Primitive binary polynomials," Math. Comp., vol. 27, Oct. 1973, pp. 977-980. N. Zierler and J. Brillhart, "On primitive trinomials (mod 2), " Inform. Contr., vol. 13, Dec. 1968, pp. 541-554. [6] N. Zierler and J. Brillhart, "On primitive trinomials (mod 2), II," Inform. Contr., vol. 14, June 1969, pp. 566-569. [7] N. Zierler, "Primitive trinomials whose degree is a Mersenne exponent," Inform. Contr., vol. 15, July 1969, pp. 67-69. [8] R. Lidl and H. Niederreiter, Finite Fields, Reading, MA: Addison-Wesley, 1983. [9] J. Brillhart, D. Lehmer, J. Selfridge, B. Tuckerman, and S. Wagstaff, Jr., Factorizations of bn + 1. Providence, RI: American Mathematical Society, vol- ume 22 in Contemporary Mathematics Series, 1983. This Page Intentionally Blank Chapter Part 2 CLASSICAL SPREAD-SPECTRUM COMMUNICATIONS This Page Intentionally Blank Chapter Chapter 1 COHERENT DIRECT-SEQUENCE SYSTEMS In its most general form a direct-sequence spread anti-jam communication system takes a binary data sequence and multiplies it by a higher rate pseudorandom (PN) binary sequence. The result is a binary sequence at the PN binary sequence rate which is then modulated. Compared to the usual modulation of the data, the data multiplied by the PN sequence causes the modulated signal spectrum to spread by a factor of N, the ratio of the PN sequence bit rate to the data bit rate. Such systems have been discussed in recent books and proceedings on spread-spectrum communications [1]-[11] and in tutorial papers [12]-[19]. Clark and Cain [9] provide the most com- plete discussion. Figure 1.1 illustrates the general direct-sequence spread modulation. The data waveform is given by d(t) = dnE{ - 1} n = integer (1.1) where {dn} is the data sequence. The PN binary waveform is c(t) = ck, kT,<1<(k+1)T, CKE - 1, 1} k = integer (1.2) where {Ck} is the PN sequence. Here, N - 1/2 (1.3) is the signal spectrum-spreading factor. Typically, N is on the order of 1000 or more. Tb is the bit time and T is referred to as the "chip" time interval. In the above multiplica