Optimal pilot placement for time-varying channels

Two major training techniques for wireless channels are the time-division multiplexed (TDM) training arid the superimposed training. For the TDM schemes with regular periodic placements (RPP), the closed-form expression of the steady-state minimum mean square error (MMSE) is obtained as a function of pilot placement for Gauss-Markov fading channels. We show that the single cluster RPP scheme (RPP-1) minimizes the maximum steady-state channel MMSE. For BPSK and QPSK signaling, we then 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 schemes with those under the optimal TDM scheme. It is shown that while RPP-1 scheme performs better at high SNR and for slow 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.