Cụ thể, Q = i 2 + ij + j 2 cho bất kỳ số nguyên dương i và j [6]. Với mô hình như vậy, nó có thể được hiển thị khoảng cách tối thiểu giữa các tần số tế bào đồng D = √ 3Qdr dr là bán kính tế bào [6]. Khoảng cách này cùng với sự can thiệp tối đa chấp nhận được xác định yếu tố tái sử dụng cho phép. | SPREAD SPECTRUM TECHNIQUES FOR CODE DIVISION MULTIPLE ACCESS 29 FIGURE Illustration of PSD of original and spread signals with DS SS. Now examining the last line in we can see that if N 1 the second term will be approximately constant over the significant values of the first term. Thus T N Sx f sinc2 fT N Tb sinc2 ộ T dộ sinc2 T N An illustrative sketch of the spectra main lobe only for the original information signal and the signal after spreading is plotted in Figure . A more concrete example is plotted in Figure for N 256. From the perspective of the spread signal the information signal Sb t appears to be a strong narrowband tone. From the perspective of the narrowband signal see inset the spread signal appears to be white noise. Further we can see that the first-null bandwidth of the spread signal is N times that of the original information signal. Thus we call N the bandwidth expansion factor which is closely related to the processing gain and which we will discuss in Section . The PSD of a bandpass signal can easily be found from the PSD its complex baseband representation as 22 Sbp f 4 Sx f fc Sx f fc 215 Thus the PSD of the DS SS BPSK signal is - PT Sbp f sin n f fc T 2 sinn f fc T 2 n f fc T n f fc T where P is the bandpass power. 30 CODE DIVISION MULTIPLE ACCESS CDMA FIGURE Comparison of original despread signal and spread signal spectra for DS SS with square pulses. Multiple Access The DS SS technique can be expanded to multiple users by providing different spreading codes ak t to each user in the system where ak t is the spreading code of the kth user. A three-user example is shown in Figure . Channels are thus defined by the spreading waveform ak t . Ideally we would like all channels to be orthogonal. The key to making the spreading waveforms orthogonal is the spreading sequences . the series of binary values used to modulate the spreading waveform. Thus we wish 1 V 1 Ri k n Vỉ a m ak m n m 0 1 i k n 0 0 i
