On the use of X2-test in signal detection

The problem considered in this work is the detection of a random signal in colored noise. A modelling approach was used to construct two hypotheses: that the received data consisted of noise alone (hypothesis H0) and that they consisted of signal plus noise (hypothesis H1). The models used were linear auto-regressive models. A log likelihood ratio was constructed, based on these hypothesis. The probability density of this ratio was approximated by a χ²- distribution, from where the threshold levels for the detector under a given probability of detection could be estimated. Computer simulations showed that the χ²-approximation provided a good basis for threshold estimation. A good detection performance was also verified.