Delay-Doppler Estimation Via Structured Low-Rank Matrix Recovery

The estimation of a narrowband time-varying channel under finite block length and transmission bandwidth is investigated. A novel method is proposed for estimation in the delay-Doppler domain by exploiting structural constraints on low-rank matrix recovery. The proposed algorithm uses Gauss-Seidel iterations on the low-rank parameterization under noisy training signal measurements. Theoretical global identifiability results for the channel leakage (due to finite block length and transmission bandwidth) are stated and the necessity of considering Doppler shift induced structure is demonstrated. Justification is provided for the choice of simulation parameters and initialization strategies to achieve good convergence rates and some ill-posed scenarios are also described. It is further shown that simple sparsity-based algorithms like basis pursuit/nuclear norm minimization do not perform well on the said constraint set for measurement operators arising out of training sequences.