Optimal-Tuned Weighted LASSO for Massive MIMO Channel Estimation with Limited RF Chains

Channel estimation (CE) in massive MIMO system with limited RF chains is known to be a challenging problem. In many cases, base station (BS) can obtain certain channel support side information (CSSI), which can be exploited to enhance the CE performance and reduce the pilot overhead. Due to imperfectness of prior information, it's very important to utilize the CSSI in an optimal way to improve the CE performance. We propose an optimal-tuned weighted LASSO algorithm which can fully exploit the imperfect CSSI to optimize the CE performance in massive MIMO system with limited RF chains. In the proposed algorithm, the weighted l_{1} norm is used as the regularization function and the weights on the known support part (as indicated by the CSSI) and the rest are different. Based on the accuracy of CSSI, we obtain closed-form solution for the optimal LASSO weights which minimize the asymptotic normalized squared error (aNSE). Moreover, we derive closed-form expression of the minimum aNSE and characterize the minimum number of required pilots to achieve stable channel recovery. The theoretical analysis and simulation both show the performance advantages of our proposed solution over various baselines.