Error Probability Estimation Using Bivariate Extreme-Value Theory

Information is ultimately conveyed by the use of some form of decision or threshold device in binary communication systems. Threshold receivers are all basically "signal present" receivers, and are used in both telemetry and command systems for deep space probes and orbital spacecraft. One attack on the problem of experimentally determining bit error rates in such systems is the standard concept of bit error testing, i.e., comparing transmitted and received digital information bit by bit. When either error rates or bit rates are low, considerable test time is required to establish error rates by this method. This paper presents an application of the statistics of extreme values to the problem of estimation of low error probabilities in binary communication systems, with special reference to systems which have "loss-of-lock" indicators. The idea of the extreme-value theory method is to record the maxima within a large group of successive independent samples of the detector analog signal just prior to quantization, and then in turn record a large number of these maxima themselves. Next, the two parameters of the double exponential extreme-value probability distribution are estimated. The probability of exceeding the error threshold is then calculated from knowledge of these two parameters. The presence of a loss-of-lock indicator reduces the error probability at the expense of introducing an "erasure" probability. Techniques are given for estimating both these probabilities using "bivariate" extreme-value theory.