SER Analysis and PDF Derivation for Multi-Hop Amplify-and-Forward Relay Systems

Author

Conne, Chris ; Ju, MinChul ; Yi, Zhihang ; Song, Hyoung-Kyu ; Kim, Il-Min

Author_Institution

Dept. of Electr. & Comput. Eng., Queen´´s Univ., Kingston, ON, Canada

Volume

58

Issue

8

fYear

2010

fDate

8/1/2010 12:00:00 AM

Firstpage

2413

Lastpage

2424

Abstract

An amplify-and-forward, multi-branch, multi-hop relay system with K relays, in which the relays broadcast to other relays as well as the destination, is analyzed. An approximate symbol-error-rate (SER) expression, which is valid for any number of relays and for several modulation schemes, is found for the multi-hop system. Also, the cumulative density function (CDF) and probability density function (PDF) are found for the random variable, Z = XY/(X + Y + c), where X and Y are sums of independent, Erlang random variables, and c is a constant. The moment generating function (MGF) of Z is found for the special case in which c = 0. It is shown that these results are generalizations of previously published results for special cases of Z. The MGF of Z is used to develop the approximate SER expression. Results for the analytic SER expression are included and compared with simulation results for various values of K, for various modulation schemes, and for two choices of system parameters (channel variances). Results for the multi-hop system are also compared to results for the two-hop system (in which relays transmit only to the destination).

Keywords

diversity reception; error analysis; frequency hop communication; modulation; probability; radio broadcasting; random processes; relays; Erlang random variables; MGF; PDF derivation; SER analysis; amplify-and-forward; cooperative diversity; cumulative density function; modulation schemes; moment generating function; multihop relay system; probability density function; relay broadcasting; symbol error rate; Analysis of variance; Analytical models; Broadcasting; Cultural differences; Density functional theory; Digital relays; Probability density function; Protocols; Random variables; Spread spectrum communication; Amplify-and-forward; cooperative diversity networks; multi-hop; symbol-error-rate;

fLanguage

English

Journal_Title

Communications, IEEE Transactions on

Publisher

ieee

ISSN

0090-6778

Type

jour

DOI

10.1109/TCOMM.2010.062510.080615

Filename

5510782