Suppose that the receiver in Figure 6.6 wanted

Authors:

James F. Kurose, Keith W. Ross

Chapter:

Wireless And Mobile Networks

Exercise:

Problems

Question:3 | ISBN:9780132856201 | Edition: 6

Question

Suppose that the receiver in Figure 6.6 wanted to receive the data being sent by sender 2. Show (by calculation) that the receiver is indeed able to recover sender 2’s data from the aggregate channel signal by using sender 2’s code.

Answer

The following formula for the receiver is indeed able to recover sender 2’s data:

$d_{i}^{2}=\frac{\sum_{m=1}^{M}Z_{i,m}^{*}.c_{m}^{2}}{M}$

Given data to time slot for 0:

The receiver in given Figure 6.6 wanted to receive the data being sent by sender 2.

$Aggregate\ channel\ signal(Z_{i,m}^{*})=(2,0,2,0,2,-2,0,0)$

$c_{m}^{2}=(1,-1,1,1,1,-1,1,1)$

M=8

Apply these values in above formula:

$d_{0}^{2}=\frac{\sum_{m=1}^{8}Z_{i,m}^{*}.c_{m}^{2}}{8}$

$d_{0}^{2}=\frac{2\times 1+0+2\times 1+0\times1+2\times1-2\times-1+0\times1+0\times1}{8}$

$d_{0}^{2}=1$

Given data to time slot for 1:

The receiver in given Figure 6.6 wanted to receive the data being sent by sender 2.

$Aggregate\ channel\ signal(Z_{i,m}^{*})=(0,-2,0,2,0,0,2,2)$

$c_{m}^{2}=(1,-1,1,1,1,-1,1,1)$

M=8

Apply these values in above formula:

$d_{0}^{2}=\frac{\sum_{m=1}^{8}Z_{i,m}^{*}.c_{m}^{2}}{8}$

$d_{0}^{2}=1$

Hence, that the receiver is indeed able to recover sender 2’s data from the aggregate channel signal by using sender 2’s code is 1.

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