Joint Multi-Band DOA Estimation Using Low-Rank Matrix Recovery

To address wideband direction of arrival (DOA) estimation problems, this paper proposes a gridless and covariance-free joint multi-band (JMB) DOA estimation method using low-rank matrix recovery. In contrast with subspace methods and sparse array-based methods, a unified frequency grid is established based on the concept of the greatest common divisor (GCD) to solve the nonlinearity of steering matrices from multiple frequencies. With the unified frequency grid, a low-rank master matrix is formed as a combination of the truncated Hankel matrices from different subbands and snapshots. Unlike convex relaxations, a nonconvex optimization problem of low-rank matrix recovery with unknown waveforms is presented with an indicator function of the rank constraint and is solved using proximal gradient descent. Numerical results demonstrate the effectiveness and efficiency of the proposed method to estimate more sources than sensors in a uniform linear array with only a few snapshots, which outperforms conventional subspace methods averaging the estimates per subband and the state-of-the-art methods using convex relaxations such as nuclear norm minimization.