nformation symbol. This is a consequence of the differential phase-encoding operation described by (2.59). Immediately, then, one observes that, in order to estimate (i) in the absence of absolute phase information, what is needed is a receiver which forms estimates of (ii) and ((i-1) and computes their difference. Furthermore, since the QASK signal set is obviously not constant envelope, the amplitude, A(), must also be estimated by the receiver in order to complete the deci- sion on S(i). Again, since absolute phase information is assumed to be unavail- able at the receiver, the estimate of A(i) is obtained from a non-coherent envelope detector. In the next section, we describe and derive the performance of a receiver which performs the above two functions, namely, differentially coherent detection of phase and non-coherent detection of envelope (amplitude). 2.3.2 Receiver Characterization and Performance Figure 2.8 depicts a receiver used to perform differentially coherent detec- tion of differentially phase-encoded QASK. The structure combines the ele- ments of a differentially coherent receiver for a constant envelope modulation such as MPSK with a non-coherent envelope detector. The out- put from these two receiver components, namely, detected envelope and dif- 3When we discuss the differentially coherent detection process in the next section, we shall switch back to the rectangular representation to accommodate the rectangular-shaped decision regions. K Level Quantizer Envelope Detector - 2 sin (wor-ta) K-Level ( )dt Phase Quantizer Estimator cos ( ) -sin () (i-1)Ts n(i)= (i) n (i-1) (1;0) 52 COS (wot-to) tan -1 visit VS Delay Ts (i-1) (i-1)Ts Figure 2.8. A receiver for differentially coherent detection of differentially phase-encoded QASK. Differentially Coherent Modulation Techniques ferential phase are then converted to equivalent in-phase and quadrature signals upon which multilevel decisions are made, as is done in the more con- ventional coherent QASK receiver. Appearing at the receiver input in the 