Nonasymptotic Analysis of Capacity in Massive MIMO Systems

In this letter, we analyze the capacity of a point-to-point massive MIMO system in the regime of a large (but finite) number of antennas. Different from previous works resorting to asymptotic random matrix theory, concentration inequalities are used in our nonasymptotic analysis for massive MIMO systems with a finite number of antennas. We first derive deterministic bounds on the ergodic capacity for massive MIMO systems. Furthermore, we obtain statistical bounds within which the instantaneous capacity falls with a falling-in probability. As the number of antennas increases, the statistical bounds on the instantaneous capacity become tighter and the corresponding falling-in probability increases, which reveals an interesting phenomenon that the instantaneous capacity has fewer random fluctuations as the number of antennas becomes larger. Simulations show that these theoretical bounds match well with our experimental results. Therefore, the bounds can be useful for the design and analysis of practical massive MIMO systems with a large but finite number of antennas.