A broadband signal reconstruction method based on sub-Nyquist sampling

Abstract

The present invention belongs to the field of cognitive radio technology, and specifically relates to a broadband signal reconstruction method based on sub-Nyquist sampling. Under the condition of known signal sparsity, the present invention aims to solve the problem that the OMP algorithm cannot reflect the relationship between the residual and the atom through the inner product under low signal-to-noise ratio. In addition, the present invention selects the correlation coefficient to replace the inner product in a mathematical sense, and combines the characteristics that the sub-band signal of the MWC system occupies at most two spectrum fragments, so that the number of iterations is halved, thereby improving the reconstruction probability of the support set and reducing the reconstruction time. The present invention replaces the inner product with the correlation coefficient as a method for finding the atom with the highest correlation, taking into account the characteristics that the signal brought by the MWC sampling structure occupies at most two spectrum fragments, thereby improving the reconstruction probability under low signal-to-noise ratio and reducing a certain reconstruction time.

Description

Technical Field

[0001] The present invention belongs to the technical field of cognitive radio, and in particular relates to a broadband signal reconstruction method based on sub-Nyquist sampling. Background Art

[0002] In today's radio communications field, with the continuous increase in signal bandwidth, sampling wideband signals has become a major challenge in modern digital signal processing. The emergence of compressed sensing theory provides a solution to this problem. Compressed sensing exploits the sparsity of signals in a certain transform domain, compressing the signal through a random measurement matrix during sampling. This allows sampling, transmission, and processing of wideband signals at a sampling rate lower than the Nyquist rate. Modulated Wideband Converter (MWC) sub-Nyquist sampling is a compressive sampling method. After compressive sampling, reconstructing the original signal is necessary to perform time-frequency analysis. The core of reconstructing MWC compressively sampled signals is obtaining the support set. Since the MWC sampling system continuously generates discrete signals as input to the reconstruction system after startup, this is an infinite measurement vector (IMV) problem. The continuous-to-finite (CTF) module is typically used to convert the IMV problem into a multiple measurement vector (MMV) problem. The support set is then obtained through a reconstruction algorithm, and the solution is finally solved to obtain the time-domain sampling sequence.

[0003] Traditional reconstruction algorithms, such as the Orthogonal Matching Pursuit (OMP) algorithm, while offering good performance, suffer from degradation at low signal-to-noise ratios. The OMP algorithm estimates the support set by selecting one or more columns with the highest correlation with the residual matrix through inner products. The residual matrix and support set are then iteratively updated until a stopping condition is met. The correlation coefficient, which ranges from -1 to 1, is essentially the covariance of two normalized vectors. This means the correlation coefficient does not consider the vector modulus, making it more objective in evaluating correlation. Selecting the column with the highest correlation with the residual matrix using the correlation coefficient better reflects the correlation between the residual and the atom. Furthermore, the MWC front-end analog sampling structure ensures that the original signal subband occupies at most two spectral segments. Therefore, after obtaining the column with the highest correlation, the more strongly correlated of the two adjacent columns can be added to the support set, thereby halving the number of iterations, increasing the probability of support reconstruction while reducing reconstruction time. Summary of the Invention

[0004] The present invention proposes a broadband signal reconstruction method based on sub-Nyquist sampling, which aims to improve the support set reconstruction probability under low signal-to-noise ratio and reduce a certain reconstruction time.

[0005] The technical solution of the present invention is:

[0006] Assuming that the signal is a sparse multi-band signal modulated by QPSK, the signal is expressed as:

[0007]

[0008] Where N s is the number of frequency bands. The spectrum of the RF signal is conjugate symmetrical, so the number of frequency bands N s It is twice the number of signals. i is the energy of each sub-signal; B i is the bandwidth of each sub-signal. I[n] and Q[n] represent the in-phase and quadrature components of the QPSK signal respectively. s(t) is composed of a sinc function, with a carrier frequency f i In [0,f nyq / 2) Random selection.

[0009] For the received broadband signal x(t), before MWC compression sampling, assume that the number of parallel channels is m and the number of signal frequency bands is N. s , the signal aliasing rate is L, the number of samples for each channel is K, and the sampling frequency is f s , T s =1 / f s .

[0010] The broadband signal reconstruction method of the present invention comprises the following steps: Figure 1 As shown:

[0011] S1, the received signal passes through m MWC parallel channels, and in each channel, the period is T p The pseudo-random sequence is mixed, and the m×L dimension matrix A is obtained by the Fourier expansion coefficient of the periodic pseudo-random sequence; then the mixing signal of each channel is passed through a cutoff frequency of 1 / 2T s The low-pass filter is then passed through the sampling frequency f s The ADC obtains the m-way compressed sampling sequence y i (n), forming an m×K dimensional matrix Y, such as Figure 2 As shown;

[0012] S2. Calculate the covariance matrix R of the MWC sampling sequence Y :

[0013]

[0014] The covariance matrix R is obtained by sampling the sequence Y , then R Y Perform eigenvalue decomposition to obtain m eigenvalues and their corresponding eigenvectors, and then use the largest 2N s eigenvalues and their corresponding eigenvectors to construct an m×2N s dimensional matrix V;

[0015] S3, initialize residual r0 = V, index set Iteration number i = 1;

[0016] S4. Find a new index ζ that satisfies in Express the correlation coefficient:

[0017]

[0018] In the formula, cov(,) means calculating covariance, and D() means calculating variance.

[0019] S5. Determine the occupancy of two adjacent spectrum fragment positions ζ-1 and ζ+1, and take the larger d k The spectrum fragment of the value is recorded as ζ', where k is the position of adjacent spectrum fragments, ||||2 means calculating the bi-norm;

[0020] S6. Update the support set Γ = Γ∪ζ∪ζ';

[0021] S7. Calculate the current estimate by the least squares method And update the residual

[0022] S8, the number of iterations i=i+1, if i <N s / 2, then return to step S4, otherwise stop the iteration and output the support set Γ;

[0023] S9, pass Solve the time domain sampling points, and the values of other rows that do not belong to the support set are all 0;

[0024] S10, z S [n] is padded with zeros and then interpolated to the Nyquist sampling rate f through a digital filter nyq , and then perform time domain modulation and superposition on all interpolated sequences to obtain the sampling sequence of the original signal.

[0025] The beneficial effects of the present invention are: replacing the inner product with the correlation coefficient as a method for finding the atoms with the highest correlation, considering the characteristic that the signal brought by the MWC sampling structure occupies at most two spectrum segments, improving the reconstruction probability under low signal-to-noise ratio, and reducing a certain reconstruction time. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 This is a system diagram of a broadband signal reconstruction solution based on sub-Nyquist sampling according to the present invention;

[0027] Figure 2 Simulate the sampling model diagram for the front end of the modulated broadband converter;

[0028] Figure 3 The method proposed by the present invention is consistent with the OMP algorithm in the case of m=50 sampling channels and N number of frequency bands. s =6, the number of sampling points K = 50, the support set reconstruction performance comparison under different signal-to-noise ratios;

[0029] Figure 4 The method proposed by the present invention is consistent with the OMP algorithm in the signal-to-noise ratio of 10dB and the number of frequency bands N. s =6, the number of sampling points K = 50, the support set reconstruction performance comparison chart under different sampling channel numbers;

[0030] Figure 5 The method proposed by the present invention is consistent with the OMP algorithm in the case of a signal-to-noise ratio of 0dB, a sampling channel number m=50, and a frequency band number N s =6, the comparison of support set reconstruction performance under different sampling points;

[0031] Figure 6 This is a comparison chart of the support set reconstruction performance of the method proposed in the present invention and the OMP algorithm under different numbers of sub-bands when the number of sampling channels is m = 50, the signal-to-noise ratio is 10dB, and the number of sampling points is K = 50;

[0032] Figure 7 The method proposed by the present invention is to achieve a signal-to-noise ratio of 10dB and a frequency band number of N. s =6, and the number of sampling points K = 50, the reconstruction time comparison of the OMP algorithm under different numbers of sampling channels. DETAILED DESCRIPTION

[0033] The technical solution of the present invention has been described in detail in the summary of the invention. The practicality of the present invention is illustrated below with reference to simulation examples.

[0034] Assume that the signal consists of three pairs of frequency bands, each with a bandwidth of 50 MHz, E i =[1 1 1], the initial simulation parameters are: compressed signal length K = 50, MWC sampling channel number m = 50, Nyquist rate f NYQ =10GHz, f s =f p =51.28MHz, aliasing rate L=195, signal-to-noise ratio SNR range is [-10:1:10]dB, and each simulation experiment is performed 1000 times of Monte Carlo experiments. The support set reconstruction performance evaluation criterion is: when the true support set Λ is the estimated support set When the subset of When the column is full rank, the support set is considered to be reconstructed successfully.

[0035] from Figure 3It can be seen from the analysis that as the signal-to-noise ratio increases, the probability of successful reconstruction of the support set increases accordingly. In a low signal-to-noise ratio environment, the reconstruction performance of the method of the present invention is greatly improved compared to the OMP algorithm under low signal-to-noise ratio. This shows that the method of the present invention can improve the reconstruction performance under low signal-to-noise ratio, and also verifies that the use of correlation coefficient can better reflect the correlation between residuals and atoms. Figure 4 It can be seen from the figure that as the number of sampling channels increases, the probability of successful reconstruction of the support set increases. When the number of sampling channels is less than 20, the reconstruction performance of the proposed method is better than that of the OMP algorithm. Figure 5 It can be seen from the results that the reconstruction performance of the proposed method is better than that of the OMP algorithm. Moreover, as the number of sampling points increases, the reconstruction performance of each method improves accordingly. When the number of sampling points increases to a certain value, the probability of successful reconstruction of the support set of each method no longer changes. Figure 6 It can be seen that as the number of signal sub-bands increases, the reconstruction performance of each method decreases. When the number of signal sub-bands is less than 14, the probability of successful reconstruction of the support set of each method is similar; when the number of signal sub-bands is more than 16, the reconstruction performance of the method of the present invention is better than the OMP algorithm. Figure 7 It can be seen that the reconstruction time increases with the increase in the number of sampling channels, wherein the reconstruction time of the method of the present invention is shorter than that of the OMP algorithm, which also proves that the method of the present invention can reduce the reconstruction time to a certain extent.

Claims

1. A broadband signal reconstruction method based on sub-Nyquist sampling. For the received broadband signal x(t), before MWC compression sampling, the number of parallel channels is defined as m and the number of signal bands is defined as N. s , the signal aliasing rate is L, the number of samples for each channel is K, and the sampling frequency is f s , T s =1 / f s , characterized in that, The method comprises the following steps: S1, the received signal passes through m MWC parallel channels, and in each channel, the period is T p The pseudo-random sequence is mixed, and the m×L dimension matrix A is obtained by the Fourier expansion coefficient of the periodic pseudo-random sequence; then the mixing signal of each channel is passed through a cutoff frequency of 1 / 2T s The low-pass filter is then passed through the sampling frequency f s The ADC obtains the m-way compressed sampling sequence y i (n), forming an m×K dimensional matrix Y; S2. Calculate the covariance matrix R of the MWC sampling sequence Y : The covariance matrix R is obtained by sampling the sequence Y , then R Y Perform eigenvalue decomposition to obtain m eigenvalues and their corresponding eigenvectors, and then use the largest 2N s eigenvalues and their corresponding eigenvectors to construct an m×2N s dimensional matrix V; S3, initialize residual r0 = V, index set Iteration number i = 1; S4. Find a new index ζ that satisfies in Express the correlation coefficient: In the formula, cov(,) means calculating covariance, D() means calculating variance; S5. Determine the occupancy of two adjacent spectrum fragment positions ζ-1 and ζ+1, and take the larger d k The spectrum fragment of the value is recorded as ζ', where k is the position of adjacent spectrum fragments, || ||2 means calculating the bi-norm; S6. Update the support set Γ = Γ∪ζ∪ζ'; S7. Calculate the current estimate by the least squares method And update the residual S8, the number of iterations i=i+1, if i <N s / 2, then return to step S4, otherwise stop the iteration and output the support set Γ; S9, pass Solve the time domain sampling points, and the values of other rows that do not belong to the support set are all 0; S10, z S [n] is padded with zeros and then interpolated to the Nyquist sampling rate f through a digital filter nyq , and then perform time domain modulation and superposition on all interpolated sequences to obtain the sampling sequence of the original signal.

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