CN115940992B - BL-DSSS signal code tracking method based on frequency domain subspace principle - Google Patents
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Abstract
The invention proposesThe BL-DSSS signal code tracking method based on the frequency domain subspace principle comprises the steps of preprocessing signals in a time domain, estimating time delay errors by adopting a modified root-MUSIC algorithm, and compensating fractional time delay by adopting a frequency domain fractional time delay filter; the time delay error estimation part adopts a modified root-MUSIC algorithm, and the tracking range can be along with N b The setting of the method is flexibly increased, and is not limited by a related error estimation principle; the modified root-MUSIC algorithm is adopted to carry out time delay error estimation, the obtained estimation result linearly changes along with the increase of the real result, and the situation that the tracking establishment time is greatly increased under the condition of large time delay error caused by nonlinear change in the traditional method is not introduced.
Description
Technical Field
The invention belongs to the technical field of communication, and particularly relates to a BL-DSSS signal code tracking method based on a frequency domain subspace principle.
Background
The Direct Sequence Spread Spectrum (DSSS) modulation technology has the characteristics of strong anti-interference capability, high-time wide bandwidth, convenience for multiple access communication and the like, and is widely applied to the fields of aerospace measurement and control, navigation, communication, radar and the like. The conventional DSSS modulation method in the fields of application, measurement and control, navigation and the like adopts square wave as the waveform of the adopted code chip. The conventional DSSS has the disadvantages of relatively simple signal generation and reception, such as low spectral efficiency and small sideband attenuation, which are inherent in square waves, and thus the requirements of modern radio systems for high spectral efficiency and low adjacent interference are gradually not met.
The band-limited direct sequence spread spectrum (BL-DSSS) modulation technology changes the square wave of the original traditional DSSS into other waveforms with limited frequency bands, such as a root raised cosine waveform, a Gaussian waveform, a long ellipsoidal wave function waveform and the like, can reduce the frequency spectrum width of a signal under the condition of the same code rate, and meanwhile, compared with the square wave, the waveform with limited frequency bands has higher sideband attenuation in practical application. Meanwhile, the frequency spectrum of the BL-DSSS is more similar to the shape of white noise, so that the anti-interference and anti-interception capabilities can be further improved compared with the traditional DSSS.
The conventional code tracking method is based on a delay locked loop method, and the implementation principle of the method is shown in fig. 1. First, the received signal is sampled and then passed through a matched filter to obtain a filtered signal. The signal is then time-delayed by an interpolator, which may use a general polynomial interpolation or a cubic interpolation. The output of the interpolator is extracted by 2 times, one path of data is obtained and sent to a next signal processing module, such as a carrier tracking loop and a data detector, and the other path of data generates leading branch data and lagging branch data. The delay phase-locked loop code tracking method obtains a delay error by square difference between the output related to the leading branch and the output related to the following branch, and the delay error outputs control signals of an interpolator through a designed loop filter and an NCO. Still other methods implement the matched filter and interpolator of fig. 1 in the frequency domain to reduce computational complexity and improve interpolation accuracy.
The existing code tracking method adopts a delay phase-locked loop principle, and takes the difference between two correlation values as an estimated signal of delay errors to control NCO. The tracking range of this method is a small fixed value under conditions that meet the performance. If the tracking range is increased by adopting the multi-correlator method, the tracking performance is reduced. In the existing code tracking method, only under the condition of smaller delay error, the delay error estimated value linearly increases along with the increase of the delay error, and when the delay error continues to increase, the delay error estimated value is reduced instead. This non-linear variation results in a significant increase in the time of track setup when the delay error is large, even if it is within the tracking range of the code tracking method.
Disclosure of Invention
In view of the above, the present invention aims to provide a frequency domain subspace principle-based BL-DSSS signal code tracking method, which performs code tracking on BL-DSSS signals through a frequency domain subspace method, wherein the time delay variance performance is the same as that of the conventional method, and the tracking range can be flexibly set. Under the condition of similar computational complexity to the traditional code tracking method, the tracking range is larger than that of the traditional code tracking method; meanwhile, the tracking range can be further increased at the expense of computational complexity; in addition, the delay error estimated value is linearly changed along with the increase of the delay error, and the track establishment time is not greatly increased due to the nonlinear change of the traditional code tracking under the condition of large delay error.
A BL-DSSS signal code tracking method based on frequency domain subspace principle includes:
step 1, assume that in the nth data period, the obtained estimated value of the time delay isBased on the estimated value +.>Carrying out integer and fractional delay compensation on a received signal, then carrying out conjugate multiplication on the received signal and a local waveform in a frequency domain, and finally realizing the dimension reduction of data by utilizing partial accumulation;
step 2, performing delay error estimation on the dimension reduced data based on a modified root-MUSIC algorithm, wherein the delay error estimation is specifically as follows:
in the delay error estimation section, the input signal is expressed as a matrix:
X n ＝Α(ε n )F n +V n
wherein ,
the covariance matrix is estimated by means of an RC integral filter, and the s-domain system function is expressed as:
wherein ,τ1 =rc is the time constant of the filter, then converting it to the z-domain is expressed as:
the estimated value of the covariance matrix is expressed as a differential equation:
wherein the initial value of covariance matrix
Eigenvalue decomposition is carried out on the covariance matrix to obtain a signal subspace estimation value thereofAnd noise subspace estimate +.>Namely:
wherein The characteristic value corresponding to the signal subspace; />The characteristic value matrix is corresponding to the noise subspace; the parameter spectrum of the delay estimate is expressed as:
by the method of S -1 S is carried out on the time delay parameter by adopting an (epsilon) root-finding method -1 (ε) is expressed as:
wherein Is a diagonal matrix; defining a coefficient matrix:
and orderAccording to frequency domain fractional delay filter H FD Expression of S -1 (ε) is expressed as:
wherein ：
wherein bm The sum of the m-th diagonal elements in B is expressed as:
and (3) making:
obtaining an estimation result of the parameter by solving the root of the D (z) closest to the unit circle; assume that the root closest to the unit circle is:
z＝z 1
then and covariance matrix estimateThe corresponding estimated value of the delay error is:
step 3, time delay estimated value:
the delay estimate for the n+1th data period can be expressed as:
wherein Gd Is the multiplier coefficient;
step 4, returning to the step 1, and utilizing the time delay estimated value of the (n+1) th data periodThe next round of signal code tracking is performed.
Preferably, the specific steps of the step 1 include:
the received signal result samples are then expressed as:
wherein ,Ts For sampling period, d=τ/T s To normalize the time delay, the number of sampling points N of the single data period s ＝T/T s The method comprises the steps of carrying out a first treatment on the surface of the Will beIs compensated by a time domain shift of the signal,/->The fractional part of (2) is compensated by a fractional delay filter of a frequency domain; the signal of the nth data period after integer delay compensation and serial-to-parallel conversion is expressed as:
through N s The point FFT operation converts the signal to the frequency domain, then it is expressed as:
wherein ,is a frequency domain fractional delay filter, and has the expression:
for transmitting the frequency domain waveform of the signal, includingPseudo code and basic waveforms, expressed as:
after integer delay compensation, the remaining uncompensated delay isBy combining R k,n And local fractional delay filter->Conjugate multiplication to complete the compensation of the fractional delay; the signal after fractional delay compensation is expressed as:
wherein ,to normalize delay errors, W k Is a frequency domain noise term; will->And local frequency domain waveform->Conjugate multiplication to complete matched filtering and despreading; wherein the frequency domain waveform is represented as:
wherein ,pR (t) is a local pulse waveform with a frequency response ofThe signal that completes matched filtering and despreading is expressed as:
wherein ,G k the corresponding time domain signal is +.>Wherein P (T) has a frequency response of P (f) =t c P N (f) The method comprises the steps of carrying out a first treatment on the surface of the Noise item->Corresponding time-domain signal->Is of the digital power spectral density of
And finally, carrying out partial accumulation in a frequency domain to realize data dimension reduction, wherein the data dimension reduction is expressed as:
wherein ,NI To accumulate points partially, N b To output the point number of the single data period after the partial accumulation, the condition N is satisfied b ＝N s /N I ；V k For noise term with partial accumulation hysteresis +.>F n ＝a n e jθ 。
Preferably, in the step 2, G d ＝4TB L ；B L Indicating ringA road bandwidth;
the invention has the following beneficial effects:
the invention provides a BL-DSSS signal code tracking method based on a frequency domain subspace principle, which comprises the steps of preprocessing signals in a time domain, estimating time delay errors by adopting a modified root-MUSIC algorithm, and compensating fractional time delay by adopting a frequency domain fractional time delay filter; the time delay error estimation part adopts a modified root-MUSIC algorithm, and the tracking range can be along with N b The setting of the method is flexibly increased, and is not limited by a related error estimation principle; the modified root-MUSIC algorithm is adopted to carry out time delay error estimation, the obtained estimation result linearly changes along with the increase of the real result, and the situation that the tracking establishment time is greatly increased under the condition of large time delay error caused by nonlinear change in the traditional method is not introduced.
Drawings
FIG. 1 is a prior art delay locked loop based BL-DSSS signal code tracking;
FIG. 2 is a diagram of a code tracking method based on the frequency domain subspace principle of the present invention;
FIG. 3 shows the steady-state delay variance of two methods under different signal-to-noise ratios;
fig. 4 (a) and fig. 4 (b) are two methods for time delay hopping to d=2.5t, respectively s and d＝3Ts Tracking the time;
FIGS. 5 (a) and 5 (b) are, respectively, N for the method of the present invention b When=8, N b Tracking case at maximum delay jump condition at=16.
Detailed Description
The invention will now be described in detail by way of example with reference to the accompanying drawings.
1. Signal model:
the transmission signal model adopted by the invention is a binary phase shift keying direct sequence spread spectrum (RRC-BPSK-DSSS) signal formed by root raised cosine pulse, and the transmission signal can be expressed as:
wherein ,ai In the form of a data symbol,BPSK symbols in the present invention; />Representing a downward rounding operation; c m The= ±1 is a spread spectrum code sequence, gold codes are adopted in the invention, and the code length is N; p is p T (t) is the transmit signal pulse waveform, in this case the Root Raised Cosine (RRC) waveform, whose frequency response can be expressed as +.> wherein Tc For chip period, P N (f) Is the frequency response of the nyquist raised cosine waveform. In the invention, we set the data symbol period equal to the pseudo-code period t=nt s 。
In code tracking, we assume that the receiving end has completed carrier frequency synchronization. The received signal is also affected by time delay, carrier phase and noise, so the received signal can be expressed as:
where θ is the carrier phase, subject to a uniform distribution over [ -pi, pi); τ is the time delay; w (t) is complex Gaussian white noise with a power spectral density of N 0/P, wherein N0 The power spectrum density of noise is single-sided, and P is the power of the received intermediate frequency signal. The partial symbols used in the present invention are shown in table 1.
Table 1: the symbols and meanings indicated in the invention
2. BL-DSSS signal code tracking method based on frequency domain subspace principle
The BL-DSSS signal code tracking method based on the frequency domain subspace principle is different from the delay phase-locked loop method based on the time domain correlation principle, obtains the time delay error of the received signal in the frequency domain through the subspace estimation method, and directly performs time delay compensation on the received signal in the frequency domain through the frequency domain fractional time delay filter. The structure of the proposed method is shown in fig. 2. The method comprises a preprocessing part for performing preprocessing and partial accumulated data dimension reduction on a received signal, a root-MUSIC algorithm for modifying time delay difference estimation and a loop part for outputting time delay estimation values afterwards.
2.1 pretreatment of received Signal
The preprocessing part mainly completes integer and fractional time delay compensation on the received signal, conjugate multiplication of the received signal and the local waveform in the frequency domain and realization of data dimension reduction by utilizing partial accumulation.
The resulting samples of the received signal may then be expressed as:
wherein ,Ts For sampling period, d=τ/T s To normalize the time delay, the number of sampling points N of the single data period s ＝T/T s . Assume that in the nth data period, the estimated value of the delay isTo achieve that in a single data period the data sign remains approximately unchanged, we will +.>Is compensated by a time domain shift of the signal,/->Is fed through a fractional delay filter of the frequency domainAnd (5) row compensation. The signal of the nth data period after integer delay compensation and serial-to-parallel conversion can be expressed as:
in the above, a n Data symbols representing the nth data period, the data symbols of the same period being identical;
through N s The point FFT operation can convert the signal to the frequency domain, then it can be expressed as:
wherein the noise termThe frequency domain fractional delay filter can be used for representing the time delay in the frequency domain, and the expression is as follows:
for the frequency domain waveform of the transmitted signal, which contains pseudo code and basic waveforms, it can be expressed as:
after integer delay compensation, the remaining uncompensated delay isWe pass R k,n And local fractional delay filter->And (5) conjugate multiplication to complete the compensation of the fractional delay. The signal after fractional delay compensation can be expressed as:
wherein ,normalized delay error; w (W) k Representing the frequency domain noise term. The power spectrum approximation of the noise is not affected by the frequency domain fractional delay filter, so the noise part in the above equation is unchanged. Delay-adjusted ∈>Still contains the relevant information of the waveform, so we pass +.>And local frequency domain waveform->Conjugate multiplication, matched filtering and despreading are completed. Wherein the frequency domain waveform can be expressed as:
wherein ,pR (t) is a local pulse waveform whose frequency response isThe signal that completes matched filtering and despreading can be expressed as:
wherein ,from the derivation we can get G k The corresponding time domain signal is +.>Wherein P (T) has a frequency response of P (f) =t c P N (f) The method comprises the steps of carrying out a first treatment on the surface of the Noise item->Corresponding time-domain signal->Is of the digital power spectral density of
Because during the course of the tracking process,the corresponding time domain signals are concentrated near the zero point, so that the data dimension reduction can be realized by carrying out partial accumulation in the frequency domain, and the subsequent processing is convenient. The signal after the dimension reduction process can be expressed as:
wherein ,NI To accumulate points partially, N b To output the point number of the single data period after the partial accumulation, the condition N is satisfied b ＝N s /N I ；V k For noise term with partial accumulation hysteresis +.>F n ＝a n e jθ . After the dimension reduction treatmentOn the one hand, the time delay error estimation is carried out by a subsequent frequency domain subspace method, and on the other hand, the signals required by data detection are output by an accumulator.
2.2 time delay error estimation based on modified root-MUSIC algorithm
The time delay difference is estimated by adopting a root-MUSIC algorithm based on modification. The classical root-MUSIC algorithm can be divided into two parts, one part being covariance matrix estimation and the other part being parameter estimation. In covariance matrix estimation, the classical root-MUSIC algorithm adopts the method of adding and averaging the sample covariance matrix to estimate the covariance matrix, but the method cannot be well applied to a tracking loop. Therefore, the covariance matrix is estimated by adopting an RC integral filter method, and the modified root-MUSIC algorithm is used for delay error estimation in code tracking.
In the delay error estimation section, the input signal matrix can be expressed as:
X n ＝Α(ε n )F n +V n
wherein ,
we estimate the covariance matrix by means of an RC-integrator filter whose s-domain system function can be expressed as:
wherein ,τ1 =rc is the time constant of the filter, then converting it to the z-domain can be expressed as:
the estimated value of the covariance matrix can be expressed as a differential equation:
wherein the initial value of covariance matrix
The covariance matrix is subjected to eigenvalue decomposition to obtain the signal subspace estimation value thereofAnd noise subspace estimate +.>Namely:
wherein For the characteristic value corresponding to the signal subspace, since in the present invention there is only one signal, therefore +.>Is a scalar; />Is a characteristic value matrix corresponding to the noise subspace, and the size is (N b -1)×(N b -1); the parameter spectrum of the delay estimate can be expressed as:
we pass through the pair S -1 The method of (epsilon) root finding estimates the time delay parameters. S is then -1 (ε) may be expressed as：
wherein ：
we can define a coefficient matrix:
and orderThen delay filter H is delayed according to the frequency domain fraction FD Expression of S -1 (ε) may be expressed as:
wherein ,represents the mth in matrix B 1 +N b /2+1,m 2 +N b 2+1 elements; b m The sum of the m-th diagonal elements in B can be expressed as:
let us let:
by finding the root of the unit circle where D (z) is closest, the estimation result of the parameter can be obtained. Assume that the root closest to the unit circle is:
z＝z 1
then and covariance matrix estimateThe corresponding estimated value of the delay error is:
the delay error estimation flow based on the modified root-MUSIC algorithm is as follows:
1) Estimating covariance matrix based on RC integral filter
2) For covariance matrixPerforming characteristic decomposition to obtain signal noise subspace +.>
3) Constructing matrix B and calculating to obtain sum { B } of diagonal elements m ,m＝-N b ,…,N b }；
4) Polynomial root-finding to obtain a covariance matrixCorresponding delay error estimate +.>
2.3 time delay estimation value
We derive an estimate of the delay through the loop. In the last part, we estimate the time delay difference to obtain the estimated value of the time delay error. And then, obtaining the estimated value of the time delay through a coefficient multiplier and an integrator. For delay compensation of subsequent data.
The delay estimate for the n+1th data period can be expressed as:
wherein Gd Is the multiplier coefficient. G d There are two roles, one is as the gain factor of the integrator and the other is as the gain factor of the whole loop, controlling the loop bandwidth.
In this section, the estimated value of the delayThe pre-processing portion of the signal is accepted for integer and fractional delay compensation in the next data cycle.
We pass through the required loop bandwidth B L Deriving multiplication factor G d And the time constant τ of the RC integration filter 1 . In general, let us let the damping coefficient of the loop be critical value ζ=0.707, then G in the present invention d 、τ 1 The relation with the loop bandwidth is:
G d ＝4TB L
in the code tracking method based on the frequency domain subspace principle, which is provided by the invention, the sampling period T s The nyquist sampling theorem is satisfied, preferably simultaneously, the requirement of an efficient FFT, i.e. the number of sampling points of a single data period is a power of 2. When the spreading codes employ M sequences or time Gold sequences, their pseudocode length satisfies n=2 n -1, where n is the order of the generation registers, so that the number of single-period sampling points and the sampling period can beThe method comprises the following steps:
N s ＝2(N+1)
in contrast, in conventional BL-DSSS signal code tracking, N is typically set s =2n so that leading and lagging leg data can be generated by decimation.
3. Computational complexity analysis
In this section, we analyze the computational complexity of the proposed feedback subspace-based code tracking method and compare it to conventional code tracking methods. We choose the number of complex multiplications required for the different code tracking methods for a single data period as an indicator of their computational complexity.
The conventional code tracking method is shown in fig. 1, meanwhile, the matched filtering part performs acceleration calculation by using FFT, and the interpolator selects cubic interpolation, so that the required calculation complexity can be expressed as follows:
C T ＝2N s log 2 (2M)+6N s +2N
wherein Ns The number of samples for a single data period, M is the matched filter length and N is the pseudo code length. The computational complexity of each part of the code tracking method based on the frequency domain subspace principle provided by the invention is shown in table 2.
Table 2: the method for tracking the code comprises the following steps of calculating complexity of each part
wherein Nb Points for that data period after the dimension reduction process. The total computational complexity of the proposed code tracking method can be expressed as:
in the following we compare the computational complexity of the two code tracking methods in specific cases. Let us let the data period be the same as the pseudo code period, the pseudo code length n=1023, N in the conventional code tracking method s =2n, N in the proposed method s =2 (n+1), matched filter length m=16. Then the number of single data cycle points N after dimension reduction b When=8, the ratio of the computational complexity of the proposed method to that of the conventional method is C P /C T =0.60, at N b When=16, C P /C T =1.65, at N b When=32, C P /C T =9.98. We can find that, at N b When=8, 16, the computational complexity of the proposed method is on the same order as that of the conventional method.
4. Simulation experiment
We first compare the steady state delay variance performance of the proposed method with that of the conventional method. In the simulation, we set the spread spectrum code length n=1023, the chip rate 1/T c The code period is equal to the data period, the RC integral filter setting parameter is set to a critical value, namely damping coefficient xi=0.707, and the loop bandwidth is set to B L =50 Hz. In the method, we set the number N of single data period points after dimension reduction b Sample rate 1/T =8 s In the conventional tracking method, we set the number of matched filter points m=16, sampling rate, =20.48 MHzThe steady-state delay variance of the two methods under different signal-to-noise ratios is obtained by 50 Monte Carlo simulations for 1s, and the result is shown in FIG. 3.
As can be seen from fig. 3, the code tracking method proposed in the present invention is the same as the conventional method in terms of steady-state delay variance performance, and the steady-state delay variance gradually becomes smaller as the signal-to-noise ratio of the input signal increases.
The following is a comparison between the tracking situation of the method proposed in the present invention and the tracking situation of the conventional method under the condition of different time delay jump. The loop bandwidths are all set to B L =10 Hz, normalized delay jump is set to d=2.5t s and d＝3Ts Wherein the first time delay jump is located in a nonlinear tracking area of the traditional code tracking method, and the second time delay jump is located outside the tracking area of the traditional method. The tracking results are shown in fig. 4.
It can be seen from fig. 4 (a) that in the nonlinear tracking area of the conventional method, the method proposed in the invention has a shorter track setup time than the conventional method, i.e., the method proposed in the invention is linear in the tracking area. As can be seen from fig. 4 (b), the method proposed in the invention has a larger tracking area than the conventional method.
In order to verify the maximum tracking area of the method, we set the number N of single period data points after dimension reduction b＝8 and Nb =16, and the tracking condition of the method proposed in the invention under the critical condition of the maximum tracking range is obtained, and the results are shown in fig. 5 (a) and 5 (b).
Maximum tracking range 3T from conventional methods s In comparison with N b When=8, the maximum tracking range of the method is 4.3T s When N b When=16, the maximum tracking range of the method is 8T s . In addition, the method provided by the invention is linear in the trackable region, namely the track establishment time is not greatly increased due to the increase of the time delay jump value.
In summary, the above embodiments are only preferred embodiments of the present invention, and are not intended to limit the scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (3)
1. The BL-DSSS signal code tracking method based on the frequency domain subspace principle is characterized by comprising the following steps:
step 1, assume that in the nth data period, the obtained estimated value of the time delay isBased on the estimated value +.>Carrying out integer and fractional delay compensation on a received signal, then carrying out conjugate multiplication on the received signal and a local waveform in a frequency domain, and finally realizing the dimension reduction of data by utilizing partial accumulation;
step 2, performing delay error estimation on the dimension reduced data based on a modified root-MUSIC algorithm, wherein the delay error estimation is specifically as follows:
in the delay error estimation section, the input signal is expressed as a matrix:
X n ＝Α(ε n )F n +V n
wherein , F n ＝a n e jθ the method comprises the steps of carrying out a first treatment on the surface of the θ is the carrier phase; a, a n A data symbol representing an nth data period; n (N) b Representing the number of single-period data points after dimension reduction;
the covariance matrix is estimated by means of an RC integral filter, and the s-domain system function is expressed as:
wherein ,τ1 =rc is the time constant of the filter, then converting it to the z-domain is expressed as:
wherein T represents a data symbol period;
the estimated value of the covariance matrix is expressed as a differential equation:
wherein the initial value of covariance matrix
Performing eigenvalue decomposition on the estimated value of covariance matrix to obtain its signal subspace estimated valueAnd noise subspace estimate +.>Namely:
wherein The characteristic value corresponding to the signal subspace; />The characteristic value matrix is corresponding to the noise subspace; the parameter spectrum of the delay estimate is expressed as:
by the method of S -1 S is carried out on the time delay parameter by adopting an (epsilon) root-finding method -1 (ε) is expressed as:
wherein ,
wherein Is a diagonal matrix; defining a coefficient matrix:
and orderAccording to frequency domain fractional delay filter H FD Expression of (. Epsilon.), S -1 (ε) is expressed as:
is a frequency domain fractional delay filter, and has the expression:
wherein bm The sum of the m-th diagonal elements in B is expressed as:
and (3) making:
obtaining an estimation result of the parameter by solving the root of the D (z) closest to the unit circle; assume that the root closest to the unit circle is:
z＝z 1
then and covariance matrix estimateThe corresponding estimated value of the delay error is:
step 3, calculating a time delay estimated value:
the delay estimate for the n+1th data period can be expressed as:
wherein Gd Is the multiplier coefficient;
step 4, returning to the step 1, and utilizing the time delay estimated value of the (n+1) th data periodThe next round of signal code tracking is performed.
2. The BL-DSSS signal code tracking method based on the frequency domain subspace principle of claim 1 wherein the specific steps of step 1 include:
the received signal result samples are then expressed as:
wherein w (t) is complex Gaussian white noise; p is p T (t) is the pulse waveform of the transmitted signal, and the frequency response isP N (f) A frequency response for the nyquist raised cosine waveform; c m = ±1 is a spreading code sequence; t (T) c Representing a pseudo code period; t (T) s For sampling period, d=τ/T s For normalized time delay, τ represents the initial time delay of the received signal; sampling point number N of single data period s ＝T/T s The method comprises the steps of carrying out a first treatment on the surface of the Will->Is compensated by a time domain shift of the signal,/->The fractional part of (2) is compensated by a fractional delay filter of a frequency domain; the signal of the nth data period after integer delay compensation and serial-to-parallel conversion is expressed as:
；
through N s The point FFT operation converts the signal to the frequency domain, then it is expressed as:
wherein ,Wk Is a frequency domain noise term;
a frequency domain waveform, which is a transmitted signal, contains pseudo code and a basic waveform, expressed as:
in the above formula, N represents a pseudo code length;
after integer delay compensation, the remaining uncompensated delay isBy combining R k,n And frequency domain fractional delay filter>Conjugate multiplication to complete the compensation of the fractional delay; the signal after fractional delay compensation is expressed as:
wherein ,normalized delay error; will->And local frequency domain waveform->Conjugate multiplication to complete matched filtering and despreading; wherein the frequency domain waveform is represented as:
wherein ,pR (t) is a local pulse waveform with a frequency response ofThe signal that completes matched filtering and despreading is expressed as:
wherein ,G k the corresponding time domain signal is +.>Wherein P (T) has a frequency response of P (f) =t c P N (f) The method comprises the steps of carrying out a first treatment on the surface of the Noise item->Corresponding time-domain signal->Is of the digital power spectral density ofWherein P is the power of the received intermediate frequency signal;
and finally, carrying out partial accumulation in a frequency domain to realize data dimension reduction, wherein the data dimension reduction is expressed as:
wherein ,NI To accumulate points partially, N b Satisfies the condition N b ＝N s /N I ；V k For noise term with partial accumulation hysteresis +.>
3. The BL-DSSS signal code tracking method based on the frequency domain subspace principle as set forth in claim 1, wherein the method is characterized in thatIn the step 2, G d ＝4TB L ；B L Representing loop bandwidth;
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