Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

MMSE Channel Estimation in Fading MIMO Gaussian Channels With Blockage: A Novel Lower Bound via Poincaré Inequality

Mohammadreza Bakhshizadeh Mohajer, Luca Barletta, Daniela Tuninetti, Alessandro Tomasoni, Daniele Lo Iacono, Fabio Osnato

TL;DR

A new lower bound based on a Poincare inequality is proposed and applied to fading MIMO AWGN channels with blockage probability, and the behavior of the lower bound at high SNR is precisely characterized.

Abstract

Integrated sensing and communication is regarded as a key enabler for next-generation wireless networks. To optimize the transmitted waveform for both sensing and communication, various performance metrics must be considered. This work focuses on sensing, and specifically on the mean square error (MSE) of channel estimation. Given the complexity of deriving the MSE, the Bayesian Cramer-Rao Bound (BCRB) is commonly recognized as a lower bound on the minimum MSE. However, the BCRB is not applicable to channels with discrete or mixed distributions. To address this limitation, a new lower bound based on a Poincaré inequality is proposed and applied to fading MIMO AWGN channels with blockage probability, and the behavior of the lower bound at high SNR is precisely characterized.

MMSE Channel Estimation in Fading MIMO Gaussian Channels With Blockage: A Novel Lower Bound via Poincaré Inequality

TL;DR

A new lower bound based on a Poincare inequality is proposed and applied to fading MIMO AWGN channels with blockage probability, and the behavior of the lower bound at high SNR is precisely characterized.

Abstract

Integrated sensing and communication is regarded as a key enabler for next-generation wireless networks. To optimize the transmitted waveform for both sensing and communication, various performance metrics must be considered. This work focuses on sensing, and specifically on the mean square error (MSE) of channel estimation. Given the complexity of deriving the MSE, the Bayesian Cramer-Rao Bound (BCRB) is commonly recognized as a lower bound on the minimum MSE. However, the BCRB is not applicable to channels with discrete or mixed distributions. To address this limitation, a new lower bound based on a Poincaré inequality is proposed and applied to fading MIMO AWGN channels with blockage probability, and the behavior of the lower bound at high SNR is precisely characterized.

Paper Structure

This paper contains 10 sections, 5 theorems, 55 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Poincaré Lower Bound
  3. Non-Canonical Exponential Family
  4. Conditional Poincaré Inequality
  5. MMSE and the Poincaré Lower Bound
  6. Channels with Blockage Probability
  7. System Model
  8. Real-Valued Scalar Model
  9. Vector Model
  10. Conclusion

Key Result

Proposition 1

For the exponential family defined in eq:exp_family we have that where $\mathbf{x} \in \mathcal{X}$ and $\mathbf{y} \in \mathcal{Y}$.

Figures (2)

  • Figure 1: Poincaré lower bound in \ref{['eq:LB_p_on_off']}, MMSE in \ref{['eq:MMSE_scalar']}, and LMMSE in \ref{['eq:LMMSE_scalar']} for different values of $\sigma_{\rm s}^2$ with $\mathsf{X}=1$, $\alpha=0.4$, and $\sigma_h^2=1$. For each value of $\sigma_{\rm s}^2$, the simulations are run for $10^8$ Monte Carlo trials.
  • Figure 2: Poincaré lower bound \ref{['eq:Poi_bound']}, MMSE \ref{['eq:MMSE_vector_case']}, and LMMSE \ref{['eq:LMMSE_vector_case']} for $100$ values of $\sigma_{\rm s}^2$, $M = N = T = 4$, $\alpha = 0.4$, $\frac{\sigma_{\mathsf{H}}^2}{2} = \frac{1}{2}$, and $\mathsf{C}_{\mathbf{X}} = I$. For each value of $\sigma_{\rm s}$, the simulations are run for $10^8$ Monte Carlo trials.

Theorems & Definitions (5)

  • Proposition 1
  • Proposition 2
  • Theorem 1
  • Theorem 2
  • Lemma 1