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Find mean and variance of Poission distribution

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Q2. (a) Discuss selection diversity in detail and show that average SNR improvement

by M branch selection diversity combiner is =

M

k k1

1

(b)

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Q3. (a) Explain ergodic capcity and outage capcity of mIMO system.

(b) What is the coding gain? What is the diversity gain?

(C) Explain spatial multiplexing. What are the differences between H-BLAST, V-BLAST and D-BLAST. Which receiver architectures can be used for these

schemes?

(d) What methods are known to reduce the peak-to-average power ratio (PAR) of QPSKs?

Solution: Generalize one of them to 8PSK. Explain whether your method of choice ismore effective with QPSK than with 8PSK and why that is.

Phase-jumps reduction technique can be used to reduce the peak-to-average ratio.

This is done be switching between different constellation to avoid 180 degree phase

jump. In 8PSK we can choose the two constellations shown below and restrict the

phase jump to 8/7 by switching between them.

The method is more efficient with QPSK since the phase jumps can be restricted to

4/3 .

Q4. (a) Differentiate between WiFi and WiMAX on the basis of their standards.

(b) Consider a static wireless ad-hoc network with symmetric traffic and Q nodesuniformly placed within a circle of radius 25 km. Assume that the number of nodes Q is

very large. Compare the throughput of this network with the throughput of another wireless

ad-hoc network that has the same density of nodes per square meter, but has a rectangular

shape of 10 km 20 km.

Solution: For the first case we have:

22 )25( km

Q

r

Qdensity

==

.

And for the other case we have:kmkm

Q

ba

Qdensity

1020

=

= .

By equating the density of nodes per meter square for the two cases we have:

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QQ =25

8

From Gupta & Kumar theorem the total throughput of the network scales like thesquare root of the number of nodes. Therefore:

CCC 32.025

8

== , whereC

andC

are the total throughput of the circular and

rectangular cases respectively.

Q5. (a) What are Wireless Sensor Networks? Discuss their applications to under watercommunication.

(b) Suppose that you are asked to select a modulation scheme for a system with the

following specifications:

1. The bandwidth of the transmit signal has to be less than the data rate.

2. The receiver must be as simple as possible.

Specify your choice out of 4 alternatives below and express your reasons.

a) DQPSK b) GMSK

c) 16QAM d) BPSK

Solution: The transmit BW is obtained as:

M

RRBW bs

2log)1()1( +=+= for M-ary modulation scheme. Where and

bR are the roll-off factor and bit rate, respectively. To meet the first requirement we

must have: 1log

)1(

2

+

M

, so BPSK and GMSK can not be used, and the second

requirement force us to choose DQPSK.