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Unit time-phase signal sets: bounds and constructions. (English) Zbl 1335.94014
Summary: Digital signals are complex-valued functions on $$\mathbb Z_n$$. Signal sets with certain properties are required in various communication systems. Traditional signal sets consider only the time distortion during transmission. Recently, signal sets taking care of both the time and phase distortion have been studied, and are called time-phase signal sets. Several constructions of time-phase signal sets are available in the literature. There are a number of bounds on time signal sets (also called codebooks). They are automatically bounds on time-phase signal sets, but are bad bounds. The first objective of this paper is to develop better bounds on time-phase signal sets from known bounds on time signal sets. The second objective of this paper is to construct four series of time-phase signal sets, one of which is optimal.

##### MSC:
 94A12 Signal theory (characterization, reconstruction, filtering, etc.)
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