Optimal Pilot Placement for Time-Varying Channels

Two major training techniques for wireless channels are time division multiplexed (TDM) training and superimposed training. For the TDM schemes with regular periodic placements (RPP), the closedform expression for the steady-state minimum mean square error (MMSE) of channel estimate is obtained as a function of placement for Gauss-Markov flat fading channels. We then show that, among all periodic placements, the single pilot RPP scheme (RPP-1) minimizes the maximum steady-state channel MMSE. For BPSK and QPSK signaling, we further show that the optimal placement that minimizes the maximum bit error rate (BER) is also RPP-1. We next compare the MMSE and BER performance under the superimposed training scheme with those under the optimal TDM scheme. It is shown that while the RPP-1 scheme performs better at high SNR and for slowly varying channels, the superimposed scheme outperforms RPP-1 in the other regimes. This demonstrates the potential for using superimposed training in relatively fast time-varying environments.