Analytical Approximation of the Channel Rate for Massive MIMO System with Large but Finite Number of Antennas

In practical massive multiple-input-multiple-output (MIMO) system, limited transmitted antennas installed at the base station (BS) cannot guarantee the ideal orthogonality and the theoretical channel rate cannot thus be achieved. In this paper, we consider the approximation of channel rate for the configuration of large but finite number of antennas at BS in a massive MIMO system. A perturbation matrix is introduced to model the non-ideal orthogonality. And then, Taylor expansion of determinant is utilized to derive the closed form of the achievable channel rate. The convergence of the Taylor expansion is theoretically proved and simulated. Numerical results show that our calculation of channel rate can get a better approximation compared with the practical rate, especially in the case of high expansion order and large number of antennas.