Channel Estimation Aware NMSE Performance Analysis for Multi-Cell Massive MIMO Systems

In this article, we investigate normalized mean squared error (NMSE) of channel estimation in multi-cell massive multiple-input multiple-output (MIMO) systems. Primarily, the whole channel estimation phase is carefully introduced via the least squares (LS) and minimum mean squared error (MMSE) estimation methods, respectively. In the second place, to effectively evaluate the channel estimation performance, its NMSE is considered. In detail, the properties of NMSE and its expectation are verified through the law of large number and large dimensional random matrix theory. It implies that the obtained closed-form expression of NMSE’s expectation, which is mainly the function of large-scale fading, number of base station antennas M , and pilot power, is the same as the limit of the instantaneous NMSE for both LS and MMSE cases as large M . Then, the asymptotic analyses about NMSE’s expectation are presented with system parameters to show its robustness. Interestingly, as the pilot power is cut down with M in a power law, the LS and MMSE cases firstly improve the channel estimation performance and then deteriorate, which the LS case is keeping worse and the MMSE case approaches to a given constant. It implies that pilot power can be set smaller for MMSE case for channel estimation. In the end, all obtained results are validated via simulations.