The Bayes' optimal receiver for digital fibre optic communication systems

El-Hadidi, Mahmoud T.; Hirosaki, B.

doi:10.1007/bf00668345

Cited by 11 publications

(11 citation statements)

References 7 publications

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“…In particular, we would now like to find the pair (θ, w) that Figure 2: MD error exponents of the optical matched correlator (blue dashed curve) and the optimal correlator (red solid curve) as functions of θ, for a random gain (ζ = 0.1), P = 10, N 0 /q 2 e = 0.0001, λ 1 = 1 and λ 2 = 10. maximizes E MD (θ, w) over all pairs such that E FA (θ, w) ≥ S, for a given S > 0 that designates the target FA exponent. 4 Equivalently, we would like to solve the problem sup θ,w…”

Section: The Case Of Positive Dark Currentmentioning

confidence: 99%

“…We will not continue any further to the full, detailed solution of this problem, beyond the following comment 4 Previously, S was given by θ 2 /N0P , so for a given P , S was proportional to θ 2 .…”

Section: The Case Of Positive Dark Currentmentioning

confidence: 99%

“…In the case of an avalanche photo-diode (APD), which is the more relevant case, there is an additional, third type of noise, namely, the excess noise, induced by the APD, which is actually a multiplicative noise process pertaining to fluctuations in the random gain associated with the avalanche mechanism, as each primary electron-hole pair (generated by a photon absorbed in the photo-diode), may generate secondary electron-holes, which in turn can generate additional electron-holes, and so on. For more details, and additional aspects of the problem area, the interested reader is referred to some earlier work, e.g., [2], [3], [4], [5], [6], [7], [13], [14], [15], [16], [17], [18], [19], [20], and [22], which is by no means an exhaustive list of relevant articles (and a book).…”

Section: Introductionmentioning

confidence: 99%

“…More recently, Helstorm and Ho [8] and Ho [10] have applied saddle-point integration and thereby studied the behavior of certain pulse shapes at the optical receiver in terms of the performance of the decoder. Other studies are guided by the approach of approximating the distribution of the shot noise of the photo-diode by the Gaussian distribution, owing to considerations in the spirit of the central limit theorem (CLT), see e.g., [3,Subsections 5.6.3,5.8.4], [4]. In this context, the well-known optical matched filter (see, e.g., [7], [9]) is the main building block of the optimal detector that simply maximizes the SNR at the sampling time, t = T .…”

Section: Introductionmentioning

confidence: 99%

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Optimal Correlators for Detection and Estimation in Optical Receivers

Merhav¹

2020

Preprint

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Motivated by modern applications of light detection and ranging (LIDAR), we study the model of an optical receiver based on an avalanche photo-diode (APD), followed by electronic circuitry for detection of reflected optical signals and estimation of their delay. This model is known to be quite complicated as it consists of at least three different types of noise: thermal noise, shot noise, and multiplicative noise (excess noise) that stems from the random gain associated with the photo-multiplication of the APD. Consequently, the derivation of the optimal likelihood ratio test (LRT) associated with signal detection is a non-trivial task, which has no apparent exact closed-form solution. We consider instead a class of relatively simple detectors, that are based on correlating the noisy received signal with a given deterministic waveform, and our purpose is to characterize the optimal waveform in the sense of the best trade-off between the false-alarm (FA) error exponent and the missed-detection (MD) error exponent. In the same spirit, we also study the problem of estimating the delay on the basis of maximizing the correlation between the received signal and a time-shifted waveform, as a function of this time shift. We characterize the optimal correlator waveform that minimizes the mean square error (MSE) in the regime of high signal-to-noise ratio (SNR). The optimal correlator waveforms for detection and for estimation turn out to be different, but their limiting behavior is the same: when the thermal Gaussian noise is dominant, the optimal correlator waveform becomes proportional to the clean signal, but when the thermal noise is negligible compared to the other noises, then it becomes logarithmic function of the clean signal, as expected.

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Section: The Case Of Positive Dark Currentmentioning

confidence: 99%

Section: The Case Of Positive Dark Currentmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimal Correlators for Detection and Estimation in Optical Receivers

Merhav¹

2020

Preprint

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“…There is a large volume of work [9][10][11][12][13][14][15][16][17] based on complex CB and MCB to handle receiver design optimization for optical fiber communication. However, the main elements of receiver optimization methodology are the filter impulse response h f (t), the photodetector internal gain (g), and the threshold for the decision unit F D (Figure 1).…”

Section: Introductionmentioning

confidence: 99%

Simple Moment Generating Function Optimisation Technique to Design Optimum Electronic Filter for Underwater Wireless Optical Communication Receiver

Ramley,

AlZhrani,

Bedaiwi

et al. 2024

Mathematics

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This paper introduces a new simple moment-generating function (MGF) design modelling method to conclude an optimum filter to maximize the Q-factor and increase the link communication span. This approach mitigates the pulse temporal dispersion, particularly the underwater wireless optical communication (UWOC) systems. Hence, some form of equalizing filter design is highly desirable. The model solution environment includes a Double Gamma Function (DGF) water channel impulse response, intersymbol interference (ISI), stochastic Poisson process, and additive Gaussian thermal noise (AGTN). The optimal filters exhibit temporal profiles comparable to those derived by published works based on complex Chernoff Bound (CB) and Modified Chernoff Bound (MCB) methods. The results show the impact of the optimum filter at a signal level and optical receiver level utilizing Eye-Diagrams and BER vs. Q-Factor, respectively. The computation involves four different UWOC propagation channel models for Coastal and Harbor waters. One of the main conclusions indicates that the optimum filter manages the temporal dispersion due to the ISI impairment correctly. Also, the proposed optimum filter reduces eye-opening and the corresponding Q-Factor by less than 15% for a five-times increase in pulse width for the same transmitted optical power level.

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A consideration on optimum direct detection optical communication receiver

Hata¹,

Morinaga²,

Namekawa³

1986

Electron. Comm. Jpn. Pt. I

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This paper presents an optimum receiver for direct detection/binary intensity modulation optical communication systems. Here, the signal‐plus‐noise model assumes a signal‐dependent nonstationary Gaussian random process. Moreover, assuming white noise and an ideal low‐pass receiver, the receiver vector is generated by sampling of signals and noise. The likelihood ratio for this receive vector is derived based on the maximum likelihood test to determine the structure of optimum receiver. This paper shows that the optimum receiver has both the usual correlation detection for additive noise in the radio wave region and noise energy detection for the signal shot noise. Next, the error rate of this receiver is derived theoretically and its characteristics are evaluated. As a result, the signal shot noise can be effectively utilized for signal detection by allowing a greater bandwidth for the receiver, elucidating treatment of the shot noise from the standpoint of statistical signal detection theory.

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The Bayes' optimal receiver for digital fibre optic communication systems

Cited by 11 publications

References 7 publications

Optimal Correlators for Detection and Estimation in Optical Receivers

Optimal Correlators for Detection and Estimation in Optical Receivers

Simple Moment Generating Function Optimisation Technique to Design Optimum Electronic Filter for Underwater Wireless Optical Communication Receiver

A consideration on optimum direct detection optical communication receiver

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