Adaptive Sequential Detection of an Unknown Signal

摘要

This paper treats the problem of sequentially detecting a signal whose amplitude is fixed but initially unknown to the system designer. Under the assumption that the signal is drawn from a Gaussian population with known parameters, the sequential likelihood-ratio detector for detecting the signal in the presence of Gaussian noise is derived. The amount of information per sample provided by this detector is then calculated and compared with that for a detector designed for a specific signal strength. This quantity provides considerable insight into the adaptive capability and the performance of the detector. Finally, the operating characteristic function (OCF) and the average sample number (ASN) are investigated using approximate analytical techniques in conjunction with computer simulation. It is shown that the detector considered in this paper provides considerably more protection against small signals than does a detector designed for a specific signal strength, at the expense of considerably longer average test lengths for such signals. (Author)