Code Division Multiple Access (CDMA) phần 3 potx

P1: IML/FFX P2: IML

MOBK023-02 MOBK023-Buehrer.cls September 28, 2006 15:54

SPREAD SPECTRUM TECHNIQUES FOR CODE DIVISION MULTIPLE ACCESS 29

Sx( f )

1 − 1

Tb Tc

Original signal and

despread signal

Spread signal

f (Hz)

B ∝ Rs = 1

BS ∝ Rc = 1

Tb

Tc

Tc

1 − Tb

1

FIGURE 2.3: Illustration of PSD of original and spread signals with DS/SS.

Now, examining the last line in (2.13), we can see that if N  1, the second term will be

approximately constant over the significant values of the first term. Thus,

Sx ( f ) ≈

Tb

N

sinc2

 f Tb

N

 ∞

−∞

Tb sinc2 (φTb ) dφ

≈

Tb

N

sinc2

 f Tb

N

(2.14)

An illustrative sketch of the spectra (main lobe only) for the original information signal and the

signal after spreading is plotted in Figure 2.3. A more concrete example is plotted in Figure 2.4

for N = 256. From the perspective of the spread signal, the information signal s b (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 2.6.

The PSD of a bandpass signal can easily be found from the PSD its complex baseband

representation as [22]

Sbp ( f ) = 1

4 (Sx ( f − fc) + Sx (− f − fc)) (2.15)

Thus, the PSD of the DS/SS BPSK signal is

Sbp ( f ) ≈

P Tc

4

sin π( f − fc)Tc

π( f − fc)Tc

2

+

sin π( f + fc)Tc

π( f + fc)Tc

2



(2.16)

where P is the bandpass power.