鲁棒自适应波束形成：基于转向矢量估计与协方差矩阵重建

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本文是一篇研究论文，针对鲁棒自适应波束成形(Robust Adaptive Beamforming, RAB)领域提出了创新的方法。传统的波束形成技术在存在较大指向向量(阵列指向矢量, Array Steering Vector, ASV)误差和协方差矩阵不确定性的情况下可能会受到影响。作者针对这一问题，设计了一种新型的鲁棒自适应算法。首先，该方法的核心是ASV估计技术。不同于常规处理，作者将ASV视为处于两个子空间交集中的一个向量，并采用一种封闭形式的公式进行精确估计。这种估计策略巧妙地考虑了实际ASV可能偏离理想值的情况，提高了算法的鲁棒性。其次，重构协方差矩阵是另一个关键步骤。在估计过程中，通过替换期望信号(Desired Signal, DS)的特征值为噪声特征值的平均值，有效地减小了DS对整体计算的影响。这种方法降低了对DS强度的依赖，使算法能够更好地抵抗噪声干扰。论文强调，实施该方法所需的先验信息仅限于天线阵列的几何结构以及实际ASV所在的角区间。这简化了系统设计的要求，使得它在实际应用中具有较高的可操作性。在实验结果部分，通过模拟仿真，作者证明了新提出的RAB技术在输出信号与干扰加噪声比(Signal-to-Interference-and-Noise-Ratio, SINR)方面表现出色。只要输入信号噪声比保持在可接受范围内，即使在存在显著的ASV误差和协方差矩阵不确定性时，该方法也能提供良好的性能。这篇论文为鲁棒自适应波束成形提供了一个有效的解决方案，它不仅提升了系统的稳定性和抗干扰能力，还降低了对系统参数精确度的依赖，对于无线通信系统，特别是在多径环境下的信号处理有着重要的实际价值。

1636 IEEE COMMUNICATIONS LETTERS, VOL. 19, NO. 9, SEPTEMBER 2015

Robust Adaptive Beamforming Based on Steering Vector Estimation

and Covariance Matrix Reconstruction

Feng Shen, Fengfeng Chen, and Jinyang Song

Abstract—In this letter, a novel robust adaptive beamforming

(RAB) technique is proposed. It offers robust performance even

with large look direction error in the array steering vector (ASV)

and an uncertainty in the covariance matrix. In essence, the

proposed ASV estimation technique treats the ASV as a vector

lying within the intersection of two subspaces, and then estimates

it using a closed-form formula. In this technique, the covariance

matrix is reconstructed after the desired signal (DS) eigenvalue

is replaced by the average value of the noise eigenvalues, thus

eliminating a large portion of the DS. Furthermore, the only prior

information necessary is knowledge of the antenna array geometry

and angular sector in which the actual ASV lies. Simulation results

indicate that the proposed method achieves good performance

in terms of output signal-to-interference-plus-noise ratio (SINR),

as long as the input signal-to-noise ratio (SNR) is not close to

the interference-to-noise ratio (INR) and the DS and interference

signals are well separated.

Index Terms—Robust adaptive beamforming (RAB), array

steering vector (ASV) estimation, closed-form formula, covariance

matrix reconstruction, large look direction error.

I. INTRODUCTION

DAPTIVE arrays are widely used in radar, sonar, wireless

communication and medical imaging. They have high

performance in interference cancellation and noise reduction,

provided that array steering vector (ASV) uncertainty of the

desired signal (DS) is accounted for and provided that an

accurate array covariance matrix estimate is available. Adaptive

arrays are very sensitive to the ASV mismatches, which will

result in serious DS cancellation problem. The presence of the

DS component in the training snapshots is also a major cause

of performance degradation in adaptive beamforming.

Many approaches such as the robust Capon beamformer

(RCB) [1], the eigenspace-based beamformer (ESB) [2], and

beamformers based on ASV estimation [3]–[6] have been

proposed to enhance robustness against ASV errors. In ad-

dition, the beamforming methods in [3]–[6] have high com-

plexity owing to the use of speciﬁc optimization software.

The interference-plus-noise (IPN) covariance matrix can be

obtained in [7], but it will be ineffective in presence of ASV

errors especially at the high input signal-to-noise ratio (SNR).

The beamformer of [6] achieves good performance in the

case of DS error due to the required IPN covariance ma-

trix reconstruction process and the optimization software. Re-

Manuscript received January 22, 2015; revised June 3, 2015; accepted

July 4, 2015. Date of publication July 13, 2015; date of current version

September 4, 2015. This work was supported by National Natural Science

Foundation of China (Grants 61102107 and 61374208) and by the Fundamental

Research Funds for the Central Universities (HEUCFX41310). The associate

editor coordinating the review of this paper and approving it for publication

was A. Ikhlef.

The authors are with College of Automation, Harbin Engineering Uni-

versity, Harbin 150001, China (e-mail: sf407@126.com; cyf1935@163.com;

cyf1935@126.com).

Digital Object Identiﬁer 10.1109/LCOMM.2015.2455503

cently, a low-complexity robust adaptive beamforming (RAB)

technique which estimates the ASV using a Low-Complexity

Shrinkage-Based Mismatch Estimation (LOSCME) algorithm

was presented in [8]. This beamforming method offers excellent

performance when the interfering sources are weak.

In this letter, a novel RAB technique is proposed. This

method is an improved version of the beamformer presented in

[7], while also being robust against large look direction error.

Firstly, two subspaces are formed where the ASV is assumed

to be a vector lying in the intersection of these subspaces and

the ASV can be easily estimated using a closed-form formula.

Then, the covariance matrix is reconstructed after the DS eigen-

value is replaced by the average value of the noise eigenvalues,

thereby eliminating a noticeable portion of the DS. Importantly,

the only prior information required is the knowledge of the

antenna array geometry and the angular sector in which the

actual ASV lies. Furthermore, the proposed technique does

not require any optimization programs which is beneﬁt by the

ASV estimation can be in a closed-form formula. Crucially, the

technique can offer good performance provided that the SNR

is not close to the interference-to-noise ratio (INR) and the DS

and interference signals can be well separated.

II. S

YSTEM MODEL

Let us consider a uniform linear array (ULA) with N sensors

impinged by M + 1 narrowband uncorrelated signals (one DS

and M interferences). The signal received at the time instant k

can be written as

x(k) = s(k) + i(k) + n(k) (1)

where s(k), i(k),andn(k) denotes the N ×1 vectors of the DS,

interference, and noise, respectively. The adaptive beamformer

output is given by y(k) = w

x(k),wherew =[ω

,...,ω

]

is the complex weighting vector, and (·)

and (·)

denote the

Hermitian transpose and transpose, respectively. The Capon

beamformer can be written as

min

w subject to w

a(θ

) = 1(2)

where R

= E{(i(k) + n(k))(i(k) + n(k))

} is the IPN covari-

ance matrix, a(θ

) ∈ C

N×1

is the presumed ASV of the DS,

where θ

is the presumed direction-of-arrival (DOA), and E{·}

is the expectation. The solution is the Capon beamformer,

w =

−1

a(θ

)

a(θ

)

−1

a(θ

)

(3)

which is a function of two factors R

and a(θ

The SINR is given by SINR = (σ

a(θ

)/(w

−1

w),

where σ

is the power of the DS. However, the IPN covariance

matrix R

is usually unavailable in practical applications and

See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

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