Published in Annampedu, V., Roganov, V.V., & Viswanathan, R. (2000). Two rank order tests for M-ary detection. IEEE Transactions on Information Theory, 46(2), 585-594. doi: 10.1109/18.825823 ©2000 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.


We consider a general M-ary detection problem where, given M groups of L samples each, the problem is to identify which unique group of L samples have come from the signal hypothesis. The optimal likelihood ratio test is unrealizable, when the joint distribution of ML samples is not completely known. In this paper we consider two rank order types of tests termed as the modified rank test (MRT) and the modified rank test with row sort (MRTRS). We examine through simulation, the small sample probability of error performances of MRT and MRTRS for detecting a signal among contaminants. Numerically computable closed –form error expressions are derived for some special cases. Asymptotic (large sample) error rate of MRT is also derived. The results indicate that MRTRS provides improved performance over other previously known rank tests.