A Novel Approximation for K Distribution: Closed-Form BER Using DPSK Modulation in Free-Space Optical Communication

TL;DR: A new analytical approximate expression for K

Abstract: A new analytical approximate expression for K distribution is proposed by expanding it in terms of orthogonal associated Laguerre polynomial. The expansion is truncated after first three terms, which yields a fairly close approximation to K distribution. The advantage of the proposed approximation is that the analytical closed form expression for bit error rate can be easily derived. KL measure is used to show the accuracy of the proposed approximation. The proposed approximate probability density function and bit error rate work well within the desired range of the channel parameter $\alpha$ , which is $1 and corresponds to the scintillation index value ranging from 2 to 3. We have also demonstrated the utility of our approximation for other quality of service metric such as fade probability.

TL;DR: In this article, the authors performed simulations and experiments on a dual-hop free-space optical (FSO) communication system with on-off keying (OOK) and differential phase-shift keying signals, focusing on the receiving sensitivity loss (RSL).

Abstract: All-optical amplify-and-forward (OAF) relaying technique can amplify and filter the attenuated optical signal in optical domain, and thus is regarded as a simple way to extend the transmission distance of free-space optical (FSO) communication systems. At the relaying node, however, the incident background radiation and the amplified spontaneous emission noise of the deployed erbium-doped fiber amplifier will deteriorate the optical signal-to-noise, therefore causing the degradation of the system's bit error ratio (BER). In this paper, we perform simulations and experiments on FSO system with on-off keying (OOK) and differential phase-shift keying (DPSK) signals, focusing on the receiving sensitivity loss (RSL) of the OAF-assisted dual-hop system. Taking the BER level of ${10^{ - 7}}$ as the reference, we find that the DPSK system suffers more than 8 dB RSL at the data rate of 5 Gb/s in simulation, while the OOK system gets less than 1 dB RSL at the same data rate. In the following experiments, the obtained results exhibit that RSL of DPSK system is nearly 10 dB, which of OOK system is less than 1.5 dB, shown similarly property to the simulations.

TL;DR: The design approach of all optical contention detection circuit based on the cross phase modulation interaction between two copropagating signal inside highly nonlinear fiber at the data rate of 120 Gbps is presented.

Abstract: This paper presents the design approach of all optical contention detection circuit based on the cross phase modulation interaction between two copropagating signal inside highly nonlinear fiber at the data rate of 120 Gbps. The error free operation has been achieved with the optimized signal power, length and effective area of optical fiber.

TL;DR: In this article, the effects of atmospheric turbulence on fiber-coupled differential phase-shift keying (DPSK) system in satellite-to-ground (STG) downlink were investigated.

Abstract: Fiber-coupled differential phase-shift keying (DPSK) modulation is potentially an effective approach for further high-speed satellite lasercom, due to the high detection sensitivity, low linewidth requirements, and uncalled-for complex phase-locked loop techniques. Nevertheless, the phase distortion caused by atmospheric turbulence will destroy the spatial coherence of the incident light field, thereby limiting the coupling efficiency of spatial light to single-mode fiber. Here, we report on the effects of atmospheric turbulence on fiber-coupled DPSK system in Satellite-to-Ground (STG) downlink. Fading characteristics of receiving signals and average BER performances have been also studied to optimize DPSK system performances by using wavefront modal compensation method based on orthonormal polynomials. An optimal receiving aperture could be obtained to achieve lowest BER in finite items of mode compensation. The analysis results can provide a reference for optimization of the receiving aperture in the STG downlink laser communication system and the reasonable system margin design.

TL;DR: In this paper, the authors used K distribution with modified Bessel function of the second kind with half integer order to obtain probability density function and cumulative distribution function in closed form in terms of elementary functions and simplifies the calculation of exact average bit error rate.

Abstract: We study modeling of wireless channel with fading and shadowing effects using K distribution with modified Bessel function of the second kind with half integer order. This allows us to obtain probability density function and cumulative distribution function in closed form in terms of elementary functions and simplifies the calculation of exact average bit error rate. The problem of Monte Carlo simulation using random variables with K distribution is also addressed.

TL;DR: Basic Forms x n dx = 1 n + 1 x n+1 (1) 1 x dx = ln |x| (2) udv = uv − vdu (3) 1 ax + bdx = 1 a ln|ax + b| (4) Integrals of Rational Functions

Abstract: Basic Forms x n dx = 1 n + 1 x n+1 (1) 1 x dx = ln |x| (2) udv = uv − vdu (3) 1 ax + b dx = 1 a ln |ax + b| (4) Integrals of Rational Functions 1 (x + a) 2 dx = −

TL;DR: In this article, the authors present a model for vector analysis based on the Calculus of Variations and the Sturm-Liouville theory, which includes the following: Curved Coordinates, Tensors.

Abstract: Vector Analysis. Curved Coordinates, Tensors. Determinants and Matrices. Group Theory. Infinite Series. Functions of a Complex Variable I. Functions of a Complex Variable II. Differential Equations. Sturm-Liouville Theory. Gamma-Factrial Function. Bessel Functions. Legendre Functions. Special Functions. Fourier Series. Integral Transforms. Integral Equations. Calculus of Variations. Nonlinear Methods and Chaos.

TL;DR: The Handbook of Mathematical Functions with Formulas (HOFF-formulas) as mentioned in this paper is the most widely used handbook for mathematical functions with formulas, which includes the following:

Abstract: (1965). Handbook of Mathematical Functions with Formulas. Technometrics: Vol. 7, No. 1, pp. 78-79.