CA2195925A1 - Fmcw radar with angular position detection - Google Patents

Abstract

This thesis describes a new FMCW radar system with digital beam-forming capabilities. A proof-of-concept prototype radar was designed, built, and tested to demonstrate the performance. The prototype contained a VCO, a transmit antenna, eight separate, identical receive channels, VCO linearization circuitry, IF amplifiers and filters, A/D converters, and a computer interface board. A new implementation of a VCO
linearization algorithm was integrated into the prototype, greatly improving the VCO
linearity.

The target angular position was determined by combining the signals from the eight receive channels in software. This process was accomplished in several steps. First.
the return signal from the target was received by the separate antennas and converted to an IF signal. Next, the IF signal from each channel was amplified, filtered, and digitized.
Then an FFT was used to determine the complex spectral components of the digitized signals. In the last step, these spectral components were combined in software to provide the angular position of the target.

Tests were performed to verify the beam-forming capabilities of the radar prototype. Several synthesized radiation patterns of the radar prototype were determined experimentally. Further tests of the prototype showed the ability to detect the angular position of multiple targets under two test configurations: Two targets at different ranges and different angles, and two targets at the same range but different angles.

Description

TITLE OF INVENTION

FMCW RADAR WITH ANGULAR POSITION DETECTION
R~ K~hO~r_~- OF INVENTION

This Invention relates to frequency modulated continuous wave (FMCW) radar, and in particular to short range FMCW radar which can provide the angular position of targets.

Frequency modulated continuous wave (FMCW) radars have been used in many applications. These such as navigation radars [1], altimeters, and various automot*e radar applications including station keeping, obstacle avoidance, and collision war~ing [2-4].
- Recent advances in microwave technology and signal processing capabilities are making automot*e applications a practical technical and commercial proposition.

For short range applications, FMCW~radar systems have- rnany advantages over other radar systems. These include simple solid state transce*ers, resistance to - interception and interference, good range resolution, and compatibility with inexpens*e and accurate signal processing techniques (namely digital signal processors performing FFTs). FMCW radars have been designed to detect the range and velocity of multiple targets[5] ,as in U.S. patent No. 5,268,692 issued December 7, 1993, to Grosch et al, which is lncorporated herein by reference.

The ability to provide angular resolution is critical for many applications. Standard beam-steering techniques can be applied to FMCW radar systems. Digitally controlled phase shifters can be incorporated into the RF transce*er, electronically steering the radar beam in space. Ferrite phase shifters can be used for the same purpose. Both of these methods change the relati~e phase of the RF signal from various elements in the antenna _ 2 array to change the main beam position. However, these standard techniques are expensive and increase the size, weight, and complexity of the hardware.

1.2 Research Obiectives and Summar~ of Results The research in this thesis describes a new method for implementing beam-steering in F~ICW radar systems. A unique radar prototype was designed, built, and tested to prove the concept. Testing procedures were developed to verify the beam-forming capabilities of the radar prototype. The VCO linearity, a critical pelroll~lance parameter of the radar, was greatly improved in the prototype by implem~nting a novel linearizing algorithm.

The F~ICW radar with digital beam-forming represents an advancement in the art of radar technology. lt has several advantages over traditional RF-based beam-forming techniques. First, the hardware costs are lower and the reliability is higher. Second, the target detection time is reduced. Third, sophisticated signal processing techniques can be applied to further improve the accuracy of the radar.

The first advantage of the digital beam-forming technique is that the hardware costs are lower than those of an RF-based system. The digital beam-forming system uses standard audio frequency components (such as analog to digital converters and op-amps).
These components are inexpensive and are very reliable. In contrast, R~-based beam-forming networks use PIN diodes and ferrite material, which are more expensive, lessefficient, and less reliable for long-term operation.

The second advantage of the digital beam-foring technique is that the target acquisition time is reduced. Only one modulation cycle is required, since the phase shifting is performed in software. In RF systems, on the other hand, one modulation cycle is required for each of the RF beam positions. This has the disadvantage of increasing the target acquisition time by a multiple of the number of switched beams.

The third advantage of the digital beam-forming technique is that sophisticated signal processing techniques can be applied to the return signals to further improve the radar accuracy. Sidelobes can be reduced by applying, in software, phase and magnitllde tapers across the receive array. Windowing functions can be also used to decrease the range ambiguity in the return signals, and im~ging techniques can be applied to provide a three dimensional output of targets (in range, angular position, and velocity).

A unique contribution of the FMCW radar prototype is its angular resolution capabilities. The results, presented in Chapter 4, show that the IF signals from different receive channels were digitized, phase shi~[ed, and combined in software to provide angular resolution. Radiation patterns from a single receive channel were measured and compared to the theoretical patterns. The returns from all receive channels were combined in software, yielding several synthesized patterns with different main beam locations. The results from the prototype were within the experimental error of the theoretical patterns.

Two additional tests indicate that the radar prototype can determine the range and angular position of multiple targets, as discussed in Chapter 4. The first test result indicates that the radar can identify two targets at different ranges and di~erent angular positions. The second test result shows that the radar can identify two targets at the same range but di~elen~ angles. This ability to identify range and angular position using digital beam-steering is a unique and significant conl~ilJulion to the radar capabilities reported in the literature.

1.3 FMCW Radar Principles This section describes the basic operation of an FMCW radar system. First, the general operation of a linearly modulated FMCW radar isillustrated. Next, a detailed analysis of the FMCW signal is presented. Then, the various types of signal processors are discussed. The section concludes with a general discussion of the non-ideal effects of an FMCW radar.

An FMCW radar is shown in Figure I [6]. The radar consists of a modulated continuous-wave source~ a transmit antenna. a receive ~n~nn~j a mixer, and an IF amplifier and f~ter stage. A portion of the transmit signal is coupled into the mixer as the local oscillator (LO). The radar uses the time delay between the transmitted wave and the received wave to deterrnine target range. This time delay results in a frequency difference between the two signals. A plot of the tr~ncmtted and received signals for a stationary target are shown in Figure 2.

VCO

~3 -10 dB \ Trarlsrmt Filter LNA / AMP LO Receive IF Output < ~) RF <

~~ Figure 1 FMCW Radar System The FMCW radar operates as follows. The VCO is linearly rarnped. A portion of the VCO output power is tr~ncmitte-~, and this wave travels to a fixed target at a distance R in a tirne t=R/c, where c is the speed of light. The wave is then reflected back to the receive antenna in time t=R/c, giving the total transit time T=2R/c. This received signal is then mixed with the .;..g VCO signal. However, since the VCO is linearly modulated, the two frequencies are slightly offset. The resultant IF signal is thus the difference between these two frequencies.

11 . 3 0 ~,, T rAnsm it 1 1.2~ Receive -26-~

, 11.24--.22 -/ -' - - \, .20 ' ' , , .
o ~ ~ v ~ ~coO~ O
o o g o o o ~o o ~O ~
o o o o o o o o o o o o Time (sec) Figure 2 Plot of FMCW Transmit and Receive Signals for St~ nqry Target A detailed analysis of a linearhy modulated FMCW signal, inrhl~ling Doppler and second order terms follows [7], This derivation is for a single target, but the effect of multiple targets can easily be included since the system is linear with respect to the received signals, The in~t~nt~neous transmit frequency,f, is given in Equation 1,1:

f =fio+ fm t, (1.1) wherefm is the modulation rate (Hz/sec) ofthe VCO, andfO is the tran~er frequency at t=O, and t is the time since the start of the sweep. The phase of the transmitted signal is shown in Equation 1 2:

~ = 2~ J fr dr = 2~r[fOt + 1/ 2fmt2], ( 1.2) assuming that ~=0 at t=(7.

~19~925 In the following portions of the analysis, aO, bo, and cO are constants that determine the absolute amplitude of the signals, but have no effect on the derivations. The in.ct~nt~neous amplitude ofthe transmitted signal is given in Equation 1.3:
a(t) = aO sin 2ir~fOt + (1/2)fm t-]. ( 1.3) The received signal re~ected back from the target is delayed and ~ n-~te~, as shown in Equation 1.4:

b(t) = bosill 2ir~fO(t-r) + (1/2)fm (t-r)~] (1.4) where ris the tirne delay between the tr~n.cm;~ted and received signal; and the IF signal is c(t) = cO cos 2~foT + fm t r- (1/2)fm ~]. (1.5) If the target is moving, then r(t) = r~ + vt (1.6) where r~ is the range of the target at t=O and v is the radial velocity of the target and r =
2r(t)/c c is the velocity of propagation. Manipulating Equation 1.5 with Equation 1.6 yields the following:
-c(t) = cO cos 2~T[2rl t(l - 2v/c)/c + 2fo vt/c + 2fm vt- (1-2v/c)/c + 2(fo - fm r~ /c)r~ /c]. ( 1. 7) The terms in Equation 1.7 can be rewritten as c(t) = cO cos 27~[ 2fo r, /c - 2fm r,~ /c~ (phase terms) ( ! 8) + 2fo l t/c + 2f n vt- /c - 2fm vt- /c~ (radial velocity terms) ( 1.9) + 2f r, t,'c (range terrn) ( 1.10) - 4r~ f h/C ~ (mixed range/velocity term) ( I . I l ) Equation 1.8 contains phase terrns which do not vary with time. The radial velocity terrns, contained in Equation 1.9, are dorninated by the Doppler shi~, ~fo Vt/c. The range term is shown in Equation 1.10, which is proportional to the range of the target. It is generally represented as f,~ = 2fr~ rO /c- ( 1.12) This relationship maps range to an audio, frequency-domain signal, from DC to fs~ where f~ is the highest IF frequency, norrnally in KHz. The final frequency term, shown in Equation 1.11, can be interpreted in two ways: first, as the chirp on the range beat due to the l~h~n~ing range, or, alternatively, as the chirp on the Doppler due to the ~ nging transmit firequency.

For the ~ ;llg portions ofthis thesis, all analysis and data will assume a f~ed target with a radial velocity of zero. This greatly simphfies the irnpl~ nt~tion of the radar system under question. However, all analysis and appl;~ ~tion~ (li~lcced in this thesis can be extended to moving targets. With this assumption, Equation 1.12 becomes the basis of our target analysis.

The audio signal given by Equation 1.12 must be analyzed in an IF signal processor.
This can take many forrns. Traditionally, the IF signal processors consist of a number of f~ters which are linked to form a spectrum ana~zer [8]. The IF filter bandwidth det~nnles the range resolution. For an IF filter bandwidth offB~,; the range resolution is g~en by Equation 1.13 [9]:

R = 2~"f ( 1.13) 219592~ - 9 Furthermore, the number of filters required isfc /fs~
There are several non-ideal effects that can degrade the pe-rul~ce of an FMCW
radar. The linearity of the frequency modulation must be m~int~ined. Any non-linearity's will result in the spreading and cmP~nng of the IF signaL System noise can also deteriorate pe-rul~ce. System noise levels are determined by the purity of the VCO, and are therefore dependent on the ramp rate and phase noise. Other factors in determining system noise are the receiver noise figure and system bandwidth, and qll~nti7~ti~n errors. These non-ideal effects will be discussed in Section 3. 5.

1.4 Di~ital Si~nal Processin~

IF signals can also be analyzed using digital signal processors (DSPs) via FFTs [10].
The IF signal is ~ ;iti7Pd using AID converters, and the spectral components of the signal are determined in so~are, providing phase and mqgnitllde information. The accuracy ofthe signal processing is determined by the A/D sampling rate (fs) the modulation bandwidth, and the number of samples [11]. The frequency resolution (and therefore the range resolution) of the ~~1 is given by Equation 1.14:

f M*~T' (1.14) where M is the total nurnber of samples and ~T is the sampling period, ~T=I/fs . Today, DSPs are fast and accurate enough to provide target determination in several milliseconds. which is ecsPnti~lly real time for many applications.

2195925 lo The analysis presented above can be extended to moving targets, as well as multiple targets, by utihzing several modulation schemes [5]. For example, for a single target, the modul~tion can ramp positive, then reverse and ramp negative, as shown in Figure 2. By con~qnn~ the IF signals dunng these t~,vo periods, the Doppler shift in the RF signaL and thus velocity of the target, can be determined. Sirnilarly, multiple targets with Doppler shifts can be detecte~l by rh~nging the modulation rate,fm, ofthe transmit signaL

There are several non-ideal effects that can degrade the pelro,~ce of a DSP. These effects include qll~nti7~tion and round-off errors. In ~ liti-n, this system uses a digital fee~ba~l~ system (discussed in Section 3.4) to lineari7e the VCO. This D/A based system increases linearity of the VCO ramp, but is limited by the hardware components. The analysis ofthese non-ideal effects will be ~iccllc~e(l in Section 3.5.

1.5 Thesis Outline Chapter 2 provides a general overview of antenna theory and beam-steering techniques. Antenna array theory is presented in Section 2.2 to show the effect of applying a progressive phase shift across the antenna. In Section 2.2, Microstrip antennas are discussed and the theoretical radiation pattenns of several antennas used in the prototype are calculated. Section 2.3 discusses various beam-forming techniques, including post-processing beam-forming techniques and phase shifter hardware. In Section 2.4, an adaptive beam-forming technique is presented. This chapter is concluded by introducing the new FMCW beam-steering technique.

In Chapter 3, a unique FMCW radar prototype is described. The first section contains a detailed description of the radar hardware. The software used to control the radar is discussed in Section 3.2. The data processing and beam-forming algorithms are discussed in Section 3.3. The novel VCO linearization technique is discussed in Section 3.4. The chapter concludes with a system noise analysis.

The expenmPnt~l results presented in Chapter 4 show the angular resolution capabilities of the radar system. Section 4.1 describes the test setup used to measure the radiation pattern of a single radar channel. The pattern is generated by measuring the Channel I retum from a target at a range of 16 m, as the target is moved from 0~ to 180~
in 1~ steps. In Section 4.2, the returns from all eight channels were combined in software to synthesize very narrow main beams at 90~, 92~, and 94~. These results show the beam-forming capabilities of the prototype, and are compared to the theoretical patterns. The results in Section 4.3 show that the radar can discriminate between two targets, one at 20 m and 88~, the other at 26 m and 90~. Section 4.4 shows that ~he radar can discriminate two targets located at a range of 30 m, but at two dilrelelll angular positions: 90~ and 94~.

Chapter 5 concludes that the FMCW radar discussed in this thesis provides angular resolution capabilities. Furthermore~ the thesis concludes that this method of beam-forming increases the capabilities reported in the literature, thus advancing the art of radar technology. A summary of the research from this thesis is provided in Section 5.1. Future work to further improve this technology is discussed in Section 5.2.

Chapter 2 ANTENNA TEEORY AND BEAM-STEERING TEC~INIQUES

This chapter discusses various beam-steering and im~ging techniques used in radar systems. Section 2.1 contains classical antenna array theory. Section 2.2 discusses the microstrip antennas and presents theoretical radiation patterns of the microstrip antenna arrays used in this thesis. Electrically steered arrays using ferrite and switched phase shifters, as well as other beam-forming techniques, are discussed in Section 2.3. Adaptive beam-forming is reviewed in Section 2.4. This chapter concludes with a section on the theory of the F~ICW radar digital beam-forming technique presented in this thesis.

2.1 Antenna Array Theory In many radar applications, the target range and velocity are the only quantities desired.
However, for a large class of radar systems, angular resolution is also needed. Several techniques can provide this information. Radar bearns can be swept across a volurne of space to providing angular resolution [8]. The antenna can also be mech~nir.~lly rotated. Monopulse radars are available, providing angular position inforrnation by comp~ring ma~i~lde and phase in two (or more) separate receiving antennas [12]. In phased array antennas, the radar bearn can be electrically swept by varying the relative phase of each radiating element [13]. This section will discuss basic antenna array theory.

An antenna array is a group of two or more radiators geometrically aligned so that the radiation from the individual elements combine or cancel (depending on the angle offboresight) at large distances to provide a desired radiation pattern. A linear array is a group of elem-Pnts aligned along a common axis. If the array has N number of PlP.mPntci equal spacing d between PlPmPntc, relative current levels L" and relative progressive phase shif't az across the array, then the array factor is given by [ 14]:

AF((9) = ~ n e~ dcos~-e~ (2. 1) n=l O
where k=27~/~, and ~ = 90~ is normal to the plane of the array. Furthermore, if each of the array PIP.rnPntC has a radiation pattem E(~), then the total array pattem is given by:
Aa(~) = E(~J) AF(O). - (2.2) The quantity Aa(~) represents the phasor addition of N PIPrnPntc at a large distance from the individu~l PlemPnt~ The relative phase shift, az, of each element can be varied, ~h~n ing the location of the main beam. The relative current levels, I " can be varied to control sidelobe levels and shape the beam. Similar analysis can be apphed to two (or more) ~imPncinnal arrays [15].

Any radar system providing angular resolution uses the phase and magnitl1de tion to determine target location. In phased arrays, the phase is changed to steer the rnain beam location. In irnaging radars, the receive signal from many different channels is combined in rnatrix forrn to ~ield a two or three ~imPncinnal image [16]. These systems will be (licc1lcc~P(l in detail in Sections 2.3 and 2.4.

2195~25 '-- 14 2.2 Microstriu Antenna Arrays Microstrip patch qnt~nnqc have been well docllm~nted in the literature [17-22]. They have rnany adv ntages, in that they are inexpensive and easy to mqmlfqctllre, they are physically thin and conr~ ,, they have relatively high gain and efficiency, and they can be easily incorporated into an array with an integrated feed structure. There are numerous disadvantages as well: They are inherently narrow band, they have high cross po!qri7qtinn, and they are sensitive to en~ onlllelllal vqri~tion~ Feed network losses also lin~it the practical size ofthe array, and therefore the upper limit on gain.

The most basic microstrip antenna element is the rect~n~ r patch radiator. The input irnpedance of this structure is several hundred ohrns, thus requiring an irnpedance m~tching network. Using a quarter-wave microstrip transformer can result in 1.5:1 VSWR bandwidths on ~he order of 1.5%, sufficient for many apphcations. The efficiency of microstrip patches is generally between 25% and 85%. The gain of a single rect~ng~ r patch is on the order of +4 to +8 dBi and the radiation pattern is broad in both azimuth and elevation, with 3dB
beamwidths of approximately 60~ [23]. The radiation pattern in the ~7irnllth~1 plane is approximated by Equation 2. 3:

sin(2~Ta- cos(~)) E(~) ~ (2 a cos(~) (2.~) where a is the patch width and ~90 ~ is norrnal to the plane of the microstrip patch.

--- 219S92~ 15 Individual microstrip patch PlPmPntc can be combined to form array ~nt~nn~c A
corporate feed structure uses ~1-l power splitters to sequential~r split (or combine) the power and feed n indin,idual elements [24]. Series feed structures use n-l tran~ro~ el~ between the individual elements [25]. Both of these feed methods have their advantages and disadvantages.
and some feed structures use a hybrid ofthese two feeds [5].

The radar descnbed in this thesis utihzes microstrip patch ~ntPnn~c as the primciple ra&tion element. The basic building block is a lx4 array PlPmPnt, shown in Figure 3, using a series feed structure. This element has an elevation 3 dB bearnwidth of approximately 16~, and an ~7imllth~1 pattem given by Equation 2.3. The transmit antenna is constructed of two of these lx4 arrays, and is shown im Figure 4. The receive ~nt~nn~ are constructed of four of these lx4 arrays, shown im Figure 5. Eight ofthese receive nt~nn~c are used in the radar, one for each channeL

The calculated :17imllth~1 ra&tion pattern of the 4x4 array is shown in Figure 6. All of the elements in this array are fed in phase, resultimg m a main beam at 90~ and a symmetrical response on both sides of the main beam The 3 dB bearnwidth is approximately 16~. The first sidelobe level is approximately -14 dB, and the secondary sidelobe level is below -22 dB. Nulls m the pattern occur at 90~ + 22~ and 90~ + 45~.

219592~ 16 300 mils x 330 mils Microstri:p Inter Patch Impedance W ~/4 Transformer L~
50Q Input Line ~

Figure 3 lx4 Microstrip Antenna Array ~0.750"~
300 mils x 330 mils Microstrip lnter-Patch Transformer ~/4 Transformer J

50Q Input Line ~

Fi~ure 4 2~4 Microstrip Antenna Array ~0.750" ~11 0.750" ~11 0.750"~

~ 300milsx 330 mils Microstrip ~ter-Patch Transformer 50Q Input Line ' ¦~

Figure 5 4x4 Microstrip Anterma Array o ~ ~ I Theoretical Pattern _ -20 -~-40 -60 : , .
ooooooooooooooooooo ~ ~ oo ~ o -- ~ ~ ~t ~ ~o _ _ Angle (degrees) Figure 6 Calculated A7imllth~l Radiation Pattem of a 4x4 Microstrip Antenna Array Eight ofthese 4x4 arrays are used as the receive ~ntrnn~ in the radar. The c~lrlll~ted radiation pattem for the 8x(4x4) array, with all rl~mrnt.s fed in phase, is shown in Figure 7. The pattem has a 3 dB beamwidth of 2~ centered at 90~. The first sidelobes are approximately -14 dB, and further sidelobes decrease as the angle increases away from the main beam.

This main beam is '~steered" by varying the relative phase ~ across the array. Equation 2.4 was modified into the following form:

)= E(H) ~ ~e~ cOs~-c~v~ ) (2.4) C'.V=I ~1 ~,vhere n varies from 4*(CN- I ) to 4*CN for the second s~mm~tion. The phase is progressively increased (or decreased) from channel-to-channel across the array. For a progressive phase shift of c~ = -35.7~, the main beam position changes to 92~. The calculated pattem for this case is shown in Figure 8. This pattern also has a 3 dB bearnwidth of 2~, and first sidelobes at approximately-14 dB. However, grating lobes appear at several angles. These gratmg lobes are present because ofthe l~rge spacing between the 4x4 arrays.

Theorehcal Pattern ooooooooooooooooooo x G~ O -- ~ ~ ~ _ _ _ _ Angle (degrees) Figllre 7 Calculated A7im..th~1 Radiation Pattern of an 8x(4x4) Microstrip Antenna Array with a 90~ Main Beam ~ I Theoreocal Pattern O O O O O O O O O O O O O O O O O O O
~ ~ ~ ~, ~ ~ 00 ~ O = ~ ~ ~ ~ ~ ~ 0~
Angle (degrees) Figure 8 Calculated A~mllth:ll Radiation Pattern of an 8x(4x4) Microstrip Antenna Array with a 92~ Main Beam - 21959~5 21 By increasing the progressive phase shift between channels to -71.4~, the main beam position was moved to 94~, as shown in Figure 9. This pattem also has a 3 dB beamwidth of 2~. The grating lobes are quite high, at -12 dB, but the close sidelobes are still appro~mately -13 dB.

Theore~ical Pattem ¦

3~ -30 -50- ~ ~ t o o o o O O O O O o o o O o o o o O o ~ ~ ~ I~ CO ~ O ~ ~ ~ ~ ~ I' X
Argle ~de~rees) Figure 9 Calculated A7iml-th~1 Radiation Pattern of an 8x(4x4) Microstrip Antenna Array with a 94~ Main Beam These calculated pattems show that the main beam ofthe 8x(4x4) array can be tilted by applying a progressive phase shift between the channels. The main beam location was changed from 90~ to 92~ and 94~. However, the sidelobe and grating lobe levels in the radiation pattems increased with increasing phase shift. The beam can also be shifted to 88~ and 86~ by apply~g a +35.7~ and +71.4~ progressive phase shiflc (respectively) across the array. In Chapter 4, these calculated radiation pattems ~ill be cornparedto the synthesized pattems derived from the radar return data.

2.3 Beam-Formin~ Techniques All radar systerns providing angular resolution manipulate the phase and m~itllde of the receive signals to locate targets. In phased array systerns, the phase delay in each channel is switched between two or more di~ values, and the receive beam is formed by s..mmnlg these delayed signals. In other systems, the received signal is amplified and then split into paths, each path with a dia~le.l~ phase delay, and the signals are then recornbined to form ~imllh~neous bearns. This section reviews these two types of beam-forming techniques.

A phased array antenna is an electrically steerable ant~nn~, where the relative phase of each element or group of elem~nts is controlled digitally [6]. By varying the relative phase shifts, the main beam position can scan a wide area of space very quickly. The relative phase differences can be achieved by diode switching of RF paths or by varying the pha~se velocity in waveguides by using ferromagnetic m~ten~l~ (known as ferrite's). Phased arrays have many advantages, which include speed and flexibility [8]. The beam can also be given ahmost any shape, swept in any fashion, or switched almost in~t~nt~neously to any desired position. The pattem can also be split into several beams. and thus track muhiple targets ~imllh~neously.

However, electronic scanning also has several key disadvantages. The systerns are generally very complex and expensive, the efficiency of phased arrays are lower than those of f~ed beam systems, the arravs suffer extreme main-beam broad~ning at extreme scan angles.
and they are also generally larger and require more space and power.

Phased arrays can use clc~,llol~ically controlled phase shifters on the transrnit ~ntonn~
receive ~ntPnn~, or both. Ferrite phase shifters are usually used on transrnitters due to the high power-h~nllling capabilities [26-28]. PIN diode switched-line-phase shi~ers are generally used with receive antenna arrays due to the low power levels [29-31]. Many phased arrays iUurninate the target area with a broad transmit beam and used a switched beam phased-array to locate the target within this area. A detailed analysis of phased array systerns is presented in the literature [6,13,16].

A post-amplification beam-forming network is shown in Figure 10 [6]. The network has three receive ~nt~nn~c, power splitters, LNAs, and three sets of phase shi~ers, as well as three power combiners. A portion of the receive signal from each of the rh~nnel.c is phase shifLed (relative to the other channels) and recombined to form a fixed antenna beam pattern.
The network forms three of these separate antenna bearns ~ h~neously. The RF signals could have been converted to a lower IF frequency and combined, so long as a common LO
signal was used to preserve phase il.fol~ion. (The advantage of pe~rul~ g phase shif~ing at lower frequencies is reduced cost.) Many other systems have been developed which provide multiple radar beams ~iml-h~neously [32-37].

In any type of beam-forming systern, the channel-to-channel amphtude and phase errors must be controlled. Sources of phase error include antenna mic~lignmPnt RF and IF
channel phase mismatches and phase incoherence due to path differences in the LO signaL RF
path lengths, etc. In addition. variations in the IF and RF channels cause amplitude differences [38]. These errors can seriously degrade the target detection capability [39].

219~25 24 Nô 2 /~) \\ I

+ ~'~ +
IAmplifi I IAm~lifi I IAmplifi I

1.1 ... ...
ISUMI ISUMI ISUM
+ + +
Beam Beam Beam No. 3 No. 2 No. I

Figure 10 Post Amplification Beamforming Network 219Sg25 2.4 Adaptive Beam-Formin~ Techniques In the systems described in Section 2.3, it was ~cqlmPd that the m~ le and phase errors in each of the receive channels were controlled and held below a determined threshold.
Furthermore, it was assumed that the relative locations of the receive elem~ntc were known? in other words the ~l.om~ts were fixed in space. In some applications, however, the element locations are not fixed over time? so the m~gn~lde and phase errors are very large. This section discusses one method of removing these errors.

Adaptive Bearn-Forming (ABF) techniques have been applied to an X-band radar system to compensate ffir geometric and electrical distortions, allowing the system to produce images of an airplane with good angular resolution [40]. In this system, the phase errors due to channel micm~t~ element location, and LO errors were grouped into a single error term for each charmeL (The m~gni~lde termc in the different receive channeLs are determined to be negligible, and are therefore ignored.) These error terms were determined by ana~yzing the complex returns of the target being imaged. Once the error terms were known, the rnatrix of complex returns was combmed to form an irnage of the target.

The ABF procedure assumed that there existed a point-like scatterer or source havmg a large radar cross-section some~hhere m the field of view of the imagmg system. The physical size ofthis source is govemed by Equation 2.4 [41,42].

AR
Ph.,sicalSi e= ~L (2.4) 2195g25-where ~ is the wavelength, R is the radar to target distance, and L is the size of the imaging qntPnn- Furthermore, the echo strength from the scatterer must exceed the total backscatter from all other sources in its range bin by at least 4 dB.

The system under questien is shown in Figure 11 [42]. The receiving array is shown distorted in t~,vo dimensions: the elPm~ntc are displaced from a datum line, and the element spacing is not uniform. During operation, an RF pulse is transmitted toward the point scatterer.
The re'dected wavefront is then sampled at each of the receivers. The measured amphtudes and phases are effected by the displ~cPmPnt of the antenna elpm-pnts from the design positions. The phase error can be significant, and must be less than a tenth of a wavelength if the gain of the antenna is to be held within I dB; smaller if the sidelobes must be controlled [41,42]. Similarly, the variation in the receiver RF and IF hardware must be held under tight controL In practice, the measured arnpl~tudes at the individu~l receivers vary little due to the geometric errors ofthe receiving array and the receiver channel variations in the individual receivers. However, the phase information is more sensitive, and is ec~Pntiqlly destroyed if the displacement error or receiver channel phase errors exceed a small fraction of a wavelength.

The application of adaptive beam-forming has been used to cornpensate for the displqcPmPnt errors and channel phase errors. Since the m,qgni1~lde variations in the receivers are minimql the signal processor searches across all range bins for the smallest variation, and d~PcignqtPs this range as the reference range. Then the signals in each channel are phase shifted such that the reference range phases are all equaL This process is called phase conjugation [43,44], and is shown as the feedback network in the lower right of Figure 11. A~er the phase errors are normqli7~, the beam-forming algorithms are applied to fficus the signals ~om all channels and form narrow beams or images.

Table I describes the ABF imaging algorithm [40,42]. In step 1, the echoes received by each antenna element are sampled, rligiti7e~1, and stored. Step 2 consists of searching through the ranges for that range bin which exhibits the smallest normqli7~d variance of the echoes across the array. This range is decignq-ted as the reference range, R". In step 3, the signal processor conyugates the phases (in each channel) at R~, to form a weight vector, and in step 4 phase shi~s echoes in other range bins by the weight vector. The array is focused at all range bins in step 5, and is scanned in a_imuth to form the two--lim~n.ci- n~l image in steps 6 and 7.
Thic algorithrn is ~om~timPC called the "~ ~;""ll~ variance algorithrn (MVA) or the dom~nt scatterer algorithm (DSA) [39].

A bistatic radar system was used to d~m-.nctrate the abihty ofthis technique to produce an aircraft image. An X-band trqn.cm~er radiated I kW peak power, in 7 ns pulses. This fixed the range resolution to I m. The radiated and received signal bandwidth was 150 MHz. The transrnit antenna was a 1.2 m parabolic dish and was mec~llq-ni~qvlly steerable to follow the target. The receive array consisted of 32 X-band receivers deployed on a laboratory rooftop, spaced approximately I m apart. The total array size was approximately 1,000 wavelengths.
Assuming the antenna is diffraction limited, the beamwidth is approximately the reciprocal of its si_e in wavel~ngths [45]. This assurnption is valid once the ABF has been performed.

~ lss~a~

- ~8-fr~i~S~n9 ~hen r~ ed in ~il~ pre ~ 219592S 29 Table l Adaptive Beam-Forming Algonthm 1. Measure and store complex envelopes of samples. Aineifin Range bin Ain.
2. Find Ro such that Ao")~A for aU channels n. Aei~n 3. Phase rotate at R{, by phase conjugate in relation to Aei~o referenceellern~nt ei(ff)~~n) 4. Phase rotate all range elements. Aj ei(fin~~
A J[fin~ll)~+kx2n/2( I/R l+ I/RO)~OB

5. Focus at each range Rj. ~n~ - in 6. Phase shift linearly with angle. Bjnexp(jkxnu) 7. Sum at each range element. . Sj(u)=SBjnexp(jkxnu) Therefore, the expected beamwidth of the array is approxi~ ely 10-3 rad or 1 mrad. At 3 km,this corresponds to a transverse resolution cell width of 3 m. Each receiver used a 19 X
14 cm hom antenna with a horizontal beamwidth of 12~.

All receivers were phase locked to a common 120 M~ master oscillator. The oscillator's output was frequency multiphed to provide the proper RF and LO power. Each antenna in the array received a modulated RF wave from the echoes of the targets and clutter.
The received waveforms were detecte-l~ coherently quadrature-demodulated, and sarnpled at 200 meg~camrles per second. Each quadrature sarnple was converted into an 8 bit digital word. Each receiver had a number associated with each range bin. Therefore, if there are m range bins, and n receivers. an ~7~X7l rnatrix was formed with the associated return signals. The function of the signal processor was to transform this matrrx into an irnage. If the array had no geometric or electrical phase errors in each of the arrays, an irnage could have been formed - ~lg5925 immP li~tP~y However, because of the sensitivities discuss,ed earlier, and the large s~e of the array, the adaptive beam-folming techniques were needed to form an image.
DETATT.~n DESCRIPTION OF ~K~r~KK~v EMBODIMENT
2.5~CVVBeam-Steer~Radar .
ThLs thesis describes a new and unique FMCW radar with bea_-steering capabilities.
This new technique combines the radar IF signaLs in software to provide angular resolution. A
system block diagram of a four-channel radar is shown in Figure 12. This system consists of a single, broad beam transmit ~mPnn~ a voltage controlled oscillator (VCO) and m u~iple receive channels. Each receiver consists of an ~nt~nn~, a mixer, and an IF filter and arnphfier stage. All mixers are driven by a common LO source (the VCO). The IF signals are synchronously (ii{~i7PIl, and an FFT is performed to det~rm~e the complex spectral components of each return signaL These complex spectral components from each channel are co~ined to provide angular resolution of the target or targets. This section outlines the principles and algorithms used in the F~ICW beam-steering radar.

In F~ICW radar with digital bear~steering, a linearly modulated CW signal is first transmitted. The energy reflects off of the target and is then retumed to the receive antennas.
The magni1~ldes of the retums should be approximately equalL, but the relative phases will be determined by the locations of the receive ~ntPnn~s within the array. These signals are then modulated to the IF frequency by the receive mixers, introducing m~gni~lde and phase errors.
These errors are due to variations in mixer conversion loss, variations in path lengths in the LO
feed network, RF receive network, etc. These signals are then amplified and filtered in the IF

amphfier and f}ter chain, adding additional phase and m~ de errors. Finally, all channels are sampled synchronously.

The digital signals from each of the channels are combined to det~.rmme the angular positions ofthe target or targets. ~-l's are used to decompose the signals from each charmel into a complex _atrix with a m~gnit~lde and phase term for each ofthe range bins. For a single target, the resultant magnitllde term is a product of the ~F signal level (which is proportional to the RF return m~gnit~lde) and the individual error ter_s ~cc~ ted in the signal due to channel variations. The resultant phase term is a ~Imm~tion of the phase of the return signal ~ and the individual phase errors which accllmlll~ted in the signal due to channel variations. The errors in these terms are removed by using a cahbration algorithm~ and the resultant complex signals are cornbined using array theory to determine the angular position of the target or targets.

A mathem~ti~l representation of the calibration process ffillows. The return signal received by the antenna is given in Equation 2.5:
Fn = MRF e , (2.5 ) where n is the channel number index, ~RF is the m~ lde of the RF signal and ~RFn is the relative RF phase angle. In general, if the target is a large distance from the array, the m~gnitlldec will be appro~imately equal. However, the RF phase angles will vary depending on the location of the target. The absolute phase angle of the return is not important, however, the relative phase di~erences between dilrerelll channels must be preserved if accurate bearns are to be produced.

A~er this signal is converted to the IF frequency, it is appro~mated by Equation 2.6:
G = M e~Fn E eSn (2.6) where C is the rnixer conversion loss, MIF = CMRF is the IF signal level, q~lFn iS the IF phase angle (in general it is proportional to the RF phase angle), En1n is the magnitude variation error associate with rnixer n, and sn is the phase error associated with the rnixer, LO and RF feed network, etc. A~er the signal is amplified by the lF chain, the signal is given by Equation 2.7:
Hn MlFe E~nn e E1FAn~Pe, (2.7) where EIFAMP is the magni~1de error introduced by the IF arnplifiers and filters, rn is the phase error due to the IF chain, and Hn is the resultant IF signaL This is rewritten with the error terms grouped, and is shown in Equation 2.8:
Hn = MIF e~Fn Etn e~n = M eAn (2.8) where Etn is the total ma~ de error m channel n, ~n is the total phase error, Mn = M~FE,n is the total m~gnitllde response, and An = ~Ifn + Tn is the total phase angle. These phase and m~gni~lde error terrns are due to hardware variations, and can be ~c.qlm~d to be time invariant.

The problem at hand is removing the error terms, leaving only the target mqgnihlfle and phase information. The phase term can be uniquely determined for by me~ mg a target at a known angle. The m~gni~lde terrns can be normqli7t d to a common m~grihlde, thus removing any variat~on errors. This is accomph hed by performing a calibration mea~ of a target - 219S~25 33 Receive ~_NA I F~3ter 1~ D I

Receive Filter 2h'l~ 2 Receive - LO
NA 3 Filter 3~D 3 Receive LO
Filter4h D4 LO
VCO
Transrnit D/A
~y ~Figure 12 Four Channel FMCW Radar with Digital Beam-Forming - 2195~25 at 90~ for each of the range bins. According to array theory, the RF ma~itlldPs and phases in each channel should be equal for targets at all 90~. Therefore, any differences in signal mqgnih~ c and phases between the channels can be attributed to the error terms. A calibration vector, comprised of a mq.~hude term and phase term, is cql~lqted from the return at 90~ and used to remove these errors. The mqgnit lde terms from each of the channels are normqli7~d by rnultiplying the mq.~ihl-le in each channel by the calibration term CM(n) = M~ / Mn for each channel n. The phase terrns are normqli7~d by adding the cahbration term CA(n) = -An from each ofthe measured phase values in each channeL

It should be noted that the channel errors are due in part to the di~e~ phase and ma~it~l(le responses of the IF filter and amplifier chain. These filters are constructed of components with moderately large tolerance values (10% for capacitors and 1% for resistors).
It is reasonable to assume that the phase and m~gnitllde errors of the dilrt;~ lF filters will vary over the IF frequency range. Therefore, in order to assure an accurate calibration vector, a ~ target calibration should be performed at each range of interest.

219532~ -The general algolilhlll ofthe FMCW radar with bea~fomnng follows:
Step 1: Measure the return of a target at range R~ at 90~.
Step 2: Perform cornplex ~-1 on retum. Determine range bin k with largest target response.
(Yields Hn = Mn eAn in range bin k.) Step 3: C~ e calibration vector for each channel for this range bin. (Yields CM(n) = M//~Mn and CA(n) = -An = -m.) Step 4: Measure retum of target at range R~ at angle ~. (Yields Hn = Mn e~Fn +rn- ) Step 5: Calibrate the retlun for each charlneL (Yields Hn(cal) = [Mn ~MI/Mn ]e~Fn +rn e-~n = Ml e~7n~ the desired result with error terms removed.) Step 6: Perform bea~steermg to det~.mine target location by cornbi~ing results of all channels.

21gS925 3~

Chapter 3 FMCW RADAR SYSTEM WITH DIGITAL BEAM-FORMING
PROTOTYPE DESCRIPTION

This thesis describes a new and unique FMCW radar with digital beam-forming capabilities. Part ofthe contribution ofthe thesis is the design, construction, and testing of a unique radar prototype to demonstrate the concept and verify the pel~o~ ce. This prototype includes a new implementation of a VCO linearization technique critical to the radar performance.

This chapter discusses the hardware and software components of the new F~fCW
radar system with digital beam-forming capabilities. Section 3.1 describes the radar hardware. Section 3.2 describes the software used to control the radar. The post-processing routines and beam-forming algorithms are described in Section 3.3, the VCO
linearization technique and implementation are described in Section 3.4, and a discussion ofthe dominant radar non-ideal effects is presented in Section 3.5.

3.1 Radar Hardware Description This section describes the hardware used in the radar system. The overall system block diagram is sho~n in Figure 13. The system is composed of a VCO (with an integrated D/A converter system), various power splitters and isolators, a transmit D/A FlFO's D/A Transmit --d~ ¦ Y'~~ -~J -3 dB LO Feed d7 'r -1~ -3 dB
4 Delayq) ~ DelayLine FIFO #l A/D #l Mixer BaDk I
do l I I ~ Rx4 d~ I r.H~
O-~tp + ('H4 ~K ~) I O Fl~n~l ~ ~< C~5 Filter/Gai~ ~tages FIFO #2 A/D #2 Mixer Bank 2 ~
dn ~ HS ~_~ Rx PC Controller ~H~
d, ~H
(~H~ ~

FigureZ Eight Cha~nel FMCW Radar with Digital Beam-Forming 21~92S 38 antenna, a bank of 8 identical receivers (each with a receive antenna, mixer, and lF filter and arnplifier chain), an overall system-control circuit with a master clock and AID
converter system, and a computer controller. The radar system also has a VCO linearizing circuit, comprised of a delay line. a coupler, a mixer, and an IF filter and gain stage.

3.1.1 VCO with Integrated D/A Converter This section describes the VCO and the integrated D/A converter system used as the frequency source for the radar system. The VCO is a Voltage Controlled/Dielectric Resonator Oscillator (VC/DRO) constructed of a FET, a dielectric resonator, a varactor diode, arld DC power supply and bypass components. The VCO is built on low-cost soft-substrate microstrip material. The circuit configuration is shown in Figure 14. The oscillator is in a series feedback configuration, with the common terminal (the drain) termin~ted with an open circuit tr~ncmi.c.cion line [46]. The oscillator frequency is determined by the resonant structure of the two rnicrostrip coupled lines on either side of the dielectric resonator, the varactor capacitance, and the resonant frequency of the dielectric resonator. The resonant frequency of this structure can be changed slightly by varying the capacitance in the varactor diode, achieved by changing the varactor voltage.
(The gate output ofthe VCO, usually terminated in a 50Q load, is instead used to feed the delay line used for linearization, as discussed in Section 3.4.) 219~925 +5.00 Volts ~, Output #l 1~

~ 20Q
Control <
Voltage Output #2 Figure 14 11.2 GHz DR/VCO with Dual Output 219Sg2S

The important characteristics of a VCO are the DC operating conditions. the frequency and tuning range, the power output and change in power level over the tuning range, the phase noise, and the spurious outputs. The DC supply voltage is +6.00 V, at 80 mA. The fun~l~m~nt~l frequency (at zero control voltage) is 1 1.176 GHz, with a power output of +15.6 dBm. The VCO tuning range is +0.0 to +7.0 V, with a bandwidth of 96 MHz. The power output, taken off of the source port, varies approximately 3.8 dB over this measured tuning range. The plots of power and frequency versus tuning voltage are shown in Figure 15. (The actual tumng range used for the radar is limited to +5.0 V, providing 80 MHz of bandwidth and less than 1.8 dB of amplitude variation. The effects ~ of this amplitude modulation are further reduced because of the use of a balanced mixer. ) The phase noise and spurious response are provided in Table 2.

.30 ~ 20.0 28 ~ - 18.0 26 ~ - - - - - 16.0 24 ~ ~ ------= - - - ~- 140 .22--~ --- .- 120 ~
11.20---- - ~ - - - loo ~.
-11 18 -/ ~ ~ ~ - 8 0 6 - - - - 6.0 .14 - - - ¦Frequ~CY (GHz) ¦ 4 0 - - - - - Power (dBm) 11.12 -- - - - ~ - - - 2.0 I 1. 10 o,o ooooooooooooooo ~ '~ ~ '~ ~ ~ O ~ o ~ o v) o v~ o VCO Voltage (volts) Figure 15 VCO Power and Frequency versus Tuning Voltage Table 2 Voltage Controlled Oscillator Characteristics Power Supply Voltage +6.00 V
Power Supply Current 80 mAmps Output Power +15.6 dBm Frequency ((~,) zero control voltage) 11.176 GHz Tuning Range (0 to +7 V tuning voltage) 96 MHz Output Power Variation over Tuning Range 3.8 dB
Phase Noise -100 dBC ~,) lOkhz offset Spurious Power <60 dBC

A custom D/A converter system was used to accurately control the VCO voltage, as shown in Figure 16. The system used a 12 bit Analog Devices D/A chip (P.N. AD7845) [47], two Dallas Semiconductor 8K x 9 bit FIFOs (P.N. DS2013) [48], various flip-flops, and a master control clock of 12.8 MHz. The converter system had five major inputs: a load pulse for the low bits, a load pulse for the high bits, a reset/initi~li7e pulse from the computer interface board, a start pulse from the overall system control circuit, and the master clock from the system control circuit.

The operation of the D/A control circuit proceeded as follows. The D/A
coefficients were loaded into the FlFOs using the computer-intelface board. The 12.8 Mhz master clock was reduced to a lower clock rate of 800 KHz (using a divide-by- 16 circuit).
A start pulse was received from the system control circuit (discussed in Section 3.1.6), and 4096 D/A samples were clocked from the FIFOs into the D/A converter. This process took approximately 5.12 msec (the radar modulation time period). The D/A output voltage was then used to sweep the VCO, providing the modulation for the radar. The output was filtered using ~ I kQ resistor and the varactor's naturaL internal capacitance.

219~92~

D(~
PC CorltrolleD/, ¦¦¦ F{FO 1 ~ 20Q 7k~ Output D7 ~, R D/A

- Dll FIFO 2 ~D

'~? D15 ~L
12.8 Mhz System Clock .16 800 Khz 4096 Counter EN

Figure~Digital-to-Analog Converter Circuitry 3.1.2 Couplers, Isolators, and Power Splitters Various couplers, isolators, and power splitters were used in the radar to provide isolation and to couple portions of the VCO power for various uses. Two 10 dB couplers were used to provide energy to the transmit antenna as well as the linearization mixer (described in Section 3.1.7). Willcinson splitters were used to provide in-phase power for the 8 receiver channels. Because load variations can cause frequency pulling and amplitude modulation, the isolators were used to buffer the VCO output.

3.1.3 Transmit Antenna and Transmit Power A 4x2 microstrip antenna array was used as the transmit antenna for the radar, as shown in Figure 4. The antenna characteristics are provided in Table 3. The operating frequency is 11.125 GHz to 11.300 GHz, with a VSWR less than 1.5:1. The gain is approximately 16 dBi, and the antenna in vertically polarized. The ~7iml1th 3 dB
beamwidth is approxirnately 30~, and the elevation beamwidth is approximately 16~. The antenna is fed via an SMA connector. A 10 dB coupler is used to provide approxirnately +3 dBm from the output of the VCO to the transmit antenna.

Table 3 Transmit Antenna Characteristics Frequency 11 .125 GHz to 11 .300 GHz VSWR(50Q) < 1.5 1 Gain >16 dBi Size 2.0"x4.0"
Connector Type SMA Female Polarization Vertical E-Field Elevation Beamwidth (3 dB) 16~
Azimuth Beamwidth (3 dB) 30~

3.1.4 Receive Antenna, Mixer, and IF ~ilters and Amplifiers This section describes the radar receiver. The receiver is co_prised of 8 identical channels. Each channel has a receive antenna, a mixer, and an IF filter and amplifier stage.
Each receive antenna is a 4x4 microstrip array made on soft substrate material, and is shown in Figure 5. The receive antenna characteristics are given in Table 4. The operating frequency is 11.125 GHz to 11.300 GHz, with a VSWR less than 1.5:1. The gain is appro~mately 18 dBi and the antenna is vertically polarized. Both the a7imllth and the elevation 3 dB beamwidths are approximately 16~. The antenna is fed via an SMA
connector, and is designed to attach directly to the mixer units.

Table 4 Receive Antenna Characteristics Frequency 11 .125 GHz to 11 .300 GHz VSWR(50Q) < 1.5:1 Gain >18 dBi Size 3.2"x4.0"
Connector Type SMA Male Polarization Vertical E-Field Elevation Beamwidth (3 dB) 16~
Azimuth Beamwidth (3 dB) 16~

The rnixer used in each receive channel is a single-balanced design. An ~' HMS3202 dual diode package cont~ining two Schottky Barrier diodes is used as the active device [49]. The mixer circuit is a "Rat Race" coupler design [50], and is made on soft-substrate material. The recommended drive level for each diode is -5 dBm to +2 dBm (or -2 dBm to +5 dBm per diode pair). The IF output is taken directly offthe common terminal between the diodes and fed into the input stage of an audio LNA (a T.I. TL084 JFET input op-amp [51]), with an input impedance of 1000Q. Each mixer has a measured conversion loss of 6. 0 to 6. 5 dB.

The 8 mixers are subdivided into t~,vo banks of four mixers, each bank cont~ining one input port for the LO and four inputs for four sets of receive antennas. The banks also contain integrated Wilkinson power spl'itters to provide equal, in-phase LO power to each mixer [52]. The total LO drive power for each bank is approximately +9 dB~

3.1.5-lF Filter, Gain, and Offset Ampliflers This section describes the IF gain and filter stages. The IF channels are constructed of five sets of arnplifiers and filters: the LNA section, a fixed gain stage, a low-pass filter stage, a variable gain stage. and a DC offset stage. All of the filters and amplifiers used precision resistors and standard capacitor values. A second-order Butterworth high-pass filter was used as the LNA [53]. The filter had a cutofffrequency of 1.0 KHz, and a rollup of +20 dB per decade from DC to the passband. The fixed gain stage provided +20 dB of gain. The low-pass filter was a fourth order Butterworth design with a cutoff frequency of - 219~925 46 10.0 KHz. This filter also acted as a Nyquist filter for the AID converter and the signal processing software. A variable gain stage provided channel-to-channel leveling, and the offset stage provided a DC offset of approximately 1.25 V to each channel. A Bode plot of the measured frequency response of the Channel 1 IF filter and gain stages is shown in Figure 17.

70.0 60 .0 ~ Gain (C H 1 ) j 40 o ---o 30.0-- - /
O~ 20.0-~
O 10.0------00 0 ---- - - ' - - - --- ' - ~ - ~ \
-10.0----- -- - ~ --- ~ \
-20.0 O ~ ~O N O 00 N ~~ o cr~ c~ ~ o O ~ ~ ~ O ~ ~ N O 0~ N C~ O
O ~ ~ ~ O ~ C~ ~ G
~ ~ C~ U~ O ~ ~ a~i O
Frequency (Hz) Figure 17 Channel 1 Filter and Gain Stage Frequency Response 3.1.6 System Control Circuit and Analog-to-Digital Converter The system control circuit and A/D converter block diagrams are shown in Figure 18. The control circuit serves the following major functions: generates the proper A/D

sarnpling rate and tirning sequence; provides means for an external reset; provides ternporary storage for sampled values; and provides the radar with a system clock rate of 12.8 MHz. The inputs to the control circuit are the reset/initi~ tion pulse, the 8 analog inputs, a system start pulse, and inputs to read the digital data stored in the FIFOs from the contro~ circuit to the cornputer.

The AID converter system uses two MAX-156 four-channeL cimlllt~neous sample and hold, 8 bit analog-to-digital converters [54]. The 8 analog inputs are .~imnlt~neously sampled at 51.2 KHz. A~er conversion, the 8 data bytes are then read from the A~D
converters into two FIFOs (DS-2013), one for each A/D converter. An on-board counter stops the process after 256 samples. The controlling software then reads the data from the FIFOs into the computer, and the control circuit awaits a new resetliniti~ tion pulse from the computer.

The control circuit provides the master clock rate of 12.8 MHz to the rest of the radar system. The circuit also provides a start pulse to the D/A converter circuit to synchronize the VCO sweep with the sampling process. All of the resets and read/write pulses to the D/A, FIFOs, and control circuit are provided through the computer interface card, and are easily controlled by the software.

2195g2!~ 18 C~ l DO
PC Controller ~ -- MAX156-1 AIN1 lll~FO 1 D7 AIN2 ~, r W ~ R W

DO
~ CLR CLR

W,~ R W

51.2 Khz rL START
12.8 Mhz System Clock Control Circuit 51.2 Kh~ 256 Counter C~$R EN

FigureA'Analog to Digital Converter Control Circuitry 3.1.7 VCO Linearizing IIardware The radar system has a VCO line~n7ing circuit, constructed of a coupler, a delay line, a mixer, and an LF filter and gain stage, as shown in Figure l9. The two outputs of the VCO, one from the gate (port 2) and one from the source (port l), are at exactly the same frequency [55]. A portion of the signal from port l is coupled off as the LO to the line~n~ng mixer. The energy from port 2 is delayed in a 39.42 m delay line and is treated as the mixer RF signal. The resultant I:F signal is then filtered, amplified, and .li~ti7Pd for processing. If the VCO modulation is exactly linear, then a perfectly sinusoidal IF
frequency is generated. However, if the VCO modulation is non-linear, then a frequency modulated IF output results.

Transmit D/A FIFO's D/A <
r~, ~ To Mixer ~ -1~
Delay (p ~ Delay Line (39.42m) IF Output Figure 19 Voltage-Controlled Oscillator Linearization Circuitry - 219592~ 50 The electrical specifications for the VCO linearizing circuit are sufficient to supply a full-scale signal at the lF output. The VCO port-2 power output level is approximately +11 dBm over the full tuning range. The delay line loss is -54.2 dB and the electrical delay is 131.5 nsec (39.421 m). The mixer conversion loss is 6.5 dB, and the LO power level for the mixer is approximately +3.0 to + 5.0 dBm over the VCO tuning range. The rF filter and amplifier stage uses a second-order Butterwolth high-pass filter with a cutoff frequency of 1.017 KHz and a fourth-order Butterworth low-pass filter with a cutoff frequency of 7.234 KHz. The IF chain also has several fLxed and variable gain stages, as well as a DC offset stage to provide +1.25 V of offset. A Bode plot of the frequency response ofthe IF chain is shown in Figure 20.

50.0 ~ ~ ~
40 0 ~ Gain (IF CKT) __ 30 o ~
20.0~
~--10.0- -/ - - ~ ~~ ~ \ ~ ~ ~
O 00.0-~ ' ~ ' ' '\ ~
o-10~0-- ~ - ~ ~ ~ . .\ ~ .
-20.0-30.0 -40.0 O ~-- tD N O C~ C~l C') O ~ C~) ~t O
O ~ ) O ~ C~ ~ 0 00 ~ C~ O
~) o r~ ~ ~ o r~ o O r~ ~ ~ o Frequency (Hz) Figure 20 Linearizing Circuit IF Filter and Gain Stage Frequency Response 219~925 3.1.8 Computer Interface Circuitry This section describes the computer interface circuitry used to communicate between the computer, the system control circuit, and the D/A converter circuit. The JDR
Microdevices PR-2 circuit board and interface circuitry was used [56]. The PR-2 is designed to be cornpatible with the IBM PC-AT computer bus architecture, providing 8 bit data transfers. The card contains an 8 bit data bus, a 10 bit address bus, and 8 decoded address lines (S0-S7). The decoded select lines can be addressed with one line of progli1."",;..g in QuickBasic. Data transfers (both input and output) can also be achieved with one line of QuickBasic Prog~ ,.,.;.-g The radar operation was controlled using 6 of the 8 decoded outputs and by transferring data on the buffered data bus. The decoded data lines, their addresses, and use are shown in Table 5.

Table 5 Decoded Address Lines (Select Lines) and Functions Select Line Computer Address System Function Select 0 (S0) H300 System Reset & Tniti~ tion Select 1 (Sl) H304 System Start Select 2 (S2) H308 Write to D/A FIFO, Low Bits (D0-D7) Select 3 (S3) H30C Write to D/A FIFO, High Bits (D8-Dl 1) Select 6 (S6) H3 18 Read A/D FIFO ffl, Channels 1-4 Select 7 (S7) H3 lC Read A/D FIFO #2, Channels 5-8 ~195925 52 3.2 Software Description This section describes the software used to control the radar. A software block-diagram is shown in Figure 21. The main software tasks are initi~li7~tion/reset, line~ri7~tinn (tli~c~lc.ced in Section 3 .4), loading of the D/A converter coefficients, starting the radar system and reading the sampled data, and data plotting and storage. The data processing routines are discussed in Section 3.3.

3.2.1 l~iti7l1i77ltion and Reset Subroutine The initi~li7~tion and reset subroutine initi~li7es all internal con~nt.~, resets the radar to proper initial values, and zero's all data arrays. Input and output addresses are set, as are the software sample rates, number of channels selected, and nurnber of samples per channel. The D/A converter is preset and latched to 0.00 V.

3.2.2 Generating and Loading D/A Coef~lcients Generating the D/A coefficients is one of the major software tasks. A total of 4096 data coefflcients, each 12 bits wide, are stored in two FIFOs and are later clocked sequentially into the D/A converter. sweeping the VCO. Each of these coefficients is between a value of 0 and ~ l (4,095). The difference between the nth and the (~I+I)'h coefficient is stored in the (n+l)'h position of an array dVolt(i). The nth coefficient is generated by summing the dVolt(i) values from i=l to n. This essenti~lly stores the instantaneous derivative of a linearized coefficient equation. For example, for a VCO with perfect frequency versus ~ oltage characteristics, all of the coefficients of the array dVolt(i) 2195g2~ ' ( Start Program rnitialize and Reset '< Linearize'~ >YES , L~nearizeVCO
\/ ' ''~ ' - 1NO ~ \
Load D/A Coeff's ~ , NO <~ave Coe~s~
\/
Start Radar 1YES
Save Coefficients Read A/D FIFO's Reset System r NO
END

Figure ~ I Sofh~are Block Diagram of Radar Prototype would be 1. The D/A coefficients are calculated, stored, and processed in this way to sirnplify the linearization process discussed in Section 3.4.

Once the data coefficients are generated, they are divided into high and low bits.
Low bits vary between 0 and 2~-1 (255), and the high bits vary between 0 and 24-l (15).
The 4,096 coefficients are then loaded into two FIFOs, and the radar is set for operation.
Loading of the low and high bits is accomplished with two lines of prog~ g OUTHIGHBITS, 15 OUT LOWBITS, 255 where HIGHBITS is Hex value 30C and LOWBITS is Hex value 308, the addresses of the two D/A FIFOs (see Table 5). (This exarnple loads all 1 's into the FIFOs.) The rarnp rate of the radar can be easily changed by scaling each value of dVolt(i).
For exarnple, the ramp rate can be doubled by multiplying each value of dVolt(i) by two.
This provides great progr Imming flexibility.

3.2.3 Sweeping the Radar and Reading the Di~ i;Ged Return Signal The radar begins a sweep-and-sample cycle by selecting the start address. This is accompli~hed by the follo~ing line of prog~g: -OUT START, ~x where START is Hex value 304, and xx can be any value, since the data bus is not activated with the Select I line (see Table 5).

A~er the radar completes the sweep-and-sample cycle (approximately 5.12 msec), the 256 samples from each of the 8 channels are read firom the storage FIFOs into the computer. This is again accomplished by using a sin~le line of pro~ n;~g~ as shown below:
DATA(I,J)=INP(ADDRI ) where ADDRI is Hex Value 318 (FIFO 1) and I and J correspond to the channel number (I to 8) and sample number (I to 256). A~er all 2 Kbytes are read (8 channels x 256 bytes), the radar is reset and initi~li7e(i 3.2.4 Data Plotting and Storage A~er the data is read into the cornputer, all 8 tirne-domain retur.ns are ternporarily plotted for comparison. The data sarnples are values between 0 and 28-l (255). These values are rescaled to represent a voltage value (0 corresponding to 0.00 V a~d 255 corresponding to +2.50 V). The data is then saved in a user-specified file. This data is later processed using an FFT and beam-forming algorithms to provide angular information about the targets. The user can then specify if another target is to be measured, and the process begins over again.

In one preferred embodiment of the invention, the computer is configured to proces6 the received data samples immediately after receiving the data so that the angular information of the targets can be determined and displayed on a real-time or near real-time basis (as is required in vehicular applications). An output device is preferably attached to the computer to allow a representation of the angular information to be displayed to a user.
3.3 Data Processin-~ Routines This section describes the data processing routines used to generate the different beam pattems from the return data. The first routine described is a standard FFT routine.
This routine generates a comple:Y vector in the frequency-domain (or range-dornain) from 2195g25 the time-domain samples. The second routine is a calibration method used to remove channel-to-channel phase and m~gni1llde errors resulting from hardware differences. The third routine uses the synthetic beam-forming algorithms to generate the effective returns from the different radiation beams.

3.3.1 FFT Routine The first data processing routine is a complex FFT. The algorithm is a standard mathematical-library subroutine [57]. The inputs are the complex time-domain samples, the number of sample points (NS), and the value NU, where NS=2~U. For this routine, there are 8 separate channels of data, each with NS=256. The real part of the complex time-domain samples are the sampled data values, and the im~gin~ry part is set to zero for all samples.

The FFT subroutine returns the complex frequency-domain value in each frequency bin. There are 128 di~rert;.l~ frequency bins, each with a 200 Hz bandwidth (~iven by Equation 1.14). For this particular application, only the first 51 frequency bins contain useful information. The other bins contain target information beyond the range of the radar (targets > 100 m or frequencies above lOKHz).

The m~gni~lde of the return for each frequency bin is calculated by taking the square root of the sum of the real part, squared plus the im:lgin~ry part, squared. The relat*e angle of the return for each frequency bin is found by taking the arctangent value of the im~ginary portion. divided by the real portion. Performing these operations results in the generation of a complex vector, with a mq~ de and phase angle in each frequency bin. Since the frequency of the IF signal is proportional to the range of the target, each of the frequency bins can be interchangeably labeled a range bin.

3.3.2 Calibration Routine The FFT routine described above calculates a complex vector for each of the 51 range bins, for all 8 channels. Since the channels are all sampled synchronously, the relative phase difference from channel-to-channel should be zero for a target at 90~. The mqgni~lde of the returns should also be equal for this target. Any phase or rllqgT itllde errors should therefore be the result of channel-to-channel differences in the hardware. RF
hardware differences can result in channel to channel errors. Slight length tolerances can cause significant phase errors. IF filter vanations, caused by capacitor and resistor tolerances, can also cause variations in phase and mq~ de responses.

A calibration measurement with a target at 90~ is taken at each range bin of interest (for a response in each frequency bin). This measurement is then used to calibrate the return signals for a target at any angular position for this ran~e. A calibration vector is derived using the following three steps: First, the target return at 90~ is measured. This results in a complex vector, consisting of a magnitude Mn and an angle An, for each channel ~1. Next, the phase calibration vector, CA, is formed for each range bin, where CA(~ An. And third, the magnitude calibration vector, C~I, is formed for each range bin, where C~l(n)=M,/,~f".

The resultant complex vector, with magnitude MA and angle CA, is used to calibrate returns from tar_ets at any angular positionfor this particular ra~lge bin. To do this, let RMn and RAn be the return m~ de and angle, respectively, for a target in channel n at any angle in the corresponding range bin. A new calibrated return, CRAn and CRMn~ is generated in the foUowing two steps:
Step 1: CRAn = RAn + CA(n);
Step 2: CRMn = RAn x CMf~l).
Note that if the measured retum is from a target at 90~, the resultant CRAn is 0~ for all -channels, and the resultant CRMn is equal to the return m~ de of Channel 1, which is the desired result.

3.3.3 Digital Beam-Forming Algorithms The final data-processing routine is the digital beam-forming algorithms. The calibrated complex returns from each of the 8 channels are combined to produce affective returns for each beam position at each of the range bins. A progressive phase shift is applied across the array for each beam position, according to the array theory discussed in Section 2.1. The result is a complex power return for each of the beam positions. The target.'s angular position can be found by comparing the m~gni~lde of these returns for each ofthe angular beam positions.

3.4 VCO Linearization Technique In an FMCW radar. the linearity of the modulation is critical. Any unwanted non-linearity will result in increased noise in the return signal [4]. If the non-linearity is large.

219592~

the target return can be spread across several range bins, making target detection difficult or impossible.

A new implem~nt~tion of a VCO linearization technique is presented in this section. First, the problems associated with a non-linearized VCO modulation are shown, then the basic theory behind the technique is reviewed. The new implem~qnt~tion is presented along with the results of the VCO linearization.

The frequency-tuning characteristics of the radar VCO were shown in Figure 3~... These characteristics indicate a non-linear frequency change per unit modulation voltage change. The output of the VCO linearization mixer for a linear voltage ra~ is shown in Figure 22 (A linear voltage ramp indicates that the modulation voltage for the VCO varies linearly with time, and a linear VCO sweep indicates the VCO frequency is ch~ging linearly with time.) This output shows several important characteristics. First, it should be obvious that the resultant sinusoidal IF signal is frequency modulated. Second, a short delay is present before the system hardware settles and the resultant "steady-state" waveform is present.
Third, there is a DC offset of 1.25 V. And finally, a small amount of low frequency modulation due to system generated clutter and system response is present in the IF signal.

2.50 r ¦ Voltage ¦
o~

0 50 ~ J v~
0.00 , ' ~ ' oooooooooooooooooo LL1 LT~ LT ~ Ll~ LL~ L~ LL~ LL1 L- L- Ll~ L~ LL~ L~ L~ LL1 L~ LT~
U~ ~ V') ~o ~ X X ~ o G~ -- O C' -- ~ 1-- 0 ~ -- ~ ~ O
Time (msec) Figure 22 VCO Linearizing Network Mixer Output for Linear Voltage Ramp The return spectrum of this signal is shown in Figure 23. The power spectrum is concentrated in range bins between 12 m and 38 m. (Since the "target" in this case is a delay line, the spectrum should have a peak corresponding to a target at one-half the delay line electrical distance, or 19.71 m.) It is clear that the spectral purity of this IF signal is very poor.

The general theory of using iterative feedback to linearize the VCO comes directly from Klimkiewicz and Grosch [58]. Figure 24 shows the general configuration of the Mixer-Delay Line (MDL) system. The VCO modulation input voltage is controlled by the computer. and is represented by the digital words V(~l). A~er a D/A converter and a low-pass filter, this digital signal becomes modulation voltage v(t). The output of the VCO is represented by x(t), and the instantaneous frequency is given by F(t). The frequency is a _ 6 ~0 30 - Power (dB) /~\
~- 20 - f ~ \
~ IO-~J ~
O--20 - : ~

Range (meters) Figure 23 Spectrurn for VCO Linearizing Network Output for Linear Voltage Ramp function of the modulahon voltage via the non-linear operator ~(v(t)). For this application, it is assumed that the goal of the linearization process is to produce a linear FM chirp of the VCO. Therefore, the product of the VCO output and a delayed portion of this output should produce a sinusoidal term, y(t) in Figure 24, dependent on the delay h and ~(v(t)).

Computer v(n), D/A , LPF v(t), VCO x(t) Output F~

LO J

y(n) ~(t) lF ~3 ' (h secs) Figure 24 FM VCO ~\,ith Digital Feedback Using a Mixer-Delay Line System The goal of the linearization process is to produce an output F(t) = G~t), where G(t) is the ideal linearly modulated RF signal. If the output F(t) is sampled directly, then let En(t) represent the error a~er the n"' modulation cycle, defined as follows:
En (t) = ¦Fn (t)--G(t)¦ (3 . I ) If the first derivativ-e of ~(v(t)) is continuous, then an iterative feedback control system can be used to reduce the error with each iteration, and En(t) = ¦Fn(t) - G(t)¦ < C¦Fn l(t) - G(t)¦, (3.2) where O<C<l, shows convergence of F(t) to G(t) for increasing n. Further_ore, En(t) approaches O for increasing n, indicating ideal modulation.

For the MDL system, the measured and ideal outputs become f(t) and g(t), respectively. If the delay line is ideaL then the following relationships hold:
f(t) = h * F '(t), (3.3 ) and g(t) = h * G '(t). (3.4) Furthermore, def~lling several terms:
S~(vo) = Fo, (3.5-a) and ~(v~) = F~ . ~ (3. 5-b) where vO and v, are the minimllm and rnaximum tuning voltages, and Fo and F, are the resultant output frequencies~ where F, - Fo (, . 6 ) V~--Vo represents the tuning band~,idth to tuning voltage ratios, and O~'<y, (3.7) where y is the maximum slope coefficient, and <~ (H /v2) (3.8) for some ~.

If the second derivative of ~(v(t)) is continuous, then iterative feedback control can be used to provide convergence of f(t) to g(t). This is accomplished by using the following relationship:
vn(t) = vn ~(t) - a[Avn ~(t)~, (3 9) where ~v" ,(t)= S h¦O[fn l(r)-g(r)]dr, (3.10) and ~z is confined by the following relationship:
o<~x ~SvlY (3.11) The implementation of Equation 3.9 is somewhat difficult, because this involves using an approximation of the modulation voltage functions vn(t) and vn l(t), and has finite accuracy. It also involves the evaluation of the integral in Equation 3.10, which can be difficult to solve and may introduce additional errors.

An improved implementation scheme has been developed as part of this thesis.
This improved scheme uses the derivatives of vn(t) and vn ,(t) and the derivative of ~[~vn./(t)~. This leads to a simple implementation scheme that does not require an approximation for Vn(t) and Vn l(t) or the evaluation of the integral in Equation 3. 10.

DiLre~ ting Equation 3.9 yields the following result:

V n (t) = v n-l (t)--~¦fn_1(t)--g(t)j, (3. 12) where ~ = ~ I [Sv*h] (3. 13) The linearization technique used with this system is based on Equation 3.12. The function v 'n(t) represents the derivative of the new modulation function for the VCO, and the function V'n l(t) represents the derivative of the previous modulation function. Note that v'(t) is implemented in software in the array dVok(i), and is already in a form for direct application of Equation 3.12. The constant ~ is a calculated constant with several constraints. The function g(t) is the desired IF output function of the mixer, and the function f(t) is the actual measured output function of the mixer. In general, f(t) and g(t) can be any measure of frequency linearity in the IF signal. This choice provides a ~reat deal of flexibility in choosing an appropriate measurement process.

The linearization technique is accomplished in five steps. First, the VCO is modulated using a linear ~oltage ramp (dVolt(i)=l for all i). Second, the resultant mixer IF signal is analyzed, and some measure of the lineanty of this signal is recorded (yielding f(t)). Third, a polynomial p(t) is fit approximating the measured linearity of the IF signal (p(t)~f(t)). Fourth, an error function is calculated (e(t)=p(t)-g(t)), providing a measure of the amount of non-linearity of the IF signal over the ramp period. Finally, a new modulation voltage is calculated using this error fimction as iterative feedback. The five steps are repeated until the IF signal is linear (and hence the VCO modulation is linear).

The first step in the linearization is to modulate the VCO using a linear voltage over time signal. This is generated by setting all values of dVolt(i)=l. (The modulation voltage at the i'h sample is produced by summing dVolt(i) from 1 to i and supplying the integer value of this number to the D/A converter. ) During this initial modulation cycle, the mixer output is recorded, and some measure of the linearity of this signal is observed. In the prototype radar system, the time between "zero crossings" of the IF signal is used to approxirnate the IF linearity. This "spacing" is termed DEL(t) (for DELta) and has units of "samples". The DEL(t) is related to the instantaneous frequency by Equation 3.14, (2* DEL(t)* Ts~ e ) (3 . 14 ) where Tsa~ e= 1/5 1,200.

For a perfectly linearly modulated VCO, the resultant output should be a perfect sinusoidal voltage (excluding DC offsets and system-generated clutter). This would also result in a constant DEL(t) for the sampled time period. By contrast, the measured DEL(t) - 219~92~ 66 values for a linear modulation voltage are shown in Figure 25. It is clear from Figure 25 that the DEL(t) values vary from values of 7 to 15 for a linear voltage ramp.

8 - - ~ ~ ~

~, 14-0 1 2 - - - - _ - - - - ~ - -8 ~
-- 6 --- - - . . . . . .
", 4 -- - - . . ~ stimate ¦-2 - ~ Meaured I
O , , ~
oooooooooooooooooo LTj LTj LS LTj L~ L~ ~ LTj L- LT LTj LTj L~ LLI Lb LTj LTj LTI
~ _ O O~ O , ~ ~ r~ g Time(sec) Figure 25 Measured DEL(t) and Estimated p(t) Values for Linear Voltage Ramp ~ he third step in the linearization process reql~ires fitting a polynomial appro~mation to the measured DEL(t) values, in other words, generating p(t). A standard library subroutine for a fifth-order polynornial regression algorithm is used. The estimated DEL(t) values are plotted in Figure 25. (Note that the smoothing properties of the regression function remove any short-term DC offset from the delta values.) 2195g2S

The fourth step in the linearization process is to calculate an error function using the approximate p(t) values and the ideal delta values (represented by DDEL, for Desired DELta). The value of DDEL is dependant on the desired modulation ra_p rate, the delay line length, and the sampling frequency. The desired radar modulation rate is 15 GHz per second. Since the delay line is 39.421 m long, the IF will be the same as a target at 1/2 this length, that is 19.21 m. Using Equation 1.12, the ideal IF frequency should be 1,971 Hz.
Plugging this into Equation 3.14, the DDEL value emerges as 12.988 sarnples.

The error function can now be calculated directly from Equation 3. 15:
e(t)=p(t)-DDEL. (3. 15) The final step in the linearization technique is to calculate the new modulation voltage function using the calculated error function as feedback. This is performed using Equation 3 . 16:
d Volt(i) =d Volt(i) + ~ e(t). (3 .1 6) This new modulation function is then used to sweep the VCO, and this iterative process continues until the desired level of linearity in the IF signal is achieved. The value of ~ iS constrained by Equation (3.13) and is determined experiment~lly. A srnall ~ value will reduce the robustness of the process, requiring a large number of iterations to achieve a given linearity, while a large ~ value can result in instabilities. An experimentally 219592~ 68 determined value of 0.0025 was used to achieve a linearity of approximately 2% in less than 10 iterations.

This modified VCO linearization technique results in an improved frequency vs.
time modulation characteristic. Figure 26 shows a plot of the estim~ted delta values for the first four iterations (Sweep-00 indicates a linear modulation voltage). Figure 27 shows a plot of the delta values for the next 6 iterations. A linearity within 5% is achieved by the fifth iteration, and this is further improved to approximately 2 % by the tenth iteration.
The time-domain response of the tenth iteration is shown in Figure 28. The measured and polynomial approximation of the delta values are shown in Figure 29, and the return spectrum for the tenth iteration is shown in Figure 30. All of these results indicate a significant improvement over the original modulation. The initial and final modulation voltage is shown in Figure 31 for co_parison.

2 _ ~

8 - - ~ - sweep-oo --6 --- ----- sweep-oI
---- SWeeP-02 ---- SWeeP-O3 a 2 -- - ~ ~ - SWeeP-04 O O o o ~ o O o o o o o o o o o o O
Lj LTj Ui Ui U~ Ui Ui Ui U L- Ui LTj LTj U; LTj L'j L'j LTj 3 -- O C~ O ~ ~ ~ ~ ~ OC -- ~ r-- C
- Time(sec) Figure 26 Estimated Delta Values (p(t)) for Linearization Iterations 1-4 21959~5 ~, 16-o1 2 - - - ~ - --- - - - ~ . . . . _~
10- : . ~
8 -- - -- we~-0: -- - - we~-O
--6 ~ wee~-0 -- wee~-g~ -2 -- - - . : :-- wee -- I
O
o o o o o o o o o o oo o o o o o o L~ LII L~l L~l LL1 Ll~ Ll~ Lr~ . L-- L-- Ll~ LI1 LI~ LI~ Lll LT~ Lll LLI
x a~ O
_ o c~ o ~ oo -- ~ ~ o Time(sec) Figure 27 Estimated Delta Values (p(t)) for LineaTi7~tinn Iterations 5-10 2.50 ~ ~
Voltage ¦
2 00 ~ - A ~

~o~so~ V
0.00 o o o O O o O O OO O O O O O O O O
L~ LI~ LL1 L~ LIJ L~ L~ L~l L~l r L~ ~ LI~ LI~ 1~ LI~ L~l LII
I~ ~ v~ oo 5~ oo X ~ ~ t ~ ~ r ~ -- -- O
G~ -- O C~ 0 ~7 ~ ~ O
Time (msec) Figure 28 VCO Linearizing Network Mixer Output for Linearized Modulation -~ 18 ~~_ 1 6 8 ~
6 - - ~ Estimate ~ 4 ---- - - . ----- Meaured a 2--- - - i . .. .. ~...... .........
O , . . .
o, o, o, o,o o o o o o o, o, o, o, o, o, o o L l LLl L~ L~L~ Ll~ LLl LU L- L- Lr~ L~l Ll~ LT~ Ll~ Ll~l Lll LL1 X C~ X ~ ~ ~-- ~
T~me(sec) Figure 29 Measured and Fstim~ted Delta Values for Linearized Modulation 30 ~ POwer(ds ~~ 20- ~/ \ ~ .. ..
~, lo-f - - \--\ - - - : - - - -: ' '' -10- ~ ~

o lo ~o 30 40 50 60 70 80 90 100 Range (meters) Figure 30 Spectrum for VCO Linearizing Network Output for Linearized Modulation 21959~S

5.00 4.00--~
", 3.50 o 3 00 2.50-0 2.00--- /
1 . 50 - --1.00 - -- -- - /~ -¦ - Initial VolTage Ramp ¦
50 / - - - I - - - - Fillal Voltage Ramp ¦
0. 00 . ~
ooooooooooooooooo L~ LTI LT~ LT~ U Ul U~ LT~ L- LT L~ LTI L~ L~ LTI LTI LT~
o o o o o o ~ ~ ~ o o ~ ~ ~ oo o ~
o ~ ~ '-0 ~ o ~1 v) 00 -- t 00 Time (sec) Figure 31 Initial and Final Modulation Voltage Rarnps 3.5 Svstem Noise AnalYsis This section includes an analysis of the dorninant noise sources in the FMCW radar systern. The received noise power is the sum of therrnal noise, receiver noise figure, IF
noise, LO phase noise, and modulation noise. The thermal nolse, receiver noise, and IF

noise analysis is well documented [59] and will not be covered. The LO phase noise is the dorninant source, and it wiU be analyzed in detail. The effect of a non-linear VCO ramp will also be examined. Ou~nti7~tion errors, due to the finite number of bits in the A/D
converters, and roundoff and truncation errors, will also contribute to the overall noise.
These effects will also be analyzed.

2195S~ 72 3.5.1 AM and FM LO Phase Noise The LO noise is the dominant noise source in the received signal [4]. This noise will have both an AM and FM cornponent. The AM noise is suppressed by using a balanced rnixer. This analysis begins by ex~mining the AM noise co~ il,ulion [7].

The AM noise on a carrier ~0 in a narrow frequency band about _ ~, is "quasi-sinusoidal," and can be expressed by Equation (3.17):
~ (t) = Eo [(I - a) + a cos(~" t)~ cos(~O t), (3.17) where cx/(a-l) is the modulation index, and Eo is the peak signal level. This can be expressed in terms of the canier and the sidebands:
E(t) = Eo (I - a) sinfc~O t) + Eo cc~2 cos(~O - c~")t + Eo a/2 cos(~O + ~",)t. (3.18) If a balanced rnixer is used to suppress the AM noise on the LO, then the local oscillator output can be represented by ELo(t) in Equation (3.17):

ELo(t) = E~o sin(~o t - ~). (3.19) The low frequency cornponent of the AM noise at the output of the mixer will be:
~IF (t) = a~O k/2 [cos(c~, t + 4~) + cos(-c~", t + ~)~, (3.20) and the ratio of the detected lF AM noise power to single sideband AM noise is:
r/,~, = 4k cos~ ~ = 4L cos~ ~, (3.21) where L is the conversion loss. This means, esst-nti ~lly, that the IF-noise power varies between zero and four times the single sideband noise level of the RF signal. This variation is caused by the variation of the relative phase of the RF and LO signals, and so the - 2195~25 sidebands either cancel or add. The mean noise power level is 2L, which is double the sideband power level multiplied by the conversion loss.

An F~I signal can be expressed as:
E(t) = Eo sin (~0 + ~a~ sin ~",t)t. (3.22) The FM noise due to the local oscillator cannot be suppressed in the mixer. However, if the modulation is narrowband, that is ~ << ~", then the LO sigllal can be represented by Equation 3.22 and rewritten as:
ELO (t) = Eo ~sin ~0 t + ~ /2~ [sin (~0 - ~t~ - ~/2CIJ", [sin (~0 + ~t~. (3.23) The RF signal has a tirne delay, r, relative to the LO, as shown in Equation 3.24:

ERF (t) = Eo ~sin ~0 (t - r) + ~J~/2c~", sin [(c~O - ~J(t - r)~
/2~, sin [(c~0 + ~(t - r)~. (3.24) The following IF cornponents are generated in the rnixer:

EIF (t) = ~Eo k/2~,~-cos[(c~ + c~")(t - r) - ~0 t~ + cos[(~ - ~(t - r~ O t]
-cos[(c~) + c~J t- c~O (t- r)~ + cos[(c~ ) t- c~O (t- r)~. (3.25) This can be reduced to:
ErF (t) = 2k(~/~Eo ~sin(c~O r) cos(~", r~2) sin[~", (t - r/2)~. (3.26) The noise power in the IF is then:
PIF = ~k~ (E2 / ZO) [sin~ (~0 r) sin(c~", r/2)~. (3.27) The detected noise power in the I:F signal relative to the RF noise level is:
= 16 L [sin~ (c~O r) sin~ (c~" r/2)~. (3.28) If we let ~ = ~Or, then Equation 3.28 can be rewritten as:

2195~5 71F~ = [4L sin~ (~)~ [45i~1- (~m r/2)~. (3.29) The first term is the phase sensitive term, equivalent to Equation 3.21, except that this term is prevalent when the LO is in phase quadrature with the RF leakage signaL and in the AM noise case, the term is prevalent when the two are in phase. This trigonometric ~imil~rity iS due to the fact that the upper and lower AM sidebands are in phase and the F~I sidebands are antiphase.

The second term in Equation 3.28 is the FM noise cancellation. If the time delay r is much less than the modulation rate (~m / 2~T), the LO and RF signals are strongly correlated and the noise output is very low. However, as the time delay increases (i.e., as the target range increases), the degree of correlation decreases and the IF noise increases.

3.5.2 Effects of Non-Linear VCO Ramp Another important source of noise is due to the non-linearity of the modulation slopefm [4]. Consider Equation 1.12 withfm replaced withfm +fe, wherefe is the slope error term. Iffe is independent of time (i.e. a constant offset in the ramp slope), then Equation 1.12 becomes:

flF = 2 (fm + fe)ro /c = 2fm rO /c + 2fe rO /c. (3 30) This shows an offset in the IF frequency which is proportional to the error in the modulation slope. This also shows that the absolute error increases with increasing range.

If the slope varies with time, then the error term must be integrated in Equation 1.2. Whenfe is decomposed into its Fourier sine components cl~F, each multiplied by t and integrated, the transmit signal becomes:
a(t) ~ aO sin[2~zfO t + ~fmt~ + 21ZCF~ /~ (Sin~Ft - ~Ft COS~Ft)~ (3 31 ) This transmit signal is delayed and mLxed with itself to produce an IF signal b(t). If CF- /~
is small compared tOfm and ~0, then the IF signal b(t) can be reduced to:
b(t) ~ bo sin[~O t + 7Tfmt + 2n~F /C~F (~0 - ~)F)t + 2~F /~F (~0 + ~)F)t~ (3.32) This introduces the following error in the IF signal:
PIF = (I6LCF/ ~F) sin (~oT) sin (~Fr/2c). (3.33) This error term is similar to the FM component of the LO phase noise shown in Equation 3.28. The error component at each Fourier frequency ~F will add phase noise to the target IF and frequencies close to it. The IF spectral peak will be spread out by this noise. Since (~Fr/2c) << I, then the IF noise power due to this source is proportional to range. As the target range increases, the spreading of the targets spectrai response will also increase.
Eventually, the range resolution of the radar will be proportional to the target range.

3.5.3 Digital Signal Processing Errors Digital signal processing errors can introduce a significant amount of noise as the received signal is processed, and seriously degrading signal-to-noise ratios. There are three main types of DSP errors [60]: the D/A converter qll~nti7~tion error, due to the finite number of bits used to represent the sampled signal, roundoff errors produced by adding two b-bit numbers (the resulting number must be represented by a single b-bit number), and truncation errors, caused by multiplying two b-bit numbers and truncating the result to a single b-bit number. The error introduced by the A/D converter will be discussed in detail, and the roundoffand truncation errors will be presented in su~ y form. It will be shown that the A/D converter qu~nti7~tion error is the dominant DSP noise source for the radar prototype.

An A/D converter is used to quanti_e a discrete time signal with finite accuracy.
This qu~nti7~tion process is nonlinear and converts the input signal into a finite set of prescribed values, each represented by b-bits. This process is represented by Equation 3.34:
*[nl = Q(x[n~) (3 34) where Q(x[n~) is the qll~nti7~tion process, and x[n~ is the qu~nti7ed sample. Figure 32 shows a typical qu~nti7~tion transfer function between x[n~ and x[n~. Several features from Figure 32 should be noted. First, the sampled values are rounded to the nearest qu~nti7~tion level. Second, the analog input signal varies from O volts and FS volts. Third, the least significant bit (lsb) is FS/2b, where b is the number of bits. Fourth, there are 2b levels, or outputs. The difference between output levels is 4 which is the value ofthe lsb. Therefore, the largest error introduced from the qll~nti7~tion process (~csllming that the input signal is not saturated) is less than FS/2J. This error e[n~ is given in Equation 3.35:
e[~l] = x[n] - x[n]- (3.35) For example, for the qll~nti7~tion represented by Figure 32, if ~1/2 < x[n~ <3~1/2, then x[n~ = a, and it follows that -a/2< e[n~ <~1/2. (3.36) Several assumptions are rnade about the error function e[n] First, e[n~ is a sample sequence of a stationary random process. Second, e[n~ is uncorrelated with x[n~ Third, the random variables of the qll~nti7~ti~ln process are uncorrelated, i.e. the error is a white noise process. Fourth, the probability distribution of e[n~ is u~ o~ over the range of the q~l~nti7~tion error.

For qll~nti7~tion processes that round to the nearest level, as shown in Figure 32, the amplitude of the error function is bounded by Equation 3.36. For small ~, it is reasonable to assume that e[n~ is a random variable u~irol~ly di~ uled from -a/2 to ~1/2. The probability density function for ehis noise is shown in Figure 33. If successive noise samples are uncorrelated with each other and e[n] is uncorrelated with x[n~ then the mean value of e[n~ is zero and the variance is given by the E~uation [60]:

~ ~2 / 12 = 2-2b F52 / 12.

_ 2ig~i925 78 Output 111111-- --- ---- --- ...............
111111- --- - ......... ~J
111111-- - - -- . .... ...

- FS=2Vref=2.5 V
~~~~~l-- r 1 LSB--FS.256=~
oooooo-- r~ ' 000000-- ~ ;
000000--~
000000 1 1 1 1 1 ~ -'AIN
3~ FS-~
0 2~ 4~ FS-2~ FS
Analog ~put (AIN) - Figure 32 MAX156 A/D Converter Transfer Function for Unipolar Operation Pen (e) ~ 2bFs b = # bits 1/~

-~12 +~12 Figure 33 Probability Density Function of Error due to Q~l~nti7~tinn For an 8 bit A/D converter, with an input signal between 0.0 and 2.5 V, the noise var;ance or power level is calculated to be 7.9473 x 10~ W.

The other rnajor DSP noise sources are due to roundoff errors, truncation errors, and errors due to the qll~nti7~tion ofthe sine and cosine multiplication constants [57]. The noise due to roundoffand truncation in the FFT are grouped together and presented below in Equation 3.38 [61-64]. The literature has shown that negligible error is introduced by the sine and cosine constant q~l~nti7~tion if these constants are rounded to the word length ofthe FFT computations [64-65].

-- 2~ 9S~25 80 The roundoff and truncation noise in each stage of a complex FFT can be grouped together. If a fixed point representation is used, then the total noise contribution at each stage is given by ~ 6 = (4 / 3) 2 , (3.38) where b is the word length of the FFT co_putations. Further_ore, for N stages, the total noise co~ il)ulion is ,~
~ C~ T ~ N (4 / 3) 2-2b / ~ ~ (3.38) For a 256 point FFT using 16 bit nurnbers, the noise power in the output spectrurn is 79.473 x 10-9 W. In floating point arithmetic, the noise depends on the mq~ de of the numbers in the FFT calculations, but in general the noise effects are reduced [65-66].

The ratio of noise due to the A~D converter and noise generated in the FFT is shown in Equation 3.39:

[ 12~/[N(4/3) 22b2~1 = [22b~-2bl~/[2c-~
where bl = nurnber of A/D bits, b2 = nurnber of FFT bits, and N = 2L. These two noise powers are equal when b2-bl = L/2-1.

The calculated noise conllil)ulions for the protot,vpe are shown in Table 6. It is clear that the A~D converter noise is the dominant noise source.
Table 6 Comparison of DSP Noise Co~ ulions of D/A Converter and FFT Algorithm Noise Source Noise Power AiD Converter Noise (FS = 2.5 V, b=8) 7.9473 x 10~ Watts FFT Processing Noise (N=256, b=16) 79.473 x 10-9 Watts 219592~ ~

Chapter 4 FMCW RADAR SYSTEM WITII DIGITAL BEAM-FORMING
PROTOTYPE PERFORMANCE

The results in this chapter show the angular resolution capabilities of the F~ICW
radar prototype. These results demonstrate the concept and efficacy of digital beam forming. In Sections 4.1 and 4.2, the radar generates narrow main beams at di~erent angles. The radar's ability to discriminate between two targets at di~eleLl~ ranges and angles is shown in Section 4.3. In Section 4.4, the ability to discrimin~te two targets at the same range but dilreLenl angles is demonstrated.

In the first test,- discussed in Section 4.1, the return from a single target located at a range of 16 m was measured from 0~ to 180~ in 1~ increments. The power measured at each of these 181 points was used to generated a radiation pattern for each of the 4x4 receive antennas. Section 4.2 describes how this measured data was combined digitally to synthesize the main beam radiation patterns of the 8x(4x4) array with beam positions at 90~, 92~, and 94~.

In the second test~ discussed in Section 4.3, two targets at di~erel-t ranges and different angles were measured and identified. This ability to uniquely identify two targets is critical in many radar applications. In automotive applications, the radar must determine if a target is directly ahead. ahead but to the right, or ahead but to the left. The results show that the radar can discriminate these targets, providing range and angular position.

The final test, ~iccllssed in Section 4.4, shows that the radar can discrirninate two targets at the same range but at di~ e~lt angular positions. Again, this ability is critical in many radar applications. The angular discrimination shown in this chapter would not be possible with conventional FMCW radars.

4.1 Measured Radiation Pattern of the 4x4 Receive Antennas This section describes the test setup and procedure used to measure the radiation patterns of the radar. The measured pattern of a single channel of the radar is presented and compared with the theoretical pattern of a single 4x4 array. First, a description of conventional pattern measurement procedures is provided, then the test setup used to measure the radar receive radiation pattern is described.

Two conventional radiation pattern test setups are shown in Figure 34. In both setups, the transmit power and the distance between transmit and receive antennas are fixed. Therefore, the incident power to the receive antenna is also fixed. In Figure 34(a), the receive antenna is rotated from ~= 0~ to ~= 180~. As this antenna is rotated, the receive power level is measured and recorded as a function of the angle ~, thus providing the radiation pattern. (This power level is sometimes measured directly at RF and is sometimes converted to an lF signal and measured.) In Figure 34(b), the receive antenna is - 219~925 83 fL~ced, and the transmit antenna is rotated along a constant arc at a fixed distance. Again, the receive power versus the angle ~ is recorded.

There are three major sources of measurement error in these setups. First, the power density incident on the receive antenna can fluctuate. Second, the receiver gain and/or IF gain can vary during the measurement. Third, there are inaccuracies in mPasllring the angle ~. All three of these errors co~ ilJule to the measurement error in the radiation pattern.

The same principles used in the conventional pattern measurements were applied to the FMCW radar to measure the receive antenna patterns. In this setup, the radar receive ~ntenn~ were fL~ced at the origin. A target was moved along an arc at a fixed range of 16 m. The target angular position was moved between 0~ and 180~ in 1~
increments. A transmit antenna tracked the target, so that the reflected power from the target was held constant. The radar was swept, and the received power was converted to an IF signal, amplified, and digitized in the radar for each angl.lar position. An FFT was performed on this data, resulting in a matrix of retum power levels at each of the 51 range bins. The radiation pattern is produced by plotting the power in the 16 m range bin (the only one of interest) as a fùnction of the target angle ~.

Transmit (fixed) ... ..

Direction of / ~=45~
~ Receive (rotaledl .
Figure 34(a) Transrnit (rotated along Direction o~
/'r \
.

~-45~ \/ Receive (fixed) Fi~re 34(b) Figure 34 Conventional Pattern Measurement Setup '- 2195925 85 The measurements were performed in an open parking lot on The Pennsylvania State University property. The area was more than 120 m long, and clear of objects visible to the radar beam in all directions. The radar test platform, contqining the radar, power supplies, and the computer interface, was set in a fixed position at zero range. An arc (centered at the test platform) with a radius of 16 m was drawn on the parking lot surface.
This arc was then sequentially subdivided into 1~ increments so as to minimi7e the error at any particular angular position.

The test proceeded by moving a target (a small corner reflector on a tripod) to each angular position, sweeping the radar, and saving the time-domain return data for each of the eight channels. During data collection, a broad beam antenna, with a 30~, 3 dB
beamwidth was used as the transmit antenna. This antenna was rotated to track the target as the target was moved to di~erenl angular position, thus mqintqining a constant reflected power level to the receive antennas.

Several errors can effect the accuracy of the measured radiation pattern: The power incident on the receive antenna can vary, the lF and RF receiver gain can fiuctuate between measurements, and there are errors associated with the measurement of angle ~.
All ofthese errors can seriously degrade the resultant radiation pattem.

The return power incident on the receive array is assumed to be the dominant cause of error in these measurements. There are several factors that can contribute to this 219~92~ 86 error. First, the comer reflector ~lignmPnt is critical. Small vertical or horizontal errors can result in significant changes (~ + 1.0 dB) in the receive power level. Also, small errors in the pavement flatness over the area of the arc can result in power fluctuation due to the vertical change in the comer reflector position. A second factor is the alignment of the transmit antenna and the target. A small error in this ~lignmPnt can result in the incident power at the target varying from 0.5 to 1.0 dB. This in tum results in a decrease in the reflected power, and therefore a decrease in the received power at the radar. The ~lignmP.nt ofthe transmit antenna was estimated to be within + 3~.

Figure 35 shows the IF voltage from Channel I for the target at 16 m and three di~elel~l angular positions. Note that the signal frequencies are the same, but the amplitude varies. This amplitude variation is due to the variation in the receive antenna gain at the particular angular position. Clearly, the return of the target at 90~ exhibits the greatest voltage level, with the return for 120~ (the first major sidelobe in the receive pattern) as the next greatest in m~gnilllde. The return from 0~ is nearly 0, indicating a deep null in the pattern of the receive antenna (as expected). Similar returns were measured for each ofthe 181 angular positions ofthe target.

An FFT was performed on the IF signal recorded for each angular position of the target. Each FFT resulted in a relative power value for each of the 51 frequency bins.
Since the frequency is proportional to range, this corresponds to a reflected power level in each range bin. The target range can be determined by comparing the power level for all range bins and identifying the peak level. Figure 36 shows the reflected power level in all - 2~ 95925 87 2. 50 1--O degrees ~ - 90 degrees ,~ ------ 120 de8rees 2 . 00 ~

o 1 50-- -O ~ t --, 0.50 - - - ' - ~ . . ' ~ .

0.00 ooooooooooooooo,oo, X '~ ~O ~ ~ ~ -- ~ ~ ~ ~ ~ ~O O
Ttme (sec) Figure 35 Time-Domain Return for Corner Reflector at 16 m and 0~, 90~, and 120~

range bins for a target at 16 m and 90~. Clearly, the peak in return power is centered in the 16 m range bin, indicating target location. All other peaks are at least 20 dB below this level.

Figure 37 shows the return power versus target range for the target at three di~e.ellL angular positions: 0~, 90~, and 120~. In this particular measurement, the only range of interest is the 16 m range bin. Again, it is clear that the target at 16 m and 90~ has the greatest measured power level.

2195g2S 88 30 - A ~ 90 degrees '~20~

, O~

Range (meters) Figure 36 Spectral Return for Corner Reflector at 16 m and 90~

O degrees 30 - -- - - - ---- t '' ' ' ' ' " - - - - ' 90 deglees 1 20 degrees _~ 20 - ~ t\
~ I \ . ~ ~

~'J ~,i~,n;\ /~l~;\ , Range (meters) Figure 37 Spectral Return for Corner Refiector at 16 m, 0~, 90~, and 120~

The radiation patterns for all eight channels were derived by calculating the power level in the 16 m range bin for all 181 angular measurements. This measured power leYel is plotted as a function ofthe target position 0. E;igure 38 shows the measured and calculated radiation pattern for Channel 1. This measured pattern shows a sidelobe level of approximately 15 dB and a first null beamwidth of approximately 40~. There is some measurement error in the main beam, due to the ~lignment errors of the transmit antenna and the target under test, and the :~lionmP.nt errors of the corner reflector. It should be noted that this measurement error is less than +1.5 dB in the worst case. Overall, there is good agreement bet~,veen the measured and calculated patterns. The sidelobes and nulls are located at the same angles in both patterns, and the pattern shapes are similar.

.' /~ Mea~red Pattem ~ Theore~cal Pattem ¦
J

~ ~ ~ OD ~-- x~ G~ O ~ ~ ~ ~ V, ~O r~ oC
_ Angle (degrees) Figure 38 Channel I Measured and Calculated Radiation Patterns 4.2 Synthesized Radiation Pattern of the 8x(4x4) Receive Antennas ~ n this section, the returns from all eight channels are combined in software to synthesize radiation paKerns of the 8x(4x4) array. The resultant patterns have 2~
beamwidths and main beam angles of 90~, 92~, and 94~. First, a calibration measurement of a target at 16 m and 90~ was taken. A calibration vector was calculated using this data, as described in Section 2.5. This calibration vector was then applied to all 181 returns from each ofthe eight channels, as described in Section 3.2. The resultant (8x181) matrix was combined, using array theory, to form digitally synthesized patterns with main beams ~ at 90~, 92~, and 94~. These synthesized patterns were then compared to the theoretical patterns that were calculated in Section 2.2.

Figure 39 shows a comparison of the synthesized radiation pattern and the calculated pattern with a main beam position of 90~. For this pattern, the m~ le at each angular position of the synthesized beam is calculated by directly sl.mming~ in vector form, the calibrated data from each of the eight channels. (rne progressive phase shift across the array is 0~.) Both patterns have a 3 dB beamwidth of approximately 2~. The measured pattern has sidelobe levels (close to the rnain beam) of approximately 19 dB.
Most other sidelobes are less than 25 dB. The measured pattern shows excellent agreement on sidelobe and null locations.

.
Figure 40 shows a comparison of the measured and calculated pattems with a main beam position of 92~. The synthesized pattern is calculated in two steps. First, a progressive phase shift is applied to the calibrated data from each of the eight channels.
(Channel 1 data has a -35.7~ phase shift applied, Channel 2- data has a -71.4~ phase shi~
applied, Channel 3 has a -107.1~ phase shift applied, etc.) Then the data at each angle is summed, in vector form, to yield the m~ de of the return signal for the synthesized pattern at angle ~. The resultant pattern beamwidth is 2~, and the sidelobe level of the synthesized beam is approximately 15 dB.

SynthesizedPattem ¦
-10 ~ - - Theoreacal Pattem ¦--,, ~

~ 40 ~J~

-60 ~ '.
ooooooooooooooooooo -- ~ ~ -t ~ ~ 1-- 00 ~ O ~ 0! ~
Angle (degrees) Figure 39 Synthesized and Theoretical Radiation Patterns for 8x(4x4) Array with a Main Beam at 90~

Synthes~zed Pattem ¦
-10 ~ - Theore~cal Patterrl ¦
- 2 0 ~

ooooooooooooooooooo -- ~ ~ ~ '~ 'D ~ 00 G' O -- ~ ~ ~ ~ ~ ~' ~~
_ Angle (degrees) Figure 40 Synthesized and Theoretical Radiation Patterns for 8X(4X4) Array with a Main Beam at 92~

Figure 41 shows a comparison ofthe measured and calculated patterns with a main beam position of 94~. Again, the synthesized pattern is calculated in two steps. First, a progressive phase shift is applied to the calibrated data from each of the eight channels.
(Channel I data has a -71.4~ phase shiflc applied. Channel 2 data has a -142.8~ phase shift applied, Channel 3 has a -214.2~ phase shift applied, etc.) Then the data at each angle is summed, in vector form, to ,vield the m l~nitl~de of the return signal for the synthesized pattern. Again, the resultant beamwidth is 2~. However, the sidelobe level of this synthesized beam is approximately 8 dB. This increasing sidelobe level is expected and is due to the increase in the progressive phase shift required to steer the rnain beam. Figure 41 shows excellent agreement between the measured and calculated grating lobe location.

- 219$9~5 93 --Measured Pattem -10 ~ - - - - Theorebcal Pattem A ~ g~l~

, .. .. .
-60 ' .
ooooooooooooooooooo ~ O ~ CC O~ O = ~ ~ ~ co Angle (degrees) Figure 41 Synthesized and Theoretical Radiation Patterns for 8x(4x4) Array with a Main Beam at 94~

A comparison of the measured radiation pattern from Channel 1 and the synthesized pattern at 90~ is shown in Figure 42. This comparison shows the beam focusing capability ofthe radar system. The beamwidth is reduced from approximately 16~
to 2~ using the digital beam forrning technique. In addition, the effective sidelobe power levels were greatly reduced.

4.3 Multiple Tar~ets at Different Ran~es and An~les The test described in this section demonstrates that the radar can distinguish two targets at different ranges and different angles. This ability is critical for many applications.

-- 219~925 94 including automotive radar. Two corner reflectors were placed at 20 m and 90~, and 26 m and 88~. The return data from the radar was calibrated, and the signals from all - ~\ Channel 1 4x4 -10 ~ - - - - Synthesized 8x(4x4) ¦

-50~
-60 ~;, ooooooooOoooooo.oooo ~ ~ ~ ~ ~ ~ 00 o~ o ~ 00 Angle (degrees) Figure 42 Comparison of Measured Patterns of Channel 1 4x4 Array and Synthesized 8x(4x4) Beam at 90~

eight channels were combined to form returns in three main beams at 88~, 90~, and 92~.
The target locations were determined by ex~mining the return spectrum in all three main beams.

In the ideal analysis~ for a target at an angle of ~72, main beams at angles ~, and ~
will have zero measured power. However, in actual operation, measured power levels will be non-zero, and will depend on sidelobe level, main beam shape, etc. Therefore? the power level in all three main beams is examined, and the beam with the highest power level is assumed to be the beam with the target. For the radar prototype, there are three main beams for this test, each with 51 range bins. All 153 power levels are examined, and the 2 peak levels are assumed to be those corresponding to targets.

The Channel l time-domain return signal for the targets is sho-,vn in Figure 43.
This signal is the combination of two IF frequencies (one from each target), each given by Equation 1.12. The frequency-domain spectrum for these signals is shown in Figure 44. It is clear that the return spectrum contains two peaks, indicating two separate targets at 20 and 26 m. However, there is no information available to indicate angular position.

2.50 Chamlel I Voltage 2.00~
~ 100 ~

0.50 ~
0.00 , ~ ~
O t 't 't o o o o o o o o o o o o o O r~ oo ~ ~O o C~ O ~ O oo G~ O
o -- ~ ) o -- U~ oo ~ o r~ ~o o Time (msec) Figure 43 Channel l Time-Domain Return for Targets at [26 m, 90~] and [20 m, 88~]

'' 219~925 96 ~o Channel I Power(dB)¦

20~

0 lO 20 30 10 50 60 70 80 90 100 Range (meters) Figure 44 Channel I Spectral Return for Targets at [26 m, 90~] and [20 m, 88~]

The signals from each of the eight channels were combined to form returns in the synthesized beam positions at 88~, 90~, and 92~. (For the main beam at 88~, a progressive phase shi~ of+35.7~ was applied across the eight channels, and for the main beam at 92~, a progressive phase shi~ of-35.7~ was applied. No phase shift was applied for the main beam at 90~.) This resulted in an effective power level fo.r each main beam at each range bitl. The target location can be determined by comparing the relative power levels in each range bin at each angular position and selecting the peak power levels.

Plots of the return spectrum for the two targets for each of the three synthesized beam positions are sho~n in Figure 45. It is clear from Figure 45 that there are t~o peaks in the power spectrums. one at a range of 20 m in the 88~ main beam, and the other at a - 21959~5 97 range of 26 m in the 90~ main beam (For each of these range bins, there is some non-zero power in the other two angular bins. These power levels are due to the antenna array sidelobes. However, these power levels are approximately 10 dB lower than the measured target retums.) ~ ~ 88 Degrees ~ 90 De~ees r ¦ . ~ ~ 92 Degrees ~~ 3 0 - - ~
c Ran~r,e (meters) - Figure 45 Spectral Retums of Synthesized Main Beams at 88~, 90~, and 92~
for Targets at [26 m, 90~] and [20 m, 88~]

4.4 Multiple Tar~ets at the Same Ran~e and Different An~les The test described in this section demonstrates that the radar can distinguish two targets at the same range but different angles. Again, this ability is critical for rnany applications, including automotive radar. Two comer reflectors were placed at 30 m, one at 90~, and the other at 94~. The return from the radar was calibrated, and the signals from all eight channels were combilled to fomm retums in five main beams at 86~, 88~, 90~, 92~.

21~13925 98 and 94~. The target locations were deterrnined by examining the return spectrum in all five of these main beams.

Figure 46 shows the Channels I and 2 time-domain return signals. The returns for Channels 3 and 4, 5 and 6, and 7 and 8 are shown in Figures 47 - 49, respectively. It is noted that the return signals have the same frequency, but the amplitude and phase varies from channel-to-channel. This amplitude variation is caused by the diaele~lt interference patterns from the reflected signals at the different receiver positions. This difference in m~gni~ldes (and slight phase difference) in each of the channels is critical for the anguiar resolution ofthe targets.

Figure 50 shows the return spectrum for each of these eight channels. All eight channels have peaks in their spectrums in the 30 m range bin, and the channel-to-channel power level varies by about 12 dB for this range bin. Once again, the target range can be ~ identified by this spectrum, but target angular position cannot. (Note the high response in the 64 m range bin for Channels 5-8. This is due to sampling noise, 51.2 KHz/8, on the second AID converter power supply. Although this noise level is high, it is still significantly lower than the target power level. In addition. this noise source-can be eliminated in future measurements.) ~1959~5 .50 --Channel I
-- - Channel ' 2.00 --~$ ,00 ~ '~ r~

0.50 -- -0.00 ~ t ~ 't r~ ~
O O O O o o o o o o o o O O O O O
O ~ I ~ 00 C~ ~ oo ~ d '~ o 00 G' O
Time (msec) Figure 46 Channel I and 2 Time-Dornain Returns for Targets at [30 m,90~] and [30 m, 94~]

2.50 Channel 3 - - - - - - Channel 4 2. 00 ~

o~ 100 ~1 0.50 - -0.00 o O O O O O O O O O O O O o o o o o ~ ~ 0~ ~ ~ O G~ O -- ~ ~ Vl ~ 0~ C~ O
O _ ~ r~ o _ v~ o~ -- ~ r~ O ~ ~O O
Time (msec) Figure 47 Channel 3 and 4 Time-Domain Returns for Targets at [30 m,90~] and [30 m~ 94~]

- 2195925 loo 2.50 --Channel 5 - - Channel 6 2.00 - - ' -0 1.50~

1.00 ~
0.50-- - - . . .

o.oo ~ ' O ~ ~ _ ", , ,, ~ ~
O O O ~, o O O o O o o o o o o, o O
O ~ ~ LT LT~ L- LT~ L ~LT~ LT~ L ~ LT L I L~ LT~ L~ LT~
O ~ oo ~ ~oo ~ o ~ ~o o T~me (msec) Figure 48 Channel 5 and 6 Time-Dornain Returns for Targets at [30 m,90~] and [30 m, 94~]

2.50 Channel 7 - - --- Cham~el 8 2.00----~ 1,00 ~ ~ ~ V:
0.50-- ~ :

0.00 o O O c ~ O O O OO O O O O o o o LT~ L~ LT~ ~LTI LT~ LTI LTI LTI LT~ LTJ L~ LTI LT~
O -- ~ r~ ~ 00 -- ~ 00 _ t V) O 00 C~ ~0 o ~ \D ~ ~ t ~ t '~
Time (msec) Figure 49 Channel 7 and 8 Time-Dornain Returns for Targets at [30 UL90~] and [30 m~ 94~]

C lanne 30 ~ ~C~anne --x--Clanne _O ,~ Clanne~ ' 3 ~ ~}CIanne ~
/110~

Range (meters) Figure 50 Spectral Return for all Eight Channels for Targets at [30 rn,90~] and [30 m, 94~]

The complex power vectors from each of the eight channels were combined to form synthesized beam positions at 86~, 88~, 90~, 92~, and 94~. This results in a two-dimensional power spectrum in the range and angle. Plots of the return spectrum for the two targets versus range for each of the five synthesized beam positions are shown in Figure 51. It is clear from this figure that there are two peaks in the power spectrum, both at a range of 30 m, but at angles of 90~ and 94~. For these range bins, there is some non-zero power in the other three angular bins. This is due to the sidelobe response in the synthesized beam at these angles. However, this power level is approximately 10-12 dB
lower than the actual target return.

h ~e ~rees e~rees ~ ~ rl ~e rees I ~ ~eVrees X--q ~e qees _~~

0 10 20 30 ~0 50 60 7080 90 100 Range (meters) Fig~e51SpectralRetu~sofS~es~ed Ma~Beam~at86~,88~,90~,92~,~d94~
forTargetsat~30 ~90~] ~d[30 ~ 94~~

Although plots of power versus range and angular position are displa~ed above, in the preferred embodiment of the invention the computer is configured to compar~ the magnitudes of the returns for each of the angular beam positions in each of the range bins and automatically select (based on the-points with the highest values~
the angular resolution of the targets and the range of the targets, and supply this information to an output device-so that it may be displayed to a user, preferably on a real-time basis.

2195925 ~o3 Chapter 5 CONCLUSION

5.1 Research Summarv The research in this thesis describes a new method for implem~onting beam-steering in FMCW radar systems. A unique radar prototype was designed, built, and tested as a proof of the concept. Testing procedures in Chapter 4 showed the beam-forrning capabilities of the radar prototype. The VCO linearity, a critical pelro~ ce parameter of the radar, was greatly improved in the prototype by implem~nting a novel linearizing algorithm, as discussed in Section 3.4.

The FMCW radar with digital beam-forming represents an advancement in the art of radar technology. This radar has several advantages over traditional RF-based beam-forrning techniques. First, the hardware costs are lower and the reliability is higher.
Second, the target detection time is reduced. Third, sophicticated signal processing techniques can be applied to further improve the accuracy of the radar.

A unique contribution of this thesis is the angular resolution capabilities of the FMCW radar prototype. The prototype hardware was described in Chapter 3. The results presented in Chapter 4 sllow that the IF signals from di~rert;lll receive channels can be digitized, phase shifted. and combined in software to provide angular resolution. Radiation patterns from a single receive channel were measured and compared to the theoretical ~195925 104 pattem. The returns from all receive channels were then combined in software to yield several synthesized pattems with a narrow rnain beam at different positions.

AfklitiQn~l tests indicated that the radar determined the range and angular position of multiple targets. In the first test, the radar identified two targets at di~,e,ll ranges and dilT~ n~ angular positions. ln the second test, the radar uniquely id~ntifie~l two targets at the same range but different angles. This ability to identify range and angular position using digital beam-steering is a unique and significant contribution to the reported radar capabilities in the literature.

5.2.1 Improve Signal Processing Capability Array tapers and FFT windowing functions can be used to improve the range and angular resolution of the radar. In the prototype discussed in Chapters 3 and 4, basic signal processing techniques were used to determine the spectral purity of the signals. A
standard FFT subroutine was used to determine the power spectrum in the range bins. To irnprove DSP capabilities, FFT windowing functions can be used to decrease the 'leakage" between range bins. In the beam-forming algorithms, uniform array tapers were used, resulting in sidelobe levels on the order of 13 dB. Array tapers can be applied during beam-forming to reduce sidelobes and grating lobes.

5.2.2 Develop Real-Time Prototype with Range, Rate, and Angular Capabilities Throughout the thesis, it was assumed that all targets were stationary. This is rarely the case in practice. The principles of digital beam-forming can be applied to detect moving targets, and the system should be able to perform target detection in rnilliseconds, which is essentially real-time for many applications. This would extend the radar operation to provide range, rate, and angular position, not just range and angular position.

It will be appreciated that the radar system disclosed above could easily be adapted for use with moving targets by using several modulation schemes. For example, the multiple receive channels and digital beam forming techniques of the present invention could be combined with the multiple modulation scheme disclosed in U.S. Patent No. 5,268,692 (referenced above), to provide a radar capable of tracking moving' targets. Data from subsequent modulation ~lopes can be matched in order to provide the velocity, range and angular resolution of moving targets.

5.2.3 Reduce l~eceive Antenna Size The receive antenn~s used in this system had an ~7imnth~1 beamwidth of 16~. This is sufficient for narrow synt_esized bearns, but it also produced grating lobes at the extreme mam beam positions. Smaller receive antennas, with broader patterns, could be used to provide wider beam-steering capabilities (though witk less angular resolution).
Errors in experimental data would be reduced due to the decreased sensit~vity of the receive antenna in the main beam.
5.2.4 lmplementing an lmaging Display The rëturn from the radar indicates power versus range and angular position. This information could then be used tO display target return in two dimensions, with color 2195g2~
~- 106 indicating intensity (and therefore target size). This would provide the user with a snapshot of the targets in view.

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Claims (3)

1. A frequency modulated continuous wave radar system with angular position detection, comprising:
an oscillator for generating continuous wave electromagnetic radar output signals;
a D/A converter system operably coupled to said oscillator to modulate said output signals;
a processor operably coupled to said converter system to cause said converter system to produce linearly modulated output signals from the oscillator;
a transmit antenna coupled to said oscillator and adapted to be located for the transmission of radar signals in a predetermined direction; and a plurality of receive channels, each said receive channel comprising a receive antenna adapted to be located to receive radar signals emanating from the transmit antenna and reflecting off objects, a mixer electrically coupled between said oscillator and the receive antenna for producing an IF output signal, and an A/D
converter means electrically coupled to the output of said mixer for sampling the IF output signal and converting the IF output signal into a digital signal;
said processor being electrically coupled to each of said receive channels for receiving said digital signals, the processor including means for performing a fast fourier transform on each of said digital signals and decomposing the transformed signals into magnitude terms and phase terms, means for calibrating the magnitude and phase terms from the different receive channels, means for combining the calibrated magnitude and phase terms from the different receive channels to synthesize receive data for a plurality of radar beam positions, means for comparing said synthesized receive data to determine the angular resolution of said objects; and an output device for indicating the angular resolution of said objects.

2. A frequency modulated continuous wave radar with angular position detection, comprising:
a modulated continuous wave-source for generating linearly modulated continuous wave electromagnetic radar output signals;
a transmit antenna electrically connected to said wave-source for transmitting radar signals;
a plurality of receive channels, each said receive channel comprising a receive antenna for receiving radar signals emanating from the transmit antenna and reflecting off objects, a mixer electrically coupled between said continuous wave-source and said receive antenna, and an A/D converter means electrically coupled to an output of the mixer for converting the mixer output signal into a digital signal;
a processor electrically coupled to each of said receive channels for receiving said digital signals, the processor including means for phase shifting the digital signals from each of the receive channels, means for combining the phase shifted signals, and means for comparing the combined signals produced by different degrees of phase shifting to produce an output indicating the angular resolution of said objects.

3. A method of determining angular resolution of target objects in a frequency modulated continuous wave radar system, the method comprising the steps of:
providing a frequency modulated continuous wave signal generating device for generating a linearly modulated radar signals;
transmitting said radar signals;
receiving in a plurality of receive channels the radar signals which are reflected off the objects;
mixing the radar signals generated by said signal generating device with the signals received in each of the receive channels to produce channel specific IF signals;
converting said channel specific signals to channel specific digital data;
performing a Fast Fourier Transform on the channel specific digital data to produce channel specific frequency domain data;
calibrating the channel specific frequency domain data;
processing the calibrated channel specific frequency domain data to determine the angular position of the objects; and generating an output indicating the angular resolution of the objects.