Sparse Channel Estimation Based on ADMM and $l_{q}$ Regularization

For the FDD downlink MIMO-OFDM system, a channel estimation algorithm based on the alternating direction method of multipliers (ADMM) and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$l_{q}, (0 &lt; q\leq 1)$</tex> regularization is proposed. The sparse channel estimation problem can be formulated as an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$l_{q},(0 &lt; q\leq 1)$</tex> norm minimization problem. Utilizing the ADMM algorithm, this non-convex optimization problem is decomposed into three simple subproblems. By alternately solving these subproblems, the optimal solution of the original problem can be gradually approximated. Simultaneously, the unique spatiotemporal joint block sparsity of the MIMO channel is exploited to further optimize the non-zero position index set selected during the algorithm's iteration process, enhancing the algorithm's stability. Simulation results demonstrate that the proposed ADMM algorithm with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$l_{q}$</tex> regularization achieves more accurate sparse channel estimation compared to algorithms based on conventional <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$l_{1}$</tex> regularization.