CN114189250B - A cross array-based undersampling method for joint estimation of carrier frequency and angle of arrival - Google Patents

Abstract

The present invention discloses a carrier frequency and arrival angle joint estimation undersampling method based on a cross array. Step 1: Use a cross array to modulate a broadband converter receiving structure for sampling to obtain the sampling values x[k] and y[k] of each channel; Step 2: Based on the number of sampling points Q of each channel in step 1, determine the trilinear model and Step 3: Use the staggered least squares method to extract the linear models from the three linear models. and Determine the estimated factor matrix and Step 4: For the matrix in step 3 and Step 5: Calculate the carrier frequency and DOA for the matrix paired in step 4 and the defined difference matrix. The present invention aims at the problem of high sampling rate and information redundancy in the joint estimation of DOA and carrier frequency of broadband sparse signals under Nyquist sampling theory.

Description

A cross array-based undersampling method for joint estimation of carrier frequency and angle of arrival

Technical Field

The invention belongs to the field of signal processing, and in particular relates to a carrier frequency and arrival angle joint estimation under-sampling method based on a cross array.

Background Art

Joint multi-parameter estimation has attracted widespread attention in recent years and has been studied in many engineering applications such as radar, sonar, and wireless communications. Carrier frequency and angle of arrival (DOA) are important features for signal recognition, and their joint estimation is a hot topic in current array signal processing research.

In practical applications, coherent signals are often generated due to multipath propagation or enemy interference. In traditional DOA estimation algorithms, the coherence of the signal will lead to rank deficiency, which seriously affects the performance of DOA. So far, many scholars have studied the carrier frequency and DOA joint estimation algorithms of coherent signals, however, these methods require the signal to be sampled at the Nyquist rate. With the development of information technology, the bandwidth of modern signals is getting higher and higher. The extremely high sampling rate brings great challenges to analog-to-digital converters (ADCs) and processing equipment.

In recent years, compressed sensing theory has been found to accurately restore sparse signals with a small number of samples, which has attracted widespread attention. Some researchers have applied CS theory to actual analog multi-band signal acquisition. Such as random demodulators, multi-coset samplers, and modulated broadband converters. Some studies have considered the joint estimation of carrier frequency and DOA under subquist sampling, which can be roughly divided into three categories: subspace, regular decomposition, and CS methods. However, current methods cannot work in the presence of coherent sources.

Summary of the invention

The present invention provides a carrier frequency and arrival angle joint estimation undersampling method based on a cross array, aiming at the problems of high sampling rate and information redundancy in joint estimation of broadband sparse signal DOA and carrier frequency under Nyquist sampling theory.

The present invention is achieved through the following technical solutions:

A carrier frequency and arrival angle joint estimation under-sampling method based on a cross array, the estimation under-sampling method comprising the following steps:

Step 1: Use the cross array modulation broadband converter receiving structure to sample and obtain the sampling values x[k] and y[k] of each channel;

Step 2: Determine the trilinear model based on the number of sampling points per channel Q in step 1 and

Step 3: Use the staggered least squares method to extract the linear models from the three linear models. and Determine the estimated factor matrix and

Step 4: For the matrix in step 3 and Pair the elements in ;

Step 5: Calculate the carrier frequency and DOA for the paired matrix in step 4 and the defined difference matrix.

Furthermore, the sampling values x[k] and y[k] of each channel in step 1 are specifically:

x[k]＝A _x w[k],

y[k]＝A _y w[k],

Wherein x[k]＝[x _-N+1 [k],...,x ₀ [k],...,x _N [k]] ^T and y[k]＝[y _-N+1 [k],...,y ₀ [k],...,y _N [k]] ^T are the sampling values of the x-axis and y-axis antennas respectively; A _x ＝[ _ax (θ ₁ ),..., _ax (θ _M )] and A _y ＝[ _ay (θ ₁ ),..., _ay (θ _M )] are (2N-1)×M array flow matrixes, where w[k] is an M×1 matrix, and the i-th element is _wi [k].

Furthermore, the step 2 specifically includes the following steps:

Step 2.1: Define a tensor based on the number of sampling points per channel Q in step 1 Determine its kth slice R _x1 [k];

Step 2.2: Define a tensor based on the number of sampling points per channel Q in step 1 Determine its kth slice R _x2 [k];

Step 2.3: Combine R _x1 [k] from step 2.1 and R _x2 [k] from step 2.2 into a trilinear model

Step 2.4: Define a tensor based on the number of sampling points per channel Q in step 1 Determine its k-th slice R _y1 [k];

Step 2.5: Define a tensor based on the number of sampling points per channel Q in step 1 Determine its k-th slice R _y2 [k];

Step 2.6: Combine R _y1 [k] from step 2.4 and R _y2 [k] from step 2.5 into a trilinear model

Furthermore, the k-th slice R _x1 [k] in step 2.1 is specifically:

The k-th slice R _x2 [k] in step 2.2 is specifically:

Step 2.3 Trilinear model Specifically:

Furthermore, the k-th slice R _y1 [k] in step 2.4 is specifically:

The k-th slice R _y2 [k] in step 2.5 is specifically:

Step 2.6 Trilinear model Specifically:

Further, the step 4 is specifically as follows: due to the CP decomposition column permutation fuzziness and scale fuzziness, it is known that the matrix Arrange and scale the columns to get the matrix make and Respectively represent matrices and The first Q rows of ; define a correlation coefficient matrix R _xy , the (i, j)th element in express and The correlation coefficient between them; by judging the size of the element |ρ| in the correlation coefficient matrix R _xy , find the matrix and The columns of correspond to the order, and the order is expressed as a permutation matrix Ξ. .

Furthermore, the step 4 also includes: the paired matrix It can be calculated by the following formula, thus obtaining the correct pairing matrix and

Define α _i =[α _1,i ,...,α _N,i ] and β _i =[β _1,i ,...,β _N,i ], where

Furthermore, the difference matrix defined in step 5 is specifically:

Calculate α _i and β _i according to the defined difference matrix:

α′ _i = mod(Dα _i ,2π)

β′ _i =mod(Dβ _i +π,2π)-π

Where α′ _i = [α′ _1,i ,...,α′ _N,i ], β′ _i = [β′ _1,i ,...,β′ _N,i ], n=1,. ..,N-1.

Calculate the carrier frequency and DOA for the paired matrix in step 4 and the defined difference matrix

Furthermore, the step 5 of calculating the carrier frequency and DOA is specifically as follows:

In step 5, the carrier frequency f _q of the coherent signal can be obtained by the average value of the sum of squares of the j-th group of coherent signals (α′ _n,p ) ² and (β′ _n,p ) ² ; and then the DOAθ _jp of each signal in the j-th group is calculated.

The beneficial effects of the present invention are:

The present invention is applicable to the situation where coherent signals and uncorrelated signals coexist, and can realize parameter estimation of coherent sources by extending the sampling sequence, while improving the robustness of the system. The matching problem between parameters caused by CP decomposition column permutation ambiguity is solved through correlation judgment.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a schematic diagram of the cross array MWC receiving structure of the present invention.

FIG. 2 is a graph showing parameter estimation results of the present invention, including (a) a graph showing RMSE of carrier frequency parameter estimation and (b) a graph showing RMSE of DOA parameter estimation.

FIG3 is a comparison diagram of true and estimated values of carrier frequencies and DOA parameters in the case of three coherent signals and two uncorrelated signals according to the present invention.

FIG. 4 is a flow chart of the method of the present invention.

DETAILED DESCRIPTION

The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

A carrier frequency and arrival angle joint estimation under-sampling method based on a cross array, the estimation under-sampling method comprising the following steps:

Step 1: Use the cross array modulation broadband converter receiving structure to sample and obtain the sampling values x[k] and y[k] of each channel;

The cross array modulation broadband converter is specifically:

Consider M continuous-time far-field narrowband signals s _i (t), where i = 1, ..., M, each with a modulated carrier frequency of Assume that these signals are mixed coherent and uncorrelated signals. In practice, such signals are common in multipath propagation environments due to factors such as enemy reflection or interference. Assume that the angle between the direction of arrival of each signal and the positive direction of the x-axis is the arrival angle where θ _i ∈(-90°,90°). To avoid array ambiguity, we assume that for i≠j,

f _i cos θ _i ≠ f _j cos θ _j

f _i sinθ _i ≠f _j sinθ _j

The cross array MWC receiving structure is shown in the figure below. It consists of two mutually orthogonal uniform linear arrays. There are 2N antenna elements along the x and y axes, represented as {x _-N+1 ,...,x ₀ ,...,x _N } and {y _-N+1 ,...,y ₀ ,...,y _N } respectively, and the two axes share one antenna at the origin. The total number of antennas is 4N-1. All antennas are connected to a single MWC channel. The signal received by the antenna is first mixed with a pseudo-random sequence p(t) with a period of T _p =1/f _p , and then sampled at a low speed at a frequency of f _s after passing through a low-pass filter with a cutoff frequency of f _s /2. For the convenience of calculation, f _s =f _p is selected.

Since the signal satisfies the narrowband assumption, s _i (t+τ _n )≈s _i (t). The signal received by the nth sensor x _n on the x-axis is Can be expressed as

Where n＝-N+1,...,0,...,N, Indicates the phase difference between the signals received by the antenna.

Similarly, for the y-axis we have

Step 2: Determine the trilinear model based on the number of sampling points per channel Q in step 1 and

Step 3: Use the staggered least squares method to extract the linear models from the three linear models. and Determine the estimated factor matrix and

Step 4: For the matrix in step 3 and Pair the elements in ;

Step 5: Calculate the carrier frequency and DOA for the paired matrix in step 4 and the defined difference matrix.

Furthermore, the sampling values x[k] and y[k] of each channel in step 1 are specifically:

x[k]＝A _x w[k],

y[k]＝A _y w[k],

where x[k]＝[x _-N+1 [k],...,x ₀ [k],...,x _N [k]] ^T and

y[k]＝[y _-N+1 [k],...,y ₀ [k],...,y _N [k]] ^T are the sampling values of the x-axis and y-axis antennas respectively;

A _x =[ _ax (θ ₁ ), ..., _ax (θ _M )] and A _y =[ _ay (θ ₁ ), ..., _ay (θ _M )] are (2N-1)×M array flow matrix, where w[k] is an M×1 matrix, and the i-th element is _wi [k].

Furthermore, the step 2 specifically includes the following steps:

Step 2.1: Define a tensor based on the number of sampling points per channel Q in step 1 Determine its kth slice R _x1 [k];

Step 2.2: Define a tensor based on the number of sampling points per channel Q in step 1 Determine its kth slice R _x2 [k];

Step 2.3: Combine R _x1 [k] from step 2.1 and R _x2 [k] from step 2.2 into a trilinear model

Step 2.4: Define a tensor based on the number of sampling points per channel Q in step 1 Determine its k-th slice R _y1 [k];

Step 2.5: Define a tensor based on the number of sampling points per channel Q in step 1 Determine its k-th slice R _y2 [k];

Step 2.6: Combine R _y1 [k] from step 2.4 and R _y2 [k] from step 2.5 into a trilinear model

Furthermore, the k-th slice R _x1 [k] in step 2.1 is specifically:

The k-th slice R _x2 [k] in step 2.2 is specifically:

Step 2.3 Trilinear model Specifically:

Furthermore, the k-th slice R _y1 [k] in step 2.4 is specifically:

The k-th slice R _y2 [k] in step 2.5 is specifically:

Step 2.6 Trilinear model Specifically:

Further, the step 4 is specifically as follows: due to the CP decomposition column permutation fuzziness and scale fuzziness, it is known that the matrix Arrange and scale the columns to get the matrix make and Respectively represent matrices and The first Q rows of ; define a correlation coefficient matrix R _xy , the (i, j)th element in express and The correlation coefficient between them; by judging the size of the element |ρ| in the correlation coefficient matrix R _xy , find the matrix and The columns of correspond to the order, and the order is represented as a permutation matrix Ξ. .

Furthermore, the step 4 also includes: the paired matrix It can be calculated by the following formula, thus obtaining the correct pairing matrix and

Define α _i =[α _1,i ,...,α _N,i ] and β _i =[β _1,i ,...,β _N,i ], where

Furthermore, the difference matrix defined in step 5 is specifically:

Calculate α _i and β _i according to the defined difference matrix:

α′ _i = mod(Dα _i ,2π)

β′ _i =mod(Dβ _i +π,2π)-π

Where α′ _i = [α′ _1,i ,...,α′ _N,i ], β′ _i = [β′ _1,i ,...,β′ _N,i ], n=1,. ..,N-1.

Calculate the carrier frequency and DOA for the paired matrix in step 4 and the defined difference matrix

Furthermore, the step 5 of calculating the carrier frequency and DOA is specifically as follows:

According to the definition of correlation coefficient, when there are j=1,...,J groups of coherent signals, the number of each group is P _j , we have According to the properties of the coherent signal, it is assumed that the carrier frequencies of the p=1, ..., P _j coherent signals in the jth group are all equal to f _j ;

In step 5, the carrier frequency _fq of the coherent signal can be obtained by the average of the square sum of the j-th group of coherent signals (α′n _,p ) ² and (β′n _,p ) ² ; and then the _DOAθjp of each signal in the j-th group is calculated. Therefore, there is no need to separate the coherent signals during the pairing process; after adding them to obtain the carrier frequency, the DOAs are calculated separately.

The simulation experiments verify the performance of the proposed method. The proposed method is compared with the ESPRIT method based on the CaSCADE system and the parallel factor analysis method (PARAFAC) based on the L-shaped array MWC system. Both methods are based on the L-shaped array MWC structure. Assume that the parameters of the three methods are the same. First consider the case of three uncorrelated sources. When the number of signals M=3 and N=10, the signal-to-noise ratio ranges from -10dB to 20dB. The simulation results show that it can be found that with the increase of the signal-to-noise ratio, the estimation accuracy of the three methods is improved. At the same time, the performance of the proposed method is better than the other two methods, especially under low signal-to-noise ratio conditions. This is because the smoothing operation in the proposed method doubles the number of available snapshots. As shown in Figure 2.

Then the ability of the proposed method to identify coherent sources is verified. Consider M = 5 mixed coherent and uncorrelated signals. The first three signals are coherent, which means that the correlation coefficient between the three sources is 1. The other two signals are independent of the coherent signals and are uncorrelated with each other. Figure 3 shows the comparison between the true and estimated values of the carrier frequencies and DOA parameters of the five signals. It is obvious that the proposed method is superior to the other two methods, which cannot estimate the parameters of the coherent signals.

Claims (7)

1. A carrier frequency and arrival angle joint estimation under-sampling method based on a cross array, characterized in that the estimation under-sampling method comprises the following steps: Step 1: Use the cross array modulation broadband converter receiving structure to sample and obtain the sampling values x[k] and y[k] of each channel; Step 2: Determine the trilinear model based on the number of sampling points per channel Q in step 1 and Step 3: Use the staggered least squares method to extract the linear models from the three linear models. and Determine the estimated factor matrix and Step 4: For the matrix in step 3 and Pair the elements in ; Step 5: Calculate the carrier frequency and DOA for the paired matrix in step 4 and the defined difference matrix; The specific step 4 is that due to the CP decomposition column permutation fuzziness and scale fuzziness, it is known that the matrix Arrange and scale the columns to get the matrix make and Respectively represent matrices and The first Q rows of ; define a correlation coefficient matrix R _xy , the (i, j)th element in express and The correlation coefficient between them; by judging the size of the element |ρ| in the correlation coefficient matrix R _xy , find the matrix and The columns correspond to the order, and the order is expressed as a permutation matrix ; The step 4 also includes: It can be calculated by the following formula, thus obtaining the correct pairing matrix and Define α _i =[α _1,i ,...,α _N,i ] and β _i =[β _1,i ,...,β _N,i ], where 2. According to the cross array-based carrier frequency and arrival angle joint estimation undersampling method of claim 1, it is characterized in that the sampling values x[k] and y[k] of each channel in step 1 are specifically: x[k]＝A _x w[k], y[k]＝A _y w[k], Wherein, x[k]＝[x _-N+1 [k],...,x ₀ [k],...,x _N [k]] ^T and y[k]＝[y _-N+1 [k],...,y ₀ [k],...,y _N [k]] ^T are the sampling values of the x-axis and y-axis antennas respectively; A _x =[ _ax (θ ₁ ),…, _ax (θ _M )] and A _y =[ _ay (θ ₁ ),…, _ay (θ _M )] are (2N-1)×M array flow matrix, where w[k] is an M×1 matrix, and the i-th element is _wi [k]. 3. According to the cross array-based carrier frequency and arrival angle joint estimation undersampling method of claim 1, characterized in that step 2 specifically comprises the following steps: Step 2.1: Define a tensor based on the number of sampling points per channel Q in step 1 Determine its kth slice R _x1 [k]; Step 2.2: Define a tensor based on the number of sampling points per channel Q in step 1 Determine its kth slice R _x2 [k]; Step 2.3: Combine R _x1 [k] from step 2.1 and R _x2 [k] from step 2.2 into a trilinear model Step 2.4: Define a tensor based on the number of sampling points per channel Q in step 1 Determine its k-th slice R _y1 [k]; Step 2.5: Define a tensor based on the number of sampling points per channel Q in step 1 Determine its k-th slice R _y2 [k]; Step 2.6: Combine R _y1 [k] from step 2.4 and R _y2 [k] from step 2.5 into a trilinear model 4. According to the cross array-based carrier frequency and arrival angle joint estimation undersampling method of claim 3, it is characterized in that the k-th slice R _x1 [k] in step 2.1 is specifically: The k-th slice R _x2 [k] in step 2.2 is specifically: Step 2.3 Trilinear model Specifically: 5. According to the cross array-based carrier frequency and arrival angle joint estimation undersampling method of claim 3, it is characterized in that the k-th slice R _y1 [k] in step 2.4 is specifically: The k-th slice R _y2 [k] in step 2.5 is specifically: Step 2.6 Trilinear model Specifically: 6. According to the cross array-based carrier frequency and arrival angle joint estimation undersampling method of claim 1, it is characterized in that the difference matrix defined in step 5 is specifically: Calculate α _i and β _i according to the defined difference matrix: α′ _i = mod(Dα _i ,2π) β′ _i =mod(Dβ _i +π,2π)-π Where α′ _i = [α′ _1,i ,...,α′ _N,i ], β′ _i = [β′ _1,i ,...,β′ _N,i ], n=1,. ..,N-1; Calculate the carrier frequency and DOA for the paired matrix in step 4 and the defined difference matrix. 7. According to the cross array-based carrier frequency and arrival angle joint estimation undersampling method of claim 6, it is characterized in that the carrier frequency and DOA are calculated in step 5 as follows: In step 5, the carrier frequency _fq of the coherent signal can be obtained by the average value of the sum of squares of the j-th group of coherent signals α′n _,p and β′n _,p ; and then the _DOAθjp of each signal in the j-th group is calculated.