Enhanced Radio Access Technologies for Next Generation Mobile Communication phần 3 doc

54 CHAPTER 2

where, each row of the matrix above except the first, can be used as orthogonal

spreading sequence. The 1st sequence of Hadamard matrix consists of all 1s and

thus cannot be used for channelization.

Earlier, in Section 2.1, we have illustrated orthogonal Walsh codes ability to

provide channelization of different users. However, this ability heavily depends on

the orthogonality of the codes during the all stages of the transmission. In practice,

the IS-95 CDMA system uses a pilot channel and sync channel to synchronize

the downlink and to ensure that the link is coherent. In the uplink, which does

not have sync and pilot channels, another type of codes, PN codes are used for

channelization, due to the noncoherent nature of the uplink

PN sequences have an important property: time-shifted versions of the same

PN sequence have very little correlation with each other, in other words low

autocorrelation property. We define the discrete-time autocorrelation of a real

valued sequence x to be

(5) Rxi =

J

−1

j=0

xjxj−1

In other words, for each successive shift i, we calculate the summation of the

product of xj and its shifted version xj−i.

PN code sets can be generated from linear feedback shift registers, as shown in

Figure 17. The register starts with an initial sequence of bits. In each step, the

content of the register is shifted one place to the right and it is also fed back to the

leftmost place, the output of the last stage and the output of the one intermediate

stage are combined and fed as input to the first stage. The output bits of the last

stage form the PN code.

0 0 1 1

1 0 0 0

0 1 0 0

1 1 0 0 1 0 1 1

0 1 1 1

1 1 1 1

p = 1 0 0 1 0 1 1

Figure 17. Example for a PN sequence generated by a linear feedback shift register of three stages

RADIO ACCESS TECHNIQUES 55

The code generated in this manner is called a maximal-length shift register code,

and the length L of this code is

(6) L = 2m−1

where m is the number of stages of the register. In example given by Figure 17 the

linear feedback shift register with three stages is shown. An initial state of [0 0 1]

is used for the register. After clocking the bits through the register, we obtain the

required PN sequence, which is p = 1001011 .

Note that at shift L=23–1=7, the state of the register returns to that of the initial

state, and further shifting of the bits yields another identical sequence of outputs.

A PN code set of 7 codes can be generated by successively shifting p, and by

changing 0s to -1s we obtain

p1 = 

+1 −1 −1 +1 −1 +1 +1

p2 = 

+1 +1 −1 −1 +1 −1 +1

p3 = 

+1 +1 +1 −1 −1 +1 −1

p4 = 

−1 +1 +1 +1 −1 −1 +1

p5 = 

+1 −1 +1 +1 +1 −1 −1

p6 = 

−1 +1 −1 +1 +1 +1 −1

p7 = 

−1 −1 +1 −1 +1 +1 +1

We can easily verify that these codes satisfy the three conditions outlined earlier.

Figure 18 shows the channelization using PN codes. Suppose the same two users

A, and B wish to send two separate messages:

• User A signal m1(t)=[+1 -1], spreading code

p1t = +1−1−1+1−1+1+1

• User B signal m2(t)=[-1 +1], spreading code

p2t = −1+1−1+1+1+1−1

Each message is spread by its assigned PN code:

• For message one:

m1tp1t = +1−1−1+1−1+1+1−1+1+1−1+1−1−1

• For message two:

m2tp2t = +1−1+1−1−1−1+1−1+1−1+1+1+1−1

The spread spectrum signals for two messages are combined to form a composite

signal s(t):

st = m1p1t+m2p2t =

= 

2 −200 −202 −220020 −2

At the receiver of user B, the composite signal is multiplied by the PN code

corresponding to the user B:

stp2t = 

−2 −200 −2 0 −22200202

56 CHAPTER 2

2 –2

1

1

1

1

1

–1 –1

1

–1

1 1

1

–1 –1

1

–1

1 1

–1

1 1

–1

1

–1 –1

1

–1 –1

1

–1

1 1

m1(t)

p1(t)

m1(t) × p1(t)

m2(t)

1

–1 –1

1

–1

1 1

p1(t)

1

–1 –1

1

–1

1 1

1

–1 –1

1

–1

1 1

m2(t) × p2(t)

–1

1 1

–1

1

–1 –1

2

–2 –2

2

s(t)

2

–2

2

2 2

–2 –2

s(t) × p2(t)

–2

–2

–2

1

1

m2(t) ~

: User 1 message

: User 1 PN code

: User 1 spread data

: User 2 message

: User 2 PN code

: User 2 spread data

: Transmitted data

: Transmitted signal

multiplied by User 2 PN code

: Recovered User 2 message

Figure 18. Example of channelization using PN code sequences

Then the receiver integrates all the values over each bit period, which results in

M2(t) = [-8 8] function for user B. After the decision threshold we obtain the result

m˜ 2t = −1 +1 for user B. may try to decode the symbols for user A in the

same manner.

The two short codes of length 215–1 and one long code length of 242–1 used in

IS-95 CDMA system. For cdma2000 Spreading Rate 3, the short code length is

3 times the short code length given above or 3x215 in length.

All base stations and all mobiles use the same three PN sequences. In uplink

direction long PN code used for channelization, by assigning different time shifted

versions of the long code to different users, whereas short PN codes used for

scrambling users data.

In downlink channel each base station is also assigned a unique, time shifted

version of the short PN code that is superimposed on top of the Walsh code. This

is done to provide isolation among the different base stations or sectors, which is