Channels with a long but sparse impulse response arise in a variety of wireless communication applications, such as high definition television (HDTV) terrestrial transmission and underwater acoustic communications. By adopting the $\ell_1$-norm as the sparsity metric of the channel response, the channel estimation is formulated as a complex-valued convex optimization problem. A fast fixed point iteration algorithm is developed to solve the resultant complex-valued $\ell_1$-minimization problem. The proposed fast channel estimation algorithm is easy to implement and has a low computational complexity of $O(N\log N)$ per iteration with $N$ the signal length. Simulation results are provided to demonstrate the performance of the proposed fixed point algorithm.
['Xue Jiang', 'Wen-Jun Zeng', 'En Cheng']
A Fast Fixed Point Iteration Algorithm for Sparse Channel Estimation