 not to the jammer, are th two pseudorandom hopping sequences fo1, fo2, fom and f11, 11, fim which represent the two possible data symbols. Two similar FH waveforms have inner product 4(fa( (1.31) Orthogonality between two such waveforms is guaranteed, regardless of the values of the phases (01,0'1) and data symbols (d,d'), provided that (1.32) where k is any non-zero integer, for all d, d' in {0, 1}. We assume that two such orthogonal frequency waveforms are used by the communication sys- tem as fon and f1n, with a different pair for each n, 1 < n < M. If the transmitter and receiver are capable of producing and observing MF distinct orthogonal tones (assume MF is even for convenience), it is clear that during each hop the jammer mmust contemplate combatting a pure SS strat- egy on an orthogonal communication system complex of multiplicity M/2. Therefore, during each hop time a single link in the orthogonal system com- plex requires four dedicated orthonormal basis functions (e.g., sines and cosines at two distinct frequencies), and uses 4MD such functions over MD hops. By the same reasoning the number of basis functions available to the entire complex is 2MFM, and hence, the energy gain of (1.18) is given by (1.33) Energy Gain Calculations for Typical Systems Example 1.3. One possible hybrid SS communication system employs TH, FH, and DS modulations to produce the wideband waveform (1.34) in which p(t) is a unit-amplitude rectangular pulse of chip time duration Tc. A total of N pulses, modulated by the sequence {Cnmd,}, are concatenated to produce a DS waveform of duration Th, which in turn is frequency-hopped to one of MF frequencies and time-hopped to one of MT time intervals within the symbol time Ts. Hence, (1.35) Modulation by the n-th M-ary data symbol dn is accomplished by switching the DS modulation to the dm-th of M orthogonal vectors Two such hybrid SS signals have inner product given by ECm m'=1 (1.36) Here 82 is the Kronecker delta function, which is one if Z = 0 and is zero otherwise. Orthogonality