Performance Analysis of the Low-Complexity Adaptive Channel Estimation   over Non-Stationary Multipath Rayleigh Fading Channels Under Carrier   Frequency Offsets
  This paper provides analytical performance of the low-complexity family of affine projection algorithms on the estimation of multipath Rayleigh fading channels in the presence of carrier frequency offsets (CFO) and random channel variations. Our analysis is based on the calculation of the error correlation matrix of the estimation, the mean-square weight error (MSWE) and the mean-square estimation error (MSE) parameters. The analysis does not use strong assumptions like small or large step-size, and explicit closed-form expressions for the MSE of estimation are obtained only from common hypotheses in wireless communication context. In this paper, the optimum stepsize parameters minimizing the MSE of estimation are analytically derived without any simplified assumptions. For the sake of comparison with other analytical approaches, we also investigate the performance of the introduced algorithms by the energy conservation relation. Likewise for exact performance analysis, we evaluate all the moment terms that appear in closed form expressions for the MSE of estimation. Simulations are conduced to corroborate the presented studies and show that the theoretical results agree well with the simulation results over non-stationary multipath Rayleigh fading channels. 
Sayed A. Hadei (Student Member, IEEE), Paeiz Azmi (Senior Member,   IEEE)
math.NA