Fast communicationAdaptive beamforming based on covariance matrix reconstruction by exploiting interferences' cyclostationarity☆
Highlights
► The interference-plus-noise covariance matrix (INCM) is reconstructed for adaptive beamforming. ► The INCM is reconstructed by exploiting the cyclostationarity of interferences. ► The proposed method needs no information of the array structure. ► The proposed method can deal with unknown array perturbations.
Introduction
Adaptive beamforming has been used in many areas, such as radar, sonar, microphone array speech processing and wireless communications [1]. Beamformers are designed for desired signal enhancement and interference suppression. The well-known minimum variance distortionless response (MVDR) beamformer is obtained by preserving a unity gain for the desired signal while minimizing the power of interference and noise [1]. Theoretically, MVDR beamformer's weight is a function of the interference-plus-noise covariance matrix (INCM). In practice, the INCM is unavailable, it is then replaced by the sample covariance matrix [2]. However, since the desired signal component is usually included in the sample covariance matrix, the resultant beamformer is known to be sensitive even to a slight mismatch between the presumed system model and the actual one [2], [3]. Such model mismatch is common in practice due to direction of arrival (DoA) mismatch, imperfect array calibration, source spreading, etc. [3].
During the past decade, many approaches by exploiting the properties or prior information of the array have been proposed to improve the performance of adaptive beamforming [2], [3], [4], [5], [6], [7], [8], [9], [10]. For example, the reduced-rank technique is used in [4] to achieve a fast convergence rate. However, the system mismatch issue is not considered in [4]. Thus, a blind and robust interference suppression algorithm is proposed in [5] which relies on the constant modulus property. In [6], [7], [8], several robust approaches against model mismatch are proposed by processing the steering vector of the desired signal. Nevertheless, the problem in the covariance matrix is not well addressed.
Besides the steering vector processing based approaches, an alternative robust beamforming design is based on the processing of the sample covariance matrix. One popular technique is the diagonal loading [2], where a scaled identity matrix is added to the sample covariance matrix. However, the desired signal is still not removed from the sample covariance matrix. Most recently, Mallipeddi et al. [9] and Gu and Leshem [10] addressed this problem by reconstructing the INCM rather than finding a diagonal level for the sample covariance matrix. Since the desired signal is removed from the reconstructed INCM, the resultant beamformers are shown to have a near optimal performance in case of steering vector mismatch of the desired signal. However, these methods need to know the array structure. When the array has unknown gain and phase errors, the interferences will be less suppressed by the beamformer, which lead to a performance penalty, especially in the case of strong interferences.
In this paper, we consider the INCM reconstruction for adaptive beamforming by exploiting the cyclostationarity of interference signals. Different from the constrained cyclic adaptive beamforming (CCAB) [12] which exploits the cyclostationarity of the desired signal, we take into account the cyclostationarity of the interferences, and use this property to estimate the steering vectors of the interferences. By further estimating the power of the interferences and noise, the INCM can be reconstructed. In contrast to the previous INCM reconstruction methods, no knowledge of array structure is needed for the proposed technique, thus, it can deal with the unknown perturbations in the array. The effectiveness of the proposed method is demonstrated by numerical simulations.
Notation: Boldfaced capital and lowercase letters denote matrices and the column vectors, respectively. is the Hermitian transpose, is the transpose, is the complex conjugate. represents the Frobenius norm.
Section snippets
Problem formulation
Consider an array of N elements. Suppose P+1 () far-field signals impinging on the array, the received signal at time k is given aswhere is the steering vector of the pth source signal sp(k), n(k) is the noise. Here, is considered as the desired signal while are interferences. The output signal-to-interference-plus-noise ratio (SINR) of the beamformer is given aswhere w is the beamformer weight, is the INCM, is the
Cyclostationarity and CCAB
A signal s(k) is said to be cyclostationary if its cyclic conjugate or cyclic correlation function is defined respectively asis nonzero at cycle frequency for some time shift [12], [11], where . Most man-made signals exhibit cyclostationarity with cycle frequency equal to the twice of the carrier frequency, multiples of the baud rate, or combinations of these [12].
For the array signal model (1), the cyclic
Simulations
To examine the performance of the proposed algorithm, simulations have been done based on a uniform linear array with N=10 sensors and inter-element spacing is half the wavelength of the desired signal. We consider one desired signal, two interferences which are all binary phase-shift keying (BPSK) signals with rectangular pulse. The baud rates for the desired signal and the interferences are respectively 1/10, 1/30 and 1/10 with respect to the 30 MHz sampling frequency. The carrier frequencies
Conclusion
An adaptive beamforming algorithm based on INCM reconstruction is proposed by exploiting the cyclostationarity of interferences. With the reconstructed INCM, the robustness of adaptive beamformer can be improved since the desired signal is removed. The proposed reconstruction method needs no information of array structure and can deal with the unknown perturbations in the array. The proposed method is shown to have a superior performance to the existing INCM reconstruction based beamformers in
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2019, AEU - International Journal of Electronics and CommunicationsPerformance of the SMI beamformer with signal steering vector errors in heterogeneous environments
2016, Signal ProcessingCitation Excerpt :Researchers have given adaptive beamforming considerable attention in the past several years [1–9].
Cyclostationarity: New trends and applications
2016, Signal ProcessingCitation Excerpt :Joint TDOA and frequency-shift estimation are made in [152–154,225,332]. Beamforming techniques are addressed in [126,148,150,211,346]. The presence of cycle frequency error is treated in [200,201].
Adaptive cyclostationary array beamforming with robust capabilities
2015, Journal of the Franklin InstituteCitation Excerpt :Adaptive beamforming utilizing signal cyclostationarity known as cyclic adaptive beamforming has been widely considered [7,10,11]. Recently, several cyclic-related techniques have been developed to deal with different realistic scenarios and applications [12–18]. The advantage of the above techniques is that they work without requiring the direction vector or the waveform of the signal considered.
Robust widely linear beamforming based on spatial spectrum of noncircularity coefficient
2014, Signal ProcessingCitation Excerpt :This robust beamforming algorithm attains a better performance over a wide range of signal-to-interference-plus-noise ratios (SINRs). Sequentially, Li et al. exploited the cyclostationarity of interferences to reconstructed INCM, which needs no information of the array structure [10]. In this communication, we develop this covariance matrix reconstruction technique in area of the WL beamformer.
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This work was supported by the National Natural Science Foundation of China (61201349, U1035003), Natural Science Foundation of Guangdong Province (s2011040001426) and Science and Technology Project of Guangzhou (2012J2200005).