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được xem là một sự thay đổi 13-chip b (sở hữu 2). Lấy một cửa sổ có chiều rộng r = 5 và trượt nó theo b (định kỳ mở rộng) cho 5-tuples 10101, 01011, 10111,. . . , 10000, 00001, 00010, 00101, 01010 (31 tổng số). Một danh sách mở rộng cho thấy rằng tất cả có thể 5-tuples Hiện nay, với ngoại lệ của 00000 (tài sản 3). Kiểm tra chặt chẽ của các b trình tự cho thấy rằng có chạy sau đây: | FUNDAMENTALS OF SPREAD SPECTRUM MODULATION 15 FIGURE 7 Autocorrelation function top and power spectral density bottom of an OT-sequence. which is seen to be a 13-chip shift of b property 2 . Taking a window of width r 5 and sliding it along b periodically extended gives the 5-tuples 10101 01011 10111 . 10000 00001 00010 00101 01010 31 total . An extended listing shows that all possible 5-tuples are present with the exception of 00000 property 3 . Close examination of the sequence b shows that there are the following runs One run of 1s of length r 5 One run of 0s of length r 1 4 One run of 1s and one run of 0s of length r 2 3 Two runs of 1s and two runs of 0s of length r 3 2 Four runs of 1s and four runs of 0s of length r 4 1 property 4 . Property 5 follows by considering the autocorrelation function at delays equal to integer multiples of a chip and noting that the autocorrelation values between these delays must be a linear function of the delay. For T 0 we get R 0 -1 L x2 t dt 31T 1 1. For a delay of 70 70 317c 16 FUNDAMENTALS OF SPREAD SPECTRUM MODULATION Tc there is one more 1 X -1 value so the result is R Tc -p Ậ which holds for 31 Tc 31 delays of 2Tc 3TC . 15T. For delays between these values the autocorrelation function must of necessity be a linear function of T the integrand involves constants . Because the sequence is periodically extended the autocorrelation function is also periodic of period 31 Tc. Note that the correlation function given by 4.2 is obtained only if integration is over a full period. In spread spectrum systems the correlation function of -sequences when integrated over less than a period is important especially for long codes. Although beyond the scope of this presentation partial-period correlation values for -sequences can be shown to be highly variable and not the nice result given by 4.2 1 . The power spectrum of b t s c t c t s is an important consideration for synchronization. This is a complex problem 1 . Example results are .
