A simplified non-Gaussian approach to digital optical receiverdesign with avalanche photodiodes: theory

A simplified theory of avalanche photodiode receiver sensitivity is presented in which the non-Gaussian nature of the avalanche multiplication process is taken into account. The theory predicts more accurately than a Gaussian theory the optimum avalanche gain and decision threshold and gives simple results for the influence of background photocurrent or dark current on receiver sensitivity, optimum gain, and threshold. For purposes of comparison, a parallel derivation using the Gaussian approximation for both the avalanche and receiver noises is given where simple expressions for the optimum avalanche gain and threshold settings are derived     

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     

Sensitivity penalty calculation for burst-mode receivers using avalanche photodiodes

This paper presents the sensitivity penalty for burst-mode receivers using avalanche photodiodes. The analysis takes into account detailed avalanche photodiode statistics, additive Gaussian noise, intersymbol interference and dc offsets in the receiver channel. The penalty has been calculated via comparison of bit-error rates (BERs), obtained using numerical integration, both in continuous- and burst-mode operation. Sensitivity penalties for burst-mode operation as a function of the mean avalanche gain are presented. The Gaussian approximation systematically underestimates the burst-mode penalty. It is shown that the penalty depends upon both the type of avalanche photodiode (APD) and the required BER. Optimum avalanche gains maximizing the sensitivity of the receiver are given. The influence of dc-offsets upon the sensitivity is studied. Furthermore, it is shown that the impulse response of the filters used to extract the decision threshold profoundly impacts the receiver performance. Finally, some important guidelines for the design of high sensitivity and wide dynamic range burst-mode receivers are given.     

Receiver Design for Digital Fiber Optic Transmission Systems Using Manchester (Biphase) Coding

An analysis of the sensitivity of an optical receiver in a digital communication system using Manchester (biphase) coding is performed. Both cases of p-i-n and avalanche photodiodes are considered. Experimental results for the sensitivity of a Manchester receiver operating at 250 Mbits/s are reported. Two types of low noise receiver amplifiers, namely the high impedance and the transimpedance amplifier, are designed and implemented for use in the receiver. A receiver sensitivity of -49.8 dBm in terms of detected optical power is obtained (at a 10^-9bit error rate and 0.1 laser extinction ratio), which corresponds to only 175 average photons per bit. It is shown that in contrast to the NRZ code, the Gaussian approximation theory tends to underestimate the Manchester receiver sensitivity. Tradeoffs between Manchester and NRZ coding are also discussed in terms of receiver sensitivity and ease of implementation. It is shown that Manchester coding is an attractive alternative to NRZ coding for optical transmission systems, particularly when an avalanche photodiode is used.     

Counting distributions and error probabilities for optical receivers incorporating superlattice avalanche photodiodes

Exact gain distributions and electron counting distributions are presented for superlattice avalanche photodiodes that operate by single-carrier transport perpendicular to the superlattice planes. The characteristic shapes of these distributions are compared with those of the single-carrier conventional avalanche photodiode and the photomultiplier tube. The electron counting distributions, which assume Poisson photocarrier injection, are used to calculate the error performance of a simple optical communication system. This performance is compared with that achievable by a single-carrier conventional APD receiver of identical quantum efficiency and gain. For simplicity of calculation, the system consists of a transmitter emitting light pulses containing a Poisson number of photons and a maximum-likelihood integrate-and-dump receiver. It makes use of binary on-off keying and is subject to noise events arising from multiplied background radiation and/or multiplied dark noise. The performance of the superlattice photodiode receiver turns out to be always superior to that of the single-carrier conventional photodiode receiver, for all values of the gain. The advantage can attain several orders of magnitude (even though the excess noise factors for the two devices lie within a factor of two). The superlattice receiver with high impact-ionization probability is shown to behave like an ideal photon counter with the same quantum efficiency, even if the device has many stages. The deleterious effects of receiver thermal noise on probability of error are examined.     

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.     

Performance evaluation of optical fiber transmission systems

A method is presented for evaluating of error probability for optical-fiber communication systems in the present of intersymbol interference and additive noise. It is based on deriving a best approximation, in a minimax sense, for the cumulative distribution function of the additive noise. The method takes into account the avalanche photodetector's non-Gaussian shot noise statistics. The additive noise is also not constrained to be Gaussian. Examples are presented for comparison to previously published techniques     

An adaptive spatial diversity receiver for non-Gaussianinterference and noise

Standard linear diversity combining techniques are not effective in combating fading in the presence of non-Gaussian noise. An adaptive spatial diversity receiver is developed for wireless communication channels with slow, flat fading and additive non-Gaussian noise. The noise is modeled as a mixture of Gaussian distributions and the expectation-maximization (EM) algorithm is used to derive estimates for the model parameters. The transmitted signals are detected using a likelihood ratio test based on the parameter estimates. The new adaptive receiver converges rapidly, its bit error rate performance is very close to optimum when relatively short training sequences are used, and it appears to be relatively insensitive to mismatch between the noise model and the actual noise distribution. Simulation results are included that illustrate various aspects of the adaptive receiver performance     

Performance of APD-based, PPM free-space optical communication systems in atmospheric turbulence

In this paper, we characterize the performance of a direct-detection, avalanche photodiode-based free-space optical (FSO) communication system in terms of the overall bit-error rate. The system of interest uses pulse-position modulation (PPM) and is subjected to scintillation due to optical turbulence. Two scenarios are considered. In one case, a weak turbulence (clear-air) scenario is considered, for which the received signal intensity may be modeled as a log-normal random process. In the other case, we consider a negative exponentially distributed received signal intensity. To arrive at the desired results, it is assumed that the system uses a binary PPM (BPPM) modulation scheme. Furthermore, it is assumed that the receiver thermal noise is nonnegligible, and that the average signal intensity is large enough to justify a Gaussian approximation at the receiver. Union bound is used to assess the performance of M-ary PPM systems using the results of the BPPM scenario. Numerical results are presented for the BPPM case to shed light on the impact of turbulence on the overall performance.     

A Detailed Comparison of Four Approaches to the Calculation of the Sensitivity of Optical Fiber System Receivers

In this paper four approaches to the calculation of error rates for optical fiber system repeaters are compared ("Exact" calculation, Monte Carlo simulation, Chernoff bounds and the Gaussian approximation). We conclude that the "Exact" and Monte Carlo calculations are in complete agreement. This allows the Monte Carlo results to be used to calibrate other methods. The relatively simple Chernoff bound is in very good agreement with the above, and should be used whenever computational facilities allow. For simpler calculations, or analytical expressions for the effects of parameter variations, the Guassian approximation gives a reasonable good estimate of the receiver sensitivity. However, it tends to underestimate the threshold setting and overestimate the optimal avalanche gain.     

Performance degradation of APD-optical receivers due to darkcurrent generated within the multiplication region

General expressions for the effective gain and effective excess noise factor associated with dark current generated within the high-field region of an avalanche photodiode (APD) are given. The influence of this background current on the performance of a uniformly multiplying APD receiver is evaluated and compared with that due to a dark current component generated outside the multiplication region (diffusion current). The results indicate clearly that the former dark current component has less effect on receiver performance than the latter, especially when hole and electron ionization rates are very different     

On adaptive minimum probability of error linear filter receiversfor DS-CDMA channels

Receiver architectures in the form of a linear filter front-end followed by a hard-limiting decision maker are considered for DS-CDMA communication systems. Based on stochastic approximation concepts a recursive algorithm is developed for the adaptive optimization of the linear filter front-end in the minimum BER sense. The recursive form is decision driven and distribution free. For additive white Gaussian noise (AWGN) channels, theoretical analysis of the BER surface of linear filter receivers identifies the subset of the linear filter space where the optimal receiver lies and offers a formal proof of guaranteed global optimization with probability one for the two-user case. To the extent that the output of a linear DS-CDMA filter can be approximated by a Gaussian random variable, a minimum-mean-square-error optimized linear filter approximates the minimum BER solution. Numerical and simulation results indicate that for realistic AWGN DS-CDMA systems with reasonably low signature cross-correlations the linear minimum BER filter and the MMSE filter exhibit approximately the same performance. The linear minimum BER receiver is superior, however, when either the signature cross-correlation is high or the background noise is non-Gaussian     

Gaussian approximation versus nearly exact performance analysis ofoptical communication systems with PPM signaling and APD receivers

A 25 Mbit/s direct-detection optical communication system that used Q=4 PPM signaling was constructed and its performance measured under laboratory conditions. The system used a single mode AlGaAs laser diode (λ=834 nm) and low-noise silicon avalanche photodiode (APD). A procedure is given to numerically compute system performance which uses the nearly exact Webb's approximation of the true Conradi distribution for the APD output that does not require excessive amounts of computer time (a few CPU minutes on VAX 8600 per system operating point). Comparison revealed that modeling the APD output as a Gaussian process under conditions of negligible background radiation and low (less than 10^-12A) APD bulk leakage currents leads to substantial underestimates of optimal APD gain and overestimates of system bit error probability. Examples are given which illustrate the breakdown of the Gaussian approximation in assessing system performance. The measured performance of the system was found to be in excellent agreement with the performance predicted by the nearly exact computational procedure. This system achieved a bit error probability of 10^-6 at a received signal energy corresponding to an average of 60 absorbed photons/bit and optimal APD gain of 700     

Effect of dead space on the excess noise factor and time responseof avalanche photodiodes

The effect of dead space on the statistics of the gain process in continuous-multiplication avalanche photodiodes (APDs) is determined using the theory of age-dependent branching processes. The dead space is the minimum distance that a newly generated carrier must travel in order to acquire sufficient energy to cause an impact ionization. Analytical expressions are derived for the mean gain, the excess noise factor, and the mean and standard deviation of the impulse response function, for the dead-space-modified avalanche photodiode (DAPD), under conditions of single carrier multiplication. The results differ considerably from the well-known formulas derived by R.J. McIntyre and S.D. Personick in the absence of dead space. Relatively simple asymptotic expressions for the mean gain and excess noise factor are obtained for devices with long multiplication regions. In terms of the signal-to-noise ratio (SNR) of an optical receiver in the presence of circuit noise, it is established that there is a salutory effect of using a properly designed DAPD in place of a conventional APD. The relative merits of using DAPD versus a multilayer (superlattice) avalanche photodiode (SAPD) are examined in the context of receiver SNR; the best choice turns out to depend on which device parameters are used for the comparison     

Performance analysis of a linear MMSE receiver for bandlimited random-CDMA using quadriphase spreading over multipath channels

This paper analyzes the bit-error-rate (P/sub e/) performance of a linear minimum mean-square error (LMMSE) receiver for bandlimited direct-sequence code-division multiple-access systems which use quadriphase spreading with aperiodic pseudonoise (PN) sequences. The analysis is based on the improved Gaussian approximation (IGA) with focus on chip pulse shaping. It shows that the IGA reduces to the standard Gaussian approximation (SGA) if 1) random quadriphase spreading is employed, 2) the spreading factor takes moderate to large values, and 3) the chip pulse excess bandwidth (BW) is zero. Hence, the SGA, known for its inaccuracy in low regions of P/sub e/, remains an accurate approximation even when the number of active users in the system is small as long as the aforementioned conditions are met. The analysis holds for either matched or different transmit and receive filters. Consequently, closed form conditional P/sub e/ expressions are derived for the coherent selective RAKE and the LMMSE receivers and verified with Monte Carlo simulations. Numerical results are presented to illustrate the performance improvement achieved by the LMMSE receiver which, in contrast to the coherent selective RAKE receiver, not only suppresses interference when the excess BW of chip pulse is nonzero, but also harnesses the energy of all paths of the desired user. Under the examined scenarios tailored toward current narrowband system settings, the LMMSE receiver achieves 60% gain in capacity over the selective RAKE receiver. A third of the gain is due to interference suppression capability of the receiver while the rest is credited to its ability to collect the energy of the desired user diversified to many paths. Future wideband systems will yield an ever larger gain.     

WDM transmission system performance: influence of non-Gaussiandetected ASE noise and periodic DEMUX characteristic

This paper presents the first unified wavelength division multiplexing (WDM) transmission model for systems incorporating cascaded optical amplifiers and a realistic demultiplexing (DEMUX) characteristic with periodic transfer function. The bit error ratio (BER) is evaluated accounting in rigorous form for the influence of non-Gaussian detected amplified spontaneous emission (ASE) noise, noise correlation between stochastic noise samples in the receiver, the bandwidth of the electrical receiver noise filter, the gain tilt and effective noise figure of optical amplifiers (with as well as without optical ASE noise filtering), channel crosstalk, signal extinction ratio and a one-or two-stage DEMUX implementation. The model is compared to the Gaussian receiver model in realistic design cases providing important information as to the validity of the Gaussian model. Practical design results indicate the link budget dependence on the DEMUX design and the ASE noise filtering     

Generalized quadratic receivers for orthogonal signals over theGaussian channel with unknown phase/fading

The orthogonal signal structure has been shown to be the superposition of an antipodal signal set and an unmodulated (pilot tone) component which can be used for channel measurement. Starting from this point of view, the quadratic receiver for orthogonal signals over the Gaussian channel with unknown phase/fading has been shown to be equivalent to a detector-estimator receiver. The estimator makes an optimum estimate of the unknown complex channel gain based on the channel measurement provided by the unmodulated component of the received signal. This channel estimate then forms a (partially) coherent reference for the detector in detecting the data carried by the antipodal signaling component of the received signal. This paper exploits this detector-estimator structure of the quadratic receiver, and generalizes it to a receiver in which the estimator makes an estimate of the channel gain in each signaling interval based on the totality of signals received over all the signaling intervals or a subset of these intervals. The generalized quadratic receiver is just as simple to implement as the conventional quadratic receiver, and theoretical and simulation results show that it can achieve substantial performance gains over the conventional receiver. A theory is presented to show that the generalized quadratic receiver is an implementable approximation to the optimum symbol-by-symbol receiver for uncoded orthogonal signals over the Gaussian channel with unknown phase/fading. The theory shows that the structure provides a unified and systematic approach to the design of coherent symbol-by-symbol receivers, and shows that the conventional carrier-loop-type receivers are ad hoc     

An Experimental 50 Mb/s Fiber Optic PCM Repeater

An experimental repeater for amplification and regeneration of 50 Mb/s fiber-optical pulses has been built and tested. For the receiver either Si p-i-n or avalanche photodiodes are used in conjunction with a high impedance FET input amplifier. The high voltage for the avalanche photodiode is generated internally and controlled by the received signal. This AGC circuit is capable of compensating for temperature changes of the avalanche gain over the range of-40 - +60degC. The optical transmitter consists of either a GaAs light emitting diode or a GaA1As laser diode coupled to optical fibers and directly modulated by a current driver with 30 percent electrical efficiency. For 10^-9error rate, the required average optical signal power for a pseudorandom signal is p-i-n diode: -41.5 dBm; avalanche diode: -56.6 dBm. The optical output power into a fiber with 1 percent index difference is LED: -17 dBm; GaAlAs laser: 0 dBm. The repeater power requirement is about 2 W.     

A Modified Receiver for Digital Optical Fiber Transmission Systems

A Percival coil connected between the photodetector and amplifier in the receiver of a digital optical communication system offers the possibility of a reduced signal power requirement for a given bit error rate. When the photodetector is an avalanche diode, the modified receiver requires a lower value of avalanche gain for optimum performance.     

Performance Analysis of GPS Receivers in Non-Gaussian Noise Incorporating Precorrelation Filter and Sampling Rate

Global positioning system (GPS) receivers find growing applications in indoor and outdoor communication environments, including urban and rural areas. Interference and noise sources for GPS receivers may assume Gaussian or non-Gaussian distributions. The GPS receiver performance under Gaussian additive noise has been studied. Non-Gaussian noise may equally contaminate the GPS satellite signals and disturb the receiver delay lock loops (DLL), producing significant tracking errors. These sources include impulsive noise, ultra-wideband (UWB) signals, and impulse and noise radar signals for target tracking and indoor imaging applications. This paper considers non-Gaussian noise of finite variance and examines its effect on the discriminator outputs for the commercial GPS receiver that uses the coarse acquisition (C/A) code. The correlator noise output components are produced from the correlation between the noise sequence and the early, late, and punctual reference C/A code. Due to the long time averaging, which is characteristic of the GPS correlation loops, these components assume Gaussian distributions. The discriminator tracking error variance is derived, incorporating the effect of noise, the front-end precorrelation filter, and the sampling rate.