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Compensation of Phase Noise in Massive-MIMO Uplink Communications Based on Expectation-Maximization Algorithm

Alberto Tarable, Francisco J. Escribano

TL;DR

This work tackles phase noise in uplink massive MIMO by introducing an EM-based, iterative receiver that jointly detects PN and demodulates data under a general oscillator-to-antenna mapping. The method alternates between a phase estimator with adaptive step size and a linear MMSE MIMO demodulator, leveraging pilot-aided initialization and hard symbol estimates within the EM framework. A Bayesian Cramér-Rao bound is derived to benchmark PN-MSE, and extensive simulations show substantial gains in both MSE and BER, often approaching PN-free performance and outperforming a GEC-SR-based alternative across diverse channel conditions, including imperfect CSI and Rician fading. The results reveal important trade-offs between performance, iteration count, and computational latency, offering guidelines for practical deployment and highlighting the method's robustness to realistic PN models such as PN masks.

Abstract

Phase noise (PN) is a major disturbance in MIMO systems, where the contribution of different oscillators at the transmitter and the receiver side may degrade the overall performance and offset the gains offered by MIMO techniques. This is even more crucial in the case of massive MIMO, since the number of PN sources may increase considerably. In this work, we propose an iterative receiver based on the application of the expectation-maximization algorithm. We consider a massive MIMO framework with a general association of oscillators to antennas, and include other channel disturbances like imperfect channel state information and Rician block fading. At each receiver iteration, given the information on the transmitted symbols, steepest descent is used to estimate the PN samples, with an optimized adaptive step size and a threshold-based stopping rule. The results obtained for several test cases show how the bit error rate and mean square error can benefit from the proposed phase-detection algorithm, even to the point of reaching the same performance as in the case where no PN is present, offering better results than a state-of-the-art alternative. Further analysis of the results allow to draw some useful trade-offs respecting final performance and consumption of resources.

Compensation of Phase Noise in Massive-MIMO Uplink Communications Based on Expectation-Maximization Algorithm

TL;DR

This work tackles phase noise in uplink massive MIMO by introducing an EM-based, iterative receiver that jointly detects PN and demodulates data under a general oscillator-to-antenna mapping. The method alternates between a phase estimator with adaptive step size and a linear MMSE MIMO demodulator, leveraging pilot-aided initialization and hard symbol estimates within the EM framework. A Bayesian Cramér-Rao bound is derived to benchmark PN-MSE, and extensive simulations show substantial gains in both MSE and BER, often approaching PN-free performance and outperforming a GEC-SR-based alternative across diverse channel conditions, including imperfect CSI and Rician fading. The results reveal important trade-offs between performance, iteration count, and computational latency, offering guidelines for practical deployment and highlighting the method's robustness to realistic PN models such as PN masks.

Abstract

Phase noise (PN) is a major disturbance in MIMO systems, where the contribution of different oscillators at the transmitter and the receiver side may degrade the overall performance and offset the gains offered by MIMO techniques. This is even more crucial in the case of massive MIMO, since the number of PN sources may increase considerably. In this work, we propose an iterative receiver based on the application of the expectation-maximization algorithm. We consider a massive MIMO framework with a general association of oscillators to antennas, and include other channel disturbances like imperfect channel state information and Rician block fading. At each receiver iteration, given the information on the transmitted symbols, steepest descent is used to estimate the PN samples, with an optimized adaptive step size and a threshold-based stopping rule. The results obtained for several test cases show how the bit error rate and mean square error can benefit from the proposed phase-detection algorithm, even to the point of reaching the same performance as in the case where no PN is present, offering better results than a state-of-the-art alternative. Further analysis of the results allow to draw some useful trade-offs respecting final performance and consumption of resources.
Paper Structure (16 sections, 1 theorem, 29 equations, 12 figures, 3 tables)

This paper contains 16 sections, 1 theorem, 29 equations, 12 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related work
  3. System description
  4. Overall channel model
  5. Pilot transmission scheme and channel estimation
  6. The EM-based receiver
  7. Phase estimator
  8. Step size optimization and stopping rule
  9. MIMO demodulator
  10. Bayesian Cramer-Rao bound
  11. Simulation results
  12. MSE simulation results
  13. BER simulation results
  14. Average number of receiver iterations and steepest-descent steps
  15. Algorithm complexity and latency
  16. ...and 1 more sections

Key Result

Proposition 1

For the channel model in eq:cha, if $\rho \ll 2\pi$, the BIM ${\bf M}$ defined in eq:info_matrix is given by where ${\bf M}_0 = {\bf J}\mathsf{^T} \widetilde{{\bf M}}_0 {\bf J}$ and ${\bf M}_1 = {\bf J}\mathsf{^T} \widetilde{{\bf M}}_1 {\bf J}$, ${\bf J}$ being the Jacobian of the transformation from sum processes to atomic processes at a given time $n$, $\widetilde{{\bf M}}_1 = -\frac{1}{\rho^2}

Figures (12)

  • Figure 1: Overall scheme of the MIMO channel and oscillator/antenna setup for the massive MIMO system.
  • Figure 2: Frame structure for the proposed massive MIMO transmission scheme. CP: channel estimation pilots. P: phase-noise estimation pilots.
  • Figure 3: Structure of the iterative receiver.
  • Figure 4: MSE results for perfect CSI. (a) Threshold $\theta=10^{-6}$ and $10$ receiver iterations. (b) Threshold $\theta=10^{-6}$ and $1$ receiver iteration. (c) Threshold $\theta=10^{-7}$ and $10$ receiver iterations. (d) Threshold $\theta=10^{-4}$ and $10$ receiver iterations.
  • Figure 5: MSE results for perfect and non-perfect CSI. In all the cases, $\theta=10^{-6}$ and we have performed $10$ receiver iterations. (a) Perfect CSI. (b) $E_C/E_s=5$ dB. (c) $E_C/E_s=10$ dB. (d) $E_C/E_s=15$ dB. (e) $E_C/E_s=20$ dB.
  • ...and 7 more figures

Theorems & Definitions (1)

  • Proposition 1