Channel estimation for PLNC under frequency flat fading scenario

In this chapter, we consider channel estimation for PLNC system in a frequency flat fading scenario. We propose a two-phase training protocol for channel estimation that can be easily embedded into the two-phase data transmission. Each terminal targets at estimating the individual channel parameters. We first derive the maximum-likelihood (ML) estimator, which is nonlinear and differs much from the conventional least-square (LS) estimator. Due to the difficulty in obtaining a closed-form expression of the mean square error (MSE) for the ML estimator, we resort to the Cramér-Rao lower bound (CRLB) of the estimation MSE to design the optimal training sequence. In the mean time, we introduce a new type of estimator that aims at maximizing the effective receive signal-to-noise ratio (SNR) after taking into consideration the channel estimation errors, referred to as the linear maximum signal-to-noise ratio (LMSNR) estimator. Furthermore, we prove that orthogonal training design is optimal for both the CRLB- and the LMSNR-based design criteria. Finally, simulations are presented to corroborate the proposed studies.