Poisson Channel Research Articles

End-to-End Learning Framework for Space Optical Communications in Non-Differentiable Poisson Channel

End-to-End Learning Framework for Space Optical Communications in Non-Differentiable Poisson Channel

Investigation of Characteristics of Ultraviolet Light Pulse Weak Signal Communication System Based on Fourth-Order Frequency-Shift Keying Modulation

In ultraviolet (UV) communication, On–Off Keying (OOK) is the primary modulation technique. Compared to OOK, frequency modulation offers stronger resistance to path attenuation. Currently, research on frequency modulation demodulation schemes for UV communication is limited, mainly employing waveform detection and laser pulse response methods, which require high detection sensitivity to light. This study presents a novel frequency modulation communication scheme using discrete Poisson channel distribution and optical pulse signal processing algorithms, enhancing the signal processing sensitivity of the existing frequency modulation scheme to the level of photons. The proposed system model is rigorously evaluated through theoretical derivations and simulations. Additionally, a hardware system integrating optical pulse counting, frequency detection, and clock data recovery algorithms is developed. Experimental results show the system achieving a 5 kbps transmission rate under frequency modulation. In non-line-of-sight (NLOS) scenarios, communication reaches up to 65 m, with the receiver elevation angle ranging from 10° to 25° and the bit error rate (BER) stabilized at 10−4, while in line-of-sight (LOS) situations, the BER remains at 10−5 up to 400 m and 10−4 up to 700 m, achieving the farthest distance and fastest communication rate achievable in the current FSK modulation scheme of ultraviolet communication systems. The integrated components enhance its applicability in communication systems. This study offers a valuable addition to UV communication technology.

Implementation of large angle low error non-line-of-sight ultraviolet communication system

Due to the strong scattering of ultraviolet (UV) communication, it is particularly suitable for scenarios involving short distance and large angle scattering, such as communication between buildings and jungles. In this paper, a system based on a single scattering model and a discrete Poisson channel pulse counting signal processing algorithm is constructed, and the effects of the number of signal photons, noise photons, and elevation angle on the system's bit error rate (BER) are simulated and analyzed. The effect of sampling rate on the system's performance is numerically analyzed. The results show that the pulse counting algorithm is suitable for systems with a small number of signal photons and a high sampling rate. The BER of the system when the number of signal photons becomes large is more dependent on the sampling rate than the signal-to-noise ratio. Additionally, we designed an outdoor test system including hardware system, pulse counting, synchronization and data recovery algorithms. The test results are consistent with the simulation results. The communication rate of the outdoor system is designed to be 10 kbps at a distance of 50 m. The BER is 10-3 when the elevation angle is 85°, while the BER is 10-5 when the elevation angle is 50°.

Benchmarking Neural Capacity Estimation: Viability and Reliability

Recently, several methods have been proposed for estimating the mutual information from sample data using deep neural networks. This approach is referred to as neural mutual information estimation (NMIE). NMIEs differ from other approaches in the literature as they are data-driven estimators. As such, they have the potential to perform well on a large class of capacity problems. To test the performance across various NMIEs, it is desirable to establish a benchmark encompassing the different challenges of capacity estimation. This is the objective of this paper. We consider three scenarios for benchmarking: (i) the classic AWGN channel, (ii) channels continuous inputs – the optical intensity and peak-power constrained AWGN channel (iii) channels with a discrete output – i.e., the Poisson channel. We also consider the extension to the multi-terminal case with (iv) the AWGN and optical MAC models. We argue that benchmarking a certain NMIE across these four scenarios provides a substantive test of performance. We study the performance of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">mutual information neural estimator</i> (MINE), <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">smoothed mutual information lower-bound estimator</i> (SMILE), and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">directed information neural estimator</i> (DINE) and provide insights into the performance of other methods as well. To summarize our benchmarking results, MINE provides the most reliable performance.

Improved response model of a superconducting nanowire array for high photon count rate communication

In high-speed photon-counting communication where the slot duration is close to the scale of detector reset time, the detection efficiency recovery characteristics of superconducting nanowire single photon detector (SNSPD) become the key factors affecting counting and communication performance. We introduced the nonlinear detection efficiency recovery model derived from the kinetic inductance model combined with the nonlinear efficiency-current relationship into the pulse position modulation (PPM) optical communication system based on the SNSPD array, and studied the impact of the recovery characteristics on the counting and communication performance of the system. On this basis, we introduce the efficiency recovery model into the correction of the channel logarithmic likelihood ratio (LLR) to estimate the SNR of each slot more accurately. Relevant results show that compared with the existing Poisson channel model, fixed deadtime model and detection efficiency exponential recovery model, this modification combined with FEC can provide the best decoding performance, especially in scenarios with high PPM order, small array pixel number and strong noise level. Besides, the nonlinear detection efficiency recovery model also reflects the best consistency with the experimental measurements of the SNSPD array in terms of response count rates near saturation.

Design and Optimization of Protograph LDPC-Coded Multipulse PPM Systems Over Poisson Channels

Combining powerful error-correction codes (ECCs) with multipulse pulse-position modulation (MPPM) has great potential to realize high-throughput and high-reliability transmissions in free-space optical (FSO) communication systems. This paper conducts an insightful investigation on protograph low-density parity-check (PLDPC)-coded MPPM systems over Poisson channels. To be specific, we first put forward a novel type of constellations, referred to as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">irregular pulse-distribution (IPD) constellations</i> , for MPPM. We also conceive a bit-level rate-adaptive (RA) scheme, which can exploit the structural property of the IPD constellations to significantly improve the convergence performance at the price of transmission-rate loss. Furthermore, with the aid of a modified protograph extrinsic information transfer (PEXIT) algorithm, we construct three enhanced PLDPC codes with code rates <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1/2, 2/3$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$3/4$</tex-math></inline-formula> that exhibit excellent decoding thresholds over Poisson channels. The proposed PLDPC-coded MPPM systems with the use of the IPD constellations, RA scheme, and enhanced PLDPC codes are superior to the state-of-the-art counterparts.

Novel Iterative Machine Learning for Accurate Photon-Counting Poisson Channel Estimation

In this work, we present a new machine learning-based framework for the accurate estimation of the shot-noise limited photon-counting Poisson channel by developing a state-of-art iterative unsupervised learning algorithm for intelligent optical communications. By accurate estimation, we mean that it achieves very low estimation error even when the effect of the received data is unpredictable. We consider a realistic situation where modulated symbols are assumed to be hidden or unobserved latent variables, thereby making conventional estimation algorithms based on maximum likelihood approach unsuitable or inefficient. In particular, we consider a probabilistic model and assume that the received data is not labeled. With this unpredictable data considered, a novel iterative machine learning framework is developed based on an expectation and maximization algorithm. The proposed algorithm avoids the need to choose an appropriate step size as required in gradient method based algorithms. It is shown that it significantly outperforms the least square and the Viterbi detection technique.

Learn the boundaries of multilevel photon-counting optical wireless channel: A machine learning approach

In this paper, we present a novel unsupervised machine learning (ML) algorithm to identify the constellation index of the received signal over a photon-counting optical wireless Poisson channel. The stochastic channel model is characterized by the mean value of the Poisson distributed photon number, corresponding to a distinct transmit power level. We show the condition where the Poisson channel can be well approximated with the normal distribution, and formulate the unsupervised ML problem as a clustering problem. To demodulate the transmitted symbol, a probabilistic model based on the Gaussian mixture model is utilized to learn the boundaries of constellation regions. The proposed algorithm avoids the measurement of channel parameters and is appropriate for applications with random channel conditions. Moreover, it is useful in scenarios where the direct maximization of the likelihood function is not possible. In addition, we demonstrate that the performance of the proposed technique is superior to the linear minimum mean square (LMMSE) estimation technique. Furthermore, the time complexity analysis is presented and compared with the LMMSE and K−means clustering algorithm. In addition, the generalization of the proposed algorithm is also presented.

Blind and Semi-Blind Channel Estimation/Equalization for Poisson Channels in Optical Wireless Scattering Communication Systems

The communication systems for Poisson channels require long pilot for channel estimation and may result in large percentage of overhead due to the signal-dependent noise of Poisson-distributed signal, i.e., both signal part and noise part experience random processes. In this paper, both blind and semi-blind channel estimation methods are studied to shorten the overhead and increase the transmission efficiency for Poisson channels. First, fractionally spaced equalizers are proposed based on modified constant modulus algorithm (CMA) and subspace (SS). Second, a data-aided iterative channel estimation (ICE) is designed and analyzed in terms of its asymptotic unbiasedness and convergence. The proposed methods are evaluated based on both a constant channel scenario and a varying channel scenario. Numerical simulation results show that the modified CMA has the worst bit-error rate performance but requires the lowest computational complexity. Besides, both SS based channel estimation and ICE have negligible overhead and comparable bit-error rate performances with respect to the conventional periodic pilot based channel estimation having 50% overhead.

Heuristic Sensing Schemes for Four-Target Detection in Time-Constrained Vector Poisson and Gaussian Channels

In this work we investigate the different sensing schemes for detection of four targets as observed through a vector Poisson and Gaussian channels when the sensing time resource is limited and the source signals can be observed through a variety of sum combinations during that fixed time. For this purpose we can maximize the mutual information or the detection probability with respect to the time allocated to different sum combinations, for a given total fixed time. It is observed that for both Poisson and Gaussian channels; mutual information and Bayes risk with 0 − 1 cost are not necessarily consistent with each other. Concavity of mutual information between input and output, for certain sensing schemes, in Poisson channel and Gaussian channel is shown to be concave w.r.t given times as linear time constraint is imposed. No optimal sensing scheme for any of the two channels is investigated in this work.

Sensing Method for Two-Target Detection in Time-Constrained Vector Poisson Channel

Sensing Method for Two-Target Detection in Time-Constrained Vector Poisson Channel

Sensing Method for Two-Target Detection in Time-Constrained Vector Poisson Channel

It is an experimental design problem in which there are two Poisson sources with two possible and known rates, and one counter. Through a switch, the counter can observe the sources individually or the counts can be combined so that the counter observes the sum of the two. The sensor scheduling problem is to determine an optimal proportion of the available time to be allocated toward individual and joint sensing, under a total time constraint. Two different metrics are used for optimization: mutual information between the sources and the observed counts, and probability of detection for the associated source detection problem. Our results, which are primarily computational, indicate similar but not identical results under the two cost functions.

Non-Asymptotic Capacity Upper Bounds for the Discrete-Time Poisson Channel With Positive Dark Current

We derive improved and easily computable upper bounds on the capacity of the discrete-time Poisson channel under an average-power constraint and an arbitrary constant dark current term. This is accomplished by combining a general convex duality framework with a modified version of the digamma distribution considered in previous work of the authors.

Low complexity receiver design for time-varying Poisson molecular communication channels with memory

This paper introduces novel approaches for the design of the linear filter and the detection algorithms in unbounded advection diffusion-based molecular communication systems affected by inter-symbol interference. The received signal samples are modeled as Poisson random variables with memory where the effect of enzymatic reactions is also included. A main characteristic of the new filter design is to allow for a real-time computation of the filter's coefficients. For the detection of the transmitted symbols, we define an averaging method suitable for time-varying channels with finite memory length. In this paper the mean value of the Poisson channel is varying with time and we quantify the memory length with a finite number, from receiver point of view. The computational burden of the proposed approaches is evaluated in terms of number of required operations and their performance is evaluated in terms of bit error rate for different sets of parameters. We show that the proposed design of the filter and of the detection algorithms enables us to achieve a performance comparable to that of the state of the art approaches in relation to their simplicity.

Transmission of a Bit Over a Discrete Poisson Channel With Memory

A coding scheme for transmission of a bit maps a given bit to a sequence of channel inputs (called the codeword associated with the transmitted bit). In this paper, we study the problem of designing the best code for a discrete Poisson channel with memory (under peak-power and total-power constraints). The outputs of a discrete Poisson channel with memory are Poisson distributed random variables with a mean comprising of a fixed additive noise and a linear combination of past input symbols. Assuming a maximum-likelihood (ML) decoder, we search for a codebook that has the smallest possible error probability. This problem is challenging because error probability of a code does not have a closed-form analytical expression. For the case of having only a total-power constraint, the optimal code structure is obtained, provided that the blocklength is greater than the memory length of the channel. For the case of having only a peak-power constraint, the optimal code is derived for arbitrary memory and blocklength in the high-power regime. For the case of having both the peak-power and total-power constraints, the optimal code is derived for memoryless Poisson channels when both the total-power and the peak-power bounds are large.

Capacity of a Lossy Photon Channel With Direct Detection

We calculate numerically the capacity of a lossy photon channel assuming photon number resolving detection at the output. We consider scenarios of input Fock and coherent states ensembles and show that the latter always exhibits worse performance than the former. We obtain capacity of a discrete-time Poisson channel as a limiting behavior of the Fock states ensemble capacity. We show also that in the regime of a moderate number of photons and low losses the Fock states ensemble with direct detection is beneficial with respect to capacity limits achievable with quadrature detection.

Covert Communication Over the Poisson Channel

We consider the problem of communication over a continuous-time Poisson channel subject to a covertness constraint: The relative entropy between the output distributions when a message is transmitted and when no input is provided must be small. In the absence of both bandwidth and peak-power constraints, we show the covert communication capacity of this channel, in nats per second, to be infinity. When a peak-power constraint is imposed on the input, the covert communication capacity becomes zero, and the “square-root scaling law” applies. When a bandwidth constraint but no peak-power constraint is imposed, the covert communication capacity is again shown to be zero, but we have not determined whether the square-root law holds or not.

Transmit power optimization over low-power Poisson channel in multiuser MISO indoor optical communications

Abstract In this paper, we address the problem of joint transmit beamforming and power control for a multiuser multiple-input single-output (MISO) indoor optical downlink channel. We adopt a shot-noise limited Poisson channel with transmitting signals subject to average and peak transmits power constraints. To minimize the total transmit power, we formulate an optimal downlink beamforming problem using convex optimization method via second-order cone programming techniques. In our approach, the total transmit power is optimized subject to the signal-to-interference-plus-noise ratio (SINR). The results verify performance improvements of the proposed technique as compared to conventional multiuser MISO indoor optical systems.

Model-Aware End-to-End Learning for SISO Optical Wireless Communication Over Poisson Channel

Faced with the challenge of transceiver design over the Poisson channel, we leverage the deep-learning technique and devise two novel end-to-end learning schemes to fulfill the design task in this paper. One of the schemes accords with the basic principle of the currently available autoencoder (AE) but is specially designed for the Poisson channel with the aid of the square root (SR) transform. The other scheme, following a different design philosophy from AE, is developed based on a double neural network (DNN) model, which regards the receiver and the transmitter as two separate networks. By these designs, the end-to-end learning task can be conducted over Poisson channel. Extensive computer simulations reveal that 1) the transceiver learned by the DNN scheme always performs better than or comparably to the currently available artificially designed transceivers, and 2) compared with the transceiver learned by DNN, the transceiver learned by SR-AE suffers performance loss in some cases, but the SR-AE scheme has a lower complexity to compute the loss function and fewer network parameters. This study takes the first step toward applying end-to-end learning techniques in the field of the Poisson channel and lays a foundation for further works on this topic.

Capacity Maximization Using Nash Bargaining in Indoor Optical Multiuser Interference-Limited Poisson Channel

In multiuser optical wireless communications (OWC), the multiuser interference becomes significant as the number of users increases. This would lead to a poor quality of service with a low signal-to-interference-plus-noise-ratio (SINR) or even a failure of service. In this paper, we consider coordination among multiple users to maximize the capacity in a multiple-input single-output (MISO) interference-limited discrete-time Poisson channel from a game-theoretic perspective. With power constraints imposed, the resource allocation problem can be interpreted as a downlink beamforming game. To improve the capacity in a power- and interference-limited channel, we model the problem as a cooperative game and propose an altruistic algorithm using the Nash bargaining, where each self-interested user attempts to maximize its capacity through cooperation. Moreover, to compare the performance with a non-game-theoretic approach, a convex optimization framework is developed. It is shown that the proposed Nash bargaining yields significant performance improvement when compared with the Nash equilibrium in the non-cooperative game. It is also found that in a power- and interference-limited channel, self-interested but cooperative users can provide a significant performance improvement over the convex optimization based non-game-theoretic approach.