On the Peak-to-Mean Envelope Power Ratio of Phase-Shifted Binary Codes

TL;DR

This paper investigates how phase shifts from a 2^h-PSK constellation can reduce the PMEPR of binary codes in OFDM systems, establishing bounds related to the code's covering radius and analyzing various code types.

Contribution

It introduces a lower bound on PMEPR reduction achievable through phase shifts, linking it to the covering radius of binary codes and evaluates this bound on multiple code families.

Findings

Most existing phase-shift designs approach the theoretical bound.

The achievable PMEPR reduction diminishes as the code's covering radius decreases.

The bound applies to various well-known codes like BCH, Reed-Muller, and convolutional codes.

Abstract

The peak-to-mean envelope power ratio (PMEPR) of a code employed in orthogonal frequency-division multiplexing (OFDM) systems can be reduced by permuting its coordinates and by rotating each coordinate by a fixed phase shift. Motivated by some previous designs of phase shifts using suboptimal methods, the following question is considered in this paper. For a given binary code, how much PMEPR reduction can be achieved when the phase shifts are taken from a 2^h-ary phase-shift keying (2^h-PSK) constellation? A lower bound on the achievable PMEPR is established, which is related to the covering radius of the binary code. Generally speaking, the achievable region of the PMEPR shrinks as the covering radius of the binary code decreases. The bound is then applied to some well understood codes, including nonredundant BPSK signaling, BCH codes and their duals, Reed-Muller codes, and convolutional codes. It is demonstrated that most (presumably not optimal) phase-shift designs from the literature attain or approach our bound.