CN104320205B - Sparse DOA algorithm for estimating in Spatial Doppler domain - Google Patents

Abstract

The invention relates to a sparse DOA estimation algorithm in the spatial Doppler domain, comprising the following steps: (1) a sparse DOA estimation algorithm under the CS architecture; (2) extending the signal strength y _m to the sparse angle domain and sparse Doppler domain; (3) sparse DOA estimation algorithm in Doppler domain. On the basis of compressed sensing theory, the present invention conducts detailed analysis and simulation on DOA estimation in space angle domain and Doppler domain, and discusses the related performance of multi-antenna spectrum sensing. Estimating the sparse DOA in the Doppler frequency domain greatly improves the resolution compared with the previous estimation results in the time domain, and the required signal elements are also reduced.

Description

Sparse DOA Estimation Algorithm in Spatial Doppler Domain

technical field

The invention relates to a compressed spectrum sensing algorithm in the case of multi-antenna arrays in the sparse angle domain and the sparse Doppler domain.

Background technique

In the past few years, the DOA (Direction Of Arrival) estimation method has been widely used in various fields, such as radar, sea traffic, underwater acoustic tracking, wireless communication and so on. Therefore, some algorithms for DOA estimation have emerged as the times require. The more common ones are Multiple Signal Classification (MUSIC), Minimum Variance Distortionless Response (MVDR), and Maximum Likelihood (Maximum Likelihood). ) and rotation-invariant signal parameter change method (Estimation of Signal Parameters via Rotational invariance techniques, ESPRIT), etc. However, these methods often need to know the prior information of the number of signals, but in today's non-cooperative communication environment, the number of wireless devices and servers has shown explosive growth, so the practicability of the above algorithms still needs to be improved. In recent years, Compressed-Sensing (CS), as a new research method and means, can better improve the spectrum sensing performance of the signal by analyzing the inherent sparse characteristics of the signal acquired at the receiver. If the CS technology is applied to DOA estimation, it can also solve the problem of too short spatial signal distance and few snapshots, and it can also alleviate the limitations caused by some parameter estimation methods, such as common coherent signals and comparative Large sample support base and other issues.

The estimation of DOA under the support of CS theory usually involves two problems, namely, the estimation of spatial signal spectrum and the selection of array flow pattern vector.

Contents of the invention

Aiming at the above-mentioned problems in the prior art, the present invention proposes compressed spectrum sensing in the case of multi-antenna arrays in the sparse angle domain and sparse Doppler domain, and performs joint sparse estimation of DOA by using the angle sparse characteristic of received signals. The sparseness of the frequency is considered in the sampling link, which can effectively reduce the burden of the entire communication system. At the same time, combined with the Doppler frequency shift, the DOA under the multi-channel antenna array is estimated.

The present invention adopts following technical scheme: sparse DOA estimation algorithm in the spatial Doppler domain, it is characterized in that, comprises the following steps:

Step 1, the sparse DOA estimation algorithm under the CS architecture,

(1) There are L electromagnetic plane waves, Among them, l=1,...L, represents the number of unknown signal directions θ _l , Indicates the projection direction;

(2) For the narrowband signal of the same frequency, the signal strength of the incoming wave signal after reaching the antenna array m is the number of antenna array elements, x _m is the position of the antenna array elements on the x-axis, f is the effective length of the antenna array elements, n _m is the additive Gaussian noise sample with a mean value of zero on the mth antenna; the above formula is variable is y=A(θ)s+n, where y=[y ₁ ,y ₂ ,...,y _M ] ^T ∈ C ^M×1 , θ=[θ ₁ ,θ ₂ ,...,θ _L ], A(θ)=[a(θ ₁ ),a(θ ₂ ),...,a(θ _L )] is an M×L-dimensional array flow pattern vector, s=[W ₁ ,W ₂ , ...,W _L ] ^T ∈C ^L×1 , n=[n ₁ ,n ₂ ,...,n _M ] ^T ∈C ^M×1 , the expansion can be expressed as

Step 2, extending the signal strength y _m described in step 1 to the sparse angle domain and the sparse Doppler domain,

(1) Perform Fourier transform on y=A(θ)s+n to obtain y _f =As _f +n _f , at this time s _f and y _f are sparse;

(2) For K non-zero signals, use ζ to represent the deterministic power value or energy value corresponding to each row of unknown parameters in the signal s _f , and the DOA estimation process is as follows: a) let L=k=1; b) When ζ _n ≠0, and θ _L =θ _k , L=L+1; c) if k<K, then k=k+1, and return to step b); otherwise, exit the calculation process of DOA;

(3) Take the block row signal of signal y _f , recover the required sparse signal from each row block, wherein the non-zero signal is the required DOA estimate;

Step 3, sparse DOA estimation algorithm,

(1) For K narrowband signals from the far field, the signal at the receiver s=[W ₁ ,W ₂ ,...,W _L ] ^T is a sparse matrix, n=[n ₁ ,n ₂ ,.. .,n _M ] ^T is a noise matrix, since only K row elements in the signal s are non-zero, y=As+n=[y(t ₁ ),...,y(t _M )] is to search The joint sparsification of y to represent the MMV problem of signal s.

(2) The objective function of the MMV problem is in When p=2, q=0, it can be written as

(3) Definition Available: In noisy environments, When there is no noise, Available where the joint row sparse matrix is therefore is further transformed into

Preferably, the value of λ in step three (3) is 0.5.

Compared with the prior art, the present invention has the following advantages and beneficial effects: On the basis of compressed sensing theory, the present invention conducts detailed analysis and simulation on the DOA estimation in the spatial angle domain and the Doppler domain, and discusses the multi-path Correlation performance of antenna spectrum sensing. Estimating the sparse DOA in the Doppler frequency domain greatly improves the resolution compared with the previous estimation results in the time domain, and the required signal elements are also reduced. The analysis results show that when the L2,0 algorithm is used, it can achieve good DOA estimation performance even when the number of signals increases. In the actual environment simulation, compared with the classic MUSIC algorithm, the L2,0-DOA estimation algorithm is different The MSE results under noise basically tend to be consistent, indicating that the L2,0 estimation algorithm is insensitive to noise interference in the test environment and has high robustness.

Description of drawings

Figure 1 is a linear adaptive antenna array;

Figure 2 is a sparse DOA power spectrum diagram with 6 sources;

Fig. 3 is a broadband DOA estimated energy spectrum diagram under the horizontal viewing angle;

Figure 4 is the energy spectrum diagram of broadband DOA estimation under any observation angle in space;

Fig. 5 is the DOA estimation error analysis result when SNR=-10dB;

Fig. 6 is the DOA estimation error analysis result when SNR=-4dB.

detailed description

In order to make the object, technical solution and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described here are only used to explain the present invention, not to limit the present invention.

The present invention analyzes the linear antenna array shown in Figure 1, specifically comprising the following steps:

Step 1: Send the spatial signal s. The spatial signal itself has a sparse characteristic, and it is not necessary to be sparse.

Step 2: For the sent spatial signal s, the corresponding received signal y=As+n is obtained at the receiving end, the array flow pattern matrix A is equivalent to the measurement matrix Φ under compressed sensing (also can be considered as the perception matrix Θ), and Similar to the measurement matrix Φ, the array flow pattern matrix A also needs to meet certain conditions. n is additive white Gaussian noise that satisfies zero mean and variance σ ² , and the channel satisfies Gaussian distribution f _σ (h)=exp(-h ² / 2σ ² ).

Step 3: Perform Fourier transform on y=As+n to obtain its frequency domain representation, and in the frequency domain, detect, extract and recover the signal, and the process of recovering the signal is mainly through the L2,0 algorithm Achieved.

Step 4: Set up the bandpass filter bank H _w is a narrow-band filter with the analog frequency w as the digital center frequency, and usually takes b=0.99, which can ensure the stability of the system while narrowing the filter bandwidth. Then analyze DOA estimation under wideband.

Step 5: Set the SNR threshold and analyze the DOA estimated power spectral density under different SNR conditions.

In conjunction with the implementation mode in the above-mentioned steps, the effectiveness of the present invention is simulated and verified as follows:

The receiving antenna array is a uniform linear array, the number of array elements is 8, the spacing between array elements is half wavelength, the number of snapshots is 100, and the noise is additive white Gaussian noise. Figure 2 shows the sparse DOA estimation diagram with 6 sources. Using the L2,0-DOA estimation algorithm can accurately measure the peak position in the actual channel without causing other peak interference, which is very important for the receiver to obtain specific It is very important to sample, quantize, and encode the signal, which can effectively improve the ability of the entire system to process useful signals and save various costs. What Fig. 3 shows is the DOA estimation of horizontal viewing angle broadband after adding a band-pass filter. Signals at -10°, -30° and 30° can be clearly detected at the receiver, and no other signals are detected at other angle positions, that is, there is basically no other interference. Figure 4 shows that in the two-dimensional space map, in addition to accurately obtaining the position of the signal, you can also roughly see the approximate distribution of the signal at a certain angle, so that the wave-of-arrival signal can be better analyzed and discussed , which is very important in real-time DOA testing. Looking at Figure 5, when the signal-to-noise is -10dB, it can be found that the angle positioning detection of the signal is not very ideal, there are many interference signals and the error is large, but when the SNR is -4dB, it can accurately locate the position at 80 The signal at the azimuth angle of ° is the transmitted signal, which reduces the error of DOA estimation, as shown in Figure 6.

The above are preferred embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any transformation or substitution that is not thought of by any person skilled in the art within the technical scope disclosed in the present invention without creative work shall be covered by the protection scope of the present invention. Therefore, the protection scope of the present invention should be determined by the protection scope defined in the claims.

Claims (2)

1. The sparse DOA estimation method in the spatial Doppler domain, is characterized in that, comprises the following steps: Step 1, the sparse DOA estimation algorithm under the CS architecture, (1) There are L electromagnetic plane waves, Among them, l=1,...L, represents the number of unknown signal directions θ _l , Indicates the projection direction; (2) For the narrowband signal of the same frequency, the signal strength of the incoming wave signal after reaching the antenna array m is the number of antenna array elements, x _m is the position of the antenna array elements on the x-axis, f is the effective length of the antenna array elements, n _m is the additive Gaussian noise sample with a mean value of zero on the mth antenna; the above formula is variable is y=A(θ)s+n, where y=[y ₁ ,y ₂ ,...,y _M ] ^T ∈ C ^M×1 , θ=[θ ₁ ,θ ₂ ,...,θ _L ], A(θ)=[a(θ ₁ ),a(θ ₂ ),...,a(θ _L )] is an M×L-dimensional array flow pattern vector, s=[W ₁ ,W ₂ , ...,W _L ] ^T ∈C ^L×1 , n=[n ₁ ,n ₂ ,...,n _M ] ^T ∈C ^M×1 , the expansion can be expressed as Step 2, extending the signal strength y _m described in step 1 to the sparse angle domain and the sparse Doppler domain, (1) Perform Fourier transform on y=A(θ)s+n to obtain y _f =As _f +n _f , at this time s _f and y _f are sparse; (2) For K non-zero signals, use ζ to represent the deterministic power value or energy value corresponding to each row of unknown parameters in the signal s _f , and the DOA estimation process is as follows: a) let L=k=1; b) When ζ _n ≠ 0, and θ _L = θ _k , L = L + 1; c) if k < K, return to step b); otherwise, exit the calculation process of DOA; (3) Take the block signal of signal y _f , recover the required sparse signal from each row block, wherein the non-zero signal is the required DOA estimate; Step 3, sparse DOA estimation algorithm design, (1) For K narrowband signals from the far field, the signal at the receiver s=[W ₁ ,W ₂ ,...,W _L ] ^T is a sparse matrix, n=[n ₁ ,n ₂ ,.. .,n _M ] ^T is a noise matrix, since only K row elements in the signal s are non-zero, y=As+n=[y(t ₁ ),...,y(t _M )] is to search The joint sparseness of y to represent the MMV problem of signal s; (2) The objective function of the MMV problem is in When p=2, q=0, it can be written as (3) Definition Available: In noisy environments, When there is no noise, Available where the joint row sparse matrix is therefore is further transformed into 2. The sparse DOA estimation method in the spatial Doppler domain according to claim 1, characterized in that λ is 0.5 in the step three (3).