WO1999014911A1 - A doubly differential detector for digital transmission with continuous phase modulation - Google Patents

A doubly differential detector for digital transmission with continuous phase modulation Download PDF

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Publication number
WO1999014911A1
WO1999014911A1 PCT/EP1997/005101 EP9705101W WO9914911A1 WO 1999014911 A1 WO1999014911 A1 WO 1999014911A1 EP 9705101 W EP9705101 W EP 9705101W WO 9914911 A1 WO9914911 A1 WO 9914911A1
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γåæ
signal
transition weights
carrier frequency
frequency error
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PCT/EP1997/005101
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French (fr)
Inventor
Marko HEINILÄ
Juha S. Korhonen
Eija Saario
Pekka Soininen
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Nokia Networks Oy
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Priority to AU44595/97A priority Critical patent/AU4459597A/en
Priority to PCT/EP1997/005101 priority patent/WO1999014911A1/en
Publication of WO1999014911A1 publication Critical patent/WO1999014911A1/en

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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
    • H04L25/03006—Arrangements for removing intersymbol interference
    • H04L25/03178—Arrangements involving sequence estimation techniques
    • H04L25/03184—Details concerning the metric
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
    • H04L25/03006—Arrangements for removing intersymbol interference
    • H04L2025/0335—Arrangements for removing intersymbol interference characterised by the type of transmission
    • H04L2025/03375—Passband transmission
    • H04L2025/03401—PSK
    • H04L2025/03407—Continuous phase

Definitions

  • the present invention relates to detection of digitally modulated radio signals. More precisely, the invention addresses differential detection of signals which are digitally modulated with methods like minimum-shift keying (MSK) .
  • MSK minimum-shift keying
  • the invention describes so-called doubly differential detection methods which are advantageous when the received microwave radio signal is directly converted to baseband.
  • the received microwave signal is first converted to an intermediate frequency (IF) by using a so-called microwave mixer system.
  • the intermediate-frequency signal is then converted to baseband and the modulated data bits are detected from the waveform. Due to the nature of the microwave components, the low- frequency part of the intermediate frequency signal is contaminated with intensive noise.
  • it is possible to avoid the low-frequency distortions caused by microwave components by simply removing the low-frequency parts of the intermediate- frequency signal with an analog high-pass filter. This is straightforward since at the intermediate frequency the received signal power is not centered at zero frequency but at the intermediate frequency.
  • the intermediate frequency is selected so that only a negligible amount of the signal power is lost due to high-pass filtering of the low-frequency part of the spectrum.
  • the IF signal is converted to baseband where the signal spectrum is centered at the zero frequency, and the data bits modulated m the signal waveform are detected. Nevertheless, savings in the overall system complexity can be achieved by a direct conversion of the microwave signal to baseband without the use of an intermediate frequency. Direct conversion of the microwave signal to baseband allows to avoid the use of intermediate frequency mixer, amplifier and filter circuits. The major drawback of this approach is that the low-frequency noise from the microwave components is then superimposed over the low- equency part of the signal spectrum. Due to this superposition, the signal waveforms are severely distorted and conventional detection methods cannot be used. A solution of this problem is facilitated by the doubly differential detection methods introduced in the document WO-A-94/28 662.
  • a doubly differential detector is a detection system which is preceded by a difference calculation as shown in the figure.
  • the appropriate detection rules depend on the intrinsic nature of the received signal which is related to the used modulation method.
  • MSK minimum-shift keying
  • Minimum-shift keying is a continuous-phase, constant- amplitude digital modulation method.
  • the popularity of MSK and its derivatives like gaussian minimum shift keying (GMSK) and tamed frequency modulation (TFM) is based on their spectral efficiency combined with the constant amplitude of the transmitted signal waveform.
  • the constant amplitude property allows to use efficient transmitter power amplifiers regardless of their typically nonuniform amplification of various signal amplitude levels.
  • the vector r n assumes four distinct values; these values comprise the MSK signal constellation.
  • the data bit b n is related to the transition between two consecutive constellation points r n _ ⁇ and r n .
  • the task of the bit detector is to find the data bits on the basis of the observed points r n .
  • Conventional detector algorithms operate directly with the quantities r n .
  • the motivation for the use of differences rather than the constellation points is that the differences are relatively immune to low-frequency noise; this property motivates the use of this approach in receivers which do not employ intermediate frequency.
  • the data bit b n could be directly determined from the angle ⁇ r . between two difference vectors.
  • the definition of the angle ⁇ n is illustrated in Fig. 3.
  • the difference vectors associated with the four possible pairs of two consecutive data bits are shown in Fig. 4.
  • An inspection of the pictures of Fig. 4 leads to the rule given in WO-A-94/28 662,
  • the drawback of this method is that it does not use all the information coded in the angle sequence ⁇ n , and is, therefore, not optimal in the presence of noise or carrier frequency error.
  • the method for detecting a digitally transmitted signal comprises the following steps: (i) differences of consecutive Cartesian constellation point vectors comprised of samples of inphase and quadrature phase components of the received signal are calculated; (ii) by using the calculated differences of the Cartesian constellation point vectors, transition weights of a feedforward network are evaluated; (iii) the data symbols are detected on the basis of the minimum weight route through the feed-forward network defined by the evaluated transition weights.
  • Fig. 1 shows a schematic system diagram of a digital radio receiver (demodulator) based on doubly differential detection.
  • Fig. 3 illustrates the definition of the angle ⁇ n between two consecutive difference vectors ⁇ n - ⁇ and ⁇ n .
  • Fig. 5 shows a trellis diagram associated with the doubly differential detection algorithm according to the present invention.
  • Fig. 6 illustrates the simulated bit error rate for the detection method of the present invention and for the previous doubly differential detection methods discussed in WO-A-94/28 662, wherein the curves for additive white gaussian noise (AWGN) channel have been obtained with pulse shaped MSK modulation and optimized receiver filters.
  • AWGN additive white gaussian noise
  • the approach of the present invention is to solve the data bits b n on the basis of the observed sequence of angle differences ⁇ n by using methods which are analogous to the maximum likelihood sequence estimation with dynamic programming. All possible data bit sequences can be described by the paths in a feed-forward network shown in Fig. 5.
  • the angle ⁇ n depends only on two data bits, b n - ⁇ and b ⁇ . Therefore, the likelihood of the transition from the state b n _ ⁇ to the state b n in the feed-forward network depends only on the angle ⁇ n : the weights w(b n - ⁇ —> b R ) are certain functions of ⁇ n .
  • the most likely data bit sequence is then obtained by calculating the minimum weight route through the feed-forward network.
  • the minimum weight path can be found, e.g., with the Viterbi algorithm.
  • the method of the present invention can be formulated also without the angles ⁇ n by using directly the pairs of difference vectors, ⁇ n _ ⁇ and ⁇ n .
  • the performance of the new method is compared with the previous algorithm in Fig. 6.
  • Fig. 5 shows the feed-forward network associated with the set of all possible data bit sequences.
  • the weight of a route in the network is given by
  • w(b n - ⁇ - b n ) indicates the contribution of the weight of transition from the node associated with the value of b n _ ⁇ to the node associated with the value of b n in the feedforward network.
  • the network weights are chosen in such a way that the minimum weight route through the network goes through the most likely transmitted data sequence.
  • the detected data bits B n are then selected so that
  • the minimum weight route can be found iteratively by using the well known methods of dynamic programming in the theory of optimization.
  • a particular method of solution in the context of real time communication systems is also known as the Viterbi algorithm (for more details, see, e.g., J.G. Proakis: Digital Communications, 3rd edition, (McGraw-Hill, New York, 1995) ) .
  • the principal content of the invention is the nature of the network transition weights w(b n - ⁇ -A b n ) .
  • the input -o-f the detector system consists of a sequence of constellation point vectors
  • the further processing is carried out with the differences of two successive constellation points:
  • ⁇ n r n - r n _ ⁇ .
  • transition weights are then constructed from the differences ⁇ n or from angles between difference vectors.
  • ⁇ n Z( ⁇ n - 1( ⁇ n ),
  • transition weights w(b n - ⁇ — b n ) may be expressed as follows:
  • ⁇ ,- - 90°, ⁇ n + 180° are interpreted by adding or subtracting a multiple of 360° so that their values are on the interval -180°, ..., +180°.
  • the angle ⁇ n is taken negative if the arc from ⁇ n _ ⁇ to ⁇ n is directed clockwise.
  • each of the four weights w(b n - ⁇ —> b n ) attains its minimum value for the bit sequence b n - ⁇ , b n .
  • one may also include digital carrier frequency error compensation by calculating the angle
  • ⁇ ⁇ C011 A (A n -. l f ⁇ n ) - f
  • f is a quantity proportional to the carrier frequency error .
  • the weights are calculated directly from the differences ⁇ r without determining any angles of the ⁇ n vectors.
  • transition weights w(b n _ ⁇ —> b n ) may be used:
  • m the weights w(b_ ⁇ —> b n ) of the formulas of equation (2) as
  • w(0 ⁇ 0) ⁇ n _! x ⁇ n - f ⁇ n _! • ⁇ n - af ⁇ I ⁇ n _ ⁇ I - + I ⁇ n
  • Z (4) w(l ⁇ 1) - ⁇ r _ ⁇ x ⁇ n + f ⁇ n _, • ⁇ r + af (
  • ') (5) w(0 ⁇ 1) ⁇ n -! • ⁇ n + f ⁇ n -!

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  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Digital Transmission Methods That Use Modulated Carrier Waves (AREA)

Abstract

A method for detecting digitally modulated radio signals is presented. In particular, a method for doubly differential detecting an MSK signal is proposed. The method of the invention involves the calculation of constellation point vectors in the Cartesian coordinate system after determination of the in-phase and quadrature phase components of the received signal. Furthermore, transition weights are calculated from the differences of two consecutive Cartesian constellation point vectors. Moreover, the transition weights may additionally be calculated on the basis of information about the carrier frequency error. These transition weights determine the minimum weight route through the feed-forward network on the basis of which the data symbols are detected. The minimum weight route is determined by one of several possible methods which include those based on dynamic programming and the Viterbi algorithm. Thus, the present invention allows to improve the preformance of the detection method in the presence of noise or carrier frequency error.

Description

A DOUBLY DIFFERENTIAL DETECTOR FOR DIGITAL TRANSMISSION WITH CONTINUOUS PHASE MODULATION
FIELD OF THE INVENTION
The present invention relates to detection of digitally modulated radio signals. More precisely, the invention addresses differential detection of signals which are digitally modulated with methods like minimum-shift keying (MSK) . The invention describes so-called doubly differential detection methods which are advantageous when the received microwave radio signal is directly converted to baseband.
BACKGROUND OF THE INVENTION
In conventional radio-link systems, the received microwave signal is first converted to an intermediate frequency (IF) by using a so-called microwave mixer system. The intermediate-frequency signal is then converted to baseband and the modulated data bits are detected from the waveform. Due to the nature of the microwave components, the low- frequency part of the intermediate frequency signal is contaminated with intensive noise. In the radio systems employing intermediate frequency, it is possible to avoid the low-frequency distortions caused by microwave components by simply removing the low-frequency parts of the intermediate- frequency signal with an analog high-pass filter. This is straightforward since at the intermediate frequency the received signal power is not centered at zero frequency but at the intermediate frequency. The intermediate frequency is selected so that only a negligible amount of the signal power is lost due to high-pass filtering of the low-frequency part of the spectrum. Only after removal of the low-frequency parts, the IF signal is converted to baseband where the signal spectrum is centered at the zero frequency, and the data bits modulated m the signal waveform are detected. Nevertheless, savings in the overall system complexity can be achieved by a direct conversion of the microwave signal to baseband without the use of an intermediate frequency. Direct conversion of the microwave signal to baseband allows to avoid the use of intermediate frequency mixer, amplifier and filter circuits. The major drawback of this approach is that the low-frequency noise from the microwave components is then superimposed over the low- equency part of the signal spectrum. Due to this superposition, the signal waveforms are severely distorted and conventional detection methods cannot be used. A solution of this problem is facilitated by the doubly differential detection methods introduced in the document WO-A-94/28 662. In the doubly differential detection methods, the data bits are detected in such a way that the distorted low-frequency part of the signal waveform is not used in the decision process. A schematic system diagram of a doubly differential demodulator is shown in Fig. 1. By definition, a doubly differential detector is a detection system which is preceded by a difference calculation as shown in the figure. The appropriate detection rules depend on the intrinsic nature of the received signal which is related to the used modulation method. In the document WO-A-94/28 662, appropriate detection rules were described for use with common digital transmission methods like minimum-shift keying (MSK) .
Minimum-shift keying is a continuous-phase, constant- amplitude digital modulation method. The popularity of MSK and its derivatives like gaussian minimum shift keying (GMSK) and tamed frequency modulation (TFM) is based on their spectral efficiency combined with the constant amplitude of the transmitted signal waveform. The constant amplitude property allows to use efficient transmitter power amplifiers regardless of their typically nonuniform amplification of various signal amplitude levels. Fig. 2 illustrates the relationship between the baseband signal samples rn = (rn x, r ) , see Fig. 1, and the data bits bn coded in the MSK signal. In general, the vector rn assumes four distinct values; these values comprise the MSK signal constellation. The data bit bn is related to the transition between two consecutive constellation points rn_ι and rn. A counterclockwise transition corresponds to bn=l while a clockwise transition indicates bn=0 as shown in Fig. 2. The task of the bit detector is to find the data bits on the basis of the observed points rn. Conventional detector algorithms operate directly with the quantities rn. The so- called doubly differential detectors use the differences Δn = rn - rn_ι as indicated in Fig. 1. The motivation for the use of differences rather than the constellation points is that the differences are relatively immune to low-frequency noise; this property motivates the use of this approach in receivers which do not employ intermediate frequency.
As described in the document WO-A-94/28 662, the data bit bn could be directly determined from the angle Δφr. between two difference vectors. The definition of the angle Δφn is illustrated in Fig. 3. The difference vectors associated with the four possible pairs of two consecutive data bits are shown in Fig. 4. An inspection of the pictures of Fig. 4 leads to the rule given in WO-A-94/28 662,
5° bn = < 0
Figure imgf000005_0001
The drawback of this method is that it does not use all the information coded in the angle sequence Δφn, and is, therefore, not optimal in the presence of noise or carrier frequency error.
SUMMARY OF THE INVENTION It is an object of the present invention to provide a method for detecting a digitally transmitted signal having an improved performance compared with the doubly differential detection methods introduced in WO-A-94/28 662.
According to the present invention, the method for detecting a digitally transmitted signal comprises the following steps: (i) differences of consecutive Cartesian constellation point vectors comprised of samples of inphase and quadrature phase components of the received signal are calculated; (ii) by using the calculated differences of the Cartesian constellation point vectors, transition weights of a feedforward network are evaluated; (iii) the data symbols are detected on the basis of the minimum weight route through the feed-forward network defined by the evaluated transition weights.
Advantageous embodiments of the present invention are defined in the dependent claims.
BRIEF DESCRIPTION OF THE DRAWINGS
The present invention will be described hereinbelow by way of example with reference to the accompanying drawings.
Fig. 1 shows a schematic system diagram of a digital radio receiver (demodulator) based on doubly differential detection.
Fig. 2 shows possible transitions between constellation points in MSK modulation wherein a counterclockwise^ rotation corresponds to bn=l while a clockwise rotation indicates bn=0.
Fig. 3 illustrates the definition of the angle Δφn between two consecutive difference vectors Δn-ι and Δn. Fig. 4 illustrates the four possible two bit sequences and the associated difference vectors (for example, Δφn « 90° implies bn-:=bn=l.
Fig. 5 shows a trellis diagram associated with the doubly differential detection algorithm according to the present invention.
Fig. 6 illustrates the simulated bit error rate for the detection method of the present invention and for the previous doubly differential detection methods discussed in WO-A-94/28 662, wherein the curves for additive white gaussian noise (AWGN) channel have been obtained with pulse shaped MSK modulation and optimized receiver filters.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
First, prior to the description of the preferred embodiments, the principle underlying the present invention will be described below.
The approach of the present invention is to solve the data bits bn on the basis of the observed sequence of angle differences Δφn by using methods which are analogous to the maximum likelihood sequence estimation with dynamic programming. All possible data bit sequences can be described by the paths in a feed-forward network shown in Fig. 5. The angle Δφn depends only on two data bits, bn-ι and bπ. Therefore, the likelihood of the transition from the state bn_ι to the state bn in the feed-forward network depends only on the angle Δφn: the weights w(bn-ι —> bR) are certain functions of Δφn. The most likely data bit sequence is then obtained by calculating the minimum weight route through the feed-forward network. The minimum weight path can be found, e.g., with the Viterbi algorithm. The method of the present invention can be formulated also without the angles Δφn by using directly the pairs of difference vectors, Δn_ι and Δn. The performance of the new method is compared with the previous algorithm in Fig. 6.
Fig. 5 shows the feed-forward network associated with the set of all possible data bit sequences. The weight of a route in the network is given by
W(..., bn-2, bn-i, bn, ...) = ∑ W(bn-1 → bn) , n
where w(bn-ι - bn) indicates the contribution of the weight of transition from the node associated with the value of bn_ι to the node associated with the value of bn in the feedforward network. The network weights are chosen in such a way that the minimum weight route through the network goes through the most likely transmitted data sequence. The detected data bits Bn are then selected so that
w r Bn-2, Bn-ι, Bn, min(...,bn,...] W ( ... ,bn-2,bn-ι,bn, .
The minimum weight route can be found iteratively by using the well known methods of dynamic programming in the theory of optimization. A particular method of solution in the context of real time communication systems is also known as the Viterbi algorithm (for more details, see, e.g., J.G. Proakis: Digital Communications, 3rd edition, (McGraw-Hill, New York, 1995) ) .
The principal content of the invention is the nature of the network transition weights w(bn-ι -A bn) . The input -o-f the detector system consists of a sequence of constellation point vectors
... , ri, r2, r3, ... The constellation point vectors rn consist of inphase (I) and quadrature (Q) phase components, so that rn = (rn x, rζj , where the x and y coordinates correspond to the I and Q components, respectively. In the doubly differential detectors, the further processing is carried out with the differences of two successive constellation points:
Δn = rn - rn_ι .
The transition weights are then constructed from the differences Δn or from angles between difference vectors.
Hereinbelow a first preferred embodiment of the present invention will be described with reference to the drawings.
According to the first embodiment of the present invention, in terms of the geometric angle Δφn between two consecutive difference vectors,
Δφn=Z(Δn-1( Δn),
see Fig. 3, the transition weights w(bn-ι — bn) may be expressed as follows:
w(0 → 0) = |Δφn + 90° |α w ( l -» 1 ) = | Δφn - 90 ° | α ( 1 ) w ( l → 0 ) = | Δφn - 180 ° | α w ( 0 A 1 ) = w ( l - 0 ) .
For simplicity, the angles are given here in degrees although other units are more convenient in practice; the notation
I ... I indicates the absolute value, and the superscript α denotes an exponent. One could select, for example, α=l in order to simplify the calculations because multiplications are not involved in this case. Another common selection is to employ quadratic expressions by taking α=2. The formulas are given with the understanding that the expressions Δφ + 90°,
Δφ,- - 90°, Δφn + 180° are interpreted by adding or subtracting a multiple of 360° so that their values are on the interval -180°, ..., +180°. The angle Δφn is taken negative if the arc from Δn_ι to Δn is directed clockwise. On the basis of Fig. 4, it is clear that each of the four weights w(bn-ι —> bn) attains its minimum value for the bit sequence bn-α, bn. In addition, one may also include digital carrier frequency error compensation by calculating the angle
Δφn in the formulas of equation (1) as
Δφπ C011 = A (An-.l f Δn) - f
where f is a quantity proportional to the carrier frequency error .
In the following, a second preferred embodiment of the present invention will be described.
According to the second embodiment, the weights are calculated directly from the differences Δr without determining any angles of the Δn vectors. The following transition weights w(bn_ι —> bn) may be used:
w(0 → 0) = Δn_ι x Δn w(l → 1) = - w(0 - 0) ( w(0 → 1) = Δn-α • Δn w(l → 0) = w(0 → 1) ,
where
Δ„_! Δn = An-AAA - Δn_!yΔn x and
Figure imgf000011_0001
and symbols * and • indicate the vectorial cross product and dot product, respectively.
An alternative set of possible weights w(bn-ι —» bn) is given as follows:
w(0 -A 0) |Δn_ + AA\a + |Δn_Z - ΔZ|α w(l - 1) \An-A - ΔA|α + |Δn-Z + AA\a o: w(l → 0) \A-A + AA\a + |Δ„_ + ΔZ|tt w(0 -> 1) w(l → 0) ,
where the notation | ... I indicates the absolute value and the superscript α denotes an exponent. In order to use weights which do not involve multiplications, one could select α=l . The selection α=2 leads to weights involving squares of sums and differences of Δn vector components.
In practical applications, one may also carry out carrier frequency error compensation as m the first embodiment. Such a correction might be included, e.g., m the weights w(b_ι —> bn) of the formulas of equation (2) as
w(0 → 0) = Δn_! x Δn - fΔn_! • Δn - af { I Δn_α I - + I Δn | Z (4) w(l → 1) = -Δr_± x Δn + fΔn_, • Δr + af (|Δn_Z' + |Δn|') (5) w(0 → 1) = Δn-! • Δn + fΔn-! x Δ, + bf (iΔπ- Z - |Δn|^ (6) w(l → 0) = Δn... • Δn + fΔ„-! x Δr - bf (|Δn_Z2 - IΔZ2) (7)
where f is proportional to the carrier frequency error and the quantities a and b are constants. A reasonable selection for a and b is, for example, a=l/4 and b=l/2. It should be understood that the above description has been made only with reference to the preferred embodiments of the present invention. Therefore, the present invention is not limited to the above described preferred embodiments, but is also intended to cover any variations and modifications to be made by a person skilled in the art within the spirit and scope of the present invention as defined in the appended claims .

Claims

1. A method for detecting a digitally transmitted signal composed of data symbols, comprising the steps of:
(a) converting the signal to the baseband m-phase (I) and quadrature (Q) components,
(b) measuring the I-Q plane constellation point vectors rn = (rx,rn yj, where the x and y coordinates rn x and rn y correspond to the m-phase and quadrature components, respectively,
(c) calculating differences Δn = rn - rn_! of two successive constellation point vectors rn and rn_ι, and
(d) detecting the data symbols bn as a minimum weight route through a feed-forward network defined by transition weights evaluated by using the differences Δn.
2. A method according to claim 1, wherein the transition weights w(b—i — > bn) are expressed by the angle Δφn = Z(Δn-:,
Δ ) between two consecutive difference vectors.
3. A method according to claim 2, wherein the digitally modulated signal is an MSK signal, and the transition weights are
w(0 → 0) |Δφ„ + 90 w(l → 1) |Δφn - 90 o i α
w(l → 0) |Δφn - 180 w(0 → 1) w(l A 0) ,
where
(a) the exponent ╬▒ > 0,
(b) the notation I ... | indicates the absolute value,
(c) the expressions Δφr + 90°, Δφr - 90°, Δφr + 180° are added to or subtracted from a multiple of 360° so that their values are on the interval -180°, ..., +180°, and (d) the angle Δφn is taken negative if the arc from Δn_ι to Δn is directed clockwise.
4. A method according to claim 1, wherein the digitally modulated signal is an MSK signal, and the transition weights
Figure imgf000014_0001
w(0 - 0) = Δn_ι x Δn w(l → 1) = - w(0 → 0) w(0 → 1) = Δn-ι • Δn w(l - 0) = w(0 → 1) ,
where
Figure imgf000014_0002
and
Δn_! • Δn = Δn_!x AA + Δn_!yΔn
where symbols x and ΓÇó indicate the vectorial cross product and dot product, respectively.
5. A method according to claim 1, wherein the digitally modulated signal is an MSK signal, and the transition weights w(bn-ι → bn) are
w(0 → 0) = |Δn-Z + ΔA|α + |Δ~A - Δn x|α w(l → 1) = |Δn_x x - Δn y|α + |Δ,A + Δn x|α w(l → 0) = iΔn-Z + AA\a + IΔ--/ + Δn y|α w(0 → 1) = w(l → 0) ,
where the notation I ... I indicates the absolute value and the superscript ╬▒ denotes a positive exponent.
6. A method according to claim 1, wherein in the step (d) , the transition weights w(bn-ι —» bn) are evaluated by using the differences Δn and information on the carrier frequency error.
7. A method according to claim 6, wherein the transition weights are expressed by the angle Δφ™rr = Z(Δn-ι, Δn) - f between two consecutive difference vectors, corrected by a quantity f related to the carrier frequency error.
8. A method according to claim 7, wherein the digitally transmitted signal is an MSK signal, and the transition weights are
w ( 0 - 0 ) = | Δφc n orr + 90 ° w ( l → 1 ) = I ΔΦ7 - 90 ° w ( l -> 0 ) = I Δφc n orτ - 180 o i α
w ( 0 A 1 ) = w ( l -> 0 ) ,
where
(a) the exponent ╬▒ > 0,
(b) the notation | ... I indicates the absolute value,
(c) the expressions Δφn corr + 90°, Δφn corr - 90°, Δφn corr + 180° are added to or subtracted from a multiple of 360° so that their values are on the interval -180°, ..., +180°,
(d) the angle Δφn included in Δφn corr is taken negative if the arc from Δn_ι to Δn is directed clockwise, and
(e) the quantity f in Δφn corr = Z(Δφn_ι, Δφn) - f is proportional to the estimated carrier frequency error.
9. A method according to claim 6, wherein the digitally modulated signal is an MSK signal, and the transition weights are w(0 - 0) = Δn-! x Δn - fΔn-i • Δn - af ( I Δn_! | 2 + |Δ»n I w(l - 1) = -Δn_ι x Δn +fΔn_ι ■ Δn + af (|Δn_ιl2 + | Δn | w(0 → 1) = Δn_! • Δr. + fΔn_: x Δn + bf (iΔn-Z - | Δn | 2 w(l → 0) = Δ„_ι • Δn + fΔn-n x Δn - bf (|Δn_!|2 - lΔn|2
where f is proportional to the carrier frequency error, and the quantities a and b are constants.
10. A method according to claim 9, wherein the constants a and b have values a = 1/4 and b = 1/2, and f = ΔωTb, where Δω is the carrier frequency error in units rad/sec and T is the bit period.
11. A method according to any of the preceding claims, wherein the minimum weight route is found with the Viterbi algorithm.
PCT/EP1997/005101 1997-09-17 1997-09-17 A doubly differential detector for digital transmission with continuous phase modulation WO1999014911A1 (en)

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PCT/EP1997/005101 WO1999014911A1 (en) 1997-09-17 1997-09-17 A doubly differential detector for digital transmission with continuous phase modulation

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Citations (2)

* Cited by examiner, † Cited by third party
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US5514998A (en) * 1994-01-27 1996-05-07 Hughes Aircraft Company Method and system for demodulating GMSK signals in a cellular digital packet data system
EP0716527A1 (en) * 1994-06-23 1996-06-12 Ntt Mobile Communications Network Inc. Maximum likelihood decoding and synchronous detecting method

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5514998A (en) * 1994-01-27 1996-05-07 Hughes Aircraft Company Method and system for demodulating GMSK signals in a cellular digital packet data system
EP0716527A1 (en) * 1994-06-23 1996-06-12 Ntt Mobile Communications Network Inc. Maximum likelihood decoding and synchronous detecting method

Non-Patent Citations (2)

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Title
ABRARDO ET AL.: "Multiple-symbol differential detection of GMSK for mobile communications", IEEE TRANSACTIONS ON VEHICULAR COMMUNICATIONS., vol. 44, no. 3, August 1995 (1995-08-01), NEW YORK, US, pages 379 - 389, XP000526028 *
SIMON, DIVSALAR: "Maximum-likelihood block detection of noncoherent continuous phase modulation", IEEE TRANSACTIONS ON COMMUNICATIONS, vol. 41, no. 1, January 1993 (1993-01-01), NEW YORK, US, pages 90 - 98, XP000367757 *

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