Performance Scaling Laws for PD Array-based Receivers in IM/DD Optical Wireless Communication Systems

TL;DR

This paper addresses performance scaling laws for PD array-based receivers in IM/DD optical wireless systems by explicitly accounting for the square-law relationship between optical and electrical powers, i.e., $P^{\mathrm{Rx,E}}_m = (R_{\mathrm{PD}} P^{\mathrm{Rx,O}}_m)^2$ and $\gamma_{\mathrm{mrc}} = \sum_{m=1}^M \gamma_m$. An analytical framework introduces a loss factor $\beta$ and an area-bandwidth trade-off to compare PD arrays against a single reference PD across Gaussian, $LG_{10}$, and uniform beam patterns. Key findings show that PD arrays provide gains only for sufficiently narrow beams and above an SNR threshold, and that increasing $M$ alone does not generally exceed the single-PD performance without optimizing beam pattern, received power, and PD placement. The results yield practical design guidelines, including when to convert higher-order modes to a fundamental Gaussian beam and why joint optimization is essential for realizing high-bandwidth PD-array receivers in next-generation IM/DD OWC.

Abstract

We study the performance scaling laws for electrical-domain combining in photodetector (PD) array-based receivers employing intensity modulation and direct detection, taking into account the inherent square-law relationship between the optical and electrical received powers. The performance of PD array-based systems is compared, in terms of signal-to-noise ratio (SNR) and achievable rate, to that of a reference receiver employing a single PD. Analytical and numerical results show that PD arrays provide performance gains for sufficiently narrow beams and above an SNR threshold. Furthermore, increasing the number of PDs alone does not enhance performance, and joint optimization of beam pattern, transverse electromagnetic mode, received power, and PD positions is necessary. Our model and derived insights provide practical guidelines and highlight the trade-offs for the design of next-generation high-bandwidth PD array receivers.

Figures (4)

• Figure 1: Illustration of the beam power distribution for Gaussian and LG$_{10}$ beams with $G=3$ rings and $\rho = 0.5$ on a PD array employing the optimal hexagonal packing. PD marked with a $\star$ denote the six corner PD in each ring.
• Figure 2: Minimum required loss factor $\beta_{\mathrm{min}}^2$ as a function of $M$ for different SNR, based on (\ref{['eqn:condopt']}).
• Figure 3: Loss factor $\beta^2$ versus the number of photodetectors $M$ for Gaussian and LG$_{10}$ beams with fixed PD-radius-to-beam-waist ratio $\rho.$
• Figure 4: Loss factor $\beta^2$ versus the number of photodetectors $M$ when the PD radius scales inversely with array size, $\rho=\rho_0/(G+1).$