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EEET 3028 Digital Communications Practical 3: Digital baseband modulation This practical deals with the simulation of a digital communication system with MAT- LAB

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EEET 3028 Digital Communications

Practical 3: Digital baseband modulation
This practical deals with the simulation of a digital communication system with MAT-
LAB. You will implement a transmitter and a receiver of a baseband system, and inves-
tigate the eect of noise to the system.
Digital modulator
The gure shows a block diagram of a digital transmitter.
Source Mapper Modulator
data bits modulation
symbols
transmit
signal
bki ak x(t)
1. Consider 4ASK with the modulation alphabet A = f?4;?2; +2; +4g, and a map-
ping from bit pairs bk1bk2 to modulation symbols ak, as given in the following table
(the index k indicates the time):
bk1bk2 ak
00 +4
. . . +2
11 ?2
. . . . . .
Fill in the gaps. (There is no unique solution.)
Write a MATLAB function that implements this mapping with a bit pair as the
input and the corresponding modulation symbol as the output. Next, write a MAT-
LAB function that maps a sequence of data bits to the corresponding sequence of
modulation symbols.
2. Assume the transmit pulse p(t) = rect
?t?Ts=2
Ts

and the symbol period Ts = 2 msec.
Sketch the transmit pulse by hand (so that you know what to expect in MATLAB).
Plot the transmit pulse with MATLAB using a time resolution of 10 sample points
per symbol period; pick a reasonable time interval. (You may use rect.m from the
course webpage.)
3. Assume a sequence of K modulation symbols: a1; a1; : : : ; aK. The corresponding
transmit signal is given by
x(t) =
XK
k=1
ak p(t ? kTs):
Sketch by hand the transmit signal for a sequence a1; a2; a3; a4 of four chosen mod-
ulation symbols.

4. Use the same modulation symbols as in the previous question. Write a MATLAB
script to plot the signal x1(t) = a1 p(t ? Ts) with MATLAB.
You may use the following code:
>> t = -2*Ts:T0:6*Ts;
>> p = @(t) rect( (t-Ts/2)/Ts );
>> x1 = a1 * p(t-1*Ts);
>> plot(t,x1);
In a similar way, plot the signals x2(t), x3(t), and x4(t) in the same gure.
5. Write a MATLAB function that implements the modulator, i.e. takes a sequence of
modulation symbols as the input and produces the transmit signal as the output.
Test your function by comparing it to the result of the previous two questions.
Digital demodulator
The gure shows a block diagram of a digital receiver.
Recv Filter Demapper
estimated
modulation
symbols
receive
signal
ˆb
aˆk ki y(t)
Sampler
z(t) zk
Decision Sink
estimated
data bits
received
samples
output of
receive filter
6. Assume that the receive lter is a matched lter, i.e., the impulse response of the
receive lter is h(t) = p(Ts ?t). Sketch by hand the impulse response of the receive
lter (with the correct time shift).
7. For the time being, assume noise-free transmission. In this case, the received signal
is y(t) = x(t). The output signal of the receive lter is z(t) = y(t) h(t). Show
analytically (by a short calculation) that
z(t) =
XK
k=1
ak

p(t ? kTs) h(t)

:
Which properties do you use to show that?
8. Use MATLAB to compute and plot the signal g(t) = p(t ? kTs) h(t) for k = 1.
Discuss if the result is expected. (See also \Joy of Convolution" on course webpage.)
9. Assume the transmit signal x1(t) from Question 4. Compute and plot the corre-
sponding signal z(t).
You may use the following MATLAB commands:
>> tp = 0:T0:(Ts-T0);
>> h = p(tp);
>> z = T0/Ts * conv(y,h);
>> tz = T0 * (1:(length(z)));
>> plot(tz,z)
Relate your result to g(t) from the previous question.
Repeat this with x2(t). Is the result as expected? Now repeat this with the full
transmit signal x(t) and interpret the result.
10. Based on the results of the previous question, discuss what are the optimal sampling
times for z(t), to determine the samples zk. Write a MATLAB function (or script)
that obtains the samples zk from z(t).
11. Assume now transmission over an AWGN channel: y(t) = x(t) + w(t). With MAT-
LAB you can obtain a noisy receive signal with the following commands:
>> varnoise = 1;
>> y = x + sqrt(varnoise) * randn(size(x));
The value of varnoise denotes the variance of the additive white Gaussian noise.
Write a MATLAB script that plots (in subplots) the transmit signal, the noisy
receive signal, the signal at the matched lter output, and prints out the samples zk.
Do experiments with various noise variance, and discuss the eect of noise on y(t),
z(t) and zk. Is it easier to estimate the transmitted modulation symbol ak from y(t)
or from z(t)?
12. Consider now the decision block. Determine the decision regions for each modulation
symbol. Then write a MATLAB function that implements the decision function,
i.e., that maps zk to ^ak.
13. Write a MATLAB function that implements the Demapper. (This is very similar
to your Mapper, written before.)
Digital transmission system
In the previous questions we have investigated the individual components required for a
baseband digital communication system. We now put all the components together.
14. Write a MATLAB script that implements the transmitter, the channel and the
receiver.
The start is a sequence of data bits (you may choose them or pick them randomly),
and the end is the sequence of estimated data bits.
15. Test your script for very low noise and for higher noise. Does the system react as
expected?