CN105302935A - Digital demodulating and measurement analysis method - Google Patents
Digital demodulating and measurement analysis method Download PDFInfo
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Abstract
The invention relates to a digital demodulating and measurement analysis method. The method comprises following steps: utilizing a modulating signal for sampling according to sampling frequency; checking based on the requirement for frequency spectrum; selecting better sampling frequency; defining functions time 2 frequency y and time 2 frequency 2 time; utilizing sampling frequency to sample an IQ quadrature modulation signal; intercepting a sequence to filter; getting phase sequences; eliminating frequency errors and calculating systematic phase deviation; eliminating frequency errors and systematic phase deviation; ultimately obtaining a new symbolic sequence; multiplying the symbolic sequence by a coefficient; and obtaining error vector magnitude (EVM), amplitude error (MagErr), phase error and other parameters by comparison operation.The digital demodulating and measurement analysis method has following beneficial effects: with the technical scheme, orthogonal multiplication operation is not relied on; and based on processing of digital signals, an original algorithm is utilized in a rapid, strict and accurate manner.
Description
Technical field
The present invention relates to a kind of digital demodulation and Measurement and analysis method, belong to Survey control field.
Technical background
Use bandpass sampling principle to sample and demodulation to signal, in prior art, have a large amount of achievements in research and scheme.But these schemes employ the demodulation structure of the orthogonal down coversion that is multiplied mostly, do not form the complete demodulation scheme of maturation of total digitalization in addition, thus Shortcomings.
Summary of the invention
The object of the invention is for above-mentioned the deficiencies in the prior art, a kind digital demodulation and Measurement and analysis method are provided.
A kind of digital demodulation and Measurement and analysis method: comprise the following steps:
(1). be f to a carrier frequency
cmodulation signal with sample rate f
ssample, if
Wherein N is integer, and Δ F ∈ (-1,1), Δ F is defined as
with
less that of middle absolute value, function mod (x, y) is the remainder asking x to be divided exactly by y, then the signal of sampling later equivalence carrier frequency is f
e, calculated by formula (2):
f
e＝ΔFf
s(2)；
(2). suppose that the spectral range of the described modulation signal be sampled is
bandwidth is B, then later spectral range of sampling becomes
and sample rate f
scorresponding sampling bandwidth is
if then meet the inequality shown in (3) formula, then think this sample frequency f
everified by spectrum requirement;
(3). in the several sample frequency by the frequency spectrum verification described in step (2), select a preferably sample frequency f
s;
(4). defined function time2frequency: the modulation signal that time span is T is with the preferably sample frequency f described in step (3)
ssample, then sampling interval dt=1/f
sdefine the sample sequence of 2N point, an inverse fast fourier (FFT) is done to this sample sequence, then rearrangement sequence: N number of point is below moved above, shown in (7), then define comprise 2N element complex spectrum sequence as shown in (8) formula:
(5). defined function frequency2time: the sample sequence of described 2N point of step (4) does an inverse fast fourier (IFFT), then rearrangement sequence: N number of point is below moved above, shown in (7);
(6). adopt the preferably sample frequency f described in step (3)
siQ orthogonal demodulation signal is sampled, defines N
rawthe sample sequence S of individual point
raw, then use the function time2frequency of step (4) to process it, define a plural spectrum sequence, then define frequency domain parameter such as formula shown in (9) formula:
Frequency axis sequence f
serycontain the arithmetic progression of 2N element, find out f
seryin with f
ethe sequence number of that numerical value that absolute difference is minimum, is designated as N
e, and natural number N
bthen tried to achieve by formula (10):
Wherein [] refers to round number;
(7). intercept described frequency axis sequence F
serymiddle N
e-N
bpoint is to N
e+ N
b-1 amounts to 2N
bthe element of individual point, forms new ordered series of numbers F
cut, suppose that the time span of measured signal is T
sym, after demodulation, the destination sample of the every symbol period of digital waveform is counted as L
am, then step-length is the object time
the definition that half of zero padding is counted is such as formula shown in (11):
To ordered series of numbers F
cutthe each supplementary N of the right and left
zerosvalue is the element of 0, forms new ordered series of numbers F
extend, then F
extendelement number be 2 (N
b+ N
zeros);
(8). to described ordered series of numbers F
extendcarry out filtering process, and then to F
extenddo mathematic(al) manipulation with function f requency2time, form the plural ordered series of numbers S of time domain
extend, by S
extendthe symbol numbers comprised is denoted as M
syms, each symbol comprises L
amindividual sampled point, in then symbol, the calculating of sample sequence general power is such as formula shown in (12)
In formula, P
lfor sample sequence general power in symbol, C
mlbe l sample sequence in m symbol, P
lsubscript l corresponding to maximal value
bestbe optimum sampling position, get l
bestcorresponding sample sequence vector, is denoted as S
baseband, the time series of its correspondence is set to 0, T
sym, 2T
sym, 3T
symm
symst
sym;
(9). to described S
basebandcompensate of frequency deviation is done to signal.First according to known modulation classification and the S calculated
basebandpower, the mathematical expectation of the constellation point amplitude that amplitude of trying to achieve is maximum, is denoted as Mag
peak, then amplitude of searching for is at interval [0.98Mag
peak, 1.1Mag
peak] S
basebandwith Mag
peakthe symbol sebolic addressing that amplitude is close, forms a new symbol ordered series of numbers S
peak, its yuan of prime number is N
peak, setting loop iteration eliminates the times N of frequency shift (FS)
eli, then a parameter is defined: the symbolic number M participating in eliminating frequency offset computations first
dev-first, and then definition increases truth of a matter factor
increase, shown in (13):
N-th
elithe secondary symbolic number participating in elimination frequency shift (FS)
shown in (14):
Wherein
round under sensing, then picks symbols ordered series of numbers S in this iteration
peakin before
individual symbol processes;
(10). try to achieve the described symbol ordered series of numbers S participating in computing
peakphase sequence, be denoted as Phase
findpeak, then adjudicate the symbol that these participate in computing, try to achieve the phase sequence Phase of judgement symbol
decided, and then the formula of use (15) tries to achieve both phase differential:
Phase
residual＝Phase
findpeak-Phase
decided(15)
By Phase
residualcorresponding time series is denoted as t
residual, then use (16) formula tries to achieve the remaining angular frequency that this computing obtains:
To time-domain signal S
peakall elements and the time series of correspondence, complex symbol S
pcorresponding time series is T
p, carry out frequency error Processing for removing, obtain new symbol S
p_lelidisposal route is such as formula shown in (17):
S
p_1eli＝S
pexp(-jω
residual_1t
p)(17)
Form outmost turns symbol sebolic addressing S
peak_1eli;
(11). to S
peak_1eliaccording to (14) formula choose new before
individual symbol carries out elimination frequency error computing, repeats step (9) and (10), in this circulation, and S
peak_1eliinstead of original S
peak, finally define new sequence S
peak_2eli, the process symbol number of its correspondence is
then by S
peak_2elibring circulation next time into and substitute S
peak_1eli, until the N of setting
elisecondary end, finally obtains remaining angular frequency successively
residual_1, ω
residual_2, ω
residual_3...
then total angular frequency error is:
(12). to the sequence that circulation last in step (11) is formed
carry out the calculating of systematic phase skew: the phase sequence of trying to achieve the symbol participating in computing, is denoted as Phase
findpeak_F, then adjudicate the symbol that these participate in computing, try to achieve the phase sequence Phase of judgement symbol
decided_F, and then (19) formula of use tries to achieve both phase differential:
Phase
diff＝Phase
findpeak_F-Phase
decided_F(19)
And then try to achieve all Phase
diffmean value, be denoted as Phase
diff_ave, i.e. systematic phase skew;
(13). eliminate frequency error and the systematic phase skew of sampling symbol sequence: to described sequence S
basebandwith the M that it comprises
symsindividual complex symbol, if wherein m
symsindividual complex symbol is
corresponding time point is m
symst
sym, then carry out processing as Suo Shi (19) to each symbol.
Thus based on S
basebanddefine new symbol sebolic addressing S
baseband_eli;
(14) by S
baseband_elibe multiplied by a coefficient, make the root mean square amplitude measuring sequence and judgement symbol sebolic addressing equal, and then pass through contrast conting, obtain the parameters such as Error Vector Magnitude (EVM), range error (MagErr), phase error (PhaseErr), and the calculating of frequency error is calculated by (21) formula based on formula (18):
wherein f
deviationfor frequency error;
Further, in described step (1) | Δ F|<0.5;
Further, described step (3) is in the several sample frequency by the frequency spectrum verification described in step (2), and select preferably one, its operation steps is: first provide measured signal from frequency f
cto f
escope in average noise level exceed the multiple N of atural beat noise
f, calculate sampling rate noise P according to formula (4)
n1, P
n1=N
fnKBT (4),
Wherein the definition of N is as shown in formula (1), and K is Boltzmann constant, gets 1.381 × 10
-23, B is signal bandwidth, and T is the thermodynamic temperature of system; And then consider the digital quantization noise of sampling system, according to the sampling bits number N of the known equivalence of hardware index of sampling system
b, then due to the quantizing noise P of digital sample formation
n2as shown in formula (5),
Wherein P
srefer to the power of sampled signal, N
bvalue is relevant with sampling rate, and comprehensive signal to noise ratio (S/N ratio) is defined as formula (6):
To multiple sample frequency f
ssNR is utilized to verify respectively, then the f of the correspondence that SNR is maximum
sbe preferably one;
Further, N in described step (6)
ecan also try to achieve in the following way: if original modulation signals is unipolar pulse modulated radio signal, and the waveform that target is recovered is baseband pulse signal, then N
etry to achieve by the following method: F
seryserial number corresponding to maximum that value of middle amplitude is N
e;
Further, in described step (8), if initial tested described modulation signal is rf modulations pulse signal, and target recovery is baseband pulse signal, then to described S
extendrealistic portion, imaginary part or absolute value obtain baseband pulse signal, and then try to achieve pulse rise time, fall time, pulse width, recurrence interval;
Further, root raised cosine filter (RRC) is adopted to carry out filtering in described step (8);
Have employed technique scheme, the present invention has following beneficial effect: the scheme that the present invention proposes, and no longer relies on orthorhombic phase multiplication, and entirety, based on digital signal processing, employs original creation algorithm, quick, rigorous, accurate.
Accompanying drawing explanation
Fig. 1 is measuring system sampling rate the result schematic diagram;
Fig. 2 is the comprehensive signal to noise ratio (S/N ratio) checking schematic diagram under different sampling rate;
Fig. 3 is the spectrum diagram of the logical radio frequency sampling of band;
Fig. 4 (a) for digital spectrum move after frequency spectrum, (b) is the spectrum diagram after symmetrical zero padding expansion;
Fig. 5 is the average power analysis schematic diagram analyzing the sequence that different sampled point is corresponding in symbol;
In Figure 66 4QAM planisphere, single symbol is always sampled the 20th corresponding planisphere, the i.e. S of 51
baseband;
Fig. 7 does the phase shift analysis that 64QAM frequency error causes, the 1st analysis result schematic diagram;
The phase shift analysis that Fig. 8 causes 64QAM frequency error, the 2nd analysis result schematic diagram;
Fig. 9 does the 2nd time to 64QAM symbol constellation peripheral point and eliminates frequency error result schematic diagram;
The phase shift analysis that Figure 10 causes 64QAM frequency error, analyzes schematic diagram the 11st time;
Figure 11 does the 11st time to 64QAM symbol constellation peripheral point and eliminates frequency error result schematic diagram;
Figure 12 is to the frequency error increment schematic diagram obtained in 64QAM frequency error analysis 11 times at every turn;
Figure 13 calculates the skew of 64QAM systematic phase, the systematic phase offset increment schematic diagram obtained;
Figure 14 eliminates frequency error and the systematic phase skew of sampling symbol sequence to 64QAM, obtains 64QAM constellation diagrams;
Figure 15 carries out the schematic diagram of standardization processing to 64QAM planisphere;
The Error Vector Magnitude of Figure 16 to 4QAM modulation sequence calculates, and obtains result sequence diagram;
The range error of Figure 17 to 64QAM modulation sequence calculates, and obtains result sequence diagram;
The phase error of Figure 18 to 64QAM modulation sequence calculates, and obtains result sequence diagram.
Embodiment
In order to make content of the present invention more easily be clearly understood, below according to specific embodiment also by reference to the accompanying drawings, the present invention is further detailed explanation.
As shown in Fig. 1-18, digital demodulation of the present invention and Measurement and analysis method, concrete operation step is as follows:
(1). be f to a carrier frequency
cmodulation signal with sample rate f
ssample, if
Wherein N is integer, and Δ F ∈ (-1,1), be then defined as Δ F
with
less that of middle absolute value.Wherein function mod (x, y) is the remainder asking x to be divided exactly by y.Obviously have | Δ F|<0.5.The signal equivalence carrier frequency of then sampling later is f
e, shown in (2).
f
e＝ΔFf
s(2)
(2). suppose that the spectral range of the described modulation signal be sampled is
bandwidth is B, then later spectral range of sampling becomes
and sample rate f
scorresponding sampling bandwidth is
if then meet the inequality shown in (3) formula, then think that this sample frequency is verified by spectrum requirement;
(3). in the several sample frequency by the frequency spectrum verification described in step (2), select preferably one.First measured signal to be provided as the case may be from f here
cto f
escope in average noise level exceed the multiple N of atural beat noise
f, then calculate because bandpass sampling includes out-of-band noise in power that wish receives signal spectrum, by P according to formula (4) accordingly
n1be referred to as " sampling rate noise ", P
n1=N
fnKBT (4),
Wherein the definition of N is such as formula shown in (1), and obvious sampling rate is higher, and N is less, and this part noise is less.K refers to Boltzmann constant, can get 1.381 × 10
-23, B is signal bandwidth, and T is the thermodynamic temperature of system, and then considers the digital quantization noise of sampling system, according to the sampling bits number N of the known equivalence of hardware index of sampling system
b, then because the sampling noiset power of digital sample formation is such as formula shown in (5).By P
n2be referred to as " quantizing noise ",
Wherein P
srefer to the power of signal, N
bvalue is relevant with sampling rate, and sampling rate is higher, N
bcan be less, this part noise can be larger.Then comprehensive signal to noise ratio (S/N ratio) is defined as formula (6):
With regard to the optional multiple sample rate f of sampling system
sverify SNR respectively, then the f of the correspondence that SNR is maximum
sbe preferably that;
(4). defined function time2frequency: the signal that T.T. length is T is sampled with preferably fs according to claim 3, obvious sampling interval dt=1/f
sdefine the sample sequence of a 2N point, N is natural number, an inverse fast fourier (FFT) is done to this sample sequence, then rearrangement sequence: N number of point is below moved above, shown in (7), then define comprise 2N element complex spectrum sequence as shown in (8) formula.
(5). defined function frequency2time: the sample sequence that a 2N (N is natural number) puts is done an inverse fast fourier (IFFT), then rearrangement sequence: N number of point is below moved above, shown in (7);
(6). adopt the sample rate f optimized
siQ orthogonal demodulation signal is sampled, defines N
rawthe sample sequence S of point
raw, then use function time2frequency to process it, define a plural spectrum sequence, then define frequency domain parameter such as formula shown in (9) formula.
Obvious frequency axis sequence f
serybe an arithmetic progression containing 2N element, find out f
seryin with f
ethe sequence number of that numerical value that absolute difference is minimum, is designated as N
eif initial tested waveform is unipolar pulse modulated radio signal, and the waveform that target is recovered is baseband pulse signal, then N
ealso can try to achieve by the following method: F
seryserial number corresponding to maximum that value of middle amplitude is N
e, and sequence number N
bthen tried to achieve by formula (10):
Wherein [] refers to round number;
(7). intercept sequence F
serymiddle N
e-N
bpoint is to N
e+ N
b-1 amounts to 2N
bthe element of individual point, forms new ordered series of numbers F
cut.The symbol period (or recurrence interval) supposing measured signal is T
sym, after supposing demodulation, the destination sample of the every symbol period of digital waveform is counted is L
am, then obviously object time step-length is
then define half of zero padding to count:
Then give ordered series of numbers F
cutthe each supplementary N of the right and left
zerosvalue is the element of 0, forms new ordered series of numbers F
extend, obvious F
extendelement number be 2 (N
b+ N
zeros).
(8). according to the concrete condition of digital demodulation, whether determine to F
extendcarry out filtering process, typically, such as use RRC (root raised cosine filter), and then to F
extenddo the mathematic(al) manipulation of frequency2time, form the plural ordered series of numbers S of time domain
extendif initial tested waveform is rf modulations pulse signal, and the waveform that target is recovered is baseband pulse signal, so just can to S
extendrealistic portion, imaginary part or absolute value obtain baseband pulse signal, and then try to achieve the information such as pulse rise time, fall time, pulse width, recurrence interval.
By S
extendthe symbol numbers comprised is denoted as M
syms, each symbol comprises L
amindividual sampled point, then by S
extendbe organized into the form of table 1.
Table 1 time-domain signal S
extendform arrange form
Sorting table 1 determines the optimum sampling position in symbol, obtains P
lmaximal value, in formula, P
lfor sample sequence general power in symbol, C
mlbe l sample sequence in m symbol, P
lsubscript l corresponding to maximal value
bestbe optimum sampling position, get l
bestcorresponding sample sequence vector, is denoted as S
baseband, the time series of its correspondence is set to 0, T
sym, 2T
sym, 3T
symm
symst
sym;
(9). based on S
basebandcompensate of frequency deviation is done to signal.First according to known modulation classification and the S calculated
basebandpower, the mathematical expectation of the constellation point amplitude that amplitude of trying to achieve is maximum, is denoted as Mag
peak, then S is searched for
basebandin with Mag
peakthe symbol that amplitude is close, such as typically, amplitude is at interval [0.98Mag
peak, 1.1Mag
peak] point, form a new symbol ordered series of numbers S
peak, first prime number is N
peak, and the time series of correspondence, as shown in table 2.
Table 2 time-domain signal S
peakand the time series of correspondence
| Symbol sebolic addressing | S p1 | S p2 | … | S pNpeak |
| Time series | t p1 | t p2 | … | t pNpeak |
The times N that loop iteration eliminates frequency shift (FS) can be set in Practical Project
eli, then a parameter is defined: the symbolic number M participating in eliminating frequency offset calculation first
dev-first, and then definition increases truth of a matter factor
increase, shown in (13).
N-th
elithe symbolic number that secondary participation frequency shift (FS) is eliminated
shown in (14):
Wherein
round under sensing, then picks symbols ordered series of numbers S in this iteration
peakin before
individual symbol processes.The symbolic number of so each process is all once many than front.And avoid being just started single treatment symbol too much, symbol is judged the algorithm caused by accident and was lost efficacy.Thus improve the stability of algorithm entirety, the flow process of process is as follows.
(10). try to achieve the phase sequence of the symbol participating in computing, be denoted as Phase
findpeak, then adjudicate the symbol that these participate in computing, try to achieve the phase sequence Phase of judgement symbol
decided, and then (15) formula of use tries to achieve both phase differential.
Phase
residual＝Phase
findpeak-Phase
decided(15)
Phase
residualalong with the part increment of linearly change causes, then by Phase due to frequency error
residualcorresponding time series is denoted as t
residual, then use (16) formula to try to achieve the remaining angular frequency that epicycle computing obtains, this process is similar to be done fitting a straight line and asks slope.
For the S of time-domain signal shown in table 2
peakall elements and the time series of correspondence, complex symbol S
pcorresponding time point is S
p, carry out frequency error Processing for removing, obtain new symbol S
p_1elidisposal route is such as formula shown in (17):
S
p_1eli＝S
pexp(-jω
residual_1t
p)(17)
Then define new outmost turns symbol sebolic addressing S
peak_1eli. if demodulation relates to wave filter, also needs also to carry out corresponding process to the time domain impulse response of wave filter.
(11). for S
peak_1eliaccording to (14) formula choose new before
individual symbol carries out elimination frequency error computing, repeats the algorithm described in claim the 9,10, in this circulation, and obvious S
peak_1eliinstead of original S
peak, finally define new S
peak_2eli(corresponding process symbol number is
).Then by S
peak_2elibring next round circulation into and substitute S
peak_1eliusually
corresponding process symbol number is
until the N of setting
elisecondary end, finally obtains remaining angular frequency successively
residual_1, ω
residual_2, ω
residual_3...
then total angular frequency error is:
(12). in step (11), last repeating query ring is formed
carry out the calculating of systematic phase skew.Try to achieve the phase sequence of the symbol participating in computing, be denoted as Phase
findpeak_F, then adjudicate the symbol that these participate in computing, try to achieve the phase sequence Phase of judgement symbol
decided_F, and then (19) formula of use tries to achieve both phase differential.
Phase
diff＝Phase
findpeak_F-Phase
decided_F(19)
Try to achieve all Phase
diffmean value, be denoted as Phase
diff_ave, be namely systematic phase skew.If necessary, the computing eliminating systematic phase skew can circulate and repeatedly add up.
(13). eliminate frequency error and the systematic phase skew of sampling symbol sequence.Symbol sebolic addressing S then with regard to mentioning in step (8)
baseband, wherein comprise M
symsindividual complex symbol.Usually, if wherein m
symssymbol is
(the corresponding time is m
symst
sym), then carry out processing as Suo Shi (19) to each symbol.
Then based on S
basebanddefine new symbol sebolic addressing S
baseband_eli.
(14). by S
baseband_elibe multiplied by a coefficient, make the root mean square amplitude measuring sequence and judgement symbol sebolic addressing equal, and then can contrast conting be passed through, according to existing normalized by definition, obtain the parameters such as Error Vector Magnitude (EVM), range error (MagErr), phase error (PhaseErr), and the calculating of frequency error is calculated by (21) formula based on formula (18):
Case study on implementation
Utilize method of the present invention to analyze digital modulation signals, signal parameter and measurement parameter as shown in table 3.
Table 3 digital modulation signals parameter and measurement parameter
| Character rate | 20Mbaud |
| Modulation system | 64QAM |
| Baseband filter | RRC |
| Carrier frequency | 2.7GHz |
| Measuring system sampling rate | 156MSa/s |
Verify measuring system sampling rate according to step (2), the result as shown in Figure 1.Obvious measured signal equivalence frequency spectrum in sampling FFT bandwidth, then have passed checking;
Then according to step (3), carry out comprehensive signal to noise ratio (S/N ratio) (SNR) checking based on measuring system known parameters, as shown in Figure 2, Fig. 3 is the frequency spectrum obtaining with logical radio frequency sampling based on step (6) to result;
Fig. 4 based on step (7) do digital spectrum move after frequency spectrum (a), and symmetrical zero padding expansion after frequency spectrum (b);
Fig. 5 analyzes the average power analysis result of the sequence that different sampled point is corresponding in symbol based on step (8);
Fig. 6 obtains 64QAM planisphere based on step (8) analysis, and single symbol is always sampled the 20th corresponding planisphere, the i.e. S of 51
baseband;
Fig. 7 does based on step (9) and (10) phase shift analysis that 64QAM frequency error causes, and analyzes for the 1st time;
Fig. 8 does based on step (9) and (10) phase shift analysis that 64QAM frequency error causes, and analyzes for the 2nd time;
Fig. 9 obtains 64QAM symbol constellation peripheral point based on step (9) and (10), eliminates frequency error the 2nd time;
Figure 10 does based on step (9) and (10) phase shift analysis that 64QAM frequency error causes, and analyzes for the 11st time;
Figure 11 obtains 64QAM symbol constellation peripheral point based on step (9) and (10), eliminates frequency error the 11st time;
Figure 12 does the analysis of 64QAM frequency error based on step (9) and (10) and amounts to 11 times, frequency error (or being referred to as residual carrier) increment at every turn obtained, and is obviously convergence, which illustrates the validity of algorithm;
Figure 13 does the calculating of 64QAM systematic phase skew based on step (12), and the systematic phase at every turn obtained skew (referred to as phase shift) increment, is obviously convergence, which illustrates the validity of algorithm;
Figure 15 carries out standardization processing based on step (14) to 64QAM planisphere, makes the root mean square amplitude measuring sequence and judgement symbol sebolic addressing equal, calculates digital modulation error parameter accordingly.
Table 4 is based on measurement demodulation result of the present invention:
Table 4
| Parameter | Demodulated methed result |
| EVM peak value | 32.01％ |
| There is position in EVM peak value | 253rd symbol |
| EVMRMS value | 3.97％ |
| MagErr peak value | 26.45％ |
| There is position in MagErr peak value | 173rd symbol |
| MagErrRMS value | 2.51％ |
| PhaseErr peak value | 13.94° |
| There is position in PhaseErr peak value | 253rd symbol |
| PhaseErrRMS value | 2.48° |
| Frequency error | 613.45Hz |
Above-described specific embodiment; object of the present invention, technical scheme and beneficial effect are further described; be understood that; the foregoing is only specific embodiments of the invention; be not limited to the present invention; within the spirit and principles in the present invention all, any amendment made, equivalent replacement, improvement etc., all should be included within protection scope of the present invention.
Claims (6)
1. digital demodulation and a Measurement and analysis method, is characterized in that: comprise the following steps:
(1). be f to a carrier frequency
cmodulation signal with sample rate f
ssample, if
Wherein N is integer, and Δ F ∈ (-1,1), Δ F is defined as
with
less that of middle absolute value, function mod (x, y) is the remainder asking x to be divided exactly by y, then the signal of sampling later equivalence carrier frequency is f
e, calculated by formula (2):
f
e＝ΔFf
s(2)；
(2). suppose that the spectral range of the described modulation signal be sampled is
bandwidth is B, then later spectral range of sampling becomes
and sample rate f
scorresponding sampling bandwidth is
if then meet the inequality shown in (3) formula, then think this sample frequency f
everified by spectrum requirement;
(3). in the several sample frequency by the frequency spectrum verification described in step (2), select a preferably sample frequency f
s;
(4). defined function time2frequency: the modulation signal that time span is T is with the preferably sample frequency f described in step (3)
ssample, then sampling interval dt=1/f
sdefine the sample sequence of 2N point, an inverse fast fourier (FFT) is done to this sample sequence, then rearrangement sequence: N number of point is below moved above, shown in (7), then define comprise 2N element complex spectrum sequence as shown in (8) formula:
(S
1S
2S
3...S
NS
N+1S
N+2S
N+3...S
2N)
→(S
N+1S
N+2S
N+3...S
2NS
1S
2S
3...S
N)(7)
F
sery＝[C
F1C
F2C
F3...C
F2N-2C
F2N-1C
F2N](8)；
(5). defined function frequency2time: the sample sequence of described 2N point of step (4) does an inverse fast fourier (IFFT), then rearrangement sequence: N number of point is below moved above, shown in (7);
(6). adopt the preferably sample frequency f described in step (3)
siQ orthogonal demodulation signal is sampled, defines N
rawthe sample sequence S of individual point
raw, then use the function time2frequency of step (4) to process it, define a plural spectrum sequence, then define frequency domain parameter such as formula shown in (9) formula:
Frequency axis sequence f
serycontain the arithmetic progression of 2N element, find out f
seryin with f
ethe sequence number of that numerical value that absolute difference is minimum, is designated as N
e, and natural number N
bthen tried to achieve by formula (10):
Wherein [] refers to round number;
(7). intercept described frequency axis sequence F
serymiddle N
e-N
bpoint is to N
e+ N
b-1 amounts to 2N
bthe element of individual point, forms new ordered series of numbers F
cut, suppose that the time span of measured signal is T
sym, after demodulation, the destination sample of the every symbol period of digital waveform is counted as L
am, then step-length is the object time
the definition that half of zero padding is counted is such as formula shown in (11):
To ordered series of numbers F
cutthe each supplementary N of the right and left
zerosvalue is the element of 0, forms new ordered series of numbers F
extend, then F
extendelement number be 2 (N
b+ N
zeros);
(8). to described ordered series of numbers F
extendcarry out filtering process, and then to F
extenddo mathematic(al) manipulation with function f requency2time, form the plural ordered series of numbers S of time domain
extend, by S
extendthe symbol numbers comprised is denoted as M
syms, each symbol comprises L
amindividual sampled point, in then symbol, the calculating of sample sequence general power is such as formula shown in (12)
In formula, P
lfor sample sequence general power in symbol, C
mlbe l sample sequence in m symbol, P
lsubscript l corresponding to maximal value
bestbe optimum sampling position, get l
bestcorresponding sample sequence vector, is denoted as S
baseband, the time series of its correspondence is set to 0, T
sym, 2T
sym, 3T
symm
symst
sym;
(9). to described S
basebandcompensate of frequency deviation is done to signal.First according to known modulation classification and the S calculated
basebandpower, the mathematical expectation of the constellation point amplitude that amplitude of trying to achieve is maximum, is denoted as Mag
peak, then amplitude of searching for is at interval [0.98Mag
peak, 1.1Mag
peak] S
basebandwith Mag
peakthe symbol sebolic addressing that amplitude is close, forms a new symbol ordered series of numbers S
peak, its yuan of prime number is N
peak, setting loop iteration eliminates the times N of frequency shift (FS)
eli, then a parameter is defined: the symbolic number M participating in eliminating frequency offset computations first
dev-first, and then definition increases truth of a matter factor
increase, shown in (13):
N-th
elithe secondary symbolic number participating in elimination frequency shift (FS)
shown in (14):
Wherein
round under sensing, then picks symbols ordered series of numbers S in this iteration
peakin before
individual symbol processes;
(10). try to achieve the described symbol ordered series of numbers S participating in computing
peakphase sequence, be denoted as Phase
findpeak, then adjudicate the symbol that these participate in computing, try to achieve the phase sequence Phase of judgement symbol
decided, and then the formula of use (15) tries to achieve both phase differential:
Phase
residual＝Phase
findpeak-Phase
decided(15)
By Phase
residualcorresponding time series is denoted as t
residual, then use (16) formula tries to achieve the remaining angular frequency that this computing obtains:
To time-domain signal S
peakall elements and the time series of correspondence, complex symbol S
pcorresponding time series is T
p, carry out frequency error Processing for removing, obtain new symbol S
p_lelidisposal route is such as formula shown in (17):
S
p_1eli＝S
pexp(-jω
residual_1t
p)(17)
Form outmost turns symbol sebolic addressing S
peak_1eli;
(11). to S
peak_1eliaccording to (14) formula choose new before
individual symbol carries out elimination frequency error computing, repeats step (9) and (10), in this circulation, and S
peak_1eliinstead of original S
peak, finally define new sequence S
peak_2eli, the process symbol number of its correspondence is
then by S
peak_2elibring circulation next time into and substitute S
peak_1eli, until the N of setting
elisecondary end, finally obtains remaining angular frequency successively
residual_1, ω
residual_2,
then total angular frequency error is:
(12). to the sequence that circulation last in step (11) is formed
carry out the calculating of systematic phase skew: the phase sequence of trying to achieve the symbol participating in computing, is denoted as Phase
findpeak_F, then adjudicate the symbol that these participate in computing, try to achieve the phase sequence Phase of judgement symbol
decided_F, and then (19) formula of use tries to achieve both phase differential:
Phase
diff＝Phase
findpeak_F-Phase
decided_F(19)
And then try to achieve all Phase
diffmean value, be denoted as Phase
diff_ave, i.e. systematic phase skew;
(13). eliminate frequency error and the systematic phase skew of sampling symbol sequence: to described sequence S
basebandwith the M that it comprises
symsindividual complex symbol, if wherein m
symsindividual complex symbol is
corresponding time point is m
symst
sym, then carry out processing such as formula (20) Suo Shi to each symbol,
Thus based on S
basebanddefine new symbol sebolic addressing S
baseband_eli;
(14) by S
baseband_elibe multiplied by a coefficient, make the root mean square amplitude measuring sequence and judgement symbol sebolic addressing equal, and then pass through contrast conting, obtain the parameters such as Error Vector Magnitude (EVM), range error (MagErr), phase error (PhaseErr), and the calculating of frequency error is calculated by (21) formula based on formula (18):
wherein f
deviationfor frequency error.
2. method according to claim 1, is characterized in that: in described step (1) | Δ F|<0.5.
3. method according to claim 1, it is characterized in that: described step (3) is in the several sample frequency by the frequency spectrum verification described in step (2), select preferably one, its operation steps is: first evaluate measured signal from frequency f
cto f
escope in average noise level exceed the multiple N of atural beat noise
f, calculate sampling rate noise P according to formula (4)
n1, P
n1=N
fnKBT (4),
Wherein the definition of N is as shown in formula (1), and K is Boltzmann constant, gets 1.381 × 10
-23, B is signal bandwidth, and T is the thermodynamic temperature of system; And then consider the digital quantization noise of sampling system, according to the sampling bits number N of the known equivalence of hardware index of sampling system
b, then due to the quantizing noise P of digital sample formation
n2as shown in formula (5),
Wherein P
srefer to the power of sampled signal, N
bvalue is relevant with sampling rate, and comprehensive signal to noise ratio (S/N ratio) is defined as formula (6):
To multiple sample frequency f
ssNR is utilized to verify respectively, then the f of the correspondence that SNR is maximum
sbe preferably one.
4. method according to claim 1, is characterized in that: N in described step (6)
ecan also try to achieve in the following way: if original modulation signals is unipolar pulse modulated radio signal, and the waveform that target is recovered is baseband pulse signal, then N
etry to achieve by the following method: F
seryserial number corresponding to maximum that value of middle amplitude is N
e.
5. method according to claim 1, is characterized in that: in described step (8), if initial tested modulation signal is rf modulations pulse signal, and target recovery is baseband pulse signal, then to described S
extendrealistic portion, imaginary part or absolute value obtain baseband pulse signal, and then try to achieve pulse rise time, fall time, pulse width, recurrence interval.
6. method according to claim 1, is characterized in that: adopt root raised cosine filter (RRC) to carry out filtering in described step (8).
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| CN108347396B (en) * | 2017-01-25 | 2022-08-16 | 三星电子株式会社 | System and method for tracking and compensating timing offset and frequency offset of modulated signal |
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| CN110113033A (en) * | 2019-04-08 | 2019-08-09 | 长春理工大学光电信息学院 | Pulse data compression sampling method |
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| CN112162152A (en) * | 2020-08-31 | 2021-01-01 | 南京亿杰明信息技术有限公司 | Sine wave coherent pulse train signal frequency estimation method based on phase straight line fitting |
| CN112162152B (en) * | 2020-08-31 | 2024-01-26 | 南京亿杰明信息技术有限公司 | Sine wave coherent pulse train signal frequency estimation method based on phase straight line fitting |
| CN112729152A (en) * | 2020-12-08 | 2021-04-30 | 广东工业大学 | Peak extraction method based on hyperbolic threshold denoising |
| CN113189403A (en) * | 2021-04-12 | 2021-07-30 | 东北大学 | Self-adaptive orthogonal demodulation method |
| CN113189403B (en) * | 2021-04-12 | 2022-11-25 | 东北大学 | Self-adaptive orthogonal demodulation method |
| CN114828370A (en) * | 2022-03-18 | 2022-07-29 | 合肥工业大学 | Self-adaptive phase difference calculation method for plasma density measurement |
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