On the WMC density as an inverse Gaussian probability density

The probability density function (PDF) used to model the statistical behavior of avalanche photodiodes (APD), known as the Webb, McIntyre and Conradi (1974) WMC density, is shown to be an inverse Gaussian density. As a consequence, a closed-form solution for the cumulative distribution function exists. A closed-form for the cumulative distribution of the WMC PDF has not been presented in the literature before. With this result, alternate methods for the generation of WMC PDF distributed random variates are now available. These methods are reviewed and discussed     

On the generation of WMC-distributed random numbers

An efficient method to generate exactly WMC-distributed random numbers on a digital computer is presented. The generation is based on the acceptance-rejection method. The WMC distribution is used to model the statistical behavior of avalanche photodiodes (APD), for example, in the simulation of optical transmission     

Effects of Ionization Velocity and Dead Space on Avalanche Photodiode Bit Error Rate

A model is presented for the bit error rate (BER) contributed by the receiver in an optical telecommunications system that includes the effects of ionizing carrier velocity and dead space in the avalanche photodiode (APD) and of additive circuit noise. The probability distribution functions of bit charge used to calculate BER are not, as is commonly assumed, Gaussian, confirming the need to directly compute the receiver statistics. Integrating the current over the central section of the bit period can minimize intersymbol interference. The assumption that carriers travel to ionization with infinite velocity underestimates BER in InP APDs with short avalanche region widths, and overestimates BER when . Models assuming constant carrier velocity or allowing for velocity enhancement predict distinctly different BER over a wide range of avalanche width and multiplication because of the manner in which the current evolves during the bit period.     

Optical wireless multiple-input multiple-output system based on avalanche photodiode receiver

With the rising demand for high data-transmission rates, optical wireless communication (OWC) is considered one of the particularly appropriate solutions. In this paper, an avalanche photodiode (APD)-based optical wireless configuration is used to approximate the receiver output. This paper also presents bit error rate (BER) evaluation statistics compared with the theoretical results for optical wireless multiple-input multiple-output (MIMO) communication systems. In particular, the simulated results show that the BER of a 4 × 4 MIMO system is significantly lower than that of other APD systems (over 10 times better when the mean energy is higher than − 165 dBJ). To summarize, the OWC-MIMO system shows enormous potential in the high-speed data-transmission field.     

Performance Characterization of Spatial Diversity Based Optical Wireless Communication over Atmospheric Turbulence Channels

Optical wireless communication is regarded as the next-generation high-speed technology. It has demonstrated its capability to deliver data faster than any other state-of-the-art wireless communication technique. This technology has drawn attention as a means of implementing reliable high capacity outdoor systems that cannot be implemented by conventional fiber optics. It has emerged recently as an efficient solution to match the larger bandwidth and high data rates requirement of the upcoming wireless communication systems. However, although FSO (free space optics) system has many appealing features, it has rather disappointing performance for long links due to the degrading effects of atmospheric turbulence-induced fading. In the presence of such type of performance impairments, the received signal exhibits random intensity fluctuations, which increase the BER (bit error-rate), where the severe weather conditions can have a detrimental impact on the performance, which may result in an inadequate availability. The MIMO wireless optical procedure, in which the spatial dimensions are used to improve the reliability and spectral efficiency of point-to-point links, provides a promising approach to mitigate turbulence effects due to its powerful performance enhancing capabilities.In this paper, we investigate a terrestrial atmospheric FSO communication system operating under the influence of strong atmospheric turbulences. Additionally, the MIMO technique with equal gain combining (EGC) is used in this work to enhance the data rate of the proposed system. Atmospheric turbulence impacts are modeled as a lognormal channel with due regard for geometric losses. With the use of NRZ line coding, an FSO highly sensitive receiver using either avalanche photodetector (APD) or PIN is designed and simulated for best system performance. The preference is achieved by using Bessel and Gaussian filters. It has been found that APD receiver using Gaussian filter is suitable for long-range links with APD gain value of 3. Also, the selection of APD gain is critical to the system performance. In addition, the optimal value of APD gain required for best system performance decreases as the size of the MIMO technique increases. The achievable performance improvements including received power levels, BER and Q-factor are also discussed. The results show that the system with optical amplifier at the transmitter gives an optimum performance. In addition the system performance is enhanced in most weather conditions by using an amplified 2×2 MIMO-FSO system with booster amplifier.     

二维大气无线光码分多址通信系统

在无线光通信系统中采用光码分多址(OCDMA)技术,可以充分利用其丰富带宽,提高系统性能。考虑背景光噪声、探测器噪声、多用户干扰和大气闪烁等影响因素,给出了二维无线光码分多址(2D-WOCDMA)系统模型,在该模型中采用了脉冲位置调制(PPM)和光纤布拉格光栅(FBG)编解码器。通过数值分析,详细讨论了该无线光通信系统的性能。结果表明,大气闪烁是影响二维无线光码分多址通信系统性能的重要因素,当其对数方差较大时,系统难以实现通信,需要采用诸如多用户检测、信道编码及阵列接收等技术提高系统的性能;二维无线光码分多址通信系统适合采用1550 nm波段;该通信系统还受背景光、雪崩光电二极管(APD)增益和调制消光比等因素的影响。     

Performance analysis of CDMA optical communication systems withavalanche photodiodes

The performance of optical code-division multiple-access (CDMA) communication systems with avalanche photodiodes (APD) is analyzed. The bit error rate (BER) can be accurately computed by using the saddlepoint method. The effects of the multiple-user interference (MUI), signal-dependent shot noise, and receiver thermal noise are investigated. Results of the numerical integration illustrate the non-Gaussian property of the receiver output distribution. Exact means and variances are derived for the Gaussian approximation. It is found that when the MUI increases, the saddlepoint approximation yields satisfactory results, but the Gaussian approximation yields higher BER floors. Prime codes and on-off keying (OOK) are considered. Examples illustrate the effects of the system parameters such as the APD gain, threshold, prime code length, and the number of simultaneous users     

无线通信系统误码率分析

无线光通信技术是当前研究的一个热点,为了对无线光通信系统的性能进行分析,采用APD探测器的Webb-Gaussian模型,对采用脉冲位置调制(PPM)方式的光通信系统性能进行分析,重点分析瞄准误差和背景光对误码率的影响,基于Matlab进行数值仿真.结果表明,要使光通信系统达到10-6的误码率,瞄准误差必须控制在0.15倍束宽以内,每个PPM时间间隙的背景光子数必须控制在20个以下.同时,计算结果表明对APD的增益系数进行优化也可以降低误码率.     

Construction and performance analysis of variable-weight optical orthogonal codes for asynchronous OCDMA systems

A construction scheme of variable-weight optical orthogonal codes （VW-OOCs） for asynchronous optical code division multiple access （OCDMA） system is proposed. According to the actual situation, the code family can be obtained by programming in Matlab with the given code weight and corresponding capacity. The formula of bit error rate （BER） is derived by taking account of the effects of shot noise, avalanche photodiode （APD） bulk, thermal noise and surface leakage currents. The OCDMA system with the VW-OOCs is designed and improved. The study shows that the VW-OOCs have excellent performance of BER. Despite of coming from the same code family or not, the codes with larger weight have lower BER compared with the other codes in the same conditions. By taking simulation, the conclusion is consistent with the analysis of BER in theory. And the ideal eye diagrams are obtained by the optical hard limiter.     

BER analysis of coherent optical CDMA communication systems with transfer function matrix

We analyze the bit error rate (BER) of coherent optical code-division multiple-access (CDMA) communication systems with a transfer function matrix (TFM). The coherent optical CDMA is a promising system for an access network due to its advantages of asynchronous transmission, information security, multiple-access capability. TFM is defined as the Fourier transform of the impulse response of an optical fiber, which interconnects each CDMA system. TFM has parameters such as the state of polarization (SOP), phase difference, power distribution between two orthogonal modes over an optical frequency range. We first analyze the statistic of a received signal via an optical fiber with TFM, and then apply the statistic to the BER analysis. The analytical results show that BER increases with the bandwidth of a signal, and that selecting a proper center frequency leads to the BER reduction.     

On improving the computational efficiency of digital lightwave linksimulation

Monte Carlo simulation can be used to estimate the bit error rate (BER) in digital lightwave communication links. However, when the link includes an avalanche photodetector (APD) receiver and is operating at a low BER, Monte Carlo simulation requires excessive execution time unless assumptions are made about the APD statistics. Techniques are presented that reduce the computational resources required to estimate the BER for these systems by two orders of magnitude. The speed-up is achieved by developing anew, more efficient random number generation algorithm for APD shot noise and by applying a tail extrapolation technique to the conditional distributions at the sample-and-decide input in the receiver. Receiver thermal noise is handled analytically. Accurate BER estimates for an NRZ direct-detection system are obtained in approximately 1.5 CPU hours on a VAXstation II using a combination of these techniques     

Turbo-coded optical PPM communication systems

A number of parallel concatenated convolutionally coded (PCCC) photon communication systems is introduced and investigated. It is assumed that the optical channel is an intensity modulated (IM) channel and that the received optical signal is detected using a direct-detection (DD) scheme. Two modes of operation are considered. In one scenario, it is assumed that the receiver is limited by shot noise (i.e., negligible receiver thermal noise, or Poisson channel). In the other case, we consider a nonnegligible receiver thermal noise where an avalanche photodetector (APD) is employed to detect the received optical signal. It is also considered that the modulation scheme is the binary pulse-position modulation (PPM). With the aid of the best available upper bounds, the performance of the rate 1/n PCCC encoded optical PPM systems is assessed in terms of the upper bound on the system bit error rate (BER) for the shot-noise-limited IM/DD systems with nonnegligible background noise and for the thermal-noise-limited systems with APD detectors when a uniform interleaver is used. Numerical results for the rate 1/3 PCCC encoded PPM channels are presented. The numerical results demonstrate the enormous potential of this novel coding scheme in enhancing the performance of the aforementioned optical channels by a sizeable margin across the board     

Efficient time gating in ultrafast optical TDM networks

Ultrafast optical communication is the backbone of high-speed global networking infrastructure. Optical time division multiplexing (OTDM) is a popular technique for embedding data from many simultaneous users on a single optical channel. This paper studies the optimal clock signal used in optical time gating to extract the data of the desired user in an OTDM network. We show that the pulse width of the clock signal can be optimized to achieve a minimum bit error rate (BER) in these networks. In this paper, we assume that the optical clock signal used for time gating has jitter, and there is therefore a delay variation between the clock and data signals. We model this delay as a zero mean Gaussian random variable. Using this model, an analytical BER expression is derived for systems with Gaussian pulses. In the numerical results, we find the optimal values of the clock pulse width by evaluating the BER versus the pulse width for different variances of the delay. Simulation results are also presented to evaluate the accuracy of the analytical expression.     

High-sensitivity Hi-Lo germanium avalanche photodiode for 1.5 ?m-wavelength optical communication

A high-sensitivity small-detectable-area Hi-Lo germanium avalanche photodiode (Ge APD) was developed for use in 1.55 ?m wavelength optical communication systems. This device has Hi-Lo (p+nn?) impurity profile. Its detectable area is 30 ?m in diameter for single-mode optical-fibre use. The minimum average received signal level obtained was ?40.5 dBm (at 450 Mbit/s, ? = 1.55 ?m, BER = 10?9, return-to-zero). This is 0.7 dB better than the value for the 80?m diameter similar structure Ge APD.     

Output Power PDF of a Saturated Semiconductor Optical Amplifier: Second-Order Noise Contributions by Path Integral Method

We have developed a second-order small-signal model for describing the nonlinear redistribution of noise in a saturated semiconductor optical amplifier. In this paper, the details of the model are presented. A numerical example is used to compare the model to statistical simulations. We show that the proper inclusion of second-order noise terms is required for describing the change in the skewness (third-order moment) of the noise distributions. The calculated probability density functions are described far out in the tails and can hence describe signals with very low bit error rate (BER). The work is relevant for describing the noise distribution and BER in, for example, optical regeneration.     

基于LDPC码的无线光通信副载波误码性能分析

为了研究信道编码技术对无线光通信副载波系统差错性能的影响,基于无线光通信链路噪声特性,建立了大气信道等效数学模型。采用低密度奇偶校验(LDPC)码作为信道编码方式引入无线光通信,在不同光强闪烁指数下对基于副载波相移键控调制无线光通信系统进行了差错性能仿真,比较分析了LDPC编码前后副载波调制系统的误比特率,并对二相相移键控及四相相移键控两种系统进行了对比。结果表明,副载波二相相移键控调制系统的差错性能优于四相相移键控系统,同时LDPC码在弱湍流信道具有优越的纠错能力,可以获得比未编码系统较高的编码增益,在无线光通信领域具有一定的应用价值。     

基于Hoyt光束指向模型的高空平台间光链路性能仿真

针对高空平台(HAP)位置不稳定特性模型,建立更符合实际的Hoyt指向误差分布模型,与理想条件下的Rayleigh指向误差分布模型比较,分析平台间光链路的差错性能。仿真结果表明,在发散角逐渐增大的条件下,Hoyt分布模型与Rayleigh分布模型的误码率(BER)曲线具有相同的变化规律;在相同发散角条件下,Hoyt分布模型的误码率低于Rayleigh分布模型;在最优发散角条件下,Hoyt分布模型误码率与Rayleigh分布模型误码率差值最大,以均方差比值因子取0.2为例,与Rayleigh分布模型相比,Hoyt分布模型的误码率减小9dB左右。     

PMD-induced fluctuations of bit-error rate in optical fiber systems

This paper presents a method that allows evaluating the performance of an optical fiber system where bit errors result from a complex interplay of spontaneous noise generated in optical amplifiers and birefringent disorder of the transmission fiber. We demonstrate that in the presence of temporal fluctuations of birefringence characteristics, the bit-error rate (BER) itself is insufficient for characterizing system performance. Adequate characterization requires introducing the probability distribution function (PDF) of the BER obtained by averaging over many realizations of birefringent disorder. Our theoretical analysis shows that this PDF has an extended tail indicating the importance of anomalously large values of BER. We present the results of comprehensive analysis of the following issues: 1) The dependence of the PDF tail shape on detection details, such as filtering and regular temporal shift adjustment; 2) the changes in the PDF of BER that occur when the first- or higher order polarization mode dispersion (PMD) compensation techniques are applied; 3) an alternative PMD compensation method capable of providing more efficient suppression of extreme outages.     

2 Gbit/s and 2.4 Gbit/s optical transmission field trial over a 32 km installed route

High-speed optical data transmission at 2Gbit/s and 2.4 Gbit/s has been demonstrated for the first time over an installed fibre-optic cable. Error-free transmission with operating margins of 15.8 dB and 12 dB over 10?9 BER was achieved over a 32 km route. The systems featured a 1.5 ?m DFB laser, Ge APD transimpedance receivers and full regeneration.     

BER performance of turbo-coded PPM CDMA systems on optical fiber

We obtain upper bounds on the bit error rate (BER) for turbo-coded optical code-division multiple-access (CDMA) systems using pulse position modulation (PPM). We use transfer function bounding techniques to obtain these bounds, so our results correspond to the average bound over all interleavers of a given length. We consider parallel concatenated coding (PCC) schemes that use recursive convolutional codes as constituent codes. We consider systems using an avalanche photodiode (APD), and treat APD noise, thermal noise, and multi-user interference using a Gaussian approximation. We compare the performance of turbo-coded systems with that of BCH-coded systems with soft-decision decoding, and that of concatenated coding systems with outer Reed-Solomon (RS) code and inner convolutional code. We show that turbo-coded systems have better performance than BCH-coded systems. We also show that concatenated systems have better performance than turbo-coded systems when the block length is small and the received laser power is somewhat large