Optimal insertion of pilot symbols for transmissions over time-varying flat fading channels

Abstract

Abstract-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.

Interplay of spectral efficiency, power and doppler spectrum for reference-signal-assisted wireless communication

“…RS are inserted periodically in the transmission [12] and the fraction thereof is denoted by α, i.e., one in every 1/α symbols is a reference while the rest are data (cf. Fig.…”

Superimposed asymmetric modulation in narrowband fading channels using orthogonal codes

“…One solution to this problem is time-divisionmultiplexed (TDM) pilot-assisted transmission (PAT) in which detection ambiguity is eliminated at the receiver. The term PAT refers to general transmission schemes that use pilot symbols to aid the process of channel estimation [5]. It is different from pilot symbol-assisted modulation (PSAM) [6] in that PSAM specifically refers to PAT with regular periodic placement of cluster size 1 (RPP-1) [5].…”

“…estimator to update its channel estimate while user data is transmitted in a separate parallel data channel. Superimposed PAT is considered in this letter because it outperforms the optimal TDM PAT scheme, the RPP-1 TDM PAT, in bit error rate (BER) and minimum mean square error (MMSE) for the majority of fading rates of practical importance [5].…”

“…A small a represents fast fading while a large a represents slow fading. The standard conditions in [5] assume that t k , d k , h k , and w k are jointly independent.…”

“…A joint CE/DD receiver consisting of a Kalman filter (KF) and a maximum-likelihood (ML) detector was proposed in [5] for the superimposed PAT. The KF operates in the pilot channel and it considers the term ρ d d k h k in y k in the first column of Table I as noise-like interference that is grouped with the AWGN w k to create the term v k in the measurement equation.…”