Probability density function of the line-of-sight angle error

The closed form probability density function (PDF) of the angle between the input and output of the time discrete AWGN channel is derived. Two N-dimensional Cartesian systems are considered. The PDF can be used for calculation of the corresponding cumulative distribution function (CDF) which determines the best known general lower and upper bounds on the decoding error probability of optimal block codes on the AWGN channel. For odd values of N/spl ges/3 this reduces to a closed form too.