Tracking Performance of Least Squares MIMO Channel Estimation Algorithm

In this paper, the tracking performance analysis of the least squares (LS) multiple-input multiple-output (MIMO) channel estimation and tracking algorithm is presented. MIMO channel estimation is a novel application of the LS algorithm that presents near-optimum performance by Karami and Shiva in 2003 and 2006. In this paper, the mean square error (MSE) of tracking of the LS MIMO channel estimator algorithm is derived as a closed-form function of the Doppler shift, forgetting factor, channel rank, and the length of training sequences. In the analysis, all training symbols are considered as randomly generated equal-power vectors on the unit circle, or in other words, phase-shift keying (PSK) signaling. By evaluating this function, some insights into the tracking behavior of the LS MIMO channel estimator are achieved. Then, the calculated tracking error is compared with the tracking error derived from Monte Carlo simulation for quaternary-PSK-based training signals to verify the validation of the presented analysis. Finally, the optimum forgetting factor is derived to minimize the error function, and it is shown that the optimum forgetting factor is highly dependent on the training length, Doppler shift, and E_b/N_o. Also, it is concluded that in low E_b/N_o values, the number of transmitter antennas has negligible effect on the optimal value of the forgetting factor.