A Unified Treatment of Optimum Pilot Overhead in Multipath Fading Channels

TLDR: It is established that the overhead optimization for multiantenna systems is effectively the same as for single-antenna systems with the normalized Doppler frequency multiplied by the number of transmit antennas.

Abstract: The optimization of the pilot overhead in single-user wireless fading channels is investigated, and the dependence of this overhead on various system parameters of interest (e.g., fading rate, signal-to-noise ratio) is quantified. The achievable pilot-based spectral efficiency is expanded with respect to the fading rate about the no-fading point, which leads to an accurate order expansion for the pilot overhead. This expansion identifies that the pilot overhead, as well as the spectral efficiency penalty with respect to a reference system with genie-aided CSI (channel state information) at the receiver, depend on the square root of the normalized Doppler frequency. It is also shown that the widely-used block fading model is a special case of more accurate continuous fading models in terms of the achievable pilot-based spectral efficiency. Furthermore, it is established that the overhead optimization for multiantenna systems is effectively the same as for single-antenna systems with the normalized Doppler frequency multiplied by the number of transmit antennas.

Figures

Figure 5: Spectral efficiency with optimum pilot overhead as function of SNR for fD = 0.001 and fD = 0.02 with a Clarke-Jakes spectrum. Also shown is the capacity with perfect CSI.

Figure 6: Optimum pilot power boost, ρ?p, as function of SNR for fD = 0.001 and fD = 0.02 with a Clarke-Jakes spectrum.

Figure 1: Spectral efficiency as function of the pilot overhead, α, for SNR = 10 dB. The Doppler spectrum is Clarke-Jakes with a maximum normalized frequency fD = 0.02 corresponding, for instance, to 100 Km/h in a WiMAX system. The pilot and data symbols have equal power.

Figure 9: Optimum pilot overhead, α?, as function of number of antennas (nT = nR) for fD = 0.001 and fD = 0.01 for a rectangular spectrum with SNR = 10 dB. Also shown is the optimal pilot overhead for the single-antenna equivalent with a normalized Doppler of nTfD.

Figure 2: Optimum pilot overhead, α?, as function of fD for SNR = 0 dB and SNR = 10 dB with a Clarke-Jakes spectrum. Relevant Doppler levels for LTE and WiMAX are highlighted.

Figure 3: Optimum pilot overhead, α?, as function of SNR for fD = 0.001 and fD = 0.02 with a Clarke-Jakes spectrum.