On the Capacity and Energy Efficiency of Training-Based Transmissions over Fading Channels

TL;DR

This paper analyzes the capacity and energy efficiency of training-based transmission schemes over unknown Rayleigh fading channels, highlighting the impact of SNR, block length, and peak power constraints on performance.

Contribution

It provides a comprehensive analysis of training-based schemes' capacity and energy efficiency, including new insights into optimal input structures and the effects of peak power constraints.

Findings

Bit energy grows unbounded as SNR approaches zero.

Flash training improves energy efficiency at low SNR.

Optimal input distribution is discrete with finite mass points.

Abstract

In this paper, the capacity and energy efficiency of training-based communication schemes employed for transmission over a-priori unknown Rayleigh block fading channels are studied. In these schemes, periodically transmitted training symbols are used at the receiver to obtain the minimum mean-square-error (MMSE) estimate of the channel fading coefficients. Initially, the case in which the product of the estimate error and transmitted signal is assumed to be Gaussian noise is considered. In this case, it is shown that bit energy requirements grow without bound as the signal-to-noise ratio (SNR) goes to zero, and the minimum bit energy is achieved at a nonzero SNR value below which one should not operate. The effect of the block length on both the minimum bit energy and the SNR value at which the minimum is achieved is investigated. Flash training and transmission schemes are analyzed and shown to improve the energy efficiency in the low-SNR regime. In the second part of the paper, the capacity and energy efficiency of training-based schemes are investigated when the channel input is subject to peak power constraints. The capacity-achieving input structure is characterized and the magnitude distribution of the optimal input is shown to be discrete with a finite number of mass points. The capacity, bit energy requirements, and optimal resource allocation strategies are obtained through numerical analysis. The bit energy is again shown to grow without bound as SNR decreases to zero due to the presence of peakedness constraints. The improvements in energy efficiency when on-off keying with fixed peak power and vanishing duty cycle is employed are studied. Comparisons of the performances of training-based and noncoherent transmission schemes are provided.