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A Spatially Non-stationary Fading Channel Model for Simulation and (Semi-) Analytical Study of ELAA-MIMO

Jiuyu Liu, Yi Ma, Rahim Tafazolli

TL;DR

A novel spatially non-stationary fading channel model is proposed for multiple-input multiple-output (MIMO) system with extremely-large aperture service-array (ELAA) that incorporates three key factors which cause the channel spatial non- stationarity: link-wise path-loss, shadowing effect and line-of-sight (LoS)/non-LoS state.

Abstract

In this paper, a novel spatially non-stationary fading channel model is proposed for multiple-input multiple-output (MIMO) system with extremely-large aperture service-array (ELAA). The proposed model incorporates three key factors which cause the channel spatial non-stationarity: 1) link-wise path-loss; 2) shadowing effect; 3) line-of-sight (LoS)/non-LoS state. With appropriate parameter configurations, the proposed model can be used to generate computer-simulated channel data that matches the published measurement data from practical ELAA-MIMO channels. Given such appealing results, the proposed fading channel model is employed to study the cumulative distribution function (CDF) of ELAA-MIMO channel capacity. For all of our studied scenarios, it is unveiled that the ELAA-MIMO channel capacity obeys the skew-normal distribution. Moreover, the channel capacity is also found close to the Gaussian or Weibull distribution, depending on users' geo-location and distribution. More specifically, for single-user equivalent scenarios or multiuser scenarios with short user-to-ELAA distances (e.g., 1 m), the channel capacity is close to the Gaussian distribution; and for others, it is close to the Weibull distribution. Finally, the proposed channel model is also employed to study the impact of channel spatial non-stationarity on linear MIMO receivers through computer simulations. The proposed fading channel model is available at https://github.com/ELAA-MIMO/non-stationary-fading-channel-model.

A Spatially Non-stationary Fading Channel Model for Simulation and (Semi-) Analytical Study of ELAA-MIMO

TL;DR

A novel spatially non-stationary fading channel model is proposed for multiple-input multiple-output (MIMO) system with extremely-large aperture service-array (ELAA) that incorporates three key factors which cause the channel spatial non- stationarity: link-wise path-loss, shadowing effect and line-of-sight (LoS)/non-LoS state.

Abstract

In this paper, a novel spatially non-stationary fading channel model is proposed for multiple-input multiple-output (MIMO) system with extremely-large aperture service-array (ELAA). The proposed model incorporates three key factors which cause the channel spatial non-stationarity: 1) link-wise path-loss; 2) shadowing effect; 3) line-of-sight (LoS)/non-LoS state. With appropriate parameter configurations, the proposed model can be used to generate computer-simulated channel data that matches the published measurement data from practical ELAA-MIMO channels. Given such appealing results, the proposed fading channel model is employed to study the cumulative distribution function (CDF) of ELAA-MIMO channel capacity. For all of our studied scenarios, it is unveiled that the ELAA-MIMO channel capacity obeys the skew-normal distribution. Moreover, the channel capacity is also found close to the Gaussian or Weibull distribution, depending on users' geo-location and distribution. More specifically, for single-user equivalent scenarios or multiuser scenarios with short user-to-ELAA distances (e.g., 1 m), the channel capacity is close to the Gaussian distribution; and for others, it is close to the Weibull distribution. Finally, the proposed channel model is also employed to study the impact of channel spatial non-stationarity on linear MIMO receivers through computer simulations. The proposed fading channel model is available at https://github.com/ELAA-MIMO/non-stationary-fading-channel-model.
Paper Structure (22 sections, 5 theorems, 50 equations, 10 figures, 5 tables, 2 algorithms)

This paper contains 22 sections, 5 theorems, 50 equations, 10 figures, 5 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Motivation of This Work
  3. State-of-the-Art Analysis
  4. Contribution of This Work
  5. Novel spatially Non-stationary Fading Channel Model for ELAA-MIMO
  6. Generating LoS/NLoS State for RUs ($\hbox{\boldmath $\beta$}_n\in\mathbf{\Phi}$)
  7. Generating LoS/NLoS State for non-RUs ($\hbox{\boldmath $\beta$}_k\in\overline{\mathbf{\Phi}}$)
  8. Channel Normalization
  9. Showcases of the Proposed spatially Non-stationary Fading Channel Model
  10. CDF of ELAA-MIMO Channel Capacity with Massive Service-Antennas
  11. MIMO Channel Capacity and Statistical Behavior
  12. CDF of The ELAA-MIMO Channel Capacity with The Proposed Model
  13. Parametric Fitting of The ELAA-MIMO Channel Capacity
  14. Linear Regression of Every Element in $\widehat{\hbox{\boldmath $\theta$}}$
  15. Numerical Results and Discussion
  16. ...and 7 more sections

Key Result

Theorem 1

Suppose that $\beta_\ell, \ell\in\{0,...,M-1\},$ obeys the Bernoulli distribution: where $\varrho_\ell=p(\beta_\ell=1)$. The probability mass function (PMF) of $\beta_m,~_{\forall m\neq\ell},$ is $\mathcal{B}(\beta_m;\varrho_m)$ with $\varrho_m$ given by where $\Delta_{\ell,m}$ is the distance between two service-antennas indexed by $\ell, m$, respectively, and $d_\textsc{los}$ is the correlatio

Figures (10)

  • Figure 1: An example of linear Wyner-type model of ELAA-MIMO system. In the proposed channel model, NLoS links can also experience the issue of visible region when the RSS of a link exceeds a certain threshold.
  • Figure 2: LoS/NLoS state and RSS from UTs to ELAA antennas. UT $\texttt{\#}1$ and UT $\texttt{\#}10$ are RUs and UT $\texttt{\#} 2$ - $\texttt{\#} 9$ are non-RUs. (a): the LoS/NLoS state of every link. (b): the RSS (normalized by the transmitted power) heat map.
  • Figure 3: Comparison of $\mathbf{H}\mathbf{H}^H$ intensity (normalized by the maximum element) between (a) the measured results in Harris2016 and (b) the proposed ELAA channel model. The absolute distance between (a) and (b) is shown in (c).
  • Figure 4: Comparison of channel correlations between (a) the measured results in 7063445 and (b) the proposed ELAA channel model. The absolute distance between (a) and (b) is shown in (c).
  • Figure 5: Standard deviation ($\sigma_{T}$) of the channel capacity. $\gamma_o = 10$$\mathrm{dB}$; $N = 20$; $d_{\perp} = 50$ m; and $T=10,000$.
  • ...and 5 more figures

Theorems & Definitions (6)

  • Definition 1
  • Theorem 1
  • Corollary 1.1: Corollary 1 in Liu2021
  • Theorem 2
  • Corollary 2.1
  • Corollary 2.2