Nonparametric Decentralized Sequential Detection via Universal Source Coding

We consider nonparametric or universal sequential hypothesis testing problem when the distribution under the null hypothesis is fully known but the alternate hypothesis corresponds to some other unknown distribution. These algorithms are primarily motivated from spectrum sensing in Cognitive Radios and intruder detection in wireless sensor networks. We use easily implementable universal lossless source codes to propose simple algorithms for such a setup. The algorithms are first proposed for discrete alphabet. Their performance and asymptotic properties are studied theoretically. Later these are extended to continuous alphabets. Their performance with two well known universal source codes, Lempel-Ziv code and Krichevsky-Trofimov estimator with Arithmetic Encoder are compared. These algorithms are also compared with the tests using various other nonparametric estimators. Finally a decentralized version utilizing spatial diversity is also proposed. Its performance is analysed and asymptotic properties are proved.