A Unified Approach to Pulse Design in Data Transmission

The problem of designing optimum pulseshapes for data transmission over randomly selected channels is examined using a meansquared error criterion. Earlier work has focused principally on SSB or VSB systems in the presence of timing and carrier phase jitter, but we extend the results here to any two-dimensional signaling scheme (including as special cases SSB, VSB, combined AM-PM, QAM, and staggered QAM) and to any type of channel dispersion. By imposing certain mild constraints on the transmitter and receiver filters, it is seen that one can solve for optimum pulses more easily than with earlier approaches, and yet the resulting system is still essentially optimum. These constraints leave design freedom only in the rolloff bands of the pulse spectra, and a major thurst of the work is to design for optimal utilization of whatever excess bandwidth is available. The approach used involves immunity to channel distortions: only the type of channel distortion to be encountered is known, and series expansions of mean-squared error are used to find sensitivity coefficients. These coefficients are then minimized by proper signal design. Closed form expressions are found for the optimum pulses, and these results are compared with previous work. A second approach, which uses as its criterion the mean-squared error averaged over all possible channel characteristics, is also discussed.