Probability of SNR Gain by Dual-Hop Relaying over Single-Hop Transmission in SISO Rayleigh Fading Channels

In this letter, we address the end-to-end signal-to-noise ratio (SNR) gain achievable by dual-hop relaying over the single-hop transmission in single-input single-output (SISO) flat Rayleigh fading channels. We deal with both nonregenerative and regenerative relaying schemes. To quantify the SNR gain, a closed-form expression of the probability of SNR gain is developed. The probability of SNR gain results in an explicit function of an average power ratio of the per-hop channel in dual-hop relaying to the channel in the single-hop transmission. We investigate impacts of the average power ratio as well as the relaying location on the SNR gain.