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Existing robust Capon beamformers achieve robustness against steering vector errors at a high cost in terms of computational complexity. Computationally efficient robust Capon beamforming approach based on the reduced-rank technique is proposed in this paper. The proposed method projects the received data snapshots onto a lower dimensional subspace consisting of the matched filters of the multistage Wiener filter (MSWF). The subsequent adaptive beamforming will then be performed within this subspace. The combination of the benefit of the robust adaptive beamforming and the reduced-rank technique improves the performance on combating steering vector errors and lowering the computational complexity.

The Capon beamformer chooses the weight vector by minimizing the array output power subject to a look direction constraint [

Based on the uncertainty set of the steering vector, some robust beamformers were recently proposed [

In this paper, we devise a computationally efficient implementation of the RCB approach using the reduced-rank technique. A framework has been proposed for combining reduced-dimension and RCB methods, producing rapidly converging, low complexity reduced-dimension RCBs [

This paper is organized as follows. In Section

Consider an

Assume that all impinging signals and noise are uncorrelated with each other. Then the covariance matrix can be expressed as

Without loss of generality, we assume that the first signal is the SOI. Then the Capon beamformer is obtained by solving the following optimization problem:

The solution to (

Based on the uncertainty set of the steering vector, the RCB approach can be formulated as follows [

The problem (

In this section, we first calculate the projection matrix using the matched filters of the MSWF, and then the adaptive reduced-rank beamforming is performed.

Let us define the reference signal and the observation data of the MSWF as

For

Decrement

We now form a matrix

Using (

Following the classic RCB approach, the proposed reduced-rank RCB approach can be expressed as

In this section, the selection of

To estimate the sample covariance matrix, a computational complexity of

In this section, simulations are carried out to investigate the performance of the proposed method compared with the SCB and the RCB. Since the signal subspace based methods will not work if the signal-plus-interference subspace is underestimated, that is,

In the first example, we consider the effect of the number of snapshots on the output SINR of the beamformers. The input signal-to-noise ratio (SNR) of the SOI is set to 5 dB and the DOA mismatch is

Output SINR versus the number of snapshots.

In the second example, we investigate the effect of the input SNR on the performance of the beamformers. The number of snapshots is fixed at

Output SINR of the beamformers versus input SNR.

In the third example, the DOA mismatch is uniformly distributed on

Output SINR of the beamformers versus DOA mismatch.

A low complexity RCB approach based on reduced-rank technique has been proposed for improving the robustness of the SCB against steering vector errors. Unlike the traditional full-rank RCB approach, the proposed method performs the adaptive beamforming within a lower dimensional subspace that consists of the matched filters of the MSWF, thereby reducing its computational complexity and the finite-sample effect. Simulation results have been presented to demonstrate the effectiveness of the proposed method.

The authors declare that there is no conflict of interests regarding the publication of this paper.

The authors are grateful to the two anonymous reviewers for their very useful suggestions and comments. This study was supported by the National Nature Science Foundation of China (nos. 61274026, 61376076, and 61377024), supported by the Science and Technology Plan Foundation of Hunan Province (nos. 2013FJ2011, 2014FJ2017) and supported by the Scientific Research Fund of Hunan Provincial Education Department (nos. 14A084, 14B060).