Industrial manufacturing of low loss optical fiber cables and their specific splicing toolings, together with recent developments of optoelectronic components will lead to real systems installations in the 1980’s. The requirements for these new systems are related to some of the fiber characteristics: 


protection against electromagnetic perturbations


radiation leakage


small size


low weight


electrical isolation


high bandwidth


low attenuation


low cost expectation



Understanding fiber optic transmission systems requires a knowledge of the characteristics of optoelectronic transmitters and receivers, which do not differ much from traditional copper pairs (choice of analog to digital modulation, total attenuation, etc.). Therefore, throughout this course we will limit our effort to descriptions of specific elements, essentially those whose parameters are directly connected to system performance.

Fiber Optic Communication Systems

An analytical solution to the problem of modeling bandpass nonlinear channels and evaluating the performance of digital communication systems operating on them is presented. A method based on a Volterra series representation of the overall channel is first proposed, which allows one to extend to nonlinearities with memory the well-known concepts of complex envelope of bandpass signals and low-pass equivalent of bandpass linear systems. The general results previously mentioned are then applied to digital satellite communication systems operating over nonlinear channels. The effect of a nonlinear amplifier located in the satellite is considered, in combination with that of transmitting and receiving filters located in the Earth stations. In addition, both uplink and downlink noise are taken into account. Basic advantages of this approach are the generality it offers to the analysis and the fact that it allows accurate evaluation of the error probability in a short computer time.

Modeling and Performance Evaluation of Nonlinear Satellite Links-A Volterra Series Approach

Digital communication systems are frequently operated over nonlinear channels with memory. The analysis of the performance of these systems is difficult and no complete analytical treatment of the problem has been obtained before. Several recent efforts have been directed toward the computation of error probabilities via Monte-Carlo simulation using a complete system model. These simulations require excessively large sample sizes and are not practical for estimating very low values of error probabilities. This paper presents a modified Monte-Carlo simulation technique for estimating error probabilities in digital communication systems operating over nonlinear channels. An importance-sampling technique is used to modify the probability density function of the noise process in a way to make simulation possible. Theoretical results as well as realistic examples are presented, showing that the number of samples needed for simulation is reduced considerably.

A Modified Monte-Carlo Simulation Technique for the Evaluation of Error Rate in Digital Communication Systems

This letter presents a new method for the evaluation of the bit error probability of a time hopping binary pulse position ultra-wideband modulation scheme, in the presence of multiuser interference. The technique permits to predict the system performance with high accuracy and reasonable complexity. A perfect agreement with simulation results is shown, and a comparison with the Gaussian approximation is presented.

Performance evaluation of TH-PPM UWB systems in the presence of multiuser interference

The probability of error in a binary symmetric channel with intersymbol interference and additive noise is efficiently calculated by numerical quadrature of a Laplace inversion integral along a contour in the complex plane passing through a saddlepoint of the integrand. For Gaussian noise, a bound is set on the truncation error incurred by necessarily restricting the integration to a finite interval. The probability of error resulting from cochannel interference is calculated by a similar technique.

Calculating Error Probabilities for Intersymbol and Cochannel Interference

A new method is presented to compute the average probability of error in the presence of intersymbol interference and additive noise for multilevel pulse-amplitude-modulation (PAM) and partial-response-coded (PRC) signaling schemes. The method is based upon nonclassical Gauss quadrature rules (GQR) and suffers no limitation on noise statistics, so that it applies also for non-Gaussian noise. Moreover it yields some remarkable advantages as compared with other methods, in particular, with the series expansion method that has recently received considerable attention. Expressions for the truncation error are also given and their derivation is reported in the Appendix. Finally, examples of applications are presented and comparisons with other methods are carried out.

Error Probability in the Presence of Intersymbol Interference and Additive Noise for Multilevel Digital Signals

Incoming data pulses from a transmission channel are differentially combined with feedback pulses from the downstream end of a cascade of (N-1) delay networks to form an updating signal fed in parallel to a first set of multipliers for weighting with respective coefficients b 1 - b N -1 . These multipliers deliver optimized signal components to the inputs of respective delay networks of the cascade, through the intermediary of adders in each instance except for the first delay network at the upstream end; a further adder downstream of the last delay network may superimpose the updating signal, weighted with a coefficient b N by an N th multiplier of the first set, upon the feedback pulse issuing from the last delay network to generate an additional signal component. At least the more significant signal components, from the inputs of the delay networks located further upstream in the cascade, are weighted in a second set of multipliers with respective coefficients a 1 , a 2 etc. before being additively combined, in a summing circuit, into a composite output signal.

Digital equalizer for data-transmission system

A class of multilevel linear-modulation data-transmission systems, over unknown, slowly time-varying, and bandlimited channels is considered. It is shown how sequence estimation in the presence of Gaussian noise and intersymbol interference can be carried out by means of a discrete Kalman estimator. Moreover, the receiver can be provided with data-aided adaptive loops for performing channel identification, carrier recovery, and timing extraction. A computational method is presented to evaluate the average probability of error of the overall system in the presence of inter-symbol interference, additive noise, and phase-and sampling-synchronization errors. The method is based upon nonclassical one-and two-dimensional quadrature rules, which are outlined in the Appendix. As an example, numerical performance results related to a phase-shift-keying (PSK) system are given. The results are obtained by means of general-purpose and system-oriented computers.

Design and Performance of an Adaptive Kalman Receiver for Synchronous Data Transmission

In multilevel bandpass data transmission there is usually a difference between the phase of the carrier signal and the phase of the receiver oscillator, thereby causing imperfect demodulation. The use of nonclassical Gauss quadrature rules (GQR's) allows: 1) a theoretical study of the joint effects of phase jitter, thermal noise, and intersymbol interference on average error probability; and 2) a maximum-precision sampling technique in the simulation of digital communication systems. On this basis, the mean-square-error and zero-forcing equalizers are considered, and their performances evaluated in terms of the average error probability for multilevel pulse-amplitude-modulation (PAM) and partial-response-coded (PRC) signaling schemes.

Application of Gauss Quadrature Rules to Digital Communication Problems

An incoming data stream in the output of a demodulator and its derivative in the output of a differentiator are passed by respective sampling gates to a pair of equalizers operating by recursive filtration. The optimized data pulses issuing from the first equalizer are quantized and, after storage in a shift register, are algebraically combined in a first adder with a reference signal x from that equalizer representing the vector sum of weighted data pulses from a succession of N preceding clock cycles; a resulting error signal e n is delivered to three cumulative multipliers forming part of three feedback loops which supply an optimized phase signal ζ to the demodulator, an optimized timing signal τ to the sampling gates and an optimized gain coefficient K to the equalizers. These three multipliers respectively receive the reference signal x from the first equalizer, an optimized differential signal dx/dτ from the second equalizer and an updating signal z from the first equalizer. A further cumulative multiplier forms part of a fourth feedback loop delivering an optimized channel coefficient G to the equalizers, this latter loop including a second adder which synthesizes another error signal e' from the incoming data pulses z and from the complex product G·x produced by the last-mentioned multiplier. Each feedback loop includes a selective delay circuit effective only during an operating phase, in contrast to an acquisition phase during which the first adder receives a locally generated test signal in lieu of the quantized data pulses.

Angelo Luvison

Papers

Error Probability in the Presence of Intersymbol Interference and Additive Noise for Multilevel Digital Signals

Digital equalizer for data-transmission system

Design and Performance of an Adaptive Kalman Receiver for Synchronous Data Transmission

Application of Gauss Quadrature Rules to Digital Communication Problems

Adaptive method of and means for recovering digital signals