Compressive beamforming

Abstract

Sound source localization with sensor arrays involves the estimation of the direction-of-arrival (DOA) from a limited number of observations. Compressive sensing (CS) solves such underdetermined problems achieving sparsity, thus improved resolution, and can be solved efficiently with convex optimization. The DOA estimation problem is formulated in the CS framework and it is shown that CS has superior performance compared to traditional DOA estimation methods especially under challenging scenarios such as coherent arrivals and single-snapshot data. An offset and resolution analysis is performed to indicate the limitations of CS. It is shown that the limitations are related to the beampattern, thus can be predicted. The high-resolution capabilities and the robustness of CS are demonstrated on experimental array data from ocean acoustic measurements for source tracking with single-snapshot data.

Snapshot Deficit Beamforming for Direction of Arrival Estimation by Compressive Sensing

“…Let 's' be the transmitted signal such that s ϵ c N . The array steering vector at each of the sensor array due to the source i can be written as in [9]: …”

“…The key idea of compressed sensing is to recover a sparse signal from very few non-adaptive, linear measurements by convex optimization. Performance of CS technique in DOA estimation under number of sources and noise conditions is presented by Malioutov et al [8] Robustness of CS in sound source localization using sensor arrays has been demonstrated in [9] with coherent arrivals and snapshot deficient case.…”

Sub-antenna sparse processing for coherence loss in underwater source localization

“…In underwater acoustics, we can also mention the use of convex-relaxation based algorithms, such as the Least Absolute Shrinkage and Selection Operator (LASSO) [4] or the Simultaneous LASSO (SLASSO) when considering multiple measurements (snapshots) [7]. All these latter techniques offer a high resolution, but are intrinsically not designed to be robust to random environmental fluctuations such as internal waves or sound speed spatiotemporal dynamics.…”

“…In order to improve its power resolution, so-called "high-resolution" techniques have then been proposed, distinguishing by the a priori information they consider on the nature and/or the number of sources. Among them, we can mention the well-known Minimum Variance Distortionless Response (MVDR) beamformer [2], the MUltiple SIgnal Classification (MUSIC) beamformer [3] and, more recently, sparse techniques [4].…”

Sparse Signal Reconstruction using Weight Point Algorithm

“…Since sparse or compressible signals have a wide range of applications, CS has been applied in many fields, such as radar and sonar [8][9][10], antenna beam forming [11,12], imaging [13,14], and video [15], to name a few. Nevertheless, there are still challenges, because CS reconstruction generally involves a heavy computational load and is time-consuming.…”