K - 1); = (2.77) where A is defined in (2.75). Averaging (2.71) over the pdf of (2.77) gives the desired result (2.78) Equivalently, letting (2.79) represent the "effective" pdf of the (i - 1)-st symbol phase, then (2.78) becomes the simple result (2.80) Figure 2.10 is a plot of Ps versus Y's in decibels as evaluated from (2.80) for K = 4 (DQASK-16). Also shown is the corresponding result for coher- ent detection of QASK which, for K = 4, is given by [8]: P,=3@(4)[1-]Q(A)]. (2.81) For comparison, the performance of coherent and differentially coherent detection of MPSK with M = 16 (i.e., PSK-16 and DPSK-16) is presented in Figure 2.10 [5]. For small Ys, the coherent PSK-16 and the DQASK-16 per- form almost identically, but for large Ys, the DQASK-16 approaches the per- formance of DPSK-16. Also, for large Ys, coherent QASK-16 is about 4 dB better than coherent PSK-16 showing the more favorable exchange of aver- age power for bandwidth with the QASK-16 than with the PSK-16. While Performance of FH/DQASK in the Presence of Partial-Band Multitone Jamming DPSK 16 DQASK-16 PSK-16 QASK-16 Figure 2.10. Symbol probability of error versus symbol SNR for coherent and dif- ferentially coherent detection of QASK-16 and PSK-16. it is true that DQASK-16 suffers a significant performance deegradation with respect to coherent QASK-16 at large Ys, we must recall our initial moti- vation, namely to use DQASK-16 along with frequency hopping (i.e., FH/DQASK) to protect a conventional QASK communication system against jamming. In the next two sections, we present the FH/DQASK per- formance in the presence of partial-band jamming and noise jamming. 2.4 PERFORMANCE OF FH/DQASK IN THE PRESENCE OF PARTIAL-BAND MULTITONE JAMMING A frequency-hopped, differentially coherent M-ary QASK modulation (FH/DQASK-M) is characterized by transmitting in the i-th symbol inter- val [(i - M possible signals of the form s(1)(t) = + (-1) + asin(whit + ((i-1))], (2.82) Differentially Coherent Modulation Techniques where who is the particular carrier freque