A Novel Beamforming and Combining Scheme for Two-Way AF Satellite Systems

We propose a novel beamforming and combining scheme for a two-way amplify-and-forward (AF) satellite system. Exchange of the data in between two multiple-antenna-based Earth stations (ESs) via a single-antenna-based satellite is performed. The transmitting ES uses beamforming for transmission of the data, and the receiving ES utilizes the combining vector for detecting the transmitted signal. By using maximum eigenvalue criterion, the beamforming and combining vectors are calculated. The satellite channels (uplink and downlink) are assumed to be shadowed Rician (SR) fading. First, we assume independent and identically distributed (i.i.d.) SR fading channels and derive the probability density function (pdf) of maximum eigenvalue to obtain the expression of moment-generating function (mgf). The closed-form expression for the symbol error rate (SER) of the scheme for $M$ - ary phase-shift keying (MPSK) is obtained by using an mgf-based approach. The diversity order of the studied scheme is also derived by exploiting the asymptotic property of the Meijer G-function. Next, we consider correlated SR fading channels and derive expressions of SER and diversity order. It is shown by simulations that the proposed scheme outperforms the existing beamforming and combining based scheme in two-way AF satellite systems. It is concluded on the basis of the diversity order analysis that the diversity of the proposed scheme linearly depends upon the minimum of the number of antennas of two ESs. Furthermore, it is also shown by simulation and analysis that correlation does not affect the diversity order of the considered scheme.