The Bit Error Performance and Information Transfer Rate of SPAD Array Optical Receivers

In this paper the photon counting characteristics, the information rate and the bit error performance of single-photon avalanche diode (SPAD) arrays are investigated. It is shown that for sufficiently large arrays, the photocount distribution is well approximated by a Gaussian distribution with dead-time-dependent mean and variance. Because of dead time, the SPAD array channel is subject to counting losses, part of which are due to inter-slot interference (ISI) distortions. Consequently, this channel has memory. The information rate of this channel is assessed. Two auxiliary discrete memoryless channels (DMCs) are proposed which provide upper and lower bounds on the SPAD array information rate. It is shown that in sufficiently large arrays, ISI is negligible and the bounds are tight. Under such conditions, the SPAD array channel is precisely modelled as a memoryless channel. A discrete-time Gaussian channel with input-dependent mean and variance is adopted and the properties of the capacity-achieving input distributions are studied. Using a numerical algorithm, the information rate and the capacity-achieving input distributions, subject to peak and average power constraints are obtained. Furthermore, the bit error performance of a SPAD-based system with on-off keying (OOK) is evaluated for various array sizes, dead times and background count levels.