Some Generalizations of the Capacity Theorem for AWGN Channels

TL;DR

This paper generalizes the Shannon-Hartley Law for AWGN channels by incorporating the linear canonical transform, showing that channel capacity depends on LCT parameters, thus broadening the classical understanding of channel capacity.

Contribution

It introduces a novel generalization of the capacity theorem for AWGN channels using the linear canonical transform, extending the classical Fourier domain analysis.

Findings

Channel capacity depends on LCT parameters

Generalized capacity formula for LCT-based channels

Broadens understanding of AWGN channel limits

Abstract

The channel capacity theorem for additive white Gaussian noise channel (AWGN), widely known as the Shannon-Hartley Law, expresses the information capacity of a channel bandlimited in the conventional Fourier domain in terms of the signal-to-noise ratio in it. In this letter generalized versions of the Shannon-Hartley Law using the linear canonical transform (LCT) are presented. The channel capacity for AWGN channels is found to be a function of the LCT parameters.