Free-space optical (FSO) communications is an important technology that will be used for supporting high data-rates in the backhaul of next generation of wireless communication networks. In this paper, we have compared the probability of error performance of two types of receivers used in FSO today: a receiver based on a single detector, and a receiver based on an array of detectors. The performance of these two receivers is compared for a number of fusion algorithms for an array of detectors such as equal gain combiner (EGC), selection combiner (SC), switched combiner (SWC) and the maximal ratio combiner (MRC). From this study, we conclude that even though the array of detectors adds more noise in the suﬃcient statistic by virtue of large number of detectors, using more computationally expensive fusion algorithms (such as SC and MRC) can help us achieve a superior probability of error performance as opposed to a single-detector receiver for practical channel conditions. Index Terms Array of detectors, equal gain combiner, free-space optics, maximal ratio combiner, probability of error, selection combiner, single-detector, switched combiner. M. -C. Tsai, M. S. Bashir and M. -S. Alouini are with the King Abdullah University of Science and Technology (KAUST), Thuwal 23955- 6900, Kingdom of Saudi Arabia. e-mail: (mingcheng.tsai@kaust.edu.sa, salman.bashir@alumni.purdue.edu, slim.alouini@kaust.edu.sa). 2 I. I/n.sc/t.sc/r.sc/o.sc/d.sc/u.sc/c.sc/t.sc/i.sc/o.sc/n.sc Free-space optics is slated to become an enabler of high data-rates in the backhaul of next generation of wireless communication networks due to the availability of large chunks of unused spectrum in the optical domain of the electromagnetic spectrum [1]. However, due to the narrow beamwidth associated with the optical signal (the beamwdith angle is proportional toλ Dwhereλis the wavelength of light andDis diameter of transmit aperture), pointing and tracking requirements become more stringent for the performance of an FSO communications link. Thus, the pointing and tracking subsystems form an important part of an FSO communication system. At the receiver, the received light is focused on a detection element—which is either a single-detector or an array of detectors—that lies in the focal plane of the aperture lens. Typically, noncoherent energy detection ( intensity modulation/direct detection or IM/DD) scheme is used in FSO receivers because of its relative simplicity as opposed to coherent receivers. Typically, IM/DD based detector arrays are used in deep-space optical communications where the link distances are so long that the transmitted signal pulse is decoded based on a few received signal photons [2], [3]. Another reason for a low number of received signal photons is the phenomenon of “blocking” associated with avalanche photodetectors (APD) that are operated in Geiger mode as photon counters. The blocking occurs because the detection of the ﬁrst photon causes an avalanche of electrons due to high gain of an APD, and this avalanche has to be quenched by an avalanche recovery circuit, and the bias has to be restored, before the next incoming signal photon can be detected. Thus, the APD gets “blocked” for a few microseconds after a single photon detection before it is ready to detect the next incoming photon. Thus, for a deep space optical communication receiver, it makes sense to spread the beam energy over an array of individual detectors in order to minimize the eﬀect of blocking, and thereby increase the number of detected photons per pulse to improve the SNR. A single-detector IM/DD receiver based on a single PIN photodiode is typically used for short link terrestrial FSO systems where the received signal power is enough for the purpose of a satisfactory bit error rate performance. The PIN diodes are not as sensitive as an APD when it comes to the detection of low-energy pulses. However, they do a satisfactory job for moderate to high amounts of received signal power. For a more detailed comparison on these two types of detectors, a good reference is [4]. Fig. 1 shows the proﬁle of the Gaussian-approximated airy pattern in the focal plane, whereas Fig. 2 depicts an array of detectors and a single-detector receiver. 3 012345 Fig. 1. Proﬁle of the incident beam in the focal plane. Gaussian BeamArray of Detectors Detector Contours of Constant Beam Intensity Fig. 2. This ﬁgure shows an array of detectors (on the left) versus a single-detector receiver (right). A. Motivation Onemightaskthefollowingquestion:"ShouldonechooseasinglePINdetector,orshouldonechoosean array of PIN detectors for short-to-medium link FSO communications /one.supin order to minimize the probability of error?" The answer to this question depends on a number of factors. So, before we answer this question, it is important that we ﬁrst understand the pros and cons of an array of detectors versus a single-detector receiver. 1) Pros of a Single Detector Versus an Array of Detectors Let us initially look at some of the pros of a single-detector receiver as opposed to an array of detectors. Firstly, the bandwidth of the detector depends on its physical size or surface area [5]. A larger surface area leads to a larger junction capacitance which implies a slower response to the changing optical signal. Thus, in order to improve the switched response of the detector, it is important to reduce its size so that the detector can detect fast changes in the received optical signal. Additionally, a small detector also adds /one.supBy short-to-medium link lengths, we mean link distances anywhere between a few kilometers to a few hundred kilometers. 4 A/D Converter AmpliﬁerArrayCentroid BlockController Unit FSM Driver TelescopeFSM AssemblyBeam Splitter Incoming Beamα 1−α DetectorBeam Output Symbol Fig. 3. This ﬁgure shows the block diagram of a single-detector receiver. Only a fraction of received energy (denoted by α) goes into the data channel, and (1−α)ﬁnds its way into the tracking channel. The parameter αcan be varied between 0 and 1 by turning a knob on a variable beam splitter. less noise in the suﬃcient statistic (the amount of dark current and background radiation captured by a detector is proportional to its area). For an array of detectors, the number of detectors M,A AwhereA is the area of the detector array, and Ais the area per detector. The area of the array Adepends on the variance of the pointing error (also called jitter in the FSO literature) or the deviation of the beam about its mean position. The magnitude of the pointing error variance depends on the physical parameters of the channel: The larger the variance of the pointing error, the larger the area Arequired in order to eﬀectively capture all the beam energy. The area of each detector Ahas to be small enough in order to support a high enough data rate of symbol transmission on the channel. Thus, it may be that a large variance of the jitter or beam deviation may lead to a large number of detectors Min the array which may be too complex—both from the hardware as well as the computational resource perspectives—to realize. Secondly, an array of detectors will also add more noise in the suﬃcient statistic since each detector in the array will be adding background radiation/thermal noise into the total noise power. In order to counter this noise resulting from each detector, a fusion algorithm—such as a maximal ratio combiner or a selection combiner—may be used that will weight the output of each detector optimally or suboptimally beforethefusiontakesplace.However,theinclusionofsuchafusiondevicewilladditsowncomputational complexity to the resulting receiver. 5 A/D ConverterAmpliﬁerBeam Tracking Beam Position InformationBeam Position InformationController Unit FSM Driver TelescopeFSM Assembly Incoming Light Array of DetectorsOutput Symbol Data Fusion (MRC or EGC) Fig. 4. This ﬁgure shows the block diagram of a detector array receiver. 2) Pros of an Array of Detectors Versus a Single Detector Now, we look at some of the pros of a detector array versus a single-detector receiver. Firstly, because of angle-of-arrival (AoA) ﬂuctuations of the beam at the receiver, the focused light beam impinging on a (small) single detector is always moving about or deviating about its mean position. We term this random deviation as the pointing error orjitterin this paper. Due to the pointing error, the beam radius has to be kept large enough so that any deviations of the beam do not lead to an outage of the signal at the detector. Additionally, even if the center of the detector and the center of the beam are aligned, the detector does not capture all the energy in the beam. If we replace this single detector with an array of detectors, and make the area of the array large enough by adding enough number of detectors, we may be able to capture all the received signal energy after the aperture lens. Secondly, for a single-detector receiver, a separate beam tracking assembly/channel is needed. The tracking assembly is typically made up of a quad-detector or a2×2detector array where each detector has an area large enough so as to accommodate for any deviation of the beam or beam wander. Thus, the net fraction of energy going into the data channel (indicated by αin Fig. 3) is reduced in order to divert a fraction of received energy into the tracking channel. For the array of detectors, a separate beam tracking assembly is not required since the same array can be used for beam tracking as well as symbol detection (please see Fig. 4). 6 Thus, in order to answer the question posed at the beginning of Section I-A, we have to make a performance comparison (bitter error rate and computational complexity comparison) between the single- detector and the detector array receivers while keeping in mind the various factors and conditions that are discussed in the pros and cons sections (Section I-A2 and Section I-A1). This comparison will highlight the advantages (or disadvantages) of one scheme over another, and will give the reader an idea of which system to choose under a given set of system parameters and conditions. This is the main motivation behind the study conducted in this paper. II. L/i.sc/t.sc/e.sc/r.sc/a.sc/t.sc/u.sc/r.sc/e.sc R/e.sc/v.sc/i.sc/e.sc/w.sc /a.sc/n.sc/d.sc M/o.sc/d.sc/e.sc/l.sc A/s.sc/s.sc/u.sc/m.sc/p.sc/t.sc/i.sc/o.sc/n.sc/s.sc A. Background Literature Review The authors in [2], [6] have proposed beam position estimation and tracking algorithms for a detector array photon-counting receiver concerning a joint beam position tracking and symbol detection scheme for PPM symbols. The authors in [7] analyze the probability of error in detail for the joint beam position tracking and symbol detection system, and show that the probability of error of a maximal ratio combining scheme is minimized if the beam is tracked accurately enough in time. The authors in [8] consider time synchronization schemes for a detector array receiver in a photon-counting channel in deep space optical communications. The authors in [9] have considered the communications performance for an array of detectors and discussed the eﬀects of the number of detectors and the beam parameter information on the performance. They showed that for a maximal ratio combining scheme, the probability of error decays monotonically with the number of detectors in the array if the area of the array is kept ﬁxed. The authors in [10] have deliberated upon the signal acquisition performance obtained with an array of detectors receiver for a photon-counting optical channel. The work [11] analyzes the performance of a free-space optical multiple-input single-output receiver for noncoherent and coherent beam combining schemes and pointing errors. For more information on the performance of an array of detectors in a deep-space optical communications,