Methods and techniques for parameter and distribution function estimation in cascaded digital channels with and without memory

Abstract

Future telecommunication networks will employ digital transmission techniques. Such networks will provide a number of benefits including the ability to integrate voice and non-voice messages. The transmission channel of this network can be represented by a cascaded channel composed of a number of elementary channels connected in series. Therefore the modelling of such a channel is of particular interest. The influence of noise and other impairments in the cascaded binary channel cause errors which may be represented by a binary signal called the error sequence. Consequently, an important step in digital channel modelling is estimation of parameters and distribution functions which characterise the statistical properties of error sequences in the channel. Thus, the development of efficient methods for this estimation is a problem of long term interest which should be properly solved. This thesis presents methods and techniques for parameter (primarily the probability of error) and distribution function (primarily the error gap complementary distribution function) estimation using the error sequences obtained by measurement or simulation in elementary or cascaded channels. Theoretical analysis and testing confirm that it is possible to control the accuracy and reliability of estimation. Two principal and practical methods for the probability of error estimation are developed: the modified Monte Carlo method (MMC); and the method based on Chebyshev inequality (MCI). In contrast to the traditional Monte Carlo method based on classical statistics, the methods developed in this thesis aim to specify the sample size required to achieve the desired accuracy. The methods developed are based on the dependence of the sample size on the estimated value of a parameter being estimated. Hence the sample size is a random variable and the confidence limits factor (which specifies the width of confidence interval in respect to the estimated value) is a constant. Based on these methods, this thesis proposes and demonstrates two techniques for parameter estimation. The traditional Monte Carlo method has been primarily used for the probability of error estimation in channels without memory. In this thesis the capabilities of this method are extended to the case of estimating the probability of error in channels with memory and cascaded channels. However, even with this extension, this method is not practical due to its complexity and limitations on the qualification and quantification of the accuracy and reliability of estimation. Also, the extended method is unable to satisfactorily estimate the probability of error in cascaded channels with memory; nor could it improve the speed of the estimation process. Two methods and two techniques for distribution function estimation are developed in this thesis. They are demonstrated by estimating the error gap complementary functions of simulated data. For this purpose, simulators of binary channels with and without memory have been developed. The methods and techniques are characterised by their simplicity in application; ability to quantify the accuracy and reliability; time efficiency; and real time capability. The wider application of the methods and techniques developed in this thesis are demonstrated on three examples: a distribution function estimation using data obtained by indoor wideband radio propagation measurement; BER characteristics measurement; and measurement of the residual probability of error in transmission systems using error correcting codes. From the results obtained in the thesis some recommendations for future work in the field of digital channel modelling and simulation are discussed.