Giancarlo Pirani

Error probability in optical fiber transmission systems

A method for evaluating the average error probability in digital fiber optic transmission systems is described. It takes into account the statistical properties of the main impairments that affect the information signal, i.e., shot noise (dark current included), thermal noise, and intersymbol interference. Unlike other methods, the analysis of shot-noise statistics does not entail the second-moment characterization alone, but uses a number of moments sufficient to evaluate the error probability with a high degree of accuracy. For this purpose it is shown how the cumulants of shot noise and intersymbol interference of any order can be computed. The baseband pulse response and the statistical distribution of the avalanche-photodetector gain are assumed to be available. Moreover, techniques for exploiting the cumulants are given; knowledge of the cumulants allows one to compute the probability of error by means of Gaussian numerical integration rules. Finally, some results and comparisons are reported.

An analytical formula for the design of quadrature mirror filters

Quadrature mirror filters have an outstanding relevance in the implementation of filter banks for dividing the speech signal into frequency bands and for reconstructing it from these subbands. An analytical formula is given, which allows one to optimize the design of the basic low-pass FIR filter by means of a straight nonlinear minimization procedure.

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

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.

Adaptive Multiplication-Free Transversal Equalizers with Application to Digital Radio Systems

Recently, multiplication-free digital filters have been proposed for different applications to digital radio systems and signal processing. The absence of multiplication is obtained by constraining each coefficient to be sum of powers of two. In this way, multipliers are substituted by shift registers and, if appropriate, some adders. The optimal power-of-two coefficients must be computed through a nonlinear optimization procedure. Until now the problem of adapting the power-of-two coefficients of base band transversal equalizers in the case of time-varying channels had not been considered. In this paper two algorithms are proposed to cope with this problem and are compared from the viewpoint of complexity, accuracy, and convergence speed. As an application example, transmission of a biphase PSK digital radio system over a multipath fading channel is considered.

A PAM-PPM signalling format in optical fibre digital communications

A combined pulse amplitude modulation (PAM) and pulse position modulation (PPM) technique is proposed and investigated as a feasible solution of the problem of line encoding in optical fibre communication systems. The basic idea is that of exploiting PAM and PPM jointly, to give rise to three different waveforms in one signalling period, without resorting to more than two signal levels. Some evaluations of the behaviour of this signalling format are reported in terms of coding efficiency, spectral density, timing information, and error probability. Alternative receiving schemes are also devised to improve system performance.

A simple timing circuit for optical PCM repeaters

A simple synchronization system is proposed for timing recovery in optical PCM repeaters. The basic idea is to exploit the spectral line at the transmission rate, which is already present in the unipolar symbol stream travelling along the fibre. Since a nonlinear circuit is no longer needed, the amplified signal at the photodetector output is directly filtered by a resonant circuit to give the clock recovery by means of a zero-crossing detector. The limits of effectiveness of this synchronization system are then discussed, especially with regard to the accumulation of timing jitter as well as of alignment error.

Timing error tolerant waveforms in optical fibre systems

The problem of pulse shaping and sensitivity to timing errors in optical fibre data communication is considered. The performance of the overall transmission system is the average probability of error, which is computed for intersymbol interference, thermal noise, and shot noise in avalanche photodiodes. An analysis of the immunity to small sampling errors of various Nyquist pulses indicates useful design criteria.

Conclusions and Future Developments

The speech understanding system that has been described in the preceding chapters represents a first prototype that is still open to evolution and improvement. Although the final result of the ESPRIT Project P26 represented a good achievement of our goals, we do believe that both the recognition and understanding stage should get better performance in order to make the overall system more accurate and robust.

Introduction to the Book

ESPRIT Project P26, “Advanced Algorithms and Architectures for Speech and Image Processing”, started in October 1984, after a one-year feasibility study (since October 1983 to September 1984) in the ESPRIT Pilot Phase, and ended in September 1988 with an overall effort of about 130 man-years.

Comments on "On Linear Receivers for Digital Transmission Systems"

In the above paper,’ Benedetto and Biglieri develop the approach proposed by Lawrence and Kaufman [l] for the equalization of digital communication systems. Specifica.lly, they consider the problem of multilevel data communication for linear-modulation systems, e.g., pulse-amplitude modul?t’ion (PAM), digital phase moddation (PSK) , and combined amplitude-phase modulation (PAM-PSK) . Moreover, they discuss some other related topics, e.g., the receiver stability. Some observations 011 the paper are made. These extensions had already been carried out bv Guardincerri.