  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.
