Optimal insertion of pilot symbols for transmissions over time-varying flat fading 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 (RPPs), the closed-form expression for the steady-state minimum mean square error (MMSE) of the 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 binary phase-shift keying (BPSK) and quadrature phase-shift keying (QPSK) signaling, we further show that the optimal placement that minimizes the maximum uncoded 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.