Imperfect CSI based maximal ratio combining in Shadowed-Rician fading land mobile satellite channels

The maximal ratio combining (MRC) scheme for Shadowed-Rician (SR) fading land mobile satellite (LMS) channels with estimated channel gains is studied, in this paper. For this set-up, a maximum-likelihood decoder is derived under the assumption of the perfectly known channel state information (CSI); then perfect CSI is replaced with the estimated CSI in the decision metric. The MRC scheme for SR fading LMS channels has been studied in existing literature mostly with the perfect CSI assumption; moreover, most of the existing analytical results are in the form of infinite power series, which are not in closed-form. In this paper, we derive approximate closed-form expressions of the probability density function and moment generating function (MGF) of the received signal-to-noise ratio of the MRC based receiver in SR fading LMS channels with estimated channel gains. Analytical expression for the symbol error rate of M-ary phase shift keying constellation is derived by using the MGF expression. We also provide approximate closed-form expression of the average capacity with estimated channel gains of the considered scheme. It is shown from analysis and simulation that estimation error does not affect the diversity order of the system.