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Abstract
Blind beamforming for extracting noncircular signals without a prior knowledge on the desired steering vector is
considered in this paper. Three second-order statistic based blind schemes, termed as subspace decomposition,
self-reference, and extraction power maximization methods, respectively, are proposed to extract one desired non-
circular signal from a number of statistically independent circular interferences in the presence of circular Gaus-
sian noise with arbitrary and unknown correlation structure. Two joint second- and fourth-order cumulant based
methods are also developed for the case of multiple noncircular interferences. One is ESPRIT (estimation of signal
parameters via rotational invariance techniques) type method. The other represents a real-valued extension of the
WL-MVDR (widely linear minimum variance distortionless response). Numerical examples are shown to illustrate
the performance of the proposed methods. The latest version of this online-only showing has also been submitted
to IET Signal Processing.
Keywords: Array signal processing, adaptive arrays, noncircular signals, blind beamforming
1. Introduction
Blind beamforming has found numerous important applications in radar, sonar, wireless communi-
cations, and biomedical imaging, mainly because it can restore one or more desired signals from multi-
ple cochannel interfering signals and noise without a prior knowledge of the array manifold and the
need for training signal [1-2]. In contrast, the non-blind beamforming techniques, such as MVDR
(minimum variance distortionless response [3]) and LCMV (linear constrained minimum variance [3]),
require the information about the steering vector of the signal-of-interest (SOI), thereby necessitating
an array calibration procedure. However, the advance calibration of the array characteristics is usually
expensive and may become uncertain especially in the presence of multipath propagation and environ-
mental changes.
The very earlier attempt for blind beamforming seems to be achieved by assuming structural proper-
ties of the array manifold. In such methods, the direction-of-arrival (DOA) of the desired signal is first
estimated by using direction finding techniques such as MUSIC (multiple signal classification [4]) and
ESPRIT (estimation of signal parameters via rotational invariance techniques [5]). The DOA estimate
then can be used to construct the desired steering vector, after which a certain beamformer can be de-
signed to extract the signal from that direction. Strictly speaking, this two-step method is not a truly
“blind” method since it requires also array calibration. More importantly, DOA estimation may be
complex and inadequate when the array is sensitive to both DOA and signal polarization, or, very fre-
quently, suffers from severe element mutual coupling. Later, new types of blind beamformers were
proposed that are not based on the receiving channel structure, but instead exploit the structural char-
acters of the signal waveform. A promising example is the constant modulus algorithm (CMA) that can
extract signals with constant amplitude (such as phase modulated signals) [6-7]. However, CMA is
very sensitive to the initialization condition, and generally poorly convergent. An analytical CMA
variant provided later in [8] was observed to be able to avoid such convergence problems.
The cyclostationarity property of many man-made communication signals can also be exploited for
blind beamforming by processing the incoming signals at the carrier frequency (i.e., without demodula-
tion). A popular cyclostationarity-exploiting blind method labeled as SCORE (spectral self-coherence
restoral [9]) can extract the signal at a known (or can be estimated to alleviate the effect of cycle fre-
quency perturbation caused by channel uncertainty such as Doppler shift [10]) cycle frequency auto-
matically. Some other interesting cyclostationarity resorted blind beamformers can be found in [11-13]
(and references therein). In the literature, there are still some efforts made on the exploitation of the
temporal correlation structure of the colored or nonstationary signals, see, for example, [14-15] and
references therein. A fundamental and necessary requirement of the algorithms there is that the incom-
This work was supported by the National Natural Science Foundation of China under Grant 60602037.
Blind Beamforming for Noncircular Signals
Yougen Xu, and Zhiwen Liu
Department of Electronic Engineering, Beijing Institute of Technology, Beijing 100081, China
E-mail: yougenxu@bit.edu.cn
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