Ee463 communications 2 - lab 2 - loren schwappach

CTU: EE 463 – Communications 2: Lab 2: MATLAB Project – Digital Modulation, Sampling RCVR, Nyquist Criterion, 1
Intersymbol Interference, Pulse Shapes

Colorado Technical University
EE 463 – Communications 2
Lab 2: MATLAB Project – Digital Modulation, Sampling RCVR,
Nyquist Criterion, Intersymbol Interference, and Pulse Shapes
December 2010
Loren K. Schwappach

ABSTRACT: This lab report was completed as a course requirement to obtain full course credit in EE463,
Communications 2 at Colorado Technical University. This Lab investigates the concepts of digital modulation, sampling
receivers, Nyquist criterion, Intersymbol Interference, and pulse shaping. If you have any questions or concerns in regards to
this laboratory assignment, this laboratory report, the process used in designing the indicated circuitry, or the final conclusions
and recommendations derived, please send an email to LSchwappach@yahoo.com. All computer drawn figures and pictures
used in this report are of original and authentic content and were created using MATLAB.

I. INTRODUCTION III. EQUIPMENT
MATLAB is a powerful utility and is helpful in the
visualization of applied mathematics, physics, and practical The following tools and or equipment were used for
engineering. The first concept of digital communications is to this lab assignment:
gain an understanding of Intersymbol Inference (ISI). To
prevent ISI signals must be sampled properly as required by 1. MATLAB version 2010a (with all features/bock sets).
the Nyquist criterion. A Nyquist pulse is a Nyquist shaped
pulse which is idealized as a way to completely eliminate ISI. 2. Simulink (Part of MATLAB)
Eye and scatter diagrams can further help by providing a
visualize indication of ISI and sampling effects. The 3. Communications Toolbox (Part of Simulink)
communication channel is the driving source of ISI due to
nonlinear frequency responses. Timing effects are another
problem encountered with digital transmission. These effects
come from duplicating delayed versions of the transmitted IV. PROCEDURE / RESULTS
signal over the communication channel.
1. Part A: Developing the basic digital modulator and
sampling receiver in Simulink:
II. OBJECTIVES
To build a digital message a new work space was
In this Communications 2 lab exercise MATLAB created in Simulink. The communication block-sets are
will be used to accomplish the following objectives: utilized as the primary source of building blocks for the digital
tools. The Bernoulli binary generator is the first tool used to
1. Gain a better understanding of the following concepts: produce a digital message by generating a randomized bit
steam based on some user defined parameters. The following
 ISI
figure shows these parameters.
 Nyquist Criterion
 Nyquist Pulse
 Eye and Scatter Diagrams
 Channel Noise & effects
 ISI due to overlapping pulses & effects
 Timing Offset & effect on eye/scatter diagrams
 Sampling Receiver


Next, an up sample block of 100 is used to generate a
continuous time sample rate of 100 samples per second
(100Hz). The Signal to Workspace blocks are used for
visualizing the signals and a Discrete Filter block is used to
modulate the incoming signal. In the Discrete Filter the Non
Return to Zero (NRZ) pulse shaping parameter is modified as
shown (Fig. 3).

Figure 1: Parameters of the Bernoulli Binary Generator.

The Bernoulli Binary Generator (Fig. 1) ensures that
a one or a zero will be occur with equal probability by the
input “Probability of a zero” of “0.5”. The sampling time is set
to 1 to ensure an output of one bit per second. So the final bit
Figure 3: Parameters of the Discrete Filter
rate is 1bps.
The Simulink workspace now resembles Fig. 4
Next a lookup table is added to Simulink. The lookup
below:
table provides a representation of the incoming bits; one or
zero provide a +1 and -1. The symbol rate is again 1symbol
per second. The following figure (Fig.2) illustrates the look-
up table parameters used in Simulink.

Figure 4: Total Block set.

After running the simulation the following signal to
workspace results were obtained (Fig. 5):

Figure 2: Parameter of the Lookup Table.

The Lookup table symbols are intended to modulate
the Bernoulli Binary Generator (BBG) pulse train. As the
BBG pulse train passes through the lookup table it is
„encoded‟ and thus needs to be sampled. This raises the
frequency and symbol rate.


Figure 5: Modulated Impulse Train. Figure 6: Modulated Impulse Train with 20%
Intersymbol Interference (ISI).
From the above figure we can conclude that the bit
rate is one bit per second and the NRZ pulse shaping is The results of Fig. 6 confirm that an overlap of
working as expected. interference has occurred. Twenty percent of each bit
overlaps with the following bit creating short additive pulses
2. Part B: Experiments with Interfering Pulses: on the top and bottom of each correct bit.
Next the NRZ pulse shaper is spread-out with the This introduced huge problems for the sampling
1bps bit rate at 100Hz a 20% overlap is introduced by receiver. It is possible to detect this Inter Symbol Interference
extending the NRZ numerator parameter to „ones(1,120)‟. (ISI) only if the impulse response of the digital filter satisfies
This results in the new output as shown (Fig. 6). the Nyquist criterion for sampling. The Discrete Filter
numerator is now changed to isipulse which is downloaded as
isipulse.mat from the MATLAB prompt. This new pulse
extends over four symbol periods as shown by the next figures
(Fig. 7 & Fig 8).


Figure 7: ISI impulse response. Figure 9: Discrete filter response of Half Sine Pulse.

Now, the numerator of the discrete filter was
modified to “hspulse”. Fig. 10 below illustrates the output of
the new “hspulse” response. With this modified configuration
the modulated pulse train will now pass symbols correctly.
Because the Nyquist pulse is at the same sample/symbol rate a
perfect shift can now occur. The intersections at -1 and +1
indicate duplicates of the symbol time.

Figure 8: Modulated signal with ISI pulse response
filtering.

Next a Half Sine (HS) pulse is created by typing in
the command “ >>hspulse = sin(pi*[0:0.01:2]/2);” via the
MATLAB prompt. This pulse shape is displayed by Fig. 9.
One observation my lab partner and I gained while performing Figure 10: The hspulse response signal output.
this is the importance of centering “hspulse” at zero. The shift
encountered was unexpected and uncorrectable.


Now the pulse train is passed through a Raised Root
Cosine (RC) pulse with thirty percent of excess bandwidth.
The function to achieve this is defined by the following
MATLAB script:

% -----------
% Matlab script for RC Pulse
function y = rcpulse(a,t)
tau = 1; % Set the symbol time
t = t + 10^(-7); %Avoids division by zero
tpi = pi/tau; atpi=tpi*a;
at = 4*a^2/tau^2;
y=sin(tpi*t).*cos(atpi*t)./(tpi*t.*(1-at*t.^2));
% -------------

The function “rcpulse” is called in MATLAB with
“rcpulse=rcpulse(.3,[-6:0.01]:6]);” command. This function
call results in a Nyquist pulse that passes through zero at each
sample time and is illustrated by Fig 12 below.

Figure 13: Updated signal using raised root cosine pulse
response.

As illustrated by Fig. 13 above the Discrete Filter is
now much more effective at producing a quality response.
Although overlapping is still observable the Nyquist criterion
is achieved.

3. Part C: Additive Noise Channel:

Additive channel noise is a common problem in
communication systems. For the next phase in this lab
additive channel noise is created by introducing zero mean
Gaussian noise into the pulse train. The Gaussian noise
generator block is now summed with the output of the discrete
filter. Yet another signal to workspace block is added for
monitoring the signal changes before and after the addition of
noise (see Fig 14).

Figure 11: The Raised Root Cosine Function (rcpulse)

Next the Discrete Filter is modified to rcpulse. This
produced Fig. 13 after passing through a Gaussian pulse.


Figure 12: Addition of new block sets for additive channel
noise.

The Gaussian Noise Generator (GNG) parameters are
altered to resemble the subsequent figure.

Figure 14: Output of signal with min. additive channel
noise.

The noise shown by Fig. 16 is illustrated by the fuzz
overcastting the signal. Additive channel noise depends upon
the parameter of variance set for in the GNG. If the varience
were increased the signal noise would also increase as shown
by Fig. 17 below.

Figure 13: Parameters of Gaussian Noise Generator

Figure 15: Large amount of additive channel noise.


4. Part D: Sampling Receiver

Changing the variance of the GNG to 0.000001 will
eliminate most of the additive channel noise. The Discrete
Time Eye Diagram Scope, DSP Constant and Discrete Time
Scatter Plots are now added to the Simulink workspace as
illustrated by Fig. 18.

Figure 18: Parameters of the Discrete Time Scatter Plot.

The new simulation results produced the following
Figure 16: Sampling Receiver Block Set outputs as illustrated by Fig. 21 & 22.

The Discrete Time Eye Diagram and a Discrete Time
Scatter Plot scope parameters were modified as shown by Fig
19 & Fig. 20.

Figure 21: Eye plot diagram with no channel noise.

Figure 17: Parameters of the Discrete Time Eye Diagram.


Figure 22: Scatter plot diagram with no channel noise. Figure 23: Eye plot diagram with triangle pulse response.

The Discrete Time Filter Numerator (DTFN) is now
modified for three different output responses. The first
response will be a triangular pulse using
“tripulse=triang(200)”. The second response will be a half
sine pulse. The third and final response will be a non-
Nyquistintersymbol interference pulse (isipulse). These
responses are illustrated by Fig. 23 – Fig. 28.

Figure 24: Scatter plot diagram with triangle pulse
response.


Figure 27: Eye plot diagram with non-Nyquist ISI
response.
Figure 25: EYE plot diagram with half sine pulse
response.

Figure 28: Scatter plot diagram with non-Nyquist ISI
response.
Figure 26: Scatter plot diagram with half sine pulse
response.


The above eye diagrams indicate the variances of
signals due to the selection of a good filter. By changing the
timing offset the impulse response is changed into the Raised
Cosine pulse. Yet another discrete filter is now added after
the introduction of channel noise to induce a twenty second
delay corresponding to twenty percent of the symbol period
due to the sample rate of one hundred samples per second.
The second filters numerator is changed to “[zeros(1,19,1]”
(see Fig. 29).

Figure 31: Scatter plots diagram with minimal channel
noise and delay.
Figure 29: Simulink block set used inducing a time delay.
As illustrated by the figures above the eye diagram is
now sampled at a place where the eye is partially closed and
The eye and scatter plot diagrams now result in the
the scatter plot is indicating multiple sample rates as shown by
following (Fig. 30 & 31):
the multiple symbols.

Additional noise is now added into the system by
increasing the GNG back to “.01” resulting in Fig. 32 & 33.

Figure 30: Eye plot diagram result with small channel
noise and delay.


V. CONCLUSIONS
This was an excellent assignment to cover some
essential concepts with digital communications. The first
concept explained was Intersymbol Inference (ISI). ISI is a
distortion of the original signal caused by one symbol
interfering with another symbol. With the proper
identification and selection of the Nyquist rate, ISI can be
effectively eliminated.
One key factor in the problem associated with ISI is
the nonlinearity of the transmission channel. An eye pattern
analyzer is a tool that addresses the issues of ISI and channel
noise. Eye plot diagrams help visualize time jitter, ISI, and
channel noise without the need of complex mathematics.
Scatter plot diagrams assist in demonstrating the
possibilities for recovering a signal and the effects of
sampling.
Additive channel noise is easily observed in eye
diagrams as overlaid fuzz.

Figure 32: Eye plot diagram result with large amounts of REFERENCES
channel noise and delay.
[1] Haykin, S., “Analog and Digital Communications 2nd
Edition” John Wiley & Sons, Haboken, NJ, 2007.

Figure 33: Scatter plot diagram result with large amounts
of channel noise and delay.

The eye and scatter plot diagrams indicate that the
noise is now so severe as to nearly close the eye.

Ee463 communications 2 - lab 2 - loren schwappach

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