ME502 Digital Communication: Analysis, Principles, Systems & MATLAB

This report delves into the analysis of digital communication systems, focusing on key aspects such as M-ary Pulse Amplitude Modulation (PAM) signaling, inter-symbol interference (ISI) mitigation, and signal reconstruction techniques. It begins by encoding a message using 8-bit ASCII and modulating it with M-PAM, addressing error detection and calculating bit and symbol rates. The report then examines ISI challenges, proposing a 3-tap linear equalizer and exploring zero-forcing (ZF) equalizers. Finally, it discusses the digitization of analog signals, determining the maximum allowable sampling period, and implementing signal reconstruction using MATLAB, complete with code and visualizations. The analysis is supported by relevant references, providing a comprehensive overview of the principles and practical applications of digital communication systems.

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TABLE OF CONTENTS
AIMS & OBJECTIVES...................................................................................................................2
QUESTION I...................................................................................................................................2
QUESTION II..................................................................................................................................4
QUESTION III................................................................................................................................7
AIMS & OBJECTIVES
(i) To apply and evaluate the principles used in the generation, transmission, and
reception of the digitally modulated signals.
(ii) To report on the characteristics of sampling and analog to digital conversion and
source coding.
(iii) Apply the techniques of, and report on, digital communication applications using
MATLAB and hardware devices.
QUESTION I
Sending a message “Start Singing” to a receiver using the baseband digital M-ary PAM
signaling where the M=16. The message signal encounters noise component during the
transmission hence the need for error detection. The first step is to convert the 8-bit ASCII code
and then partition the bit stream to symbols (Sevenhans, verstraeten, & Taraborrelli, 2012). The
message signal is modulated using the M-PAM signal prior to transmission.
(i) Encoding the message into a series of bits using 8-bit ASCII encoding including the
odd-parity bit.
start singing
S T A R T S I N G I N G
0101
0011
0101
0100
0100
0001
0101
0010
0101
0100
0101
0011
0100
1001
0100
1110
0100
0111
0100
1001
0100
1110
0100
0111
(ii) The total number of bits in the message.
For an 8 bit ASCII message for each character,
¿ characters ¿∗bitspercharacter
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¿ 12∗8=96 bits
(iii) Determining the symbols obtained in the bit string.
S T A R T S I N G I N G
0101
0011
0101
0100
0100
0001
0101
0010
0101
0100
0101
0011
0100
1001
0100
1110
0100
0111
0100
1001
0100
1110
0100
0111
83 84 65 82 84 83 73 78 71 73 78 71
The m-bit segments for the symbol of 16-PAM,
m=log2 16=2k
m=4=k
There are about 24 symbols when the system is separated.
(iv) Determining the gross bit rate and symbol rate for 16-PAM
The symbol rate is based on the N bits and they are conveyed per symbol (Tsun-I,
Liao, 2005). The gross rate is given as R which captures the channel coding
overheard. The symbol rate is given as,
f s= R
N , M =2N
f s=212=4096 bps=4.096 kbps
The gross bit rate, R, also the data signaling rate or line rate, is given as,
R=f s log2 M
The value of f S =baud rate, with an error message for about 8 microseconds
R=4096∗log2 16=16384 bps
(v) The effective bit rate and symbol rate for the 16-PAM
W =1
2 ( 1+ α ) Rs
¿ 16.384 kHz= ( 1+α ) 4.096 kHz
16.384 kHz= ( 1+α ) 4.096 kHz
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α =0.3
DISCUSSION
For an analog to digital converter, the sampling and quantization of a signal will be
performed in the discretization. The signal can be sample by impulse sampling, natural sampling,
or the sample and hold operation. The M-ary coding or signaling is performed on the binary state
where the data rate denotes the bit rate and the symbol rate (Quadri, & Tete, 2009). The signaling
technique requires transmission rate that is low as well as a low bandwidth. Unfortunately, the
low signal to noise ratio is caused by the multiple amplitude pulses. The M-ary signals reduce
required bandwidth instead of transmitting single pulses for the bits and they transmit one
multilevel pulse for the group of k-bits in the signaling technique (Chia-An & Lai, 2012).
The M-ary PAM performs multi-level signaling for the different symbols in the message
signal where the M value provides the allowable amplitude levels for the message being sent.
Depending on the data rate, the M-ary PAM, especially for values of M>2, less bandwidth is
required for transmission.
QUESTION II
The Inter-symbol interference is a great challenge for the digital communications
systems. There is an impulse response for the transmission medium between the transmitter and
the receiver is p(t). There is a Dirac impulse function given for the practical situations and the
transmission medium is not ISI-free.
p [ n ] =δ [n ]−0.2 δ [ n−1 ]+0.5 δ [n−2]
Part a
Transfer function of the 3-tap linear equalizer that forces the ISI caused by this transmission
medium to zero.
The equalizer eliminates the inter symbol interference as well as any additive noise that may
have added during transmission (Gandhira, Ram, & Soman, 2012). The ISI is as a result of the
spreading of the transmitted pulse as a result of the dispersive nature of a channel. The signals
overlap and cause the adjacent pulses to change.
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There are linear and non-linear equalizers. The linear equalizer has transversal and lattice
techniques. The 3-tap delay lines are generated using the finite impulse response and the infinite
impulse response.
For the zero forcing equalizer, the filter taps are changes so as to obtain the equalizer output
which is forced to be zero at N sample points on both ends:
{ Cn }n=− N
N → z ( k ) = { 1 ,k =0
0 , otherwise
This linear equalizer does not have a feedback path to adapt the equalizer which is linear.
Part b
The impulse response f or the 3-tap ZF-LE designed as in part a. the zero-forcing design of E(z)
is implemented in a manner that the ISI is totally removed.
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Part c
To reduce the computation complexity, e=R−1 p. the lest mean square algorithm and the
recursive least squares algorithms are implemented to determine the tracking ability of the RLS
equalizer. The ZF equalizer eliminates the ISI at the slicer input.
yk=h0 ak +h1 ak−1 +h2 ak−2+ h3 ak−3 +…+(wk−noise)
c ( z )=H−1 ( z )
The finite impulse response filter,
H ( z )=h0 +h1 z−1 +h2 z−2
The result is turned to an infinite impulse response filter such that,
C (z)= 1
h0+ h1 z−1 +h2 z−2
The channel mode is obtained as a case of fractionally spaced equalization,
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yk=h0 ak +h1 ak−1 +h2 ak−2
yk + 1
2
=h1
2
ak +h3 /2 ak−1 +h5/ 2 ak−2
The result is obtained as,
The resulting set of equations exists as the finite impulse response inverse for the channel mode
opted. The minimum filter length is obtained for the zero-forcing equalization filter.
Part d
The ZF-LE can be improved especially under the constraint of zero-ISI at the slicer input.
The linear equalizer has a whitened matched filter front-end that is optimal and it minimizes the
noise at the slicer input (Nguyen, Patin, Friedrich, & Vilain, 2011). A matched filter bound is
important to improve the figure of merit for the ZF-linear equalizer. The figure of merit is given
as,
γ¿ ≤ γ DFE ≤ γmlse ≤ γ mf
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At the improved ZF-LE, the receiver has a higher figure of merit with lower error probability.
The equalizer minimizes the noise at the slicer input while under zero-ISI constraint. The results
are observed by using an oscilloscope to determine the eye diagram. A close eye illustrates a bad
ISI and the open eye is a good ISI.
QUESTION III
The digitization of the analog signal expressed as,
s ( t )=5 sin (500 t+ π
5 )+cos (200 t+ π
4 )
The signal is transferred over a digital communication system and it is received at the receiver.
Part a
The maximum allowable sampling period for the ADC and the reconstruction of the signal at the
receiver is obtained as,
500 t=2 πft ; f 1 =79.577 Hz
200 t=2 πft ; f 2=31.83 Hz
The sampling rate used is f1 such that,
f S ≤2 f 0
f S ≤2∗79.577 Hz
f S ≤159.154 Hz
The maximum allowable sampling period is given as,
T s ≤ 1
f s
T s ≤ 1
159.154 ≤ 0.00628 seconds
Part b
The reconstruction is based on the nyquist theorem for sampling at the receiver.
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f 0 < f s
2
The entire spectrum overlaps for the frequency spectrum and does not correspond with
the frequency spectrum of the signal. To determine the correct frequency spectrum of the
continuous signal it is important to measure the period of the signal at least twice. The sampling
frequency should be at least twice the highest frequency contained in the signal.
Part c
The number of samples used in the analog signals to reproduce the 10 π seconds from the
continuous analog signal,
T s ≤0.00628 seconds
Samples are obtained as,
Sample= 10 π
T s
= 10 π
0.00628 =5002.536 samples
Part d
Using MATLAB code to implement the solutions,
%% Section 2: Part D
Ts=1/159.154; %sampling period
t=0:0.35:10*pi;
S1=5*sin(500*t+pi/5);
S2=cos(200*t+pi/4);
S=S1+S2;
figure(1)
plot(t,S,'g-.')
grid on
title('The message signal s(t)')
xlabel('Time(s)')
ylabel('Message Signal, S(t)')
figure(2)
y=stem(S)
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grid on
The signal obtained at the receiver is as shown below,
0 5 10 15 20 25 30 35
Time(s)
-6
-4
-2
0
2
4
6
Message Signal, S(t)
The message signal s(t)
The stem plot shows the sampled signal which denotes the discrete form of the received message
signal,
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-6
-4
-2
0
2
4
6
0 10 20 30 40 50 60 70 80 90
The stem plot in MATLAB implementation is used in the representation to determine the
discrete plot of the system. The PCM sequences are obtained when the continuous signals are
reconstructed at the receiver end. The signals may be distorted by noise signals. The signal is
obtained with different frequencies as shown in the signal before the signal is received. The
signal developed is a periodic signal and the signal is plotted against the time frame of up to 10-
pi seconds. This is the estimated reconstruction timeframe for this case scenario.
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REFERENCES
Sevenhans, B. Verstraeten, and S. Taraborrelli, (2012) “A contraction of modulator/demodulator
Trends in Silicon Radio Large ScaleIntegration,” IEEE Commun. Mag., Vol. 38, pp. 142–147.
Tsun-I Chien and Teh-Lu Liao, (2005) “Design of secure digital communication systems using
chaotic modulation, cryptography and chaotic synchronization” Chaos, Solitons, and Fractals.
241– 255.
Quadri, F. and Tete, A.D. (2009) “FPGA implementation of digital modulation techniques”
IEEE International Conference on Communications and Signal Processing (ICCSP), 3-5. Pp. 913
– 917.
Chia-An Yeh and Yen-Shin Lai, (2012) “Digital Pulse width Modulation Technique for a
Synchronous Buck DC/DC Converter to Reduce Switching Frequency” IEEE Transactions on
Industrial Electronics Volume: 59 , Issue: 1. 550 – 561.
Gandhiraj, R, Ranjini, Ram and K. P. Soman, (2012) “Analog and Digital Modulation Toolkit
for Software Defined Radio” International Conference on Communication Technology and
System Design 2011 Procedia Engineering 30. 1155 – 1162.
Dung Nguyen , Hobraiche, J. , Patin, N., Friedrich, G. and Vilain, J. (2011) “A Direct Digital
Technique Implementation of General Discontinuous Pulse Width Modulation Strategy” IEEE
Transactions on Industrial Electronics Volume: 58 , Issue: 9. Page(s): 4445 – 4454.
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