MIMO Capacity Analysis and Channel Estimation for Electromagnetic Information Theory

TL;DR

The paper addresses the discrete-continuous gap in electromagnetic information theory (EIT) by establishing PSWF-based discrete–continuous correspondence lemmas that link practical discrete MIMO systems to continuous operator models. This enables applying a PSWF ergodic-capacity bound to continuous-field MIMO architectures (CAP-MIMO, XL-MIMO) and reveals a capacity saturation phenomenon with a finite upper bound, rather than unbounded growth with aperture. Building on this framework, the authors design a PSWF-based MIMO channel estimator (PSWF-CE) that outperforms traditional MMSE and compressed sensing approaches by exploiting bandlimited structure in the wavenumber domain, demonstrated via simulations at 3.5 GHz. The work provides both fundamental limits and practical estimation gains, offering a unified view of capacity saturation and a principled approach to discrete-channel estimation in electromagnetically compliant MIMO systems.

Abstract

Electromagnetic information theory (EIT) is an interdisciplinary subject that serves to integrate deterministic electromagnetic theory with stochastic Shannon's information theory. Existing EIT analysis operates in the continuous space domain, which is not aligned with the practical algorithms working in the discrete space domain. This mismatch leads to a significant difficulty in application of EIT methodologies to practical discrete space systems, which is called as the discrete-continuous gap in this paper. To bridge this gap, we establish the discrete-continuous correspondence with a prolate spheroidal wave function (PSWF)-based ergodic capacity analysis framework. Specifically, we state and prove some discrete-continuous correspondence lemmas to establish a firm theoretical connection between discrete information-theoretic quantities to their continuous counterparts. With these lemmas, we apply the PSWF ergodic capacity bound to advanced MIMO architectures such as continuous-aperture MIMO (CAP-MIMO) and extremely large-scale MIMO (XL-MIMO). From this PSWF capacity bound, we discover the capacity saturation phenomenon both theoretically and empirically. Although the growth of MIMO performance is fundamentally limited in this EIT-based analysis framework, we reveal new opportunities in MIMO channel estimation by exploiting the EIT knowledge about the channel. Inspired by the PSWF capacity bound, we utilize continuous PSWFs to improve the pilot design of discrete MIMO channel estimators, which is called as the PSWF channel estimator (PSWF-CE). Simulation results demonstrate improved performances of the proposed PSWF-CE, compared to traditional minimum mean squared error (MMSE) and compressed sensing-based estimators.

Figures (7)

• Figure 1: Organization of this paper.
• Figure 2: The ergodic capacity saturation phenomenon of H-MIMO with $L_t=L_r=1\,{\rm m}$, $P_{\rm T}/\sigma_z^2 = 10\,{\rm dB}$, and 300 Monte Carlo trials.
• Figure 3: The ergodic capacity saturation phenomenon of XL-MIMO with $\lambda_c/2$ antenna spacing, $P_{\rm T}/\sigma_z^2 = 10\,{\rm dB}$, and 300 Monte Carlo trials.
• Figure 4: The NMSE performance of MIMO channel estimators with aperture $L_t = L_r = 0.5\,{\rm [m]}$ and $N_{\rm P}=40$. The number of Monte Carlo trials is 100.
• Figure 5: The NMSE performance of MIMO channel estimators with aperture $L_t = L_r = 1.0\,{\rm [m]}$ and $N_{\rm P} = 120$. The number of Monte Carlo trials is 100.

Theorems & Definitions (13)

• Remark 1
• Theorem 1: Simultaneous orthogonalization ihara1993information
• Remark 2
• Definition 1: $k$-dimensional PSWFs
• Theorem 2: Properties of 1D-PSWFs nam2014capacity
• Lemma 1
• Definition 2: Contraction operator
• Proposition 1: Discrete spectral dominance horn2012matrix
• Proposition 2: Continuous spectral dominance
• Lemma 2: Capacity dominance