Communication Systems With Amplitude Detection: An Asymptotic Approach

Abstract

Amplitude detection (AD) is a low-complexity nonlinear scheme for information retrieval, as it only considers the envelope of the received signal. This makes it ideal in applications with low-cost low-power devices such as the Internet of Things (IoT). We consider a basic Point-to-Point (P2P) setup and develop a unified analytical framework for the asymptotic symbol error rate (SER) performance of the maximum-likelihood (ML) decoder with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> -ary amplitude-shift keying (ASK). The developed framework is general and can be applied for a large class of fading channels. The SER can be characterized by two parameters: the diversity order and the coding gain at a sufficiently high signal-to-noise regime. We derive closed-form expressions for the exact diversity order along with a lower and upper bound on the coding gain. We show that the diversity order is equal to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> for Nakagami- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> fading, whereas for the other considered models, it is equal to one. We also prove that among all possible binary modulations with equal power, the modulation with one symbol equal to zero [i.e., on–off keying (OOK)] achieves the minimum asymptotic SER. The mathematical framework developed for the P2P setup is extended for cooperative relay networks. Specifically, we consider a basic amplify-and-forward (AF) three-node relay topology that employs AD at both the relay and the destination. We analytically derive the ML decoder and study asymptotic bounds on the SER by showing that the proposed AF-AD relay setup can be transformed into an equivalent P2P-AD with respect to the ML decoder.