CN105302935B - Digital demodulation and measurement analysis method - Google Patents
Digital demodulation and measurement analysis method Download PDFInfo
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Abstract
The present invention relates to a kind of digital demodulation and measurement analysis method, use and modulated signal is sampled with sample frequency, spectrum requirement verifies, selection is more excellent, defined function time2frequency and frequency2time, IQ orthogonal demodulation signals are sampled using sample frequency, interception sequence is filtered, ask for its phase sequence, carry out eliminating frequency error and systematic phase calculations of offset, eliminate frequency error and systematic phase skew, finally obtain new symbol sebolic addressing, the symbol sebolic addressing is multiplied by coefficient, pass through comparison calculation, obtain Error Vector Magnitude（EVM）, range error（MagErr）, phase error（PhaseErr）Deng parameter.Scheme proposed by the present invention, orthogonal multiplication operation is eliminated the reliance on, it is overall to be based on Digital Signal Processing, original creation algorithm has been used, it is quick, rigorous, accurate.
Description
Technical Field
The invention relates to a digital demodulation and measurement analysis method, belonging to the field of measurement control.
Technical Field
There have been a number of research efforts and solutions in the prior art for sampling and demodulating signals using the bandpass sampling principle. However, these schemes mostly use the demodulation structure of quadrature multiplication down-conversion, and furthermore, a fully digital mature complete demodulation scheme is not formed, so that the problems exist.
Disclosure of Invention
The present invention is directed to a method for digital demodulation and measurement analysis, which overcomes the above-mentioned shortcomings of the prior art.
A digital demodulation and measurement analysis method: the method comprises the following steps:
(1) For a carrier frequency of f c At a sampling rate f s Sampling is carried out, and
where N is an integer, Δ F ∈ (-1, 1), Δ F is defined asAndif the function mod (x, y) is the remainder of dividing x by y, the equivalent carrier frequency of the sampled signal is f e Calculated from equation (2):
f e ＝ΔFf s (2)；
(2) Assume that the spectral range of the modulation signal being sampled isThe bandwidth is B, the spectral range after sampling becomesAnd a sampling rate f s The corresponding sampling bandwidth isThe sampling frequency f is considered to be the sampling frequency f if the inequality shown in equation (3) is satisfied e Passing the spectrum requirement check;
(3) Selecting a preferred sampling frequency f from the plurality of sampling frequencies that pass the spectrum check of step (2) s ；
(4) Defining a function time2frequency for the modulated signal of time length T and the preferred sampling frequency f as described in step (3) s Sampling is carried out, then the sampling interval dt =1/f s Forming a sampling sequence of 2N points, performing inverse Fast Fourier Transform (FFT) on the sampling sequence, and then rearranging the sequence: moving the next N points to the front, as shown in equation (7), a complex spectrum sequence containing 2N elements is formed as shown in equation (8):
(S 1 S 2 S 3 ... S N S N+1 S N+2 S N+3 ... S 2N )
(7)
→(S N+1 S N+2 S N+3 ... S 2N S 1 S 2 S 3 ... S N )
F sery ＝[C F1 C F2 C F3 ... C F2N-2 C F2N-1 C F2N ] (8)；
(5) Defining a function frequency2time, performing Inverse Fast Fourier Transform (IFFT) on the sampling sequence of the 2N points in the step (4), and then rearranging the sequence: moving the back N points to the front, as shown in formula (7);
(6) Using the preferred sampling frequency f of step (3) s The IQ quadrature modulation signal is sampled to form N raw Sampling sequence S of points raw And (3) processing the frequency domain data by using the function time2frequency in the step (4) to form a complex frequency spectrum sequence, wherein the defined frequency domain parameter is as shown in the formula (9):
frequency axis sequence f sery Includes 2N element arithmetic progression to find f sery In and f e The number of the value with the smallest absolute difference is marked as N e And a natural number N B Then, the following equation (10) is used:
wherein [ ] means rounding off and taking an integer;
(7) Intercepting said frequency axis sequence F sery In N e -N B Point to N e +N B -1 point totaling 2N B Elements of dots forming a new array F cut Assuming that the time length of the signal to be measured is T sym The target sampling point number of each symbol period of the demodulated digital waveform is L am Then the target time step isThe definition of the number of half zero padding points is shown as formula (11):
given sequence F cut The left and right sides are respectively supplemented with N zeros Element with value 0, forming a new sequence F extend Then F is extend The number of elements of (2) (N) B +N zeros )；
(8) For said array F extend Performing filtering process to F extend Performing mathematical transformation by using the function frequency2time to form a time domain complex number sequence S extend A 1, S extend The number of symbols contained is marked as M syms Each symbol containing L am For each sampling point, the calculation of the total power of the sampling sequence in the symbol is shown in the formula (12)
In the formula, P l For the total power of the sample sequence within the symbol, C ml For the l-th sample sequence, P, in the m-th symbol l Subscript l corresponding to the maximum value of best I.e. the best sampling position, take l best The corresponding sample sequence vector, denoted S baseband Set its corresponding time series to 0,T sym ，2T sym ,3T sym …M syms T sym ；
(9) To the S baseband Performing frequency offset compensation on the signal, firstly, according to the known modulation system and S obtained by calculation baseband Power, to obtain the mathematical expected value of the amplitude of the constellation point with the maximum amplitude, which is recorded as Mag peak Then the search amplitude is in the interval [0.98Mag ] peak ,1.1Mag peak ]S of baseband And Mag peak The symbol sequences with similar amplitudes form a new symbol sequence S peak The number of elements is N peak Setting the frequency offset elimination number N of loop iteration eli Then, a parameter is defined: number of symbols M participating in calculation of frequency offset cancellation for the first time dev-first Further define the growth base factor increase As shown in formula (13):
n th eli Number of symbols participating in frequency offset cancellationAs shown in equation (14):
whereinPointing to round down, then choose the symbol sequence S in this iteration peak Front of (5)Processing each symbol;
(10) Find the sequence S of symbols involved in the calculation peak Phase sequence of (2), denoted as Phase findpeak Then, these symbols involved in the operation are judged, and the Phase sequence Phase of the judged symbols is obtained decided Further, the phase difference between the two is obtained by using equation (15):
Phase residual ＝Phase findpeak -Phase decided (15)
will Phase residual The corresponding time series is denoted t residual Then, the residual angular frequency obtained by the operation is obtained by using the formula (16):
for time domain signal S peak All elements of (2) and their corresponding time series, complex symbols S p The corresponding time series is T p Performing frequency error elimination to obtain new symbol S p_leli The treatment method is shown as the formula (17):
S p_1eli ＝S p exp(-jω residual_1 t p ) (17)
wherein, t p For the time sequence, an outermost-circle symbol sequence S is formed peak_1eli ；
(11) To S peak_1eli Selecting a new preamble according to equation (14)The symbol is subjected to a calculation for eliminating the frequency error, steps (9) and (10) are repeated, in this cycle, S peak_1eli Replaces the original S peak Finally, a new sequence S is formed peak_2eli Corresponding processing thereofThe number of symbols isThen S is peak_2eli Carry over to the next cycle to replace S peak_1eli Up to the set Nth eli After the second time, the successive residual angular frequency is finally obtainedThe total angular frequency error is then:
(12) For the sequence formed in the last cycle in step (11)Systematic phase offset calculation is performed: determining the Phase sequence of the symbols involved in the calculation, denoted Phase findpeak_F Then, these symbols involved in the operation are judged, and the Phase sequence Phase of the judged symbols is obtained decided_F Further, the phase difference between the two is obtained by using the equation (19):
Phase diff ＝Phase findpeak_F -Phase decided_F (19)
further find all the phases diff Average value of (2) is denoted as Phase diff_ave I.e. systematic phase offset;
(13) Removing the frequency error and systematic phase offset of the sampled symbol sequence: for the sequence S baseband And M contained therein syms A complex number symbol of which m is syms A plurality of symbols isCorresponding time point is m syms T sym Then each symbol is processed as shown in equation (20),
(20)
thereby based on S baseband A new symbol sequence S is formed baseband_eli ；
(14) Will S baseband_eli Multiplying a coefficient to make the amplitude root mean square value of the measurement sequence and the amplitude root mean square value of the decision symbol sequence equal, and obtaining parameters such as error vector amplitude (EVM), amplitude error (MagErr), phase error (PhaseErr) and the like through comparison calculation, wherein the calculation of the frequency error is obtained through the formula (21) based on the formula (18):
wherein f is deviation Is the frequency error;
further, the | Δ F | in the step (1) is less than 0.5;
further, the step (3) selects a better one of the plurality of sampling frequencies passing through the spectrum check of the step (2), and the operation steps are as follows: firstly, the slave frequency f of the measured signal is given c To f e In a range where the average noise level exceeds the natural thermal noise by a multiple N F The multiple sampling rate noise P is calculated according to the formula (4) N1 ，P N1 ＝N F ·N·K·B·T em (4),
Wherein N is defined as formula (1), K is Boltzmann constant, and is 1.381 × 10 -23 B is the signal bandwidth, T em Is the thermodynamic temperature of the system; furthermore, the equivalent sampling bit number N can be known according to the hardware index of the sampling system by considering the digital quantization noise of the sampling system b Due to quantization noise P formed by the digital samples N2 As shown in the formula (5), the,
wherein P is s Refers to the power, N, of the sampled signal b The value is related to the sampling rate, and the signal-to-noise ratio is integratedDefined by formula (6):
for a plurality of sampling frequencies f s Using SNR to check respectively, the corresponding f with the maximum SNR s The better one is;
further, N in the step (6) e It can also be obtained by: if the initial modulation signal is a unipolar pulse modulated radio frequency signal and the target recovered waveform is a baseband pulse signal, then N e The method comprises the following steps: f sery The sequence number corresponding to the value with the maximum amplitude is N e ；
Further, in the step (8), if the modulated signal to be measured initially is a radio frequency modulated pulse signal and the target recovery is a baseband pulse signal, then the S is measured extend Solving a real part, an imaginary part or an absolute value to obtain a baseband pulse signal, and further solving the rise time, the fall time, the pulse width and the pulse period of the pulse;
further, a root raised cosine filter (RRC) is used for filtering in the step (8);
by adopting the technical scheme, the invention has the following beneficial effects: the scheme provided by the invention does not depend on orthogonal multiplication operation, is based on digital signal processing as a whole, uses an original algorithm, and is rapid, precise and accurate.
Drawings
FIG. 1 is a schematic diagram of a sample rate verification result of a measurement system;
FIG. 2 is a schematic diagram illustrating verification of the integrated SNR at different sampling rates;
FIG. 3 is a schematic spectrum diagram of bandpass RF sampling;
FIG. 4 (a) is the shifted spectrum of the digital spectrum, and (b) is the left-right symmetric zero-filling expanded spectrum;
FIG. 5 is a schematic diagram of an average power analysis of sequences corresponding to different sampling points within an analysis symbol;
the 20 th corresponding constellation of 51 points of a total sampling of a single symbol in the constellation of fig. 6 64QAM, i.e. S baseband ；
FIG. 7 is a schematic diagram showing the 1 st analysis result of the phase shift analysis caused by the 64QAM frequency error;
FIG. 8 is a schematic diagram of the results of the phase shift analysis and the 2 nd analysis caused by the 64QAM frequency error;
FIG. 9 is a schematic diagram illustrating the frequency error elimination result of 2 nd time for peripheral points of a 64QAM symbol constellation diagram;
FIG. 10 is a schematic diagram of the analysis of phase shift caused by 64QAM frequency error, analysis 11;
FIG. 11 is a diagram illustrating the 11 th frequency error removal for peripheral points of a 64QAM symbol constellation diagram;
FIG. 12 is a schematic diagram of frequency error increments obtained in each of 11 64QAM frequency error analyses;
FIG. 13 is a schematic diagram of systematic phase shift increments obtained by calculating the systematic phase shift of 64 QAM;
fig. 14 is a diagram of a 64QAM constellation diagram obtained by eliminating the frequency error and systematic phase shift of a sampled symbol sequence for 64 QAM;
fig. 15 is a schematic diagram of a 64QAM constellation diagram being normalized;
fig. 16 is a schematic diagram of a result sequence obtained by calculating the error vector magnitude of a 64QAM modulation sequence;
fig. 17 is a schematic diagram of a result sequence obtained by calculating an amplitude error of a 64QAM modulation sequence;
fig. 18 calculates the phase error of the 64QAM modulation sequence, and obtains a result sequence diagram.
Detailed Description
In order that the present invention may be more readily and clearly understood, a more particular description of the invention briefly described above will be rendered by reference to specific embodiments that are illustrated in the appended drawings.
As shown in fig. 1-18, the digital demodulation and measurement analysis method of the present invention comprises the following steps:
(1) For a carrier frequency of f c At a sampling rate f s Sampling is carried out, and
where N is an integer, and Δ F ∈ (-1, 1), then Δ F is defined asAndthe smaller absolute value of the two. Where the function mod (x, y) is the remainder of dividing x by y. Clearly, | Δ F | <0.5. The equivalent carrier frequency of the sampled signal is f e As shown in formula (2).
f e ＝ΔFf s (2)
(2) Assuming that the spectral range of the modulation signal being sampled isThe bandwidth is B, the spectral range after sampling becomesAnd the sampling rate f s The corresponding sampling bandwidth isIf the inequality shown in the expression (3) is met, the sampling frequency is considered to pass the spectrum requirement check;
(3) Selecting a comparison among the plurality of sampling frequencies passing the spectrum check of step (2)The best one. The measured signal is first given from f according to the specific situation c To f e In a range where the average noise level exceeds the multiple N of the natural thermal noise F Then, the power of the band-pass sampling to bring out-of-band noise into the spectrum of the signal to be received is calculated according to the formula (4), and P is N1 Referred to as "multiple sample rate noise", P N1 ＝N F ·N·K·B·T em (4),
Where N is defined as formula (1), it is obvious that the higher the sampling rate, the smaller N and the smaller the noise. K is Boltzmann constant, and can be 1.381 × 10 -23 B is the signal bandwidth, T em The thermodynamic temperature of the system is taken into consideration, the digital quantization noise of the sampling system is further considered, and the equivalent sampling bit number N can be known according to the hardware index of the sampling system b Then the sampled noise power due to the digital samples is shown as equation (5). Will P N2 Referred to as "quantization noise",
wherein P is s Refers to the power of the signal, N b The value is related to the sampling rate, the higher the sampling rate, N b The smaller the noise will be, the larger this part will be. The integrated signal-to-noise ratio is defined as equation (6):
multiple sampling rates f selectable for a sampling system s Checking SNR respectively, the corresponding f with the maximum SNR s The one that is the preferred one;
(4) Defining a function time2frequency sampling a signal of total time length T with the preferred fs of claim 3, obviously with a sampling interval dt =1/f s Forming a 2N-point sampling sequence, where N is a natural number, performing inverse Fast Fourier Transform (FFT) on the sampling sequence, and then rearranging the sequence: move the next N points to the front, e.g. formula(7) As shown, a complex spectrum sequence including 2N elements is formed as shown in equation (8).
(S 1 S 2 S 3 ... S N S N+1 S N+2 S N+3 ... S 2N )
(7)
→(S N+1 S N+2 S N+3 ... S 2N S 1 S 2 S 3 ... S N )
F sery ＝[C F1 C F2 C F3 ... C F2N-2 C F2N-1 C F2N ] (8)
(5) Defining a function frequency2time, performing Inverse Fast Fourier Transform (IFFT) on a sampling sequence of 2N (N is a natural number) points, and then rearranging the sequence: moving the back N points to the front, as shown in formula (7);
(6) Using the preferred sampling rate f s Sampling the IQ quadrature modulated signal to form N raw Sampling sequence S of points raw Then, the function time2frequency is used to process it, a complex frequency spectrum sequence is formed, and then the defined frequency domain parameter is expressed by the formula (9).
Apparent frequency axis sequence f sery Is an arithmetic sequence containing 2N elements to find f sery In and f e The number of the value with the smallest absolute difference is marked as N e If the initial measured waveform is a unipolar pulse modulated radio frequency signal and the target recovered waveform is a baseband pulse signal, then N e The following method may be used: f sery The sequence number corresponding to the value with the maximum amplitude is N e And number N B Then, the following equation (10) is used:
wherein [ ] means rounding off and taking an integer;
(7) Intercept sequence F sery In N e -N B Point to N e +N B 1 points totaling 2N B Elements of dots forming a new array F cut . Suppose that the symbol period (or pulse period) of the signal under test is T sym Assuming that the number of target sampling points per symbol period of the demodulated digital waveform is L am Then obviously the target time step isThen define the number of half zero padding points:
then give the array F cut The left and right sides are respectively supplemented with N zeros Elements with a value of 0, forming a new series F extend Is apparent from F extend The number of elements of (2) is 2 (N) B +N zeros )。
(8) According to the specific case of digital demodulation, decide whether to F extend Performing a filtering process, typically using RRC (root raised cosine filter), for example, and then filtering F extend Performing mathematical transformation of frequency2time to form a time domain complex number sequence S extend If the original measured waveform is a RF modulated pulse signal and the target recovered waveform is a baseband pulse signal, then S can be measured extend And obtaining a real part, an imaginary part or an absolute value to obtain a baseband pulse signal, and further obtaining information such as pulse rising time, pulse falling time, pulse width, pulse period and the like.
Will S extend The number of symbols contained is marked as M syms Each symbol containing L am A sampling point, then S extend Collated into the form of Table 1.
TABLE 1 time-domain signal S extend Form arrangement form of
Sorting Table 1 to determine the best sample position within a symbol, and finding P l Maximum value of (1), wherein P l For the total power of the sample sequence within the symbol, C ml For the l-th sample sequence, P, within the m-th symbol l Subscript l corresponding to the maximum value of best I is the best sampling position, take l best The corresponding sample sequence vector, denoted S baseband Set its corresponding time series to 0,T sym ，2T sym ,3T sym …M syms T sym ；
(9) Based on S baseband Performing frequency offset compensation on the signal, firstly, according to the known modulation system and S obtained by calculation baseband Power, to obtain the mathematical expected value of the amplitude of the constellation point with the maximum amplitude, which is recorded as Mag peak Then search for S baseband Neutralizing Mag peak Symbols of similar amplitude, e.g. typically in the interval 0.98Mag peak ,1.1Mag peak ]Forming a new symbol sequence S peak The number of elements is N peak And its corresponding time series, as shown in table 2.
TABLE 2 time-domain signal S peak And corresponding time series
The number N of times of eliminating frequency offset by loop iteration can be set in practical engineering eli Then, a parameter is defined: symbol number M for first participating in frequency offset elimination calculation dev-first Further define the growth base factor increase As shown in formula (13).
N th eli Number of symbols secondary to frequency offset cancellationAs shown in equation (14):
whereinPointing to round down, then choose the symbol sequence S in this iteration peak Front of (5)Each symbol is processed. So that more symbols are processed each time than before. And the algorithm failure caused by symbol misjudgment because of too many symbols processed at the beginning is avoided. Therefore, the stability of the whole algorithm is improved, and the processing flow is as follows.
(10) Determining the Phase sequence of the symbols involved in the calculation, denoted Phase findpeak Then, these symbols involved in the operation are judged, and the Phase sequence Phase of the judged symbols is obtained decided Then, the phase difference between the two is obtained by using the equation (15).
Phase residual ＝Phase findpeak -Phase decided (15)
Phase residual The portion of the increment that varies linearly with time is due to frequency error, and Phase will be residual The corresponding time series is denoted t residual Then, the residual angular frequency obtained by the calculation of the current round is obtained by using the equation (16), and the process is similar to the process of obtaining the slope by fitting a straight line.
For the time domain signal S shown in table 2 peak All elements of (2) and their corresponding time series, complex symbols S p The corresponding time point is S p Performing frequency error elimination to obtain new symbol S p_1eli The treatment method is shown as the formula (17):
S p_1eli ＝S p exp(-jω residual_1 t p ) (17)
wherein, t p For time series, a new outermost circle symbol sequence S is formed peak_1eli If demodulation involves a filter, the time domain impulse response of the filter also needs to be correspondingly processed.
(11) To S peak_1eli Selecting a new front according to equation (14)Performing a frequency error cancellation calculation for each symbol, repeating the algorithm of claim 9,10, and during this cycle, it is apparent that S is peak_1eli Replaces the original S peak Finally, a new S is formed peak_2eli (the number of corresponding processing symbols is). Then the S is peak_2eli Substituting S for next cycle peak_1eli 8230am in generalThe corresponding number of processing symbols isUp to the Nth of setting eli The second time is finished, and the successive residual angular frequency is finally obtainedThe total angular frequency error is then:
(12) Formed in the last cycle of step (11)A systematic phase offset calculation is performed. Determining the Phase sequence of the symbols involved in the calculation, denoted Phase findpeak_F Then, these symbols participating in the operation are judged, and the Phase sequence Phase of the judged symbols is obtained decided_F Then, the phase difference between the two is obtained by using the expression (19).
Phase diff ＝Phase findpeak_F -Phase decided_F (19)
Find all the phases diff The average value of (1) is denoted as Phase diff_ave I.e. a systematic phase shift. The operation of removing the systematic phase offset can be accumulated cyclically, if necessary.
(13) Removing the frequency error and systematic phase offset of the sampled symbol sequence. Then the symbol sequence S mentioned in step (8) is applied baseband Wherein contains M syms A plurality of complex symbols. Generally, let us say that m syms Symbol is(corresponding time is m) syms T sym ) Then each symbol is processed as shown in equation (20),
is based on S baseband A new symbol sequence S is formed baseband_eli .
(14) Will S baseband_eli Multiplying a coefficient to make the amplitude root mean square value of the measured sequence and the judgment symbol sequence equal, and further obtaining error vector amplitude (EVM) and amplitude error according to the existing standardization definition through comparison calculation(MagErr), phase error (PhaseErr), and the like, and the frequency error is calculated by the equation (21) based on the equation (18):
example of the implementation
The digitally modulated signals were analyzed using the method of the present invention, and the signal parameters and measurement parameters are shown in table 3.
TABLE 3 digitally modulated Signal parameters and measurement parameters
And (3) verifying the sampling rate of the measurement system according to the step (2), wherein the verification result is shown in figure 1. Obviously, the equivalent frequency spectrum of the measured signal is in the sampling FFT bandwidth, and the verification is passed;
then, according to the step (3), carrying out comprehensive signal-to-noise ratio (SNR) verification based on the known parameters of the measurement system, wherein the result is shown in figure 2, and figure 3 shows the frequency spectrum of the band-pass radio frequency sample obtained based on the step (6);
fig. 4 shows a spectrum (a) after the digital spectrum shift based on step (7) and a spectrum (b) after the left-right symmetric zero-padding expansion;
FIG. 5 is based on the average power analysis results of the sequence corresponding to different sampling points within the analysis symbol of step (8);
FIG. 6 is a diagram of a 20 th corresponding constellation of a 64QAM constellation based on the analysis in step (8), wherein the total sampling point of a single symbol is 51 points, namely S baseband ；
FIG. 7 is a phase shift analysis based on steps (9) and (10) caused by a 64QAM frequency error, analysis 1;
fig. 8 is a 2 nd analysis of the phase shift caused by the 64QAM frequency error based on steps (9) and (10);
fig. 9 is based on steps (9) and (10) to obtain peripheral points of a constellation diagram of 64QAM symbols, and eliminate the frequency error for the 2 nd time;
FIG. 10 is a diagram illustrating phase shift analysis caused by frequency error of 64QAM in accordance with steps (9) and (10), and 11 th analysis;
fig. 11 is based on steps (9) and (10) to obtain peripheral points of a constellation diagram of 64QAM symbols, and the frequency error is eliminated 11 th time;
fig. 12 makes 64QAM frequency error analysis 11 times in total based on steps (9) and (10), and each increment of frequency error (or called residual carrier) obtained is obviously convergent, which illustrates the effectiveness of the algorithm;
fig. 13 is a diagram illustrating the calculation of the systematic phase shift of 64QAM according to step (12), and the systematic phase shift (abbreviated as phase shift) increment obtained each time is obviously convergent, which illustrates the effectiveness of the algorithm;
fig. 15 normalizes the 64QAM constellation diagram based on the step (14) so that the rms values of the amplitudes of the measured sequence and the decision symbol sequence are equal, thereby calculating a digital modulation error parameter.
Table 4 shows the measured demodulation results based on the present invention:
TABLE 4
The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are only exemplary embodiments of the present invention, and are not intended to limit the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (6)
1. A digital demodulation and measurement analysis method, characterized by: the method comprises the following steps:
(1) For a carrier frequency of f c At a sampling rate f s Sampling is carried out, and
wherein N is an integer,. DELTA.F.epsilon. (-1, 1), and. DELTA.F is defined asAndif the function mod (x, y) is the remainder of dividing x by y, the equivalent carrier frequency of the sampled signal is f e Calculated from equation (2):
f e ＝ΔFf s (2)；
(2) Assuming that the spectral range of the modulation signal being sampled isThe bandwidth is B, the spectral range after sampling becomesAnd the sampling rate f s The corresponding sampling bandwidth isThe sampling frequency f is considered to be the sampling frequency f if the inequality shown in equation (3) is satisfied e Passing the spectrum requirement check;
(3) Selecting a preferred sampling frequency f from the plurality of sampling frequencies that pass the spectrum check of step (2) s ；
(4) Defining a function time2frequency for the modulated signal of time length T and the preferred sampling frequency f as described in step (3) s Sampling is carried out, and then the sampling interval dt =1/f s Forming a sampling sequence of 2N points, performing inverse Fast Fourier Transform (FFT) on the sampling sequence, and then rearranging the sequence: moving the next N points to the front, as shown in equation (7), a complex spectrum sequence containing 2N elements is formed as shown in equation (8):
(S 1 S 2 S 3 ...S N S N+1 S N+2 S N+3 ... S 2N )
→(S N+1 S N+2 S N+3 ... S 2N S 1 S 2 S 3 ... S N ) (7)
F sery ＝[C F1 C F2 C F3 ... C F2N-2 C F2N-1 C F2N ] (8)；
(5) Defining a function frequency2time, performing Inverse Fast Fourier Transform (IFFT) on the sampling sequence of the 2N points in the step (4), and then rearranging the sequence: moving the back N points to the front, as shown in formula (7);
(6) Using the preferred sampling frequency f of step (3) s Sampling the IQ quadrature modulated signal to form N raw Sampling sequence S of points raw And (3) processing the frequency domain data by using the function time2frequency in the step (4) to form a complex frequency spectrum sequence, wherein the defined frequency domain parameter is as shown in the formula (9):
frequency axis sequence f sery Includes 2N element arithmetic progression to find f sery In and f e The number of the value with the smallest absolute difference is marked as N e And a natural number N B Then, the following equation (10) is used:
wherein [ ] means rounding off and taking an integer;
(7) Intercepting the frequency axis sequence F sery In N e -N B Point to N e +N B -1 point totaling 2N B Elements of dots forming a new array F cut Assuming that the time length of the measured signal is T sym The target sampling point number of each symbol period of the demodulated digital waveform is L am Then the target time step isThe definition of the number of half zero padding points is shown as formula (11):
given sequence F cut The left and right sides are respectively supplemented with N zeros Elements with a value of 0, forming a new series F extend Then F is extend The number of elements of (2) (N) B +N zeros )；
(8) For said array F extend Performing filtering processing to F extend Performing mathematical transformation by using the function frequency2time to form a time domain complex number sequence S extend Will S extend The number of symbols contained is marked as M syms Each symbol containing L am For each sampling point, the calculation of the total power of the sampling sequence in the symbol is shown in formula (12)
In the formula, P l For the total power of the sample sequence within the symbol, C ml For the l-th sample sequence, P, within the m-th symbol l Subscript l corresponding to the maximum value of best I is the best sampling position, take l best The corresponding sample sequence vector, denoted S baseband Will beWith its corresponding time series set to 0,T sym ，2T sym ,3T sym …M syms T sym ；
(9) To the S baseband Performing frequency offset compensation on the signal, firstly, according to the known modulation system and S obtained by calculation baseband Power, calculating the mathematical expected value of the amplitude of the constellation point with the maximum amplitude, and recording the mathematical expected value as Mag peak Then the search amplitude is in the interval [0.98Mag ] peak ,1.1Mag peak ]S of baseband And Mag peak The symbol sequences with similar amplitudes form a new symbol sequence S peak The number of elements is N peak Setting the frequency offset elimination number N of loop iteration eli Then, a parameter is defined: number of symbols M participating in calculation of frequency offset cancellation for the first time dev-first Further define the growth base factor increase As shown in formula (13):
n th order eli Number of symbols participating in frequency offset cancellationAs shown in equation (14):
whereinPointing to round down, then choose the symbol sequence S in this iteration peak Front of (5)Processing each symbol;
(10) Find the sequence S of symbols involved in the calculation peak Phase sequence of (2), denoted as Phase findpeak Then, these symbols participating in the operation are judged, and the Phase sequence Phase of the judged symbols is obtained decided Further, the phase difference between the two is obtained by using equation (15):
Phase residual ＝Phase findpeak -Phase decided (15)
will Phase residual The corresponding time series is denoted t residual Then, the residual angular frequency obtained by the operation is obtained by using the formula (16):
for time domain signal S peak And corresponding time series, complex symbols S p The corresponding time series is T p Performing frequency error elimination to obtain new symbol S p_leli The treatment method is shown as the formula (17):
S p_1eli ＝S p exp(-jω residual_1 t p ) (17)
wherein, t p For the time sequence, an outermost circle symbol sequence S is formed peak_1eli ；
(11) To S peak_1eli Selecting a new front according to equation (14)The symbol is subjected to a calculation for eliminating the frequency error, and steps (9) and (10) are repeated, in this cycle, S peak_1eli Replaces the original S peak Finally, a new sequence S is formed peak_2eli The number of the corresponding processing symbols isThen the S is peak_2eli Carry over to the next cycle to replace S peak_1eli Up to the set Nth eli After the second time, the successive residual angular frequency omega is finally obtained residual_1 、ω residual_2 、The total angular frequency error is then:
(12) For the sequence formed in the last cycle in step (11)Systematic phase offset calculation is performed: determining the Phase sequence of the symbols involved in the calculation, denoted Phase findpeak_F Then, these symbols involved in the operation are judged, and the Phase sequence Phase of the judged symbols is obtained decided_F Further, the phase difference between the two is obtained by using equation (19):
Phase diff ＝Phase findpeak_F -Phase decided_F (19)
further obtain all the Phase diff The average value of (1) is denoted as Phase diff_ave I.e. systematic phase offset;
(13) Removing the frequency error and systematic phase offset of the sampled symbol sequence: for the sequence S baseband And M contained therein syms A plurality of symbols, wherein m is syms A complex number of symbols ofCorresponding time point is m syms T sym Then each symbol is processed as shown in equation (20),
thereby based on S baseband A new symbol sequence S is formed baseband_eli ；
(14) Will S baseband_eli Multiplying a coefficient to make the RMS value of the measured sequence and the decision symbol sequence equal, and further comparing and calculating,parameters such as Error Vector Magnitude (EVM), magnitude error (MagErr), and phase error (PhaseErr) are obtained, and the frequency error is calculated by equation (21) based on equation (18):
wherein f is deviation Is the frequency error.
2. The digital demodulation and measurement analysis method according to claim 1, wherein: the | Δ F | <0.5 in the step (1).
3. The digital demodulation and measurement analysis method according to claim 1, wherein: the step (3) selects a better one of the plurality of sampling frequencies passing through the spectrum verification in the step (2), and the operation steps are as follows: first, the measured signal is evaluated from the frequency f c To f e In a range where the average noise level exceeds the multiple N of the natural thermal noise F Calculating the multiple sampling rate noise P according to the formula (4) N1 ，P N1 ＝N F ·N·K·B·T em (4),
Wherein N is defined as formula (1), K is Boltzmann constant, and is 1.381 × 10 -23 B is the signal bandwidth, T em Is the thermodynamic temperature of the system; furthermore, the equivalent sampling bit number N can be known according to the hardware index of the sampling system by considering the digital quantization noise of the sampling system b Due to quantization noise P formed by the digital samples N2 As shown in the formula (5),
wherein P is s Refers to the power, N, of the sampled signal b The value is related to the sampling rate, and the integrated signal-to-noise ratio is defined as formula (6):
for a plurality of sampling frequencies f s Check with SNR respectively, so that f corresponding to SNR is maximum s I.e. the one that is preferred.
4. The digital demodulation and measurement analysis method according to claim 1, wherein: n in the step (6) e It can also be obtained by: if the initial modulation signal is a unipolar pulse modulated radio frequency signal and the target recovered waveform is a baseband pulse signal, then N e The method comprises the following steps: f sery The sequence number corresponding to the value with the maximum amplitude is N e 。
5. The digital demodulation and measurement analysis method according to claim 1, wherein: in the step (8), if the initial measured modulation signal is a radio frequency modulation pulse signal and the target recovery is a baseband pulse signal, then the S is processed extend And solving a real part, an imaginary part or an absolute value to obtain a baseband pulse signal, and further solving the rise time, the fall time, the pulse width and the pulse period of the pulse.
6. The digital demodulation and measurement analysis method according to claim 1, wherein: and (5) filtering by adopting a root raised cosine filter (RRC) in the step (8).
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| CN103532906A (en) * | 2013-06-20 | 2014-01-22 | 工业和信息化部通信计量中心 | Digital modulation error parameter metering method and system based on waveform design |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN103532906A (en) * | 2013-06-20 | 2014-01-22 | 工业和信息化部通信计量中心 | Digital modulation error parameter metering method and system based on waveform design |
Non-Patent Citations (2)
| Title |
|---|
| 一种新的伴随调相测量方法;周峰 等;《电子学报》;20120331;第40卷(第3期);第592-594页 * |
| 一种适用于正交振幅调制(QAM)信号的符号定时同步算法;林素红 等;《科学技术与工程》;20140131;第14卷(第1期);第214-217页 * |
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