Joint channel estimation and data recovery of communication systems with sub-Nyquist receiver

Consider a multicarrier communication scenario where both the information (data) and channel have sparse structure. To exploit such sparse structure, we propose to use a receiver working at sampling rate much lower than Nyquist rate (sub-Nyquist sampling) to acquire the data corrupted by noise as well as multipath channel. With the sub-Nyquist rate samples, the joint channel estimation and data recovery is formulated as a sparse maximum likelihood estimation (MLE) problem which maximizes the associated non-concave likelihood function under the sparsity constraints on channel and data. This Sparse MLE framework is proved to provide solutions with bounded error w.r.t. the true value of channel and data under certain restricted isometry property (RIP) conditions. We propose an alternating sparse matching pursuit (ASMP) algorithm to solve the non-convex Sparse MLE problem. We also establish the sufficient conditions for ASMP to converge to solution with bounded error under certain restricted isometry property (RIP) conditions. Simulations show that when sparse structure is exploited, a low rate sub-Nyquist receiver using ASMP performs nearly as well as a Nyquist rate receiver.