Digital Communications and Signal Processing by K Vasudevan

Author:K Vasudevan [Vasudevan, K]
Language: eng
Format: azw3
Tags: Digital Communications and Signal Processing
Publisher: Universities Press (India) Private Limited
Published: 2017-01-17T16:00:00+00:00

Figure 4.9 The baseband equivalent model of a CDMA transmitter

Figure 4.10 Receiver for users 1 and 2

where the autocorrelation of ṽ(t) is given by (4.53). The output of the matched filter for user 1 is

x̃1(t) = ∑ k=-∞∞S 1,kh11(t - kT) + ∑ k=-∞∞S 2,kh21(t - kT) + Z̃1(t) (4.83)

where h11(t) and h21(t) are shown in Figure 4.10 and

Z̃1(t) = ṽ(t) ⋆ pl(-t). (4.84)

The output of the sampler is

x̃1(iT) = S1,ih11(0) + Z̃1(iT)

= S1,iA2T+Z̃1(iT)

= S1,i + z̃1(iT) (4.85)

where we have set A2T = 1 for convenience. Note that the autocorrelation of Z̃1(iT) is given by (4.68). Using the union bound, the probability of symbol error for user 1 is

P(e) = erfc d2 8N0. (4.86)

The probability of symbol error for the second user is the same as above.

Solution 2: Consider the alternate model for the CDMA transmitter as shown in Figure 4.11.

Note that here the transmit filter is the same for both users. However, each user is alloted a spreading code as shown in Figure 4.11. The output of the transmit filter of user 1 is given by

S̃1(t) = ∑ k=-∞∞∑ n=0Nc-1S 1,c,k,np(t - kT - nTc) (4.87)

where Nc = T∕Tc (in this example Nc = 2) denotes the spread factor and

S1,c,k,n = S1,kc1,n -∞ < k < ∞,0 ≤ n ≤ Nc - 1. (4.88)

The term S1,k denotes the symbol from user 1 at time kT and c1,n denotes the chip at time kT + nTc alloted to user 1. Note that the spreading code is periodic with a period T, as illustrated in Figure 4.12(c). Moreover, the spreading codes alloted to different users are orthogonal, that is,

∑ n=0Nc-1c i,ncj,n = NcδK(i - j). (4.89)

This process of spreading the symbols using a periodic spreading code is referred to as direct sequence CDMA (DS-CDMA).

Let us now turn our attention to the receiver. The baseband equivalent of the received signal is given by

ũ(t) = ∑ k=-∞∞∑ n=0Nc-1S 1,c,k,np(t - kT - nTc)

+ ∑ k=-∞∞∑ n=0Nc-1S 2,c,k,np(t - kT - nTc) + ṽ(t) (4.90)

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