Performance Analysis of Multi-Node Two-Hop Relay Cooperative Diversity in Rayleigh Channels Using Harmonic Mean Method

In this paper, we employ the harmonic mean method to analyze the performance of multi-node two-hop relay cooperative diversity in Rayleigh fading channels. This statistical approach helps characterize the end-to-end signal-to-noise ratio (SNR) in cooperative relay networks, where the harmonic mean effectively captures the bottleneck effect in serial relay connections. Our implementation involves calculating the equivalent SNR using the harmonic mean of individual link SNRs, which can be coded as: harmonic_mean_SNR = num_links / sum(1/SNR_i) where SNR_i represents the SNR of each relay hop. This method provides crucial insights into data transmission processes in multi-hop relay networks and demonstrates how to maximize data transmission efficiency in such network topologies. We conduct an in-depth investigation of cooperation among relay nodes, analyzing how this coordination affects signal strength and transmission rates through diversity combining techniques like selection combining or maximal ratio combining. The study examines various data transmission schemes, including decode-and-forward and amplify-and-forward protocols, to achieve optimal performance across different network environments. Through MATLAB simulations, we implement key functions for: - Generating Rayleigh fading channels using Rayleigh random variable generators - Calculating harmonic mean of SNRs across multiple relay paths - Evaluating bit error rate (BER) performance with different combining schemes This research enhances understanding of multi-hop relay network operation principles and provides guidance for future network design and optimization, particularly in implementing efficient cooperative diversity algorithms for wireless communication systems.