# Error Rate Analysis of Amplitude-Coherent Detection over Rician Fading Channels with Receiver Diversity

## TL;DR

This paper analyzes the error rates of amplitude-coherent detection methods for M-ary amplitude shift keying over Rician fading channels with receiver diversity, deriving analytical expressions and comparing performance with other detectors.

## Contribution

It introduces new AC detector designs, derives their SER analytically, and compares their performance with coherent and noncoherent detectors in Rician channels.

## Key findings

- SER of AC and coherent detectors are similar at high Rician K-factors.
- Optimal AC detector's SER matches that of the coherent detector.
- Heuristic AC detector outperforms noncoherent detectors and is immune to phase noise.

## Abstract

Amplitude-coherent (AC) detection is an efficient detection technique that can simplify the receiver design while providing reliable symbol error rate (SER). Therefore, this work considers AC detector design and SER analysis using M-ary amplitude shift keying (MASK) modulation over Rician fading channels. More specifically, we derive the optimum, near-optimum and a suboptimum AC detectors and compare their SER to the coherent, noncoherent and the heuristic AC detectors. Moreover, the analytical SER of the heuristic detector is derived using two different approaches for single and multiple receiving antennas. One of the derived expressions is expressed in terms of a single integral that can be evaluated numerically, while the second approach gives a closed-form analytical expression for the SER, which is also used to derive a simple formula for the asymptotic SER at high signal-to-noise ratios (SNRs). The obtained analytical and simulation results show that the SER of the AC and coherent MASK detectors are comparable, particularly for high values of the Rician K-factor, and small number of receiving antennas. Moreover, the obtained results show that the SER of the optimal AC detector is equivalent to that of the coherent detector. However, the optimal AC detector complexity is prohibitively high, particularly at high SNRs. In most of the scenarios, the heuristic AC detector significantly outperforms the optimum noncoherent detector, except for the binary ASK case at low SNRs. Moreover, the obtained results show that the heuristic AC detector is immune to phase noise, and thus, it outperforms the coherent detector in scenarios where system is subject to considerable phase noise.