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Hardware-Impaired Rician-Faded Cell-Free Massive MIMO Systems With Channel Aging

Venkatesh Tentu, Dheeraj N Amudala, Anish Chattopadhyay, Rohit Budhiraja

TL;DR

This work derives a closed-form spectral efficiency (SE) expression for this system, and proposes two novel optimization techniques to optimize the non-convex SE metric by exploiting the minorization-maximization (MM) method.

Abstract

We study the impact of channel aging on the uplink of a cell-free (CF) massive multiple-input multiple-output (mMIMO) system by considering i) spatially-correlated Rician-faded channels; ii) hardware impairments at the access points and user equipments (UEs); and iii) two-layer large-scale fading decoding (LSFD). We first derive a closed-form spectral efficiency (SE) expression for this system, and later propose two novel optimization techniques to optimize the non-convex SE metric by exploiting the minorization-maximization (MM) method. The first one requires a numerical optimization solver, and has a high computation complexity. The second one with closed-form transmit power updates, has a trivial computation complexity. We numerically show that i) the two-layer LSFD scheme effectively mitigates the interference due to channel aging for both low- and high-velocity UEs; and ii) increasing the number of AP antennas does not mitigate the SE deterioration due to channel aging. We numerically characterize the optimal pilot length required to maximize the SE for various UE speeds. We also numerically show that the proposed closed-form MM optimization yields the same SE as that of the first technique, which requires numerical solver, and that too with a much reduced time-complexity.

Hardware-Impaired Rician-Faded Cell-Free Massive MIMO Systems With Channel Aging

TL;DR

This work derives a closed-form spectral efficiency (SE) expression for this system, and proposes two novel optimization techniques to optimize the non-convex SE metric by exploiting the minorization-maximization (MM) method.

Abstract

We study the impact of channel aging on the uplink of a cell-free (CF) massive multiple-input multiple-output (mMIMO) system by considering i) spatially-correlated Rician-faded channels; ii) hardware impairments at the access points and user equipments (UEs); and iii) two-layer large-scale fading decoding (LSFD). We first derive a closed-form spectral efficiency (SE) expression for this system, and later propose two novel optimization techniques to optimize the non-convex SE metric by exploiting the minorization-maximization (MM) method. The first one requires a numerical optimization solver, and has a high computation complexity. The second one with closed-form transmit power updates, has a trivial computation complexity. We numerically show that i) the two-layer LSFD scheme effectively mitigates the interference due to channel aging for both low- and high-velocity UEs; and ii) increasing the number of AP antennas does not mitigate the SE deterioration due to channel aging. We numerically characterize the optimal pilot length required to maximize the SE for various UE speeds. We also numerically show that the proposed closed-form MM optimization yields the same SE as that of the first technique, which requires numerical solver, and that too with a much reduced time-complexity.
Paper Structure (21 sections, 9 theorems, 64 equations, 5 figures, 3 tables, 1 algorithm)

This paper contains 21 sections, 9 theorems, 64 equations, 5 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Channel model
  4. Uplink training
  5. Uplink Transmission
  6. Spectral efficiency Analysis
  7. SE Optimization of Hardware-Impaired CF System With Channel Aging
  8. Minorization-maximization approach
  9. Closed-form MM approach
  10. Simulation Results
  11. Validation of closed-form SE
  12. Impact of velocity on the length of the resource block $\tau_c$
  13. Impact of channel estimation on SE
  14. Impact of number of APs and UEs on SE
  15. Effect of channel aging on the power of desired and interference terms
  16. ...and 6 more sections

Key Result

Theorem 1

For a hardware-impaired CF mMIMO system with spatially-correlated Rician fading and phase-shifts, the linear minimum mean square error (LMMSE) estimate of $\mathbf{h}_{mk}[\lambda]$ is given as The matrix $\boldsymbol{\Psi}_{mk} = \!(\sum_{i\in \mathcal{P}_k}\!\mathbf{A}_{m} \alpha_{d,i}(1+\kappa_{t,i}^{2})\tilde{p}_{i}\mathbf{\overline{R}}_{mk}\mathbf{A}_{m}^H \! +\!\left(\mathbf{B}_{a}^{m}+ \ka

Figures (5)

  • Figure 1: Structure of resource block of length $\tau_c$ time instants.
  • Figure 2: LSFD architecture for CF mMIMO system.
  • Figure 3: a) Validation of closed-form SE; b) SE versus time instant $n$; c) SE versus the length of resource block $\tau_c$; and d) SE versus pilot length $\tau_p$.
  • Figure 4: a) Comparison of LSFD and SLD for different UE configuration; Effect of channel aging on the power of desired and interference terms for b) LSFD; and c) SLD; and d) SE versus number of antenna per AP for different UE velocities.
  • Figure 5: a) Comparison of different ADC architectures; b) SE versus UE transmit power; c) SE versus time instant $n$; d) CPU and average run time for different optimization techniques.

Theorems & Definitions (12)

  • Theorem 1
  • Corollary 1
  • Remark 1
  • Lemma 1
  • Theorem 2
  • Lemma 2
  • Corollary 2
  • Corollary 3
  • Remark 2
  • Lemma 3
  • ...and 2 more