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Improved SINR Approximation for Downlink SDMA-based Networks with Outdated Channel State Information

Maria Cecilia Fernández Montefiore, Gustavo González, F. Javier López-Martínez, Fernando Gregorio

TL;DR

This work addresses SINR statistics for downlink MU-MIMO with outdated CSIT and RSMA. It introduces an enhanced Gamma-based SINR approximation that explicitly accounts for cross-correlation terms through a parameter $\mu_k$, yielding better variance estimation without increasing analytic complexity. The proposed model, with $X_G\sim\mathcal{G}(D,\Theta)$, provides accurate ergodic-rate predictions across a wide range of $N_t$, $K$, and CSIT staleness, and mitigates the optimistic bias of prior Gamma approaches in massive MIMO regimes. The results support RSMA as a robust DL strategy under CSIT imperfections and enable more reliable performance analysis for next-generation networks.

Abstract

Understanding the performance of multi-user multiple-input multiple-output (MU-MIMO) systems under imperfect channel state information at the transmitter (CSIT) remains a critical challenge in next-generation wireless networks. In this context, accurate statistical modeling of the signal-to-interference-plus-noise ratio (SINR) is essential for enabling tractable performance analysis of multi-user systems. This paper presents an improved statistical approximation of the SINR for downlink (DL) MU-MIMO systems with imperfect CSIT. The proposed model retains the analytical simplicity of existing approaches (e.g., Gamma-based approximations) while overcoming their limitations, particularly the underestimation of SINR variance. We evaluate the proposed approximation in the context of Rate-Splitting Multiple Access (RSMA)-enabled MIMO DL systems with outdated CSIT. The results demonstrate excellent accuracy across a wide range of system configurations, including varying numbers of users, antennas, and degrees of CSIT staleness.

Improved SINR Approximation for Downlink SDMA-based Networks with Outdated Channel State Information

TL;DR

This work addresses SINR statistics for downlink MU-MIMO with outdated CSIT and RSMA. It introduces an enhanced Gamma-based SINR approximation that explicitly accounts for cross-correlation terms through a parameter , yielding better variance estimation without increasing analytic complexity. The proposed model, with , provides accurate ergodic-rate predictions across a wide range of , , and CSIT staleness, and mitigates the optimistic bias of prior Gamma approaches in massive MIMO regimes. The results support RSMA as a robust DL strategy under CSIT imperfections and enable more reliable performance analysis for next-generation networks.

Abstract

Understanding the performance of multi-user multiple-input multiple-output (MU-MIMO) systems under imperfect channel state information at the transmitter (CSIT) remains a critical challenge in next-generation wireless networks. In this context, accurate statistical modeling of the signal-to-interference-plus-noise ratio (SINR) is essential for enabling tractable performance analysis of multi-user systems. This paper presents an improved statistical approximation of the SINR for downlink (DL) MU-MIMO systems with imperfect CSIT. The proposed model retains the analytical simplicity of existing approaches (e.g., Gamma-based approximations) while overcoming their limitations, particularly the underestimation of SINR variance. We evaluate the proposed approximation in the context of Rate-Splitting Multiple Access (RSMA)-enabled MIMO DL systems with outdated CSIT. The results demonstrate excellent accuracy across a wide range of system configurations, including varying numbers of users, antennas, and degrees of CSIT staleness.

Paper Structure

This paper contains 6 sections, 1 theorem, 32 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. System Model
  3. Main results
  4. Numerical Results
  5. Conclusion
  6. Proof of Lemma \ref{['lemma1']}

Key Result

Lemma 1

Let the random variable (RV) $X$ be defined as in eq:Xexpand. Then, $X\approx X_{\rm{G}}$ such that the RV $X_{\rm{G}} \sim \mathcal{G}(D,\Theta)$, with and where $\mu_k$ is:

Figures (3)

  • Figure 1: Empirical PDF of $X$ and approximated PDFs of $X_{\rm{G}}$ (Lemma 1) and $X_{\rm{D}}$Dizdar2021Zhu2024, for different values of $N_{\rm t}$, $K$, and $\epsilon$.
  • Figure 2: MSE for the Gamma approximations $X_{\rm{G}}$ (Lemma 1) and $X_{\rm{D}}$Dizdar2021, as a function of the ratio $N_{\rm t}/K$ for different values of $K=\{4,6,10\}$. Parameter values are: $\epsilon=0.5$, and 1.0e5 runs for MC simulations.
  • Figure 3: Ergodic sum-rate as a function of the power allocation factor $1-\alpha_{c}$. The exact sum-rate obtained by \ref{['eq:esr']}, in solid blue line, is compared to the sum-rates obtained by the proposed Gamma approximation $X_{\rm G}$ and the existing Gamma approximation $X_{\rm D}$ in Dizdar2021Zhu2024. The lower bound (LB) proposed in Dizdar2021 is also evaluated when using $X_{\rm G}$ and $X_{\rm D}$ approximations. Parameter values are $N_{\rm t}=16$, $K=4$, with $\epsilon=\{0.3,0.5\}$

Theorems & Definitions (5)

  • Lemma 1
  • proof
  • Remark 1
  • Remark 2
  • Remark 3