The Elimination Game or: Beam Selection based on M-ary Sequential Competition & Elimination

To solve the problem of deciding which among M unknown amplitude levels is the strongest one in a scenario where exact knowledge of the underlying PDFs and in particular the current SNR value is not available a so-called sequential competition test was proposed recently. By comparing the sequence metrics of M observation sequences to a 'no signal'- hypothesis the one which first crosses a termination threshold is selected. This amounts to a variable length test that adapts itself to an unknown SNR in contrast to a fixed length test. In this work we demonstrate that the average test length can be further reduced by eliminating stochastical paths (=competitors) already during the competition if these have become highly unlikely to be selected. In addition we investigate how the termination and elimination thresholds should be set in order to fulfill a given performance constraint defined as an average fraction of the maximum achievable rate.