Pilot-Symbol-Assisted Communications with Noncausal and Causal Wiener Filters

TL;DR

This paper analyzes pilot-assisted transmission over flat fading channels using causal and noncausal Wiener filters, optimizing training and power allocation to maximize achievable rates, and compares their performance.

Contribution

It provides a detailed comparison of causal and noncausal Wiener filters in pilot-assisted fading channel estimation, including rate optimization and energy efficiency analysis.

Findings

Noncausal filters yield slightly better performance than causal filters.

Optimal training period and power allocation significantly improve achievable rates.

Causal filtering performance loss is small compared to noncausal filtering.

Abstract

In this paper, pilot-assisted transmission over time-selective flat fading channels is studied. It is assumed that noncausal and causal Wiener filters are employed at the receiver to perform channel estimation with the aid of training symbols sent periodically by the transmitter. For both filters, the variances of estimate errors are obtained from the Doppler power spectrum of the channel. Subsequently, achievable rate expressions are provided. The training period, and data and training power allocations are jointly optimized by maximizing the achievable rate expressions. Numerical results are obtained by modeling the fading as a Gauss-Markov process. The achievable rates of causal and noncausal filtering approaches are compared. For the particular ranges of parameters considered in the paper, the performance loss incurred by using a causal filter as opposed to a noncausal filter is shown to be small. The impact of aliasing that occurs in the undersampled version of the channel Doppler spectrum due to fast fading is analyzed. Finally, energy-per-bit requirements are investigated in the presence of noncausal and causal Wiener filters.