Optimal training length for MIMO frequency-selective channels with time-variation

In this paper, we investigate the multiple-input-multiple-output (MIMO) frequency-selective channel estimation performance under the impact of both channel time-variation and noise contamination. The total mean square error (MSE) using orthogonal training sequences is derived so that the optimal training length can be easily determined numerically instead of by extensive simulation. We prove that the overall MSE is irrelevant to the type of orthogonal training sequences employed and only depends on the time-varying channel model under some, fairly general, conditions. Our results are validated by considering two types of orthogonal sequences: cyclically shifted Chu sequences and zero-correlation-zone (ZCZ) sequences using Jake´s model. Applications to underwater acoustic(UWA) communications are considered.