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HW 8

The document is the solution to a homework problem about digital communication systems over a multipath fading channel. It answers questions about: 1) Using the available bandwidth to achieve frequency diversity and determining the amount of diversity available. 2) The approximate SNR required per diversity branch to achieve an error probability of 10-6. 3) The number of taps required for a RAKE receiver given the multipath spread. 4) The approximate SNR required to achieve an error probability of 10-6 using binary orthogonal signals with square law post detection combining.

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Djamel Teg
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29 views2 pages

HW 8

The document is the solution to a homework problem about digital communication systems over a multipath fading channel. It answers questions about: 1) Using the available bandwidth to achieve frequency diversity and determining the amount of diversity available. 2) The approximate SNR required per diversity branch to achieve an error probability of 10-6. 3) The number of taps required for a RAKE receiver given the multipath spread. 4) The approximate SNR required to achieve an error probability of 10-6 using binary orthogonal signals with square law post detection combining.

Uploaded by

Djamel Teg
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as DOC, PDF, TXT or read online on Scribd
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S-72.

227 Digital Communication Systems


Spring 2002 Solution to Homework#8, 29.04.2002

A multipath fading channel has a multipath spread of Tm=1 s and a


Doppler spread of Bd=0.01 Hz. The total channel bandwidth at band
pass available for signal transmission is W=5 Hz. To reduce of effects of
inter-symbol interference, the signal designer selects a pulse duration
T=10 s.
a) Suppose that the channel is used to transmit binary data via
(antipodal) coherently detected PSK in a frequency diversity
mode. Explain how would you use the available channel
bandwidth to obtain frequency diversity and determine how
much diversity is available.
b) For the case in (a), what is the approximate SNR required
per diversity to achieve an error probability of 10-6?
c) Suppose that a wideband signal is used for transmission
and a RAKE-type receiver is used for demodulation. How
many taps would you use in the RAKE receiver?
d) If binary orthogonal signals are used for the wideband
signal with square law post detection combining in the
RAKE receiver, what is the approximate SNR required
achieving an error probability of 10-6? (Assume that all taps
have the same SNR).

ANSWER:
Given, Tm=1 sec, Bd=0.01Hz,W=5Hz,T=10 sec
a) The desired data rate is not specified in this problem, and must be
assumed to solve the problem.
Note that with a pulse duration of T=10 sec, the binary PSK signals
can be spaced at 1/T=0.1Hz apart.
With bandwidth 5Hz, we can form 50 subchannel, or carrier
frequencies. On the other hand, the amount of diversity available in the

channel is

Suppose the desired data rate is 1bps


Then the adjacent carriers can be used to transmit the data in
parallel & the information is repeated 5 times using the total number of
50 subcarriers to achieve 5th order diversity.
A subcarrier diversity of 1Hz is maintained to achieve independent
fading of subcarriers covering the same information.

Course Assistant: Muhammad Imadur Rahman, Phone: 09-4514905, e-mail: imad@cc.hut.fi 1


b) Use the approximation for maximal ratio combining,

c) The tap spacong between adjacent taps is 1/5=0.2 sec.


The total multiptah spread is Tm=1 sec
hence we employ a RAKE receiver with at least 5 taps
d) For an error rate of 10-6, we have

Course Assistant: Muhammad Imadur Rahman, Phone: 09-4514905, e-mail: imad@cc.hut.fi 2

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