#### Abstract

The concept of an open loop Adaptive Communication link is established as one which is capable of monitoring the medium through which it must perform while simultaneously transmitting information and continuously adjusting its modes of operation so as to optimize its performance with respect to a performance criterion chosen a priori. Statistical methods are applied to the adaptive communication problem. Communicating through a random multipath channel with additive noise is considered. The transmitter is specified as one which transmits one of two possible noise-like waveforms which are assumed to be known at the receiver. At any time, it is postulated that the receiver is to make its decision in accordance with the Bayes Rules which appropriately fits the amount of channel knowledge stored at the receiver. The knowledge concerning the channel state is derived a posteriori at the receiver from the information bearing signal. Consequently, as the a posteriori information changes (corresponding to changing propagation medium characteristics) the receiver’s decision circuitry also changes. Hence, the receiver is one which continuously adapts itself to yield optimum performance under the measured channel parameters. These random parameters are taken to be: channel gain, channel multipath structure, and the channel phase characteristic. Probability of error is evaluated in closed form for three different modes of operation. A major conclusion taken from these expressions is that the probability of error in no ease depends directly on the channel gain, but lather is a function of the total average energy received from all propagation modes, numerical evaluation of the error expressions enables comparisons to be made among the various systems modes of operation. These results show that measurement of the channel gain is the least important of these quantities. Given the multipath structure, the channel phase characteristic is the most important, In the optimum case a gain of about 6 db to 8 db (depending on the signal-to-noise ratio) is accomplished over the Receiver mode which performs only the multipath measurement. It is shown that the information gain concerning the multipath structure increases rapidly for a few bauds of identification time after which information build up begins to saturate. This is important because there will be available at the receiver only a finite time for which to identify this channel condition. The variance of the channel estimates are computed for maximum and minimum identification time. It is shown that the bandwidth of the transmitted waveform is the important parameter for accurate measurement of the multipath structure, while a sinusoid is sufficient for measuring the channel gain. By combining the channel measurement techniques and signal detection results, two Adaptive Receiver structures are formulated and their operation discussed. Finally, commentaries on future research are made and conclusions given about the above work.

#### Date of this Version

5-1-1962