Approximation of Multi-Hop Relay to Dual-Hop Relay and Its Error Performance Analysis

In this letter, we develop a novel analytical framework in order to derive average symbol error rate (ASER) as a tractable form in multi-hop amplify-and-forward (AF) relay systems with cooperative diversity. In the proposed analytical approach, we modify multi-hop relay systems to dual-hop schemes over Rayleigh fading channels. The received signal in the l th relay can be expressed as a single signal from the source, and the probability density function (pdf) of its signal-to-noise ratio (SNR) can be equivalently modeled as a summation of the pdfs of the SNRs among the source and (l-1) relays. Based on this, the ASERs are then analyzed as approximated bounds, which are verified by comparison with simulation results. The derived ASER expressions show that the diversity order of multi-hop AF relay systems with L relays is (L+1), which is identical to that of dual-hop systems.