23-01-2013, 10:53 AM
Avalanche Photodiode Arrays for Optical Communications Receivers
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ABSTRACT
An avalanche photodiode (APD) array for ground-based optical communications
receivers is investigated for the reception of optical signals through the turbulent
atmosphere. Kolmogorov phase screen simulations are used to generate realistic
spatial distributions of the received optical ¯eld. It is shown that use of an APD
array for pulse-position modulation detection can improve performance by up to
4 dB over single APD detection in the presence of turbulence, but that photoncounting
detector arrays yield even greater gains.
Introduction
Ground-based reception of optical signals from space su®ers from degradation of the optical phase
front caused by atmospheric turbulence, leading to a reduction in the e®ective diameter of the receiving
telescope and to random °uctuations of the point-spread function in the focal plane. A proportional
increase in the receiver's ¯eld of view in order to collect all of the signal also causes a corresponding increase
in the amount of interfering background radiation, resulting in degraded communications performance.
These problems may be mitigated through the use of an optical detector array assembly in the focal
plane that can adaptively select areas of higher signal density while ignoring areas predominated by
background noise. In [1], the performance of a detector array composed of photon-counting detectors
was evaluated and found to yield up to a 5 dB improvement over a conventional single-detector photoncounting
receiver. However, the current baseline receiver design for deep-space optical communication
utilizes readily available avalanche photodiode detectors (APDs) rather than photon-counting detector
arrays, which are still in the development stage at the wavelengths of interest for optical communications.
In this article, we extend some of the results obtained in [1] to the APD array case.
APD Output Model
In [1], the derivations of signal models for the single photon counter and the photon-counting array were
given in considerable detail in order to obtain the optimally weighted photon-counting array performance.
It was then shown that a suboptimal array (referred to as the adaptive synthesized detector or 0-1
subarray) consisting of the optimal number of unweighted array elements (i.e., weights of zero or one)
yielded performance very near to that of the optimally weighted array.
Adaptive Synthesd Arizeray
If we consider a rectangular array of detectors consisting of K£L detector elements, the optical signal
intensity incident upon each array element may be denoted
the APD modeling described above and assuming that each array element observes the sum of a signal
¯eld plus multimode Gaussian noise ¯eld with an average noise count per mode much less than one, the
outputs of the APD array may be modeled as conditionally independent Gaussian processes, conditioned
on the average signal intensity over each detector element [7,8]. Given the APD array-element observables,
the optimum maximum-likelihood detection scheme may be derived, consisting of a weighted sum of array
outputs [1]. We consider a simpler real-time suboptimum detector whose array weights are either zero or
one, i.e., the array-element outputs are either included or excluded at any given time in making a PPM
symbol decision. We therefore list the detector elements in decreasing order of average signal intensity, ¹nij ,
and compute the probability of error for the ¯rst detector element's signal intensity plus the background
incident upon that element, then form the sum of signal energies from the ¯rst two detector elements
(plus background for two detector elements), and so on, until the minimum error probability is reached.
Each set of detectors may be e®ectively considered to be a single detector, so that no weighting is applied
to account for variations in the signal distribution over the detector elements included in that set. The
set of detector elements that achieves the minimum probability of error is the best \synthesized single
detector" matched to the signal-intensity distribution. As in [1], a sample signal-intensity distribution may
be generated using Kolmogorov phase-screen algorithms [9]. Note also that the process of optimizing the
subarray requires calculation of the PPM symbol-error probability for each number of detectors, as well
as knowledge of signal and background energy levels. A practical real-time implementation of this array
detection scheme will involve additional parameter-estimation algorithms that have yet to be developed.