On the Exact and Asymptotic SER of Receive Diversity With Multiple Amplify-and-Forward Relays

• Published in: IEEE transactions on vehicular technology Vol. 59; no. 9; pp. 4602 - 4608
• Main Authors: Elkashlan, Maged, Phee Lep Yeoh, Louie, Raymond H Y, Collings, Iain B
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-11-2010; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Access methods and protocols, osi model; Amplification; Antennas; Applied sciences; Array signal processing; Asymptotic properties; Beamforming; Cellular networks; Connection and protection apparatus; Detection, estimation, filtering, equalization, prediction; Diversity methods; Electrical engineering. Electrical power engineering; Exact sciences and technology; Exact solutions; Fading; fading channels; Hops; Information, signal and communications theory; Mathematical analysis; Rayleigh channels; Relaying; Signal and communications theory; Signal to noise ratio; Signal, noise; Studies; Symbols; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Teleprocessing networks. Isdn; Transmission and modulation (techniques and equipments); wireless relays; Performance evaluation; Relaying; Parameter estimation; Relay; Current source converter; Wireless telecommunication; Diversity; Unbalanced conditions; Cell network; Beam forming; M ary modulation; diversity methods; wireless relays; Channel estimation; Routing protocols; Symbol error rate; cellular networks; Antenna; Fading channels; Mobile radiocommunication; Generating function; Transmission protocol; Beamforming; Telecommunication network; Rayleigh fading; Gain; Signal to noise ratio
• ISSN: 0018-9545; 1939-9359
• DOI: 10.1109/TVT.2010.2076306

Receive diversity with multiple amplify-and-forward (AF) relays is analyzed over unbalanced hops with independent but not necessarily identically distributed Rayleigh fading. We consider two main AF protocols: 1) fixed-gain relaying, which requires partial channel-state information (CSI), and 2) variable-gain relaying, which requires full CSI. Exact closed-form expressions are derived for the moment-generating function of the end-to-end signal-to-noise ratio (SNR). Our analysis is valid for arbitrary numbers of relays and arbitrary numbers of antennas at the destination. Based on the derived results, we determine the symbol error rate with M-ary phase-shift keying. In addition, we carry out an asymptotic analysis in the high-SNR regime. Our results provide fundamental insight into the impact of the number of antennas on the performance of multiple AF relaying. We explicitly reveal that the diversity order is equal to the sum of two parameters: 1) the number of relays and 2) the number of antennas at the destination.