Time-Varying Narrowband Channel Estimation: Exploiting Low-Rank And Sparsity Via Bilinear Representation

In this paper, the estimation of a narrowband time-varying channel under the practical assumptions of finite block length and finite transmission bandwidth is investigated. It is shown that the signal, after passing through a time-varying narrowband channel reveals a particular parametric low-rank structure that can be represented as a bilinear form. To estimate the channel, we propose two structured methods. The first method exploits the low-rank bilinear structure of the channel via a non-convex strategy based on alternating direction optimization between delay and Doppler directions. Due to the non-convex nature of this approach, it is sensitive to local minima. Motivated by this issue, a novel convex approach based on the minimization of the atomic norm using measurements of signal at time domain is proposed. Numerical results show that the performance of proposed algorithm is independent of the leakage effect and the new methods can achieve moe than 5 dB improvement in average compared to l(1)-based sparse approximation method.