Signal design for a coded communication system

In many practical communication systems it is often necessary to transmit over a single radio frequency channel N binary data signals, one pseudo-noise binary sequence, and a carrier reference signal. This dissertation develops general design criteria for realizing such a multiplexing system, and answers a number of previously unresolved questions concerning the choice and performance of the data detector and the effect of probabilistic coding of the data signals. The general problem of the choice of modulation and multiplexing techniques is first examined. It is shown that a frequency division multiplexed system is in a sense optimum for this signal set. It is also shown that two good modulation techniques are amplitude modulation and phase modulation, but that it is not possible to categorically choose one over the other. The effect of a noisy phase reference and noisy timing signals on the performance of the phase shift keyed PSK data signals is analyzed. The optimum detector for receiving such signals with a noisy phase reference is derived. The performances of two practical detectors, the squaring loop and the Costas loop, are analyzed and compared with the optimum detector. It is shown that for all practical purposes the Costas loop closely approaches the performance of the optimum detector for all signal to noise ratios. It is also shown that the effects of timing errors are relatively insignificant when compared with phase reference errors. The effect of probabilistic coding of the PSK channel is discussed. The criterion for rating coded systems, the computational cutoff rate R[subscript 0], is derived for the noisy PSK channel. R[subscript 0] is then used to compare the performance of a number of coded and uncoded systems.