Efficient Noise Variance Estimation Under Pilot Contamination for Massive MIMO Systems

Massive multiple input multiple output (MIMO) is expected to be one of the enabling technologies for fifth-generation cellular networks. One of the major challenges in massive MIMO systems is the accurate joint estimation of the channel and noise variance, which significantly affects the performance of wireless communications in practical scenarios. In this paper, we first derive a novelmaximum likelihood estimator for the noise variance at the receiver of massive MIMO systems considering practical impairments such as pilot contamination. Then, this estimate is used to compute the minimum mean square error estimate of the channel. In order to measure the performance of the proposed noise variance estimator, we derive the corresponding Cramer-Rao lower bound (CRLB). Simulation results show that the estimator is efficient in certain scenarios, outperforming existing approaches in the literature. Furthermore, we develop the estimator and the CRLB for equal and different noise variance at the receive antennas. Although the proposed estimator is valid for all antenna array sizes, its use is particularly effective for massive MIMO systems.