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The performance of multi-channel Compressive Sensing (CS)-based Direction-of-Arrival (DOA) estimation algorithm degrades when the gains between Radio Frequency (RF) channels are inconsistent, and when target angle information mismatches with system sensing model. To solve these problems, a novel single-channel CS-based DOA estimation algorithm via sensing model optimization is proposed. Firstly, a DOA sparse sensing model using single-channel array considering the sensing model mismatch is established. Secondly, a new single-channel CS-based DOA estimation algorithm is presented. The basic idea behind the proposed algorithm is to iteratively solve two CS optimizations with respect to target angle information vector and sensing model quantization error vector, respectively. In addition, it avoids the loss of DOA estimation performance caused by the inconsistent gain between RF channels. Finally, simulation results are presented to verify the efficacy of the proposed algorithm.

Compressive Sensing (CS) theory, deduced from signal processing and information theories [

The strong scatter centers of target in interested area only occupy finite angle resolution cells and the target is sparse in space-domain, so that CS theory has been widely applied in Direction-of-Arrival (DOA) estimation [

In addition, all the aforementioned algorithms utilize multi-channel data so that the estimation performance degrades seriously in the presence of inconsistent gain between RF channels of the array.

In this paper, we derive a single-channel CS-based DOA estimation algorithm via sensing mode optimization to solve the above mentioned problems. Firstly, a DOA estimation model is set up considering mismatch error between system sensing model and target angle information. Secondly, a single-channel array system, which can avoid gain inconsistency between RF channels, is introduced. Meanwhile, it can be proved that the sensing matrix of the single-channel array system meets the RIP condition. Finally, on the basis of Robust Smooth L_{0} (RSL0) algorithm [

The paper is organized as follows. Section II formulates the problem of interest. Section III develops the proposed algorithm. Section IV provides the simulation results that demonstrate the efficacy of the proposed algorithm. Section V concludes the paper.

Consider K far-field narrow-band signals impinging upon a uniform linear array (ULA) of L elements. The receive signal can be represented as

where

For CS processing, the angle field-of-view of the interested area is sampled uniformly at

where

Obviously, since N is finite, the target angle

Let

where

where

is denoted as angular quantization error.

Considering the quantization error, Equation (2) can be modified as

The introduced RF single-channel array is shown in

Unlike previously developed multi-channel CS-based algorithms, this paper will, for the first time, derive a single-channel CS based algorithm for DOA estimation. First, a

where

As the target is sparse in space, we assume that the target does not cross angle resolution cells within M snapshots. Then, the M snapshots measured value of the target can be denoted as

where

By observing (8), we can conclude that sampling of space-domain signals through single channel array can be regarded as performing random projection of measurement matrix

It is found from (8) that the influences of measurement noise and sensing model mismatching error on DOA estimation can be summed up to two parts: “additive” disturbance and “productive” disturbance. Conventional CS-based algorithms only have constraint on “additive” disturbance, but do not consider the influence of “productive” disturbance on the accuracy of target angle information reconstruction. Therefore, these algorithms are not robust in the presence of sensing model mismatching since they cannot effectively reduce the effect of quantization errors.

To overcome these problems, we present a novel CS-based DOA estimation algorithm using single-channel array. The insight of the proposed algorithm is to combine RSL0 algorithm and LASSO algorithm to achieve valid DOA estimates by performing alternative iterative optimization separately on target angle information vector and sensing model quantization error. The basic step of the proposed algorithm can be summarized as follows. The parameters to be optimized are separated into two sets: target angle information set and quantization error set. Each time, a CS cost function that depends only on one set is minimized. With the solution of this CS problem, the subsequent stages of the proposed algorithm consist of applying the same principle on another set of parameter. The algorithm iterates, changing from one set to the next, until the variation of the cost function or of the parameters is less than a predefined convergence criterion.

To initiate the algorithm, we set the sensing model quantization error

where constant

Insert the estimate

where

where

From (5), we know that the sensing model quantization error vector

which can be perfectly solved by LASSO algorithm.

Finally, inserting the estimate

where

Assuming that the number of signals is known or correctly estimated, the proposed algorithm can be summarized as follows.

1) Initialize with

2) Solve (9) to get the estimate

3) Solve (13) to get the estimate

4) Stop the iteration if expression (14) is satisfied. Otherwise go back to step 2).

Performance of the proposed algorithm is evaluated by comparing to the CS-based algorithm in [

where

In the first simulation, we study the performance of the proposed algorithm in the presence of sensing model mismatching.

Next, we consider the presence of gain inconsistency between RF channels. The gains of RF channels are assumed to be of Gaussian distribution with mean value

Then, we study the performance on randomly generated DOAs. Suppose that the directions of the input three signals are uniformly generated within the intervals

In the last simulation, we consider the ability of the proposed method to represent the true signals with different angle resolution cells. The angle resolution cells are set as

We have proposed a novel CS-based DOA estimation algorithm via sensing model optimization using single-channel array to solve the problems of sensing model mismatching and channel gain inconsistency, from which most conventional multi-channel CS-based algorithms would suffer. The key idea of the proposed algorithm is to iteratively solve two CS optimizations with respect to target angle information vector and sensing model quantization error vector, respectively. Simulation results have also been presented to verify the efficacy of the proposed algorithm.

This work was supported by the National Natural Science Foundation of China (Grant no. 61401204), Postdoctoral Science Foundation of Jiangsu Province (Grant no. 1501104C), Technology Research and Development Program of Jiangsu Province (Grant no. BY2015004-03), and the Fundamental Research Funds for the Central Universities (Grant no. 30916011319).

Li, H.T. and Yuan, Z.S. (2017) Single-Channel Compressive Sensing for DOA Estimation via Sensing Model Optimization. Int. J. Communications, Network and System Sciences, 10, 191-201. https://doi.org/10.4236/ijcns.2017.105B019