ed quadrature amplitude-shift-keyed signals (DQASK) [2] which when augmented with an FH modulation can be used to protect the system from RFI or the intentional jammer [3]. Since we have already seen many times before that the performance of an FH modulation technique in the presence of a partial-band noise jammer is directly obtained from the corresponding performance of the unspread modulation over the AWGN channel, we begin our discussion by first considering the symbol error prob- ability performance of DQASK in such a Gaussian noise environment. 2.3.1 Characterization of the Transmitted Signal As a brief review of our presentation in the previous chapter, an M-ary (QASK-M) is characterized by transmitting in each symbol interval one of M possible signals of the form s(t) = V28[bn cos wot + am sin wot]=V2Re{semwot} = (2.55) where w0 is the carrier radian frequency. The total number of signals M is typically the square of an even number K, and the quadrature amplitudes am and bn take on equally likely values m and n with m,n = =1, =3, + - 1). Here, 8 is a parameter which is related to the average power S of the signal set by S = }(K2 - 1)82. (2.56) Differentially Coherent Modulation Techniques In order to describe the manner in which a QASK signal may be differ- entially phase encoded SO that differentially coherent phase detection may be performed at the receiver, a polar coordinate representation of the sig- nal set is preferable to the rectangular coordinate representation in (2.55). In particular, if in the i-th signalling interval (i - 1)Ts < < iTs, it is desired to transmit a signal corresponding to the signal point vector (2.57) the differentially phase-encoded QASK signal in this interval would then appear as s(1)(t) = (2.58) where (2.59) Note that, while (i) is restricted to take on values n=+1,3,..+(K-1), = (2.60) the actual transmitted phase, (ii) in the i-th interval has no such restriction. Consequently, an estimate of (ii) alone conveys no information regarding the phase, (i) of the transmitted i