e following examples illustrate the energy gain calculation for basic SS systems. In each case, the SS system is viewed (in the terminology of Section 1.2) as replacing an orthogonal communication system complex, and its mul- tiplicity factor K determined, thereby evaluating the energy gain of the sys- tem via (1.18). Example 1.1. Let's examine a SS system using binary (+1) DS spreading modulation as in (1.22), multiplicative data modulation (1.24), and single- channel phase-synchronous detection (solid line portion of Figure .3(a)) over the data symbol duration Ts of N chip times, i.e., Ts = NCT Hence, the pseudorandom quantities which are known to the receiver, but unknown to the jammer, are the DS pulse modulation sequence C1,C2, CN and the car- rier phase . The inner product of two such waveforms with different pseudorandom variables and data modulations is given by (1.29) For any particular choice of [C1,...CN.] and , and regardless of the val- ues of the data modulation d and d', constants over (0, Ts), the two signals are orthogonal if either - O' T = T1/2 or [C'1, ... C'N.] is orthogonal to [C1, .cn] Since the set of real N--tuples forms an N.-dimensional space (and furthermore an orthogonal basis of vectors with 1 entries can be found when N is a multiple of 4), and since carrier phase differences of A Spread-Spectrum Overview magnitude T1/2 cause orthogonality, the jammer is forced to view his wave- form selection problem as being defined for an orthogonal communication system complex with multiplicity factor K given by K = 2N = 2T, T. = = (1.30) Example 1.2. Suppose that two independently hopped SS waveforms, c(0)(t) and c(1)(t), of the form (1.20) are employed in a switching modulation scheme as in (1.26) to transmit binary data. The data symbols' duration Ts spans MD hop times. Frequency-synchronous correlation computations in the receiver are then carried out over individual hop times, and the correlator's sync clock produces a pulse every Th seconds. The signal parameters, known to the receiver but