Taming the Bessel Landscape: Joint Antenna Position Optimization for Spatial Decorrelation in Fluid MIMO Systems

Abstract

When the concept of fluid antenna system (FAS) is applied to multiple-input multiple-output (MIMO) systems, this gives rise to MIMO-FAS, a.k.a.~fluid MIMO. Under rich scattering, the spatial correlation matrices are governed by the zeroth-order Bessel function $J_0(\cdot)$ through the continuously adjustable antenna positions, creating a highly non-convex landscape for optimization with fluctuating local optima -- the \emph{Bessel landscape}. In this paper, we tackle the joint transmitter (TX) and receiver (RX) antenna position optimization problem in fluid MIMO to maximize the ergodic capacity by shaping this landscape. Using Kronecker channel decomposition, we firstly develop a suite of analytical results that expose the problem's intrinsic structure: (i) a high signal-to-noise ratio (SNR) capacity approximation that decomposes the objective into separable log-determinant terms of the TX and RX correlation matrices, $\mathbf{R}_T$ and $\mathbf{R}_R$, respectively, (ii) a closed-form capacity loss bound linking $\det(\mathbf{R}_T)\det(\mathbf{R}_R)$ to the performance gap relative to the independent and identically distributed (i.i.d.) ideal MIMO channel, and (iii) the globally optimal inter-element spacing when the number of fluid elements at the TX is $N=2$ at the first zero of $J_0$. Guided by these insights, we propose two algorithms within an alternating optimization (AO) framework. The first algorithm is AO with particle swarm optimization (PSO) which deploys a particle swarm to explore the Bessel landscape globally without gradient information. Then in the second method, we use successive convex approximation (SCA) to obtain the gradient in closed form via $J_1(\cdot)$ to construct convex surrogates for orders-of-magnitude faster convergence.

Figures (10)

• Figure 1: Convergence of the proposed AO-PSO algorithm at three SNR levels ($10$, $20$, and $30$ dB). The $x$-axis starts at $k=0$, which represents the ergodic capacity at the initial uniform-spacing positions before any optimization. With weakened PSO parameters ($Z=10$ particles, $I_{\rm PSO}=20$ iterations per AO step), the algorithm exhibits gradual improvement over approximately $5$--$8$ outer AO iterations before stabilizing, confirming the monotonic convergence guaranteed by Proposition \ref{['prop:highSNR']}. Moreover, higher SNR yields a larger absolute gain from optimization because the capacity is more sensitive to the eigenvalue distribution of $\mathbf{R}_T$ and $\mathbf{R}_R$ at high SNR.
• Figure 2: Ergodic capacity versus SNR for five schemes: the i.i.d. MIMO upper bound ($\mathbf{R}=\mathbf{I}$), the proposed AO-PSO with joint TX+RX FAS optimization, TX-FAS only (RX fixed at $d_{\min}$ spacing), random FAS (best of $50$ random feasible placements), and FPA (both TX and RX fixed at $d_{\min}$ spacing). The proposed AO-PSO consistently outperforms all other practical schemes, with a widening performance gap at higher SNR.
• Figure 3: Ergodic capacity versus normalized aperture size $A/\lambda=B/\lambda$ at SNR $=20$ dB. The i.i.d. MIMO upper bound (dashed) is the capacity achieved when $\mathbf{R}_T=\mathbf{R}_R=\mathbf{I}$. As the aperture grows, both AO-PSO and FPA improve, but AO-PSO achieves the upper bound more rapidly because it can spread the antennas to minimize spatial correlation.
• Figure 4: Optimized antenna positions (blue filled markers) versus uniform $d_{\min}=0.3\lambda$ spacing (orange dashed markers) at SNR $=20$ dB, $A/\lambda=B/\lambda=2$. The AO-PSO algorithm spreads antennas across the full aperture to maximize inter-element spacing and reduce spatial correlation.
• Figure 5: Ergodic capacity versus antenna spacing $d/\lambda$ for $N=M=2$ at SNR $\in\{10, 20, 30\}$ dB. Solid lines with markers: Monte-Carlo simulation ($S=3000$). Dashed lines: high-SNR approximation from Proposition \ref{['prop:highSNR']}. Dotted horizontal lines: i.i.d. MIMO upper bound. The vertical dashed line marks the optimal spacing $d^*\!\approx\!0.383\lambda$ from Proposition \ref{['prop:N2']}.

Theorems & Definitions (19)

• Remark 1: Properties of the Bessel Correlation Function
• Remark 2: Correlation as a Position Function
• Remark 3: Monte-Carlo Capacity Estimation
• Remark 4: Non-Convexity
• Remark 5: Capacity Bounds
• Remark 6: Decoupled TX/RX Structure
• Proposition 1: High-SNR Capacity Approximation
• Corollary 1: Capacity Loss
• Remark 7: Determinant Maximization Interpretation
• Proposition 2: Optimal Spacing for $N = 2$