Digital Data Signal Space Diagrams

Many different kinds of modulated carrier signals arc being used in digital communication systems. All these various data signals can be expressed in the general form .4(0 cos [wj. + (t)] where a carrier cos u)ct is varied in amplitude by .4 (/) and in phase by (p(t). The various modulation methods impart different patterns of amplitude and phase variation. The characteristic pattern of a given modulation method can be portrayed by a polar plot of /I and / coet. This type of plot will be referred to as a "signal space diagram." Signal space diagrams will be described for several kinds of carrier modulation. Only synchronous signals consisting of sequences of evenly spaced symbols will be considered. In each case the received symbols can be thought of as a sequence of carrier pulses or bursts, each with an envelope shape determined by the channel characteristic. In such a view the differences among the types of modulation are due to the number of pulse amplitudes and phases which are used, the particular phase sequences used, and the spacing between pulses. In order to obtain the simplest signal space diagram it is desirable to choose the reference ojc as the center of the received pulse spectrum so that the phase variation of a single isolated pulse will be minimized. With a symmetrical pulse spectrum and a linear phase characteristic this reduces the pattern of a single isolated pulse to a radial line. When the phase of the carrier varies from pulse to pulse and the pulses overlap, more complicated 2973