Structured sparse approximation via generalized regularizers: With application to V2V channel estimation

In this paper, we consider the estimation of a signal that has both group- and element-wise sparsity (joint sparsity); motivated by channel estimation in vehicle-to-vehicle channels. A general approach for the design of separable regularizing functions is proposed to adaptively induce sparsity in the estimation. A joint sparse signal estimation problem is formulated via these regularizers and its optimal solution is computed based on proximity operations. Our optimization results are quite general and they can be applied in the context of hierarchical sparsity models as well. The proposed recovery algorithm is a nested iterative method based on the alternating direction method of multipliers (ADMM). Due to regularizer separability, key operations can be performed in parallel. V2V channels are estimated by exploiting the joint sparsity (group/element-wise) exhibited in the delay-Doppler domain. Simulation results reveal that the proposed method can achieve as much as a 10 dB gain over previously examined methods.