M.Sc Thesis
M.Sc Student Carmon Yair Information-Estimation Analysis of the ISI Channel Department of Electrical Engineering ? 18? Shlomo Shamai )Shitz( Professor Tsachy Weissman

Abstract

The discrete-time ISI channel is studied, with the practical constraint of finite-alphabet i.i.d. channel inputs. We focus on the fundamental limit on the maximum achievable rate of reliable communications under this constraint. Two modulation schemes are considered - single-carrier (SC) modulation and orthogonal frequency-division multiplexing (OFDM). The main tools used in our analysis are Estimation-Theoretic bounds and Information-Estimation results relating them to achievable rates.

For SC modulation, we investigate the approximation put forth by Shamai and Laroia as a conjectured lower bound for the input-output mutual information after application of a minimum mean squared error decision-feedback receiver. A low-SNR expansion is used to prove that the conjectured bound does not hold under general conditions, and to characterize inputs for which it is particularly ill-suited. One such input is used to construct a counterexample, indicating that the Shamai-Laroia approximation does not always bound even the achievable rate of the channel, thus excluding a natural relaxation of the original conjectured bound. However, this relaxed bound is then shown to hold for any finite entropy input and ISI channel, when the SNR is sufficiently high. Additionally, new simple bounds for the achievable rate are proven, and compared to other known bounds.

Turning to OFDM, we show that the Shamai-Laroia approximation is essentially an upper bound the OFDM achievable rate. We apply Information-Estimation relations in order to rigorously establish this result for both general input distributions and to sharpen it for commonly used PAM and QAM constellations. To this end, novel bounds on estimation of PAM inputs in a scalar Gaussian channel are derived, which may be of independent interest. Thus, the Shamai-Laroia approximation is generally “sandwiched” between the SC and OFDM achievable rates, indicating that the former tends to be higher than the latter. This leads to the interesting conclusion that, under reasonable assumptions, sufficiently optimized single-carrier schemes can offer spectral efficiency superior to that of OFDM, motivating further research of such systems.