Signal design for sequential detection systems with feedback

We consider a coherent white Gaussian channel, through which one of two signals is sent to a receiver which operates as a sequential detector. A noiseless delayless feedback link is assumed, which continuously informs the transmitter of the state of the receivers uncertainty concerning which signal was sent, and which also synchronizes the transmitter when the receiver has reached a decision. The transmitter, in turn, uses the output of the feedback link to modify its transmission so as to hasten the receiver's decision. The following problem is posed: Given average- and peak-power constraints on the transmitter and a prescribed error probability for the receiver, what signal waveforms should the transmitter use in order to minimize the average transmission time, and how should it utilize the fedback values of the receiver's uncertainty to modify these waveforms while transmission is in progress? We give partial solutions to these questions. In particular, we have shown that if the peak-to-average power ratio is allowed to be sufficiently large, substantial improvement of performance may be achieved through the use of uncertainty feedback.