[Paper Review] Evaluation of the Spatial Consistency Feature in the 3GPP GSCM Channel Model

Martin Kurras, Sida Dai+2 more|arXiv (Cornell University)|Aug 10, 2018

Advanced MIMO Systems Optimization11 references6 citations

TL;DR

This paper evaluates the spatial consistency feature in the 3GPP Geometry-based Stochastic Channel Model (GSCM), which enhances correlation between small-scale fading parameters across spatially separated users. The feature ensures that angular parameters (AoA, AoD) and covariance matrices of users converge as distance decreases, with normalized metric $d_{ ext{CMD}}$ approaching 1 at 1 m for $d_ ext{λ} \ ext{≥q} 15$ m, confirming reliable user clustering for 5G MIMO systems.

ABSTRACT

Since the development of 4G networks, Multiple-Input Multiple-Output (MIMO) and later multiple-user MIMO became a mature part to increase the spectral efficiency of mobile communication networks. An essential part of simultaneous multiple-user communication is the grouping of users with complementing channel properties. With the introduction of Base Station (BS) with large amount of antenna ports, i.e. transceiver units, the focus in spatial precoding is moved from uniform to heterogeneous cell coverage with changing traffic demands throughout the cell and 3D beamforming. In order to deal with the increasing feedback requirement for Frequency-Division Duplex (FDD) systems, concepts for user clustering on second order statistics are suggested in both the scientific and standardization literature. Former 3rd Generation Partnership Project (3GPP) Geometry-based Stochastic Channel Model (GSCM) channel models lack the required spatial correlation of small-scale fading. Since the latest release of 3GPP Geometry-based Stochastic Channel Model this issue is claimed to be solved and hence our contribution is an evaluation of this spatial consistency feature.

Motivation & Objective

• To evaluate the spatial consistency feature introduced in the latest 3GPP GSCM to improve correlation of small-scale fading across users.
• To address the lack of spatial correlation in earlier GSCM versions, which hindered accurate user clustering for massive MIMO and coordinated transmission.
• To validate that the spatial consistency feature enables consistent user grouping based on second-order statistics in FDD systems.
• To quantify the impact of the decorrelation distance $d_\lambda$ on angular and covariance similarity between users.
• To support reliable performance evaluation of JSDM and similar user clustering schemes using the QuaDRiGa channel model.

Proposed method

• Simulates a 2-user scenario with one user moving toward another in a 3D urban macro environment using QuaDRiGa-based GSCM.
• Employs angular distance metrics $\Delta\phi$ and $\Delta\theta$ to measure differences in azimuth and elevation AoA across MPCs.
• Uses chordal distance $d_C(\mathbf{R}_1, \mathbf{R}_2)$ to compare covariance matrices of user channels, dependent on path loss and LSPs.
• Applies normalized metric $d_{\text{CMD}}$ to assess similarity of covariance matrices, with values from 0 (orthogonal) to 1 (identical).
• Varying $d_\lambda$ from 0 to 20 m to control spatial correlation of scattering cluster positions.
• Analyzes convergence of angular and covariance metrics as user separation decreases to 0 m.

Experimental results

Research questions

• RQ1 How does the spatial consistency feature affect angular differences (AoA, AoD) between two users as their distance decreases?
• RQ2 To what extent does the chordal distance $d_C$ between user covariance matrices decrease with decreasing user separation?
• RQ3 How does the normalized $d_{\text{CMD}}$ metric converge toward 1 as users approach each other, and what role does $d_\lambda$ play?
• RQ4 What is the residual similarity in covariance matrices when $d_\lambda = 0$ m, indicating no spatial consistency?
• RQ5 Can $d_{\text{CMD}}$ be used as a reliable threshold-based criterion for user clustering in JSDM or similar schemes?

Key findings

• The angular distance $\Delta\phi$ and $\Delta\theta$ between users decrease with decreasing separation, with a notable slope change at $d_\lambda = 5$ m.
• The chordal distance $d_C$ decreases toward zero as user separation drops, with a significant change in slope at $d_\lambda = 20$ m around 5 m separation.
• The normalized $d_{\text{CMD}}$ metric approaches 1 at approximately 1 m separation when $d_\lambda \geq 15$ m, indicating high covariance similarity.
• Even with $d_\lambda = 0$ m (no spatial consistency), $d_{\text{CMD}}$ saturates at $\approx 0.64$ due to correlation in large-scale parameters (K-factor, delays, spreads).
• The $d_{\text{CMD}}$ metric enables large-scale parameter-independent clustering thresholds, with $\epsilon_{\text{CMD}} = 0.95$ achievable at 1 m for $d_\lambda \geq 15$ m.
• The spatial consistency feature effectively enables reliable user clustering in FDD massive MIMO systems by ensuring coherent fading correlation across users.