Bounds for Multihop Relayed Communications in Nakagami- Fading
George K. Karagiannidis, Theodoros A. Tsiftsis, Ranjan K. Mallik · 2006
Abstract— We present closed-form lower bounds for the perfor-mance of multihop transmissions with nonregenerative relays overnot necessarily identically distributed Nakagami- fading chan-nels. The end-to-end signal-to-noise ratio is formulated and upperbounded by using an inequality between harmonic and geometricmeans of positive random variables (RVs). Novel closed-formexpressions are derived for the moment generating function, theprobability density function, and the cumulative distribution func-tion of the product of rational powers of statistically independentGamma RVs. These statistical results are then applied to studyingthe outage probability and the average bit-error probability forphase- and frequency-modulated signaling. Numerical examplescompare analytical and simulation results, verifying the tightnessof the proposed bounds. Index Terms— Average bit-error probability (ABEP), Gammarandom variables (RVs), multihop relayed communications, Nak-agami- fading, outage probability.