Optimum receiver design for transmitted-reference signaling

Autocorrelation receiver (AcR) is usually used as the general receiver for transmitted reference (TR) communication systems on a quite intuitive basis. In this paper, we apply the principle of statistical invariance to obtain the optimum TR receiver on a decision-theoretic basis, and it is shown that the autocorrelation receiver is optimal only in a special case. Performance of the optimum receiver and the suboptimum AcR for some important modulation schemes is also evaluated. The results imply that allocating a part of the transmitted energy and bandwidth to reference pulses would not help improve the performance of the system and the optimal performance might be achieved via much simpler non-TR transceiver structures. However, it is shown that differential TR and some other generalizations might be used to boost the performance, and numerical results are provided to assess the degree of performance improvement achieved in each case.