E-3 2.59E-2 2.06E-2 1.75E-2 1.52E-2 1.34E-2 N = 4096 to,so=2 2.00E-3 1.53E-4 2.96E-5 6.24E-6 1.34E-6 2.06E-3 3.49E-4 1.20E-4 4.57E-5 1.78E-5 2.50E-3 8.36E-4 4.28E-4 2.38E-4 1.37E-4 3.87E-3 2.00E-3 1.31E-3 9.17E-4 6.60E-4 6.99E-3 4.67E-3 3.57E-3 2.86E-3 2.34E-3 1.36E-2 1.06E-2 8.92E-3 7.73E-3 6.81E-3 Chapter Chapter 5 PSEUDONOISE GENERATORS 5.1 THE STORAGE/GENERATION PROBLEM Pseudonoise (PN) sequences are used as spectrum-spreading modulations for direct sequence SS designs, as hopping pattern sources in frequency and/or time hopping systems, and as filter section controllers in matched fil- ter SS systems. Ideally, most of the PN sequence design problems would be solved if it were possible to produce a sample of a sequence of independent random variables, uniformly distributed on the available alphabet, for use at the SS transmitter, and an identical sample sequence at the receiver for use in the detection process. This is the SS equivalent of the one-time pad used in cryptographic systems requiring the highest level of security. Unfortunately, the generation, recording, and distribution of these sample sequences at a rate (per information bit to be communicated) equal to the processing gain of the SS system, is generally not feasible. Once the one-time pad is discarded as a viable approach, the designer must come to grips with the problem of storing/generating a signal which looks random (e.g., like a one-time pad), despite the fact that it must be done with a real system possessing finite storage capacity/generating capability. Let's illustrate the possibilities by considering methods for the generation of a specified binary (0 or 1) sequence (bm, n = 1, 2, N}. If N bits of the random sequence are not sufficient to complete the communication process, the sequence must be reused, i.e., bn+n = bn for all n, (5.1) where N is the period of the extended sequence. Any other method of reusing the stored sequence other than periodic extension as indicated above, will require additional memory to supervise the reuse alg