L-Orthogonal Signal Transmission and Detection

This paper investigates the detail capabilities and performance characterization of systems that employ
L
-orthogonal signaling techniques.
L
-orthogonal signals represent a unified set of signals wherein the polyphase and orthogonal (biorthogonal) signal sets are included as special cases. This fact is important since orthogonal (biorthogonal) and polyphase signaling sets represent opposing forces as far as tradeoffs between error probability, energy-to-noise ratio, and bandwidth requirements are concerned. Bounds on the performance of the optimum receiver and the performance of various suboptimum (practical) receiver structures are given. Coherent and differentially encoded signals are also pursued. Various comparisons and tradeoffs are made by means of numerical evaluation of the error-probability expressions.