Statistical Modeling of Single-Photon Avalanche Diode Receivers for Optical Wireless Communications

In this paper, a comprehensive analytical approach is presented for modeling the counting statistics of active quenching and passive quenching single-photon avalanche diode (SPAD) detectors. It is shown that, unlike ideal photon counting receiver for which the detection process is described by a Poisson arrival process, photon counts in practical SPAD receivers do not follow a Poisson distribution and are highly affected by the dead time caused by the quenching circuit. Using the concepts of renewal theory, the exact expressions for the probability distribution and moments (mean and variance) of photocounts in the presence of dead time are derived for both active quenching and passive quenching SPADs. The derived probability distributions are validated through Monte Carlo simulations and it is demonstrated that the moments match with the existing empirical models for the moments of SPAD photocounts. Furthermore, an optical communication system with on-off keying and binary pulse position modulation is considered and the bit error performance of the system for different dead time values and background count levels is evaluated

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

Time-Gated Photon Counting Receivers for Optical Wireless Communication

Photon counting detectors such as single-photon avalanche diode (SPAD) arrays are commonly considered for reliable optical wireless communication at power limited regimes. However, SPAD-based receivers suffer from significant dead time induced intersymbol interference (ISI) especially when the incident photon rate is relatively high and the dead time is comparable or even larger than the symbol duration, i.e., sub-dead-time regime. In this work, we propose a novel time-gated SPAD receiver to mitigate such ISI effects and improve the communication performance. When operated in the gated mode, the SPAD can be activated and deactivated in well-defined time intervals. We investigate the statistics of the detected photon count for the proposed time-gated SPAD receiver. It is demonstrated that the gate-ON time interval can be optimized to achieve the best bit error rate (BER) performance. Our extensive performance analysis illustrates the superiority of the time-gated SPAD receiver over the traditional free-running receiver in terms of the BER performance and the tolerance to background light

Single-Photon Avalanche Diodes in CMOS Technologies for Optical Communications

As optical communications may soon supplement Wi-Fi technologies, a concept known as visible light communications (VLC), low-cost receivers must provide extreme sensitivity to alleviate attenuation factors and overall power usage within communications link budgets. We present circuits with an advantage over conventional optical receivers, in that gain can be applied within the photodiode thus reducing the need for amplification circuits. To achieve this, single-photon avalanche diodes (SPADs) can be implemented in complementary metal-oxide-semiconductor (CMOS) technologies and have already been investigated in several topologies for VLC. The digital nature of SPADs removes the design effort used for low-noise, high-gain but high-bandwidth analogue circuits. We therefore present one of these circuit topologies, along with some common design and performance metrics. SPAD receivers are however not yet mature prompting research to take low-level parameters up to the communications level

A SPAD-Based Photon Detecting System for Optical Communications

A small array of single photon avalanche detectors (SPADs) has been designed and fabricated in a standard 0.18 μm CMOS process to test a new photon detecting system for optical communications. First numerical results are presented which show that using arrays of SPADs reduces the optical power density required at the receiver. Experimental results then show that the new system preserves the photon counting ability of the SPADs. Finally a simple method is presented which can be used to estimate the size of array needed to achieve a particular target bit error rate at a specific optical power density. Together these results indicate that by replacing the avalanche photodiode in a receiver with the new system it will be possible to count the received photons

SPAD-Array Contention Signal and Noise Model Suitable for Multilevel Modulation Schemes with Signal Processing

The first signal model for a single photon avalanche diode (SPAD)-array communication receiver for multilevel modulation schemes is reported. This paper proposes a novel, generalised SPAD array signal and noise model for both digital and analogue, synchronous and asynchronous SPAD readout arrays, which includes the competition between the input photons, dark counts and after-pulsing counts. With this contention signal and noise model, multilevel signals including the signal variation after distortion or equalisation can be evaluated. Also, we report the first numerical investigation for SPAD-based, high data rate, free space, visible light communication using higher order pulse amplitude modulation (PAM) with matched filter, linear and non-linear Volterra post-equalization. Simulations have been carried out to analyze and compare the bit error rate (BER) performances under a variety of conditions. The model is verified by comparison with published experimental results.UK EPSRC via the TOWS project (EP/S016570/1