Noncoherent Detection of Constant-Envelope Signals for Mobile Edge Applications -- Optimum Detectors and Intelligent Decision Rule

TL;DR

This paper develops a theoretical framework for noncoherent detection of constant-envelope signals, proving the optimality of energy detectors at low SNR and introducing amplitude detectors for high SNR, with an adaptive rule for unknown SNRs.

Contribution

It provides the first rigorous proof of energy detector optimality at low SNR and introduces a simple amplitude detector for high SNR, along with an adaptive decision rule for unknown SNRs.

Findings

Energy detector is optimal at low SNR.

Amplitude detector is optimal at high SNR.

Reliability-based adaptive decision rule improves detection robustness.

Abstract

Constant-envelope signals are widely used in mobile edge applications and wireless communication systems for their hardware-friendly design, energy efficiency, and reliability. However, reliable detection with simple, power-efficient receivers remains challenging. Coherent methods offer superior performance but require complex synchronization, increasing complexity and power use. Noncoherent detection is simpler, avoiding synchronization, but traditional approaches rely on in-phase and quadrature-phase (IQ) demodulators for signal magnitudes and assume energy detectors without theoretical justification. This paper proposes a framework for optimal detection using a bandpass-filter envelope-detector (BFED) with Bayes criterion and generalized likelihood ratio test (GLRT) under unknown amplitudes. Using modified Bessel function approximations, we show the optimal detector shifts based on SNR: in the low-SNR regime, we rigorously prove for the first time that the well-known energy detector (ED) is the Bayesian-optimal solution, thus providing a firm theoretical foundation for its widespread use; in high-SNR regimes, a novel amplitude detector (AD) compares estimated amplitude to noise deviation, leading to a simple yet optimal detection strategy. For unknown SNR, a reliability-based intelligent decision (RID) rule adaptively selects detectors, leveraging their strengths across SNR ranges. Simulations confirm energy and amplitude detectors minimize errors in their domains, with RID providing robust gains. The proposed framework provides a rigorous theoretical foundation and enables low-complexity implementations for resource-constrained, interference-limited mobile edge applications, including wireless sensor networks (WSNs) and Internet of Things (IoT) systems.