A signal spectrum sensing and DOA estimation method based on cooperative MWC

Abstract

The application provides a signal spectrum sensing and DOA estimation method based on cooperative MWC. The method is based on a non-uniform array MWC sampling structure with arbitrary array element positions, and each receiving channel has a different mixing sequence. In combination with the different mixing information and spatial phases in each receiving channel, a sparse model is constructed to realize simultaneous joint estimation of the carrier frequency and the DOA. Compared with the traditional subspace-based method, the method does not need to make a uniform array assumption, and relaxes the restriction on the array manifold. Through the space-time distribution characteristics of the spectrum and the DOA, the parameter estimation problem can be solved when the coherent signals and the source ambiguity exist, and the method has a wide application prospect.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of signal processing, and particularly relates to a signal spectrum sensing and DOA estimation method based on cooperative MWC. BACKGROUND

[0002] Spectrum measurement and direction of arrival (DOA) estimation are important research topics in radar, sonar, cognitive radio and other engineering measurement applications. At present, many scholars consider the joint estimation of frequency and DOA based on Nyquist sampling theory. However, in many modern applications, the spectrum of the monitored signal is very wide.

[0003] The sampling scheme based on the traditional Nyquist theory has a high sampling rate and large data volume, which brings challenges to hardware devices and signal processing. In order to overcome the bottleneck of the sampling rate, scholars have proposed many under-sampling structures based on compressed sensing (CS), such as multi-coreset samplers, modulated wideband converters (MWCs) and the like. These methods can sample and reconstruct signals at a sampling rate much lower than the Nyquist rate. However, the array signal under-sampling method based on time delay under-sampling or multi-coreset sampling has practical problems, that is, the analog bandwidth of the low-rate ADC must be greater than the bandwidth of the input signal, and the time delay accuracy is required to be high. These problems are difficult to realize in the current radio frequency hardware. The MWC structure truly reduces the analog bandwidth of the ADC and does not require accurate delay, and has greater application potential.

[0004] At present, many array parameter estimation methods based on MWC have been proposed. However, almost all existing methods assume that there is no source ambiguity and coherent signal. Source ambiguity is caused by the same electronic angle of different sources, resulting in linear correlation of steering vectors. In actual applications, due to multipath propagation or enemy interference, coherent signals are often generated. These two problems will cause the rank of the array manifold matrix or the cross-correlation matrix to be insufficient, thereby causing the under-sampling estimation method to fail.

[0005] Therefore, it is of great practical significance to combine the MWC technology with array signal processing to realize spectrum sensing and DOA estimation when ambiguous sources and coherent signals exist under under-sampling. SUMMARY

[0006] The application aims to solve the problems of high sampling rate and large data volume of the spectrum measurement and direction of arrival (DOA) estimation method based on the traditional Nyquist theory, and proposes a signal spectrum sensing and DOA estimation method based on cooperative MWC.

[0007] The application is implemented by the following technical scheme, and the application proposes a signal spectrum sensing and DOA estimation method based on cooperative MWC, which specifically comprises:

[0008] Step 1: Sample using linear array modulated wideband transducer receiving structure to obtain per-channel sample value x n [k], expressed in discrete Fourier form as:

[0009]

[0010] where S i (f) is the Fourier transform of s i (t), is the smallest integer containing all non-zero elements of X n (f) ; considering that the spectrum of a complex-valued signal contains only positive frequencies, i.e. l = -L0,..., -1, S i (f - f i -lf p ) = 0, thus only the part for L > 0 is kept;

[0011] Step 2: Assume the electronic angle τ i is located on a grid , δ is a parameter of the estimation algorithm defining the grid resolution, and define S i (f - f i ) corresponding to the grid τ p = δp as S p (f) ;

[0012]

[0013] where when δp = τ i , has

[0014] Write equation (2) in matrix form:

[0015]

[0016] where, is the Kronecker product, is the steering vector of the n-th sensor; is an unknown vector of L0P x 1 containing all L0spectrum slices corresponding to the electronic angle of each grid point p ∈ [1,..., P]; the element in is expressed as is a joint sparse vector of 2M;

[0017] Step 3: Combine the sampling data of all sensors to obtain:

[0018]

[0019] Where ⊙ is the Khatri-Rao product; C is an N×L0 matrix containing the mixed sequence p n The Fourier series coefficients of (t), n=1,...,N, where the element in the nth row is c. n A is an N×P array manifold matrix, where the element in the nth row is a. n G = (C T ⊙A T ) T It is an N×L0P matrix, where the (n, l·p)th element is represented as

[0020] Step 4, calculate the perception matrix G:

[0021]

[0022] Step 5, for Execute the Synchronous Orthogonal Matching Pursuit (SOMP) algorithm to obtain The index set Z of non-zero items;

[0023] Step 6: Calculate the grid position index of the signal spectrum support set and the electronic angle:

[0024]

[0025]

[0026] Z odd Represents the element at an odd index in Z; and These represent the grid position indices for the estimated spectral support set and the electronic angle, respectively.

[0027] Step 7, calculate the electron angle:

[0028]

[0029] in

[0030] Step 8: Calculate the spectrum of the sub-band where the signal is located:

[0031]

[0032] in Only contains The items are supported by the Z-index. It is G Z Yes, it's a false reversal;

[0033] Step nine, signal s i The spectrum of (t) is expressed as:

[0034]

[0035] Step ten, the power spectrum of the signal is calculated by Welch method, and the power spectrum is twice smoothed, and the center frequency f is obtained by frequency centering method i,0 ; Then, combined with the sub-band support set S i , the carrier frequency of the i-th signal is:

[0036]

[0037] Step eleven, calculate the DOA:

[0038]

[0039] Step twelve, for i=1,...,M, repeat steps nine to eleven, respectively, to obtain the sub-band spectrum of M target signals carrier frequency and

[0040] Further, the linear array modulation wideband converter receiving structure is composed of a linear array MWC of N sensor elements, and the signal u n (t) received by each channel is first multiplied by a mixed sequence p p (t) with a period T p =1 / f n , wherein f p is the period rate, then the signal is filtered by a low-pass filter with a cutoff frequency of 1 / (2T s ), and then the filtered signal is sampled by an ADC at a rate of f s =1 / T s .

[0041] Further, under the narrowband assumption, the signal u n (t) received by the n-th sensor can be expressed as:

[0042]

[0043] The electronic angle is defined as:

[0044] τ i = f i sinθ i (12)

[0045] Wherein, τ i d n / c represents the spatial delay of the i-th signal at the n-th sensor relative to the reference sensor.

[0046] Further, the mixed sequence p n (t) of the n-th sensor isThe Fourier expansion of (t) is:

[0047]

[0048] where is p n The Fourier series coefficients of (t).

[0049] The beneficial effects of the present application are:

[0050] The present application proposes a signal spectrum sensing and DOA estimation method based on collaborative MWC, compared with the traditional subspace-based method, the method does not need to make uniform array assumption, and relaxes the restriction on array manifold. Through the space-time distribution characteristics of spectrum and DOA, the parameter estimation problem when coherent signals and ambiguous sources exist can be solved, and the method has broad application prospect. BRIEF DESCRIPTION OF DRAWINGS

[0051] Figure 1 is a schematic diagram of a linear array MWC receiving structure;

[0052] Figure 2 is an estimation performance diagram under different signal-to-noise ratios SNR; wherein (a) is the carrier frequency parameter estimation NMSE curve, (b) is the DOA parameter estimation NMSE curve, and (c) is the reconstructed signal MSE curve;

[0053] Figure 3 is a real and estimated parameter result diagram under coherent signals and ambiguous sources. DETAILED DESCRIPTION

[0054] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0055] The present application proposes a new array collaborative modulation wideband transformer (ACMWC) sub-Nyquist sampling receiving structure for spectrum sensing and DOA estimation, aiming at the problems in the prior art. Based on the linear array collaborative MWC sampling receiving structure of arbitrary array element position, the mixing information and spatial phase of multiple array elements with different mixing sequences in each receiving channel are combined to construct a sparse model, and the simultaneous estimation of carrier frequency and DOA is realized.

[0056] Consider M far-field narrowband signal sources s i (t), which are distributed in a wide frequency spectrum range, have a Nyquist sampling rate f nyq and an unknown carrier frequency f iWhere i = 1, ..., M. Signal bandwidth Assumption From different DOA directions θ i When incident on a linear receiving array, the positions of the N elements can be represented as d = [d1, d2, ..., dn]. N ], where d1=0, d n This is the distance of the nth sensor relative to the first sensor. Unlike previous methods, this invention does not require the sensors to be uniformly arranged. Furthermore, this invention does not require any correlation between the signals; that is, the signal sources can be correlated or even coherent, which often occurs in practice due to multipath propagation. In addition, this invention does not strictly require the absence of source ambiguity; that is, this invention does not require f... i sinθ i ≠f j sinθ j For any i ≠ j. In contrast, the assumptions of this invention impose significantly fewer restrictions on array manifolds and signal models, and are more consistent with practical applications.

[0057] Combination Figures 1-3 This invention proposes a signal spectrum sensing and DOA estimation method based on cooperative MWC, the method specifically including:

[0058] Step 1: Sampling is performed using a linear array modulation broadband converter receiver structure to obtain the sampled value x for each channel. n [k], in discrete Fourier form, is:

[0059]

[0060] Where S i (f) is s i Fourier transform of (t), It contains X n (f) is the smallest integer containing all non-zero elements; considering that the spectrum of a complex signal contains only positive frequencies, i.e., l = -L0,...,-1, S i (ff i -lf p Since L = 0, only the part with L ≥ 0 is retained;

[0061] Step 2, assume the electron angle τ i Located in the grid Above, δ is a parameter defining the estimation algorithm for grid resolution, and the signal S is defined as follows: i (ff i ) corresponds to grid τ p =δp is S p (f);

[0062]

[0063] where when δp=τ i there is

[0064] Write equation (2) in matrix form:

[0065]

[0066] where, is the Kronecker product, c n = [c n,0 ,..., c n,L0 ], is the steering vector of the nth sensor; is an unknown vector of L0P x 1, containing all L0 spectral slices corresponding to the electron angle of each grid point p e [1,..., P]; The element in is denoted as is a joint sparse vector of 2M;

[0067] Step three, combine the sampling data of all sensors to get:

[0068]

[0069] where is the Khatri-Rao product; C is an N x L0 matrix containing the Fourier series coefficients of the mixing sequence p n (t), n = 1,..., N, the element of the nth row is c n ; A is an N x P array manifold matrix, the element of the nth row is a n ; G = (C T ⊙ A T ) T is an N x L0P matrix, the (n, l-p)th element is denoted as

[0070] Step four, calculate the perception matrix G:

[0071]

[0072] Step five, perform the synchronous orthogonal matching pursuit SOMP algorithm on to get the index set Z of the non-zero items of ;

[0073] Step six, calculate the signal spectral support set and the grid position index of the electron angle:

[0074]

[0075]

[0076] where Z odd denotes the element at the odd index position in Z; and denote the estimated spectral support set and the grid position index of the electronic angle, respectively;

[0077] Step seven, calculate the electronic angle:

[0078]

[0079] where

[0080] Step eight, calculate the sub-band spectrum where the signal is located:

[0081]

[0082] where only contains the item indexed by the support set Z in G Z is the pseudo-inverse of G

[0083] Step nine, the spectrum of the signal s i (t) is represented as:

[0084]

[0085] Step ten, calculate the power spectrum of the signal using the Welch method, and perform quadratic smoothing on the power spectrum to obtain the center frequency f i,0 using the frequency centering method; then, combined with the sub-band support set S i , the carrier frequency of the i-th signal is:

[0086]

[0087] Step eleven, calculate the DOA:

[0088]

[0089] Step twelve, repeat steps nine to eleven for i = 1, …, M, to obtain the sub-band spectrum carrier frequency and

[0090] The linear array modulated wideband transducer receiving structure is composed of a linear array MWC of N sensor elements, as shown in Figure 1 The signal u n (t) received by each channel is first multiplied by a periodic function with a period T​p = 1 / f p The mixing sequence p n (t) where f p is the periodic rate, then the signal is filtered with a low-pass filter with a cutoff frequency of 1 / (2T s ), then the filtered signal is sampled by the ADC at a rate of f s = 1 / T s .

[0091] Under the narrowband assumption, the signal u n (t) received from the nth sensor can be expressed as:

[0092]

[0093] The electronic angle is defined as:

[0094] τ i = f i sinθ i (12)

[0095] where τ i d n / c represents the spatial delay of the ith signal at the nth sensor relative to the reference sensor.

[0096] The Fourier expansion of the mixing sequence p n (t) of the nth sensor is:

[0097]

[0098] where are the Fourier series coefficients of p n (t).

[0099] Simulation experiments verify the performance of the proposed ACMWC system based on the collaborative MWC signal spectrum sensing and DOA estimation method. The method is compared with the ESPRIT method based on the L-type array MWC system, the CS method, the PARAFAC method and the PASS-FD system based on the delay array. Figure 2The NMSE curves of carrier frequency and DOA estimation, and the MSE curves of signal reconstruction when the signal-to-noise ratio is-20 dB to 20 dB are given. Since the PASS-FD system reconstructs the power spectrum rather than the signal itself, the signal reconstruction experiment is not compared with it. It can be seen that the carrier frequency estimation and signal reconstruction performance of the ACMWC proposed in the application are obviously better than those of the other four array sub-Nyquist sampling methods, and the DOA estimation performance is slightly better than that of the other methods. This is because the application simultaneously utilizes the different mixing information and spatial phases of each channel to estimate the parameters, rather than relying only on the spatial phase as in other methods, so that the estimation result is more accurate and reliable. Different mixing sequences enhance the randomness of the sensing matrix, thereby enhancing the robustness of the system. However, the estimation of DOA is not as accurate as that of the carrier frequency, because the estimation of the electronic angle depends on the size of the grid, and when the target signal is not on the grid, a certain grid error will be generated. At the same time, the error of the grid will cause the deviation of the sensing matrix from the theoretical value, so the signal reconstruction performance is slightly worse than that of the traditional MWC structure.

[0100] Then, the estimation ability of the five under-sampling methods in the presence of source ambiguity and coherent sources is tested. It is assumed that M=5 signals, and the electronic angle τ=[-0.08, 0.10, -0.08, -0.08, 0.30]. The carrier frequencies of the five sources are given by f1=1.6 GHz, f2=1.6 GHz, f3=3.2 GHz, f4=1 GHz, and f5=3.6 GHz. The corresponding DOA is set as θ1=-30°, θ2=40°, θ3=-14.5°, θ4=-53.1°, and θ5=55°. Signals 1 and 2 are coherent. Signals 1, 3, and 4 are linearly related in the steering vector, which are ambiguous sources, and signal 5 is unrelated to the other signals. Figure 3 The real parameters and the estimated parameters among the five signals are given. It can be found that this method can distinguish two groups of coherent signals, while the other two methods cannot identify coherent signals. Due to the correlation of the steering vector, the rank of the array manifold matrix is insufficient, so the ESPRIT, PARAFAC, and CS methods cannot correctly estimate the parameters in the case of source ambiguity. However, the ACMWC and PASS-FD methods can distinguish ambiguous sources, and obviously the performance of the ACMWC in estimating the parameters is better.

[0101] The above describes in detail the signal spectrum sensing and DOA estimation method based on collaborative MWC proposed in the application. The principles and implementation modes of the application are described by applying specific examples in this paper. The above example is only used to help understand the method and core idea of the application; at the same time, for those skilled in the art, according to the idea of the application, the specific implementation mode and application range will be changed, and the above description should not be understood as a limitation of the application.

Claims

1. A signal spectrum sensing and DOA estimation method based on cooperative MWC, characterized in that: The method specifically includes: Step 1: Sampling is performed using a linear array modulation broadband converter receiver structure to obtain the sampled value x for each channel. n [k], in discrete Fourier form, is: Where S i (f) is s i Fourier transform of (t), It contains X n (f) is the smallest integer containing all non-zero elements; considering that the spectrum of a complex signal contains only positive frequencies, i.e., l = -L0,...,-1, S i (ff i -lf p Since L = 0, only the part with L ≥ 0 is retained; Step 2, assume the electron angle τ i Located in the grid Above, δ is a parameter defining the estimation algorithm for grid resolution, and the signal S is defined as follows: i (ff i ) corresponds to grid τ p =δp is S p (f); in When δp=τ i From time to time Equation (2) can be written in matrix form: in, For Kronecker product, It is the steering vector of the nth sensor; It is an L0P×1 unknown vector containing all L0 spectral slices corresponding to the electronic angles at each grid point p∈[1,...,P]. The elements in are represented as It is a 2M joint sparse vector; Step 3: Combine the sampling data from all sensors to obtain: Where ⊙ is the Khatri-Rao product; C is an N×L0 matrix containing the mixed sequence p n The Fourier series coefficients of (t), n=1,...,N, where the element in the nth row is c. n A is an N×P array manifold matrix, where the element in the nth row is a. n G = (C T ⊙A T ) T It is an N×L0P matrix, where the (n, l·p)th element is represented as Step 4, calculate the perception matrix G: Step 5, for Execute the Synchronous Orthogonal Matching Pursuit (SOMP) algorithm to obtain The index set Z of non-zero items; Step 6: Calculate the grid position index of the signal spectrum support set and the electronic angle: Z odd Represents the element at an odd index in Z; and These represent the grid position indices for the estimated spectral support set and the electronic angle, respectively. Step 7, calculate the electron angle: in Step 8: Calculate the spectrum of the sub-band where the signal is located: in Only contains The items are supported by the Z-index. It is G Z Yes, it's a false reversal; Step nine, signal s i The spectrum of (t) is expressed as: Step 10: Calculate the power spectrum of the signal using the Welch method, perform secondary smoothing on the power spectrum, and obtain the center frequency f using the frequency centering method. i,0 Then, combined with the sub-band support set S i The carrier frequency of the i-th signal is obtained as: Step 11, Calculate DOA: Step 12: For i = 1, ..., M, repeat steps 9 to 11 to obtain the sub-band spectra of the M target signals respectively. carrier frequency and 2. The method according to claim 1, characterized in that, The linear array modulation broadband converter receiving structure consists of a linear array MWC with N sensor elements, and each channel receives a signal u. n (t) is first multiplied by a period of T. p =1 / f p The mixed sequence p n (t), where f p The periodic rate is then used, and the cutoff frequency is 1 / (2T). s The low-pass filter filters the signal, and then the ADC outputs the signal at f... s =1 / T s The filtered signal is sampled at a rate of [a certain rate].

3. The method according to claim 2, characterized in that, Under the narrowband assumption, the signal u received from the nth sensor n (t) can be expressed as: The electron angle is defined as: t i =f i sinth i (12) Where, τ i d n / c represents the spatial delay of the i-th signal relative to the reference sensor at the n-th sensor.

4. The method according to claim 3, characterized in that, The nth sensor mixing sequence p n The Fourier expansion of (t) is: in It is p n Fourier series coefficients of (t).

Images