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Channel Estimation Performance Analysis of Massive MIMO IoT Systems With Ricean Fading

Pei Liu,Tao Jiang

Published 2021 in IEEE Internet of Things Journal

ABSTRACT

This article analyzes the channel estimation performance of massive multiple-input–multiple-output (MIMO) Internet-of-Things (IoT) systems with Ricean fading. First, by utilizing the least squares (LSs) and minimum mean squared error (MMSE) estimation methods, we consider the relative channel estimation error (RCEE) between the IoT device and base-station, and provide the approximations of the expectation of RCEE (<inline-formula> <tex-math notation="LaTeX">${\text {Exp}}_{\textrm {rcee}}$ </tex-math></inline-formula>). Then, it is found that when the number of antennas <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> becomes infinite, pilot contamination (PC) exists in both cases. However, for MMSE case, <inline-formula> <tex-math notation="LaTeX">${\text {Exp}}_{\textrm {rcee}}$ </tex-math></inline-formula> scales down by the inverse of Ricean <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula>-factor, and hence PC phenomenon disappears with a large Ricean <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula>-factor. Moreover, as <inline-formula> <tex-math notation="LaTeX">$M\rightarrow \infty $ </tex-math></inline-formula>, the power scaling laws show that the pilot sequence power can be scaled down proportionally to <inline-formula> <tex-math notation="LaTeX">$1/M^{\alpha }$ </tex-math></inline-formula> (<inline-formula> <tex-math notation="LaTeX">$\alpha >0$ </tex-math></inline-formula>) with the MMSE case, where the performance is determined only by the Ricean <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula>-factor. Next, the channel hardening and favorable propagation effects are examined via analyzing the approximations of the variance of RCEE (<inline-formula> <tex-math notation="LaTeX">${\text {Var}}_{\textrm {rcee}}$ </tex-math></inline-formula>). Analysis implies that <inline-formula> <tex-math notation="LaTeX">${\text {Var}}_{\textrm {rcee}}$ </tex-math></inline-formula> decreases by <inline-formula> <tex-math notation="LaTeX">$1/M$ </tex-math></inline-formula> when <inline-formula> <tex-math notation="LaTeX">$M\rightarrow \infty $ </tex-math></inline-formula>. For a large Ricean <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula>-factor, <inline-formula> <tex-math notation="LaTeX">${\text {Var}}_{\textrm {rcee}}$ </tex-math></inline-formula> approaches a nonzero constant for the LS case and scales down by the inverse of the square of Ricean <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula>-factor for the MMSE case. Finally, all results are verified via Monte Carlo simulations.

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