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 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 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 .
