Large System Analysis for Amplify & Forward SIMO Multiple Access Channel with Ill-conditioned Second Hop

Relaying has been extensively studied during the last decades and has found numerous applications in wireless communications. The simplest relaying method, namely amplify and forward, has shown potential in MIMO multiple access systems, when Gaussian fading channels are assumed for both hops. However, in some cases ill conditioned channels may appear on the second hop. For example, this impairment could affect cooperative BS systems with microwave link backhauling, which involve strong line of sight channels with insufficient scattering. In this paper, we consider a large system analysis of such as model focusing on both optimal joint decoding and joint MMSE filtering receivers. Analytical methods based on free probability are presented for calculating the ergodic throughput, the MMSE error and the average SINR. Furthermore, the performance degradation of the system throughput is evaluated considering second hop impairments such as ill-conditioning and rank deficiency, while highand low-SNR limits are calculated for the considered performance metrics. Finally, the cooperative BS system is compared to a conventional channel resource division strategy and suitable operating points are proposed.