Computing error probabilities over fading channels: A unified approach

Abstract

Abstract This paper is a tutorial on the calculation of error probabilities for fading channels. The method we advocate is centered on the evaluation of the Laplace transform Φ δ ( s ) of the probability density function of the difference A between the metrics of two competing signal sequences. In some cases, knowledge of the function Φ δ ( s ) allows one to determine error probabilities exactly in closed form, or asymptotically as the signal‐to‐noise ratio grows to infinity. The general technique t hat we describe here allows their computation in numerical form to any desired degree of accuracy. Coded as well as uncoded transmission can be considered in this unified framework. For illustration's sake, some examples of calculations are provided for frequency‐flat slow‐fading channels in which coherent detection is used, and the channel state information is perfect, or unavailable, or obtained from a noisy pilot tone.