EM-Based Optimal Maximal Ratio Diversity Combiner for Constant Envelope Signals

Ahmed El-Sayed El-Mahdy*
Electrical Engineering Department, MTC, Cairo, Egypt

© 2009 Ahmed El-Sayed El-Mahdy.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Electrical Engineering Department, MTC, Cairo, 821 Zahraa Nasr City, Flat 31, Nasr City, Cairo, Egypt; Tel: +2 02 24098320; E-mail:


An optimal maximal ratio combiner (MRC) based on the expectation-maximization (EM) algorithm is developed for noisy constant envelope signals transmitted over a Rayleigh fading channel. Instead of using a transmitted pilot signal with the data to estimate the combiner gains, the EM algorithm is used to perform this estimation. In the developed MRC, estimation of the transmitted data sequence is performed also by the EM algorithm. Estimation using the EM algorithm provides an iterative solution to the maximum likelihood (ML) approach. Therefore, the resulting receiver is optimum and does not suffer from the difficulties resulted from direct application of the ML procedure. One of these difficulties is the computational complexity which depends exponentially on the data sequence length. Introducing an iterative structure in the developed MRC achieves a linear computational complexity and enables efficient data extraction by the Viterbi algorithm when trellis coding is used.

Keywords: Diversity, Expectation-maximization algorithm, Maximal ratio combiner.