Structured estimation of time-varying narrowband wireless communication channels

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, under these assumptions, reveals a particular low-rank structure. The rank in this structure is governed by the number of dominant paths in the channel. Moreover, it is shown that this low-rank structure can be represented as a summation of few rank-one atoms (matrix) that are fully described by the channel and leakage key parameters. To estimated the channel, a novel approach based on minimization of 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 method can achieve significant gains over previously proposed methods.