Sparse Array Beamforming Design for Wideband Signal Models

TL;DR

This paper introduces a novel sparse array beamforming design for wideband signals, optimizing MaxSINR performance by leveraging advanced optimization techniques and matrix completion methods to handle practical constraints.

Contribution

It formulates the sparse array design as a QCQP and solves it with SDR and SCA, incorporating matrix completion for real-world implementation.

Findings

Sparse array design improves array aperture utilization.

Proposed methods outperform suboptimal array configurations.

Matrix completion enables effective correlation estimation with missing data.

Abstract

We develop sparse array receive beamformer design methods achieving maximum signal-to-interference plus noise ratio (MaxSINR) for wideband sources and jammers. Both tapped delay line (TDL) filtering and the DFT realizations to wideband array processing are considered. The array sparsity stems from the limited number of available RF transmission chains that switch between the sensors, thereby configuring different arrays at different times. The sparse array configuration design problem is formulated as a quadratically constraint quadratic program (QCQP) and solved by using SDR (semidefinite relaxation). A computationally viable approach through SCA (successive convex relaxation) is also pursued. In order to realize an implementable design, in presence of missing autocorrelation lags, we propose parameter-free block Toeplitz matrix completion to estimate the received data correlation matrix across the entire array aperture. It is shown that the optimum wideband sparse array effectively utilizes the array aperture and provides considerable performance improvement over suboptimal array topologies.