On sequential sign detection of a constant signal

In fixed sample size signal detection, the sign detector is easier to implement and requires much less knowledge of the noise density than does the optimum fixed sample size detector. These advantages accrue at a cost of more observations needed to achieve the same performance. By utilizing the sign detector sequentially, it is shown that considerable saving in the (average) number of observations is obtained over the corresponding optimal fixed sample size detector. The asymptotic relative efficiencies, as the signal-to-noise ratio and both probabilities of error approach zero, of the sequential sign detector compared to fixed sample size detectors are derived. The possibility of truncating the test to avoid excessively large numbers of observations is considered.