PEP-based optimal training for MIMO systems in wireless channels

In this paper, PEP (pairwise error probability) is derived for MIMO systems in the presence of channel estimation error, where the channel is estimated using training insertion and linear channel estimation. This training-based PEP expression is utilized to design the training sequence and for optimal power allocation between the training and data symbols. The loss of coding gain due to the training is quantified at high SNR. It is shown that both the proposed PEP-based and the existing capacity-based optimal training approach of B. Hassibi and B. Hochwald (IEEE Trans. Inform. Theory, vol. 49, no. 4, pp. 951-963, 2003) reveal the same power allocation for constant modulus (CM) constellations. The performance of our optimal power allocation scheme falls between the nonoptimized equal power allocation and perfectly known channel cases, and converges to the latter for larger data transmission intervals. Numerical and simulation results are presented to justify the usefulness of our analytical findings.