Importance sampling for analysis of direct detection optical communication systems

Journal PaperAnalytical solutions of the performance of optical communication systems are difficult to obtain and often, Monte Carlo simulations are used to achieve realistic estimates of the performance of such systems. However, for high performance systems, this technique requires a large number of simulation trials for the estimates to be in a reasonable interval of confidence, with the number of trials increasing linearly with the performance of the system. We apply an importance sampling technique to estimate the performance of direct detection optical systems, where the "gain" of importance sampling over Monte Carlo simulations is shown to increase linearly with the system performance. Further, we use this technique to study the performance of optical communication systems employing avalanche photodetectors as well as fibre-optic code division multiple access systems (FO-CDMA). We also show that the quick simulation technique developed can be used for a wide variety of coding schemes, and for the first time, we present a comparative analysis of the performance of FO-CDMA systems employing optical orthogonal codes and prime sequences. In all cases, it is shown that importance sampling simulations require less than 50-100 trials for estimating error probabilities of 10^-10 and below

Gradient estimation for stochastic optimization of optical code-division multiple-access systems. II. Adaptive detection

Journal PaperFor pt.I see ibid., vol.15, no.4, p.731-41 (1997). We develop infinitesimal perturbation analysis (IPA)-based stochastic gradient algorithms for deriving optimum detectors with the average probability of bit error being the objective function that is minimized. Specifically, we develop both a class of linear as well as nonlinear (threshold) detectors. In the linear scheme, the receiver despreads the received optical signal with a sequence that minimizes the average bit-error rate. In the case of the threshold detector, the detection threshold for the photoelectron count is optimized to achieved minimum average bit-error rate. These algorithms use maximum likelihood estimates of the multiple access interference based on observations of the photoelectron counts during each bit interval, and alleviate the disadvantage of previously proposed schemes that require explicit knowledge of the interference statistics. Computer-aided implementations of the detectors derived are shown to outperform the correlation detector. Sequential implementations of the adaptive detectors that require no preamble are also developed, and make them very viable detectors for systems subject to temporal variations

Gradient Estimation for Sensitivity Analysis and Adaptive Multiuse Interface Rejection in Code-division Multiple-access Systems

Journal PaperIn this paper, we consider a direct-sequence code-division multiple-access (DS-CDMA) system in the framework of a discrete-event dynamic system (DEDS) in order to optimize the system performance. Based on this formulation, we develop infinitesimal perturbation analysis (IPA) for estimating the sensitivity of the average probability of bit error to factors ranging from near-far effects to imperfections in power control. The above estimates are shown to be unbiased, and this technique is then further incorporated into a stochastic gradient algorithm for achieving adaptive multiuser interference rejection for such systems, which is also subject to frequency nonselective slow fading. We use an IPA-based stochastic training algorithm for developing an adaptive linear detector with the average probability of error being the minimization criterion. We also develop a practical implementation of such an adaptive detector where we use a joint estimation-detection algorithm for minimizing the average probability of bit error. A sequential implementation that does not require a stochastic training sequence or a preamble is also developed

Gradient Estimation for Stochastic Optimization of Optical Code-Division Multiple-Access Systems: Part I -- Generalized Sensitivity Analysis

Journal PaperFor optimizing the performance of optical code-division multiple-access (CDMA) systems, there is a need for determining the sensitivity of the bit-error rate (BER) of the system to various system parameters. Asymptotic approximations and bounds, used for system bit-error probabilities, seldom capture the sensitivities of the system performance. We develop single-run gradient estimation methods for such optical CDMA systems using a discrete-event dynamic systems (DEDS) approach. Specifically, computer-aided techniques such as infinitesimal perturbation analysis (IPA) and likelihood ratio (LR) methods are used for analyzing the sensitivity of the average BER to a wide class of system parameters. It is shown that the above formulation is equally applicable to time-encoded and frequency-encoded systems. Further, the estimates derived are unbiased, and also optimality of the variance of these estimates is shown via the theory of common random variates and importance sampling techniques