An Experimental Approach to CDMA and Interference Mitigation phần 5 doc

3. Design of an All Digital CDMA Receiver 97

BB

BB

0.61 0.1525

4

c

d c

B R

f R E , (3.38)

which does not depend on the chip rate. Figure 3-12 shows the generic

frequency response G f ( ), as compared with the various (wanted and

unwanted) spectral components of the received signal.

… z

-1

Stage 2

Decimation

U

Stage ( UM-1)

fs fd

z

-1

z

-1 z

-1

Stage 1

FIR 1

FIR 2

FIR 3

…

FIR N

fs

S(z) H(z)

Figure 3-11. Equivalent model for the CIC decimation filter.

It is apparent that the amplitude response G f ( ) of the CIC filter is not

flat within the useful signal bandwidth, and therefore some compensation, by

means of a subsequent equalizer, is required in order to minimize signal

distortion. We also see that the particular value of the decimation factor U

determines the location of the frequency response’s nulls at the frequencies

/ mf m f d s U . Such nulls reveal crucial for rejecting those spectral

components that, owing to the decimation, are moved into the useful signal

baseband. The differential delay M causes the appearance of intermediate

nulls in between two adjacent nulls at mfd . These additional nulls are of

98 Chapter 3

little utility and do not significantly increase the alias rejection capability of

the CIC filter. This feature is highlighted in Figure 3-12, where the case

M =1 (dashed line) is compared with the case M =2 (solid thick line).

Actually, an increase of M does not yield any improvement in the rejection

of the unwanted spectral components, while it requires an increase in the

storage capability of the CIC filter. Therefore according to [Hog81] and

[Har97] we will restrict our attention in the sequel to the case M =1.

G(f)

f

fd 2fd Ufd=fs

fd/M

1

M=1

… fs/2

M=2

f '=0.455fs f "=0.545fs

Spectral Images from

Down-Conversion

BBB=0.1525fd

Useful

Signal

Spectrum

Spectral Images from

Decimation

Figure 3-12. Generic normalized frequency response of the CIC decimation filter.

The order N of the CIC filter determines the sharpness of the notches at

mfd and the amplitude of the relevant sidelobes, therefore it must be

carefully selected, taking into account the required attenuation of the

unwanted spectral components. Assuming that a white noise process is

superimposed on the signal at the CIC filter input, the shape of the frequency

response G f ( ) is proportional to the amplitude spectral density (i.e., the

square root of the power spectral density) of the noise process at the output

of the CIC, prior to decimation. Decimation causes the (normalized)

amplitude spectral density G f ( ) to be translated onto / mf m f d s U . As a

consequence the useful signal spectrum will suffer from aliasing caused by

the lobes of the spectral replicas, as clarified in Figure 3-13.

The total contribution of the aliasing spectral replicas, that we call alias

profile [Har97], is made of the contribution of U terms, and is bounded from

above by the function

   2

2

0

d

k

k

A f G f kf

U

U

z

 ¦ . (3.39)

3. Design of an All Digital CDMA Receiver 99

The parameter N therefore keeps the alias profile A f ( ) as low as

possible within the useful signal’s bandwidth BBB .

Figure 3-14 shows the frequency response G f ( ) for the different

decimation ratios U in Table 3.2, for M 1, and N 4 , while Figure 3-15

reports G f ( ) for different orders of the filter N , for M 1, and U 8 . In

both the figures G f ( ) is plotted versus the normalized frequency / s f f .

G(f)

f

fd 2fd Ufd=fs

1

-2fd -fd … fs/2

BBB=0.1525fd

Useful

Signal

Spectrum

Aliases

Figure 3-13. Aliasing effect of the CIC filter caused by decimation.

As already mentioned, the spectrum of the signal at the output of the CIC

filter, at the decimated rate df , suffers from amplitude distortion, owing to

the non-constant frequency response H f ( ) (or, equivalently, G f ( )). This

calls for the use of a compensation filter (also termed equalizer) having a

frequency response ( ) H f eq given by

sin /

sin /

N

d

eq

d

f f H f Mf f

ª º S U « »

S ¬ ¼

(3.40)

such that

H fHf eq   1. (3.41)

We will consider the compensation filter ( ) G f eq for the normalized

frequency response G f ( ), that is