Spread Spectrum Modulation - Digital Communication: Principles and System Modelling - page 160

any two sequences of 4 digits, arbitrarily, result of addition of bit by bit product
would be 0.

S 1 = 1,1,1,1 S 1 = 1,1,1,1

/4 Ch0 [1 Æ +1] Σ [+1 Æ 1] Ch0

S 2 = 1,1,−1,−1 S 2 = 1,1,−1,−1

/4

Σ

Ch1 [0 Æ −1] [ − 1 Æ 0] Ch1

S 3 = 1,−1,1,−1 S 3 = 1,−1,1,−1

Σ /4

Ch2 [1 Æ +1] [+1 Æ 1] Ch2

S 4 = 1,−1,−1,1 S 4 = 1,−1,−1,1

Σ /4

Ch3 [1 Æ +1] [+1 Æ 1] Ch3

Fig. 7.18 DSSS based CDMA

As for an example (Fig. 7.18 ), take any two sequences 1010 and 1100.

4

1

. ∗ ( SOP cross _ bit = ( 1, − 1, 1, − 1 ) 1, 1, − 1, − 1 ) ,

where, . ∗ is the bit by bit product (analog multiplication) operator

4 (1 ∗ 1)

1)

1

1 ∗ 1) (1 ∗ − 1 ∗ −

∴ SOP cross _ Bit = + ( − + 1) + ( −

1
4 {

= 1 − 1 − 1 + 1 } = 0

We can test the claim by choosing another pair, say 1001, 1100

4

1

. ∗ ( SOP cross _ Bit = ( 1, − 1, − 1, 1 ) 1, 1, − 1, − 1 )

4 (1 ∗ 1)

1)

1

1 ∗ 1) 1 ∗ − (1 ∗ − = + ( − + ( − 1) +

1
4 {

} =

= 1 − 1 + 1 − 1 0

(ii) Auto-correlation Sum of Product is 'One':
Now, if we choose any sequence of 4 digits (N = 4), result of addition of bit by bit

product would be.
As for an example, take any two sequences 1010.