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Direction Finding with Sparse Arrays Based on Variable Window Size Spatial Smoothing

Wesley S. Leite, Rodrigo C. de Lamare, Yuriy Zakharov, Wei Liu, Martin Haardt

TL;DR

This work tackles direction-of-arrival (DOA) estimation for sparse linear arrays using coarray-based processing and spatial smoothing. It introduces a variable-window size spatial smoothing (VWS) framework that shrinks the smoothing aperture by an integer parameter $a$ and replaces part of the perturbed outer products with an unperturbed low-rank term, preserving the signal-subspace span while boosting subspace separation. Two algorithms, VWS-CA-MUSIC and VWS-CA-rMUSIC, are developed, with complexity scaling as $\mathcal{O}((M-a)^3)$ due to the reduced aperture and identifiability bounds on $a$ (e.g., $a < \frac{\text{UDOF}+1-2D}{2}$) and a minimum rank condition $a \ge D$ for the additive term. Extensive simulations on sparse geometries (NAQ2, SNAQ2, MRA) demonstrate substantial RMSE improvements and reduced computational load compared with fixed-window CA-MUSIC, especially in data-limited scenarios.

Abstract

In this work, we introduce a variable window size (VWS) spatial smoothing framework that enhances coarray-based direction of arrival (DOA) estimation for sparse linear arrays. By compressing the smoothing aperture, the proposed VWS Coarray MUSIC (VWS-CA-MUSIC) and VWS Coarray root-MUSIC (VWS-CA-rMUSIC) algorithms replace part of the perturbed rank-one outer products in the smoothed coarray data with unperturbed low-rank additional terms, increasing the separation between signal and noise subspaces, while preserving the signal subspace span. We also derive the bounds that guarantees identifiability, by limiting the values that can be assumed by the compression parameter. Simulations with sparse geometries reveal significant performance improvements and complexity savings relative to the fixed-window coarray MUSIC method.

Direction Finding with Sparse Arrays Based on Variable Window Size Spatial Smoothing

TL;DR

This work tackles direction-of-arrival (DOA) estimation for sparse linear arrays using coarray-based processing and spatial smoothing. It introduces a variable-window size spatial smoothing (VWS) framework that shrinks the smoothing aperture by an integer parameter and replaces part of the perturbed outer products with an unperturbed low-rank term, preserving the signal-subspace span while boosting subspace separation. Two algorithms, VWS-CA-MUSIC and VWS-CA-rMUSIC, are developed, with complexity scaling as due to the reduced aperture and identifiability bounds on (e.g., ) and a minimum rank condition for the additive term. Extensive simulations on sparse geometries (NAQ2, SNAQ2, MRA) demonstrate substantial RMSE improvements and reduced computational load compared with fixed-window CA-MUSIC, especially in data-limited scenarios.

Abstract

In this work, we introduce a variable window size (VWS) spatial smoothing framework that enhances coarray-based direction of arrival (DOA) estimation for sparse linear arrays. By compressing the smoothing aperture, the proposed VWS Coarray MUSIC (VWS-CA-MUSIC) and VWS Coarray root-MUSIC (VWS-CA-rMUSIC) algorithms replace part of the perturbed rank-one outer products in the smoothed coarray data with unperturbed low-rank additional terms, increasing the separation between signal and noise subspaces, while preserving the signal subspace span. We also derive the bounds that guarantees identifiability, by limiting the values that can be assumed by the compression parameter. Simulations with sparse geometries reveal significant performance improvements and complexity savings relative to the fixed-window coarray MUSIC method.
Paper Structure (5 sections, 13 equations, 5 figures, 2 algorithms)

This paper contains 5 sections, 13 equations, 5 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Measurement Model and Problem Formulation
  3. Variable Window Size Spatial Smoothing for Coarray DOA estimation
  4. Simulation Results
  5. Conclusions

Figures (5)

  • Figure 1: VWS-CA-MUSIC: RMSE comparison for multiple values of $a$ against SNR. SNAQ2 geometry. $a=0$ corresponds to the CA-MUSIC (coarray MUSIC) algorithm with a fixed window size Pal2010-1.
  • Figure 2: VWS-CA-rMUSIC: RMSE comparison for multiple values of $a$ against SNR. NAQ2 geometry.
  • Figure 3: VWS-CA-MUSIC: RMSE against snapshots. SNAQ2 geometry.
  • Figure 4: VWS-CA-rMUSIC: RMSE against snapshots. NAQ2 geometry.
  • Figure 5: RMSE against SNR comparing multiple geometries: NAQ2, SNAQ2, and MRA using VWS-CA-MUSIC algorithm.