Digital, Microwave, and Optical Communications Assignment Solution

This document presents a comprehensive solution to a Digital, Microwave, and Optical Communications assignment (CIS117-6). The digital communications section covers entropy in information theory, explaining its role in digital systems and key components with a diagram. It further explores digital modulation techniques, including Amplitude Shift Keying (ASK), Frequency Shift Keying (FSK), and Phase Shift Keying (PSK). The solution also includes Huffman and Shannon-Fano coding examples, detailing code design, tree sketching, average codeword length, and efficiency calculations. The microwave communications section focuses on the design of a microstrip patch antenna for a Wireless Local Area Network (WLAN) operating at 2.45 GHz, detailing the antenna's dimensions and resonance frequency. Finally, the optical communications section presents a Radio-over-Fibre System design for a four-story hospital building, including a block diagram with component justifications and assumptions. The assignment covers a range of topics, including fundamental principles, critical analysis, and system design in digital, microwave, and optical communications.

Digital communications https://www.slideshare.net/lineking/digital-communication-system
Q1 a) Explain the concept of entropy (information theory) with respect to digital
communications (5 marks)
The digital communication systems has various components that are used to transmit the
information message from source to the target destinations, therefore the messages are generated
by the source of the system and then get transmitted through the system channel to the desired
destination.
The generated message is first encoded for it to be transmitted through the communications
channels, where finally is decoded at the desired destinations. Below is a simple model of the
digital communication system.
The informtion theory is scienctific branch that is used in the analysis of the digital
communication systems where it highlights the informtion communications from the source to
the desired destinations. The informtion theory is also refered to as the entropy which is the
representation of the randomness of communication degrees where the higher the entropy the
higher the signaling errors and is directly proportional to the maximum attainable data speeds
represented in bits per seconds, noise and bandwidth.
However the entropy signals in the communication systems tends to be inversely proportional to
compressibility where the higher the entropy the lower the factor to cmpress the data and
therefore the entropy is a type of disorder that is added into the data to enable the encryption
process.

In the digital communication there are some events that can occur and they are determined by
some conditions as described below.
i. Uncertainity condition. Thisis type of condition that happens if no event is to happen.
ii. Surprise condition.This is the type of condition where a certain event had just
occured.
Therefore these conditions are used to give the probability of occurrence of some events in the
communication system
Therefore the entropy is the measure of the avarage data per the source symbol and is
represented using the following fomular.
Where pi is the probabilty of the occurrence of I from a stream of character b which is log based
and therefore the conditional entropy represents the measure uncertainity in the input after
making observations to channels outputs.
Q1 b) Using a diagram, explain the key components of a digital communications system (10
marks)
The digital communication system is a communication model where system information or
thoughts are encoded in digital form as discrete type of signals and then transferred electronically
to the desired recipients.
The figure below represents the diagram of the digital communication components and their
functions.

Source
This is the analog signal sent from the source which can be like sound or voice signal.
Input Transducer
It is type of transducers that take the physical inputs and then converts them into an electric
signal , for example this can be a microphone which has both analog to digital converter that is
used in processing the digital signals further which in represented in binary form of 1s and 0s
sequence.
Source Encoder
This is the component that is used in compression of the data to a least number of bits to ensure
the bandwidth is effectively utilized and also helps in the removal of the redundant bits which are
not necessary.
Channel Encoder
This is the component that codes to correct errors which may occur during the transmission
process as a result of the noise in the communication channels which as results make alterations
to the signals, therefore the encoder is used in adding the redundant bits to the data being
transmitted and they are referred to error correcting bits.
Digital Modulator
This is the component that modulates the signals to be transmitted the carrier ,however it helps in
the conversion of the signals from digital to analog sequence for them to be travelled through the
channels or mediums.
Channel
This is the component that allows the analog signals to be transmitted from the transmitter end to
the receiver’s end.

Digital Demodulator
This is the component at the initial step at the receiver end where the signals received is
demodulated and get reconverted from analog to digital form and then get reconstructed again
here.
Channel Decoder
This is the component that corrects errors after the detecting the sequence ,this is by correcting
any form of distortions that may occur during the transmission by introduction of redundant bits
and as a result the original signal is recovered.
Source Decoder
This is the component that helps in digitizing the resultant signals through sampling and
quantization in order to obtain pure digital outputs without losing any information and therefore
the decoder is used in recreating the source outputs.
Output Transducer
This is the component that is used in the conversion of the signals into original physical forms as
it was in the transmitter’s input and therefore all electrical signals are converted into physical
output, example of the transducer is the loud speakers.
Output Signal
This is the whole process outputs and this can be like the sound signal that is received.
Q2 a) What is digital modulation used for within a digital communications system? (5 marks)
The digital modulation is the variation of one or more parameters of the carriers signals
according to the instantaneous values of the messages signals where the messages signals
represents the signals that are transmitted for communication while the carrier signals are the
high frequency signals without any data but is used in transmission for long distance.

The digital modulation is used in the digital communication systems due to the following
reasons:
i. It is able to provide more information capacity.
ii. It provides high data security.
iii. It offers quick system availability.
iv. And it offers great quality communications.
Therefore the digital modulation is used in the digital communication systems due ability of
conveying large amounts of data compared to analog modulation techniques.
Q2 b) Explain three different ways of modulating a signal when only one degree of freedom is
modulated (10 marks)
Below are the three different types of modulating techniques that are used in the digital signals.
i. Amplitude Shift Keying (ASK).
This is an amplitude modulation that represents the binary data in variation manner in the
signal’s amplitudes, however the modulated signals happen to have higher frequency carriers
where the binary signals which are ASK modulated give a 0 value for any low inputs and
carrier’s output for the high inputs.
The figure below shows the ASK modulated waveforms together with the inputs.

ii. Frequency Shift Keying (FSK).
This is a digital communications technique where there is variation in frequency of the
carrier signals depending on the changes of the digital signals and therefore the FSK is used
as one of the scheme for signal frequency modulations.
The frequency of the FSK modulated wave is quite high for the binary high inputs and is also
low in the binary low inputs ,however the 1s and 0s are refered to as the spaces and marks
frequencies , the below is the diagram representing the FSK modulated waveforms together
with its inputs.
iii. Phase Shift Keying (PSK)
This is a type of digital modulation technique where the phases of carrier’s signals are changed
through the variation of sine and cosines inputs in a given period of time , this technique is
therefore mainly used in the wireless LANS, biometrics, contactless operations, and the RFID
and Bluetooth communication systems.
Q3) Consider a DMS where output is generated from an alphabet {a,b,c,d,e,f,g,h} with
respective with probabilities {0.25, 0.1, 0.02, 0.05, 0.25, 0.03, 0.25, 0.05}.
a) Design a Huffman code and sketch the corresponding coding tree. Explain the codewords
for each character in the alphabet (10 marks)

Huffman code
Characters Frequency Fixed length code Code length
a 0.25 0 1
b 0.1 1 1
c 0.02 10 2
d 0.05 11 2
e 0.25 100 3
f 0.03 101 3
g 0.25 110 3
h 0.05 111 3
Code tree
P (a, b, c, d, e, f, g, h) =1
P (a, c, d, e, f, g, h) =0.99 P (b)=0.1
P (a, d, e, f, g, h) =0.97 P (c)=0.02
P (a, e, f, g, h) =0.92 P (d)=0.05
P (a, f, g, h) =0.67 P (e)=0.25
P (a, g, h) =0.64 P (f)=0.03
P (a, h) =0.39 P (g)=0.25
P (a) =0.34 P (h)=0.05

b) Calculate the average length of the codeword if the Huffman code you generated (5
marks)
Average length of codeword= ((freq(a)* codelength(a)+ (freq(b)* codelength(b) )+ (freq(c)*
codelength(c) )+ (freq(d)* codelength(d) )+ (freq(d)* codelength(d) )+ (freq(e)* codelength(e) )+
(freq(f)* codelength(f) )+ (freq(g)* codelength(g) )+ (freq(h)* codelength(h)+)/total caharacters
=(0.25*1+0.1*1+0.02*2+0.05*2+0.25*3+0.03*3+0.25*3+0.05*3)/8=2.23/8=0.2788
c) Calculate the efficiency of your Huffman code (5 marks)
HU=(-0.25log(0.25)+-0.1log(0.1) + -0.02log(0.02) + -0.05log(0.05) + -0.25log(0.25) + -
0.03log(0.03) + -0.25log(0.25) + -0.05log(0.05))
=0.151+0.1+0.3398+0.06505+0.1505+0.04569+0.1505+0.0351=0.9375
L=(0.25*1+0.1*1+0.02*2+0.05*2+0.25*3+0.03*3+0.25*3+0.05*3)=2.23
Efficiency= 0.9375/(2.23*log2)
=(0.9375/2.23)*100%=42.04%
Q4) Design a Shannon-Fano code and sketch the corresponding coding tree where the alphabet is
{a,b,c,d,e,f} with corresponding probabilities {0.5, 0.1, 0.05, 0.05, 0.25, 0.25} (10 marks)
Shannon-Fano code
Symbol Probabilities Code
a 0.5 00
b 0.1 01
c 0.05 10
d 0.05 11
e 0.25 100
f 0.25 101
Coding tree

BA C D E F
Microwave communications
Q1) Antennas play a vital role in the performance of wireless communications systems.
Microstrip patch antennas are very widely used in wireless applications due to their inherent
features of simple design,low complexity, ease of fabrication and low cost to meet the design
requirements.
The objective of this assignment is the design of a resonance frequency microstrip patch antenna
for a practical Wireless Local Area Network (WLAN) application operating at ISM band in the
range of 2.45 GHz. The antenna is excited using a microstrip transmission line.
a) The important dimensions that need to be optimised include length and width of the ground
plane, patch and feed, and width and length of the two matching cuts on each side of the feed.
1. You need to design an antenna that needs to be matched such that the resonance frequency
is: fr = 2.45GHz + (last 3 digits of your student ID / 2)Mhz

For example, if your student ID number is 1322350 then the antenna working frequency should
be as follows:
350⎛ ⎞
f r = 2.45GHz + (300/2)MHz
= 2.45GHz +150MHz = 2.6GHz
(20 marks)
The below is the design of the microstrip patch antenna that match the resonance frequency
where the student ID is 1819067
Fr =2.45Ghz+ (067/2)MHZ
=2.45GHz+33.5MHz
=2.7852.4835GHz.
The above is the microstrip patch antenna designed to match the resonance frequency with
frequency less than 2.7852.4835GHz.
This microstrip patch antenna consists of various component parts which includes the following:
i. Radiating patch.
ii. Dielectric substrate.
iii. Ground plane
The radiating patch will have some specific width, length and thickness and the designed
rectangular microstrip patch antenna has the following measurements.

Width =8.0 mm
Length=8.5 mm
Thickness= 2.5
Optical communications
You have to design a Radio-over-Fibre System for a four storey hospital building that has 20
rooms per floor. The communication link is to be used for a wide variety of functions including
locating physicians, requesting test results, checking patient records of patients and calling for
mobile test data.
a) Show a block diagram of your designed system, justifying your selection of all the
Components. Clearly define all assumptions.
(10 marks)
Components selection and justification
The figure below shows the Radio-over-Fibre System design for the hospital which is located in
a four story building which has ground floor, first floor, second floor and third floor.
There are various components that had been used in the entire system which has specific purpose
as follows:
i. Radio Access Unit (RAU)
This is the device that receives the transmission and then passes them to the network connection
switch.
ii. Distributed antenna system (DAS)
This is a network device of the separated antennae node that makes connections to common
sources through the transport media which is used in provision of wireless services within a
certain geographical area and on the entire building.
iii. Indoor antennae

This is the device that is installed in the floors to send signals to the donor antennae for
retransmission to the nearest satellites.
iv. Donor(roof) antennae
This is a device used to send and receive signals to the nearest satellite for the entire network
system.
v. Computer and laptops
These are the devices that are used in the departments to capture the client details and also to
search the client details as well.
vi. Wireless routers
This is the device that is used to supply wireless internet service to the various departments, the
wireless can be accessed using the computers or mobile devices.
vii. Splitters
These are the devices selected to connect the network sections in the various floors on the
hospital building.
viii. Switches
The switches are the network devices selected to make connections to the other devices in the
various floors and departments.
ix. Fibre optic cables
These are cables that are selected to make connections to the devices that are installed in the
network system they are selected due to their high transmission speed and efficiency.
x. Fibre patch panel
xi. Server
The server is the network device that is fitted in each floor to store the information relevant for
the patients.
xii. Phones
The phones are the devices used to make calls to either floor departments to enquire or request
for any given service.
xiii. Patch panel hub.