PEP Analysis of the SDP Based Joint Channel Estimation and Signal Detection

In multi-antenna communication systems, channel information is often not known at the receiver. To fully exploit bandwidth resources of the system and ensure practical feasibility of the receiver, channel parameters are often estimated blindly and then employed in the design of signal detection algorithms. Instead of separating channel estimation from signal detection, in this paper we focus on the joint channel estimation and signal detection problem in a single-input multiple-output (SIMO) system. It is well known that finding solution to this optimization requires solving an integer maximization of a quadratic form and is, in general, an NP hard problem. To solve it, we propose an approximate algorithm based on the semi-definite program (SDP) relaxation. We derive a bound on the pairwise probability of error (PEP) of the proposed algorithm and show that, the algorithm achieves the same diversity as the exact maximum-likelihood (ML) decoder. The computed PEP implies that, over a wide range of system parameters, the proposed algorithm requires moderate increase in the signal-to-noise ratio (SNR) in order to achieve performance comparable to that of the ML decoder but with often significantly lower complexit