Theoretical Validation of the Latent Optimally Partitioned-ℓ2/ℓ1 Penalty with Application to Angular Power Spectrum Estimation

This paper demonstrates that, in both theory and practice, the latent optimally partitioned (LOP)-ℓ2/ℓ1 penalty is effective for exploiting block-sparsity without knowledge of the concrete block structure. More precisely, we first present a novel theoretical result showing that the optimized block partition in the LOP-ℓ2/ℓ1 penalty satisfies a condition required for accurate recovery of block-sparse signals. Motivated by this result, we present a new application of the LOP-ℓ2/ℓ1 penalty to estimation of angular power spectrum, which is block-sparse with unknown block partition, in MIMO communication systems. Numerical simulations show that the proposed use of block-sparsity with the LOP-ℓ2/ℓ1 penalty significantly improves the estimation accuracy of the angular power spectrum.