Multiobjective Bilevel Evolutionary Approach for Off-Grid Direction-of-Arrival Estimation

TL;DR

This paper introduces a multiobjective bilevel evolutionary method for off-grid DOA estimation that simultaneously identifies the number of sources and estimates their directions, improving accuracy especially in challenging noise conditions.

Contribution

It proposes a novel multiobjective off-grid DOA model with direct source number identification using the $l_0$ norm, solved by a bilevel evolutionary algorithm with a non-approximate grid refinement strategy.

Findings

Outperforms existing methods in source number accuracy

Achieves lower root mean square error in DOA estimation

Effective in impulsive noise environments

Abstract

The source number identification is an essential step in direction-of-arrival (DOA) estimation. Existing methods may provide a wrong source number due to inferior statistical properties (in low SNR or limited snapshots) or modeling errors (caused by relaxing sparse penalties), especially in impulsive noise. To address this issue, we propose a novel idea of simultaneous source number identification and DOA estimation. We formulate a multiobjective off-grid DOA estimation model to realize this idea, by which the source number can be automatically identified together with DOA estimation. In particular, the source number is properly exploited by the $l_0$ norm of impinging signals without relaxations, guaranteeing accuracy. Furthermore, we design a multiobjective bilevel evolutionary algorithm to solve the proposed model. The source number identification and sparse recovery are simultaneously optimized at the on-grid (lower) level. A forward search strategy is developed to further refine the grid at the off-grid (upper) level. This strategy does not need linear approximations and can eliminate the off-grid gap with low computational complexity. Simulation results demonstrate the outperformance of our method in terms of source number and root mean square error.