Capacity Results for Multiple-Input Multiple-Output Optical Wireless Communication With Per-Antenna Intensity Constraints

TL;DR

This work studies the capacity of MIMO optical intensity channels under per-antenna peak and average constraints, formalized as 0 ≤ X_k ≤ 1 with E[X_k] = α_k, and extends to bounded-cost variants. By channel-reduction to a rank- r model and introducing a channel-graph concept, the authors prove that when the channel graph is strongly connected the strongest eigen-subchannel has positive gains, enabling a dominant rank-1 transmission perspective. They derive multiple capacity bounds using linear precoding, generalized entropy power inequalities, and QR-based receivers, and obtain an equivalent capacity expression for the rank-(n_T−1) case via convex-geometry arguments, along with max-entropy-based high-SNR bounds. The results are validated numerically in indoor VLC and outdoor fading scenarios, showing tight performance of the proposed schemes and bounds, and illustrating practical implications for per-antenna dimming and lighting control in VLC systems.

Abstract

In this paper, we investigate the capacity of a multiple-input multiple-output (MIMO) optical intensity channel (OIC) under per-antenna peak- and average-intensity constraints. We first consider the case where the average intensities of input are required to be equal to preassigned constants due to the requirement of illumination quality and color temperature. When the channel graph of the MIMO OIC is strongly connected, we prove that the strongest eigen-subchannel must have positive channel gains, which simplifies the capacity analysis. Then we derive various capacity bounds by utilizing linear precoding, generalized entropy power inequality, and QR decomposition, etc. These bounds are numerically verified to approach the capacity in the low or high signal-to-noise ratio regime. Specifically, when the channel rank is one less than the number of transmit antennas, we derive an equivalent capacity expression from the perspective of convex geometry, and new lower bounds are derived based on this equivalent expression. Finally, the developed results are extended to the more general case where the average intensities of input are required to be no larger than preassigned constants.

Figures (4)

• Figure 1: Room layout and receiver structure. Four LED fixtures are fixed in the ceiling of a $4\, \text{m} \times 4\, \text{m} \times 3.2 \,\text{m}$ room with LED coordinates (in the $xyz$ system) $\left(\pm 1, \pm 1, 3.2\right)$ (unit: m), and two PDs are placed on one side of the user equipment with PD coordinates (in the $x'y'z'$ system) $(\pm 0.05, 0 ,0 )$ (unit: m).
• Figure 2: Capacity bound with the receiver locating at $O$ (upper left), $P_1$ (upper right), $P_2$ (lower left), and $P_3$ (lower right). The involved capacity lower bounds \ref{['eq:linear_precoding']} and \ref{['eq:ec_oic_qr']} are optimized over all possible permutations of transmitters.
• Figure 3: Bounds on the ergodic capacity of a $6\times 4$ MIMO BC-OIC with $\bm{\alpha}=(0.4,0.4,0.3,0.3,0.2,0.2)^{\textnormal{\tiny T}}$ and lognormal fading. The involved lower bounds \ref{['eq:linear_precoding2']} are optimized over all possible permutations of transmitters.
• Figure 4: Probability density functions of maximum-entropy distributions for $2\times 1$ EC-OICs (upper) and $2\times 1$ BC-OICs (lower).

Theorems & Definitions (21)

• Remark 1
• Definition 1: Channel Graph
• Theorem 1: Positivity of Strongest Eigen-subchannel
• Example 1
• Theorem 2: chaabanrezkialouini18_2
• Corollary 1: chaabanrezkialouini18_2
• Proposition 1
• Proposition 2
• Lemma 1
• Proposition 3: GEPI-Based Lower Bound