An Improved Approach to Robust Capon
Beamforming with Enhanced Performance
Huiping Huang, Bin Liao, Chongtao Guo, Lei Huang
College of Information Engineering, Shenzhen University, Shenzhen, China
hhp994800082@outlook.com,{binliao, ctguo, lhuang}@szu.edu.cn
Abstract—In this paper, the approach of robust Capon beam-
forming (RCB) in the presence of steering vector mismatch is
studied. A new method to enhance the robustness is presented.
More specifically, it is proposed herein to remove the component
of the desired signal from the array covariance matrix by esti-
mating the corresponding steering vector and signal power, such
that the influence caused by the presence of desired signal in the
training data can be reduced, especially in the case of high signal-
to-noise ratio (SNR). Furthermore, the uncertainties involved in
the resulting interference-plus-noise covariance matrix estimate
is taken into account by formulating a min-max optimization
problem. Simulation results demonstrate that the performance of
the RCB algorithm can be improved by the proposed approach.
Index Terms—Robust Capon beamformer, covariance matrix
reconstruction, steering vector mismatch
I. INTRODUCTION
Adaptive beamforming with sensor array has been success-
fully applied to many fields such as radar, sonar, navigation,
medical imaging, and wireless communications during the past
several decades [1], [2]. Typically, there are some critical prob-
lems which may occur in adaptive beamforming including the
mismatch between the presumed and actual steering vectors,
the uncertainties of the array covariance matrix estimate, and
the presence of the desired signal in the training snapshot-
s. In traditional adaptive beamformers, such as the Capon
beamformer, the array covariance matrix is replaced by the
sample covariance matrix. Thus, the gap between the actual
and estimated covariance matrices, especially when the sample
size is small [3], results in performance loss. Moreover, this
beamformer may fail to work properly in the presence of the
steering vector mismatch.
According to the uncertainty set of the steering vector, a
large number of robust beamformers have been proposed. For
instance, using the worst-case performance optimization, an
novel method based on the second-order cone programming
(SOCP) was proposed in [4]. On the other hand, the worst-
case performance optimization-based method presented in [2]
is developed for the general case of an arbitrary dimension of
the desired signal subspace. The solution to this problem is
an eigendecomposition problem that can be efficiently solved
without optimization software such as CVX [5] which can be
adopted for solving the SOCP problems in [4]. In [6] and
[7], a robust Capon beamforming (RCB) algorithm has been
introduced. The key concept of this approach is to estimate the
desired steering vector in an uncertainty set by maximizing the
array output power. In the presence of large direction-of-arrival
(DOA) mismatch, the RCB approach requires a large size of
uncertainty set to achieve sufficient robustness. Therefore, it is
proposed in [8] to design the robust beamformer by imposing
constraints on the array magnitude response with flexibly
controllable beamwidth and response ripple. In order to deal
with the performance degradation caused by the presence of
desired signal in the training data, many efforts have been
made to reconstruct the interference-plus-noise covariance
matrix (INCM), for example, by 1) utilizing the Capon spatial
spectrum [3], [9], [10], and 2) taking into account of the
special structures of the covariance matrices, such as low-rank
structure [11], Toeplitz structure [12], [13], eigen-structure
[14], [15] and circulant structure [16].
In this paper, an improved robust Capon beamforming
algorithm to deal with the array imperfections is introduced.
This method determines the steering vector and power of
the desired signal by using the RCB algorithm. Thus, the
component of the desired signal can be removed from the
array covariance matrix to achieve a reliable estimate of the
INCM. Furthermore, the uncertainty of the INCM estimate
is taken into account to improve the robustness. Simulation
results demonstrate the improvement of the robustness over
the traditional algorithms.
II. PROBLEM FORMULATION
Consider a uniform linear array with M sensors receiving
signals from multiple narrow-band sources. The array obser-
vation vector x(k) at time k can be modeled as
x(k) = s(k) + i(k) + n(k) (1)
where s(k), i(k) and n(k) are assumed to be statistically
independent, and stand for the desired signal, interference and
noise, respectively. In the case of a single point signal source,
the desired signal can be rewritten as s(k) = as(k), where
a ∈ C
M
denotes the steering vector associated with the DOA
of the desired signal and s(k) is the signal waveform. The
array covariance matrix R can be expressed as
R = E{x(k)x(k)
H
} = R
s
+ R
i+n
(2)
where E{·} represents the statistical expectation operator, (·)
H
represents the Hermitian transpose, R
s
= E{s(k)s(k)
H
} =
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