Performance Analysis of Decode-and-Forward Multi-Hop Communication: A Difference Equation Approach

The performance of decode-and-forward multi-hop communication is analyzed in a Rayleigh fading environment. Analytical expressions for the end-to-end symbol error probability are derived in the cases of M-ary phase-shift keying with coherent detection and orthogonal M-ary frequency-shift keying with non-coherent detection using a difference equation approach. When the path loss exponent is greater than one, each node transmits with the same power as that of a direct transmission source, and the relays are equispaced along the line joining the source and the destination, the performance improves with increasing number of hops. Furthermore, for fixed average signal-to-noise ratio per hop, the incremental degradation in performance when adding more hops decreases with each extra hop.