6.973 Communication System Design
03/06/06
Problem Set 3 Bluespec Introduction
Getting Started
To use the Bluespec compiler, add the following lines to your .cshrc.mine file:
1.
2.
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add 6.375
setenv BSPATH /mit/6.375/tools/bluespec/current
s
5.8
COlVﬂVIUNICATION SYSTEMS: Analysis and Design
E
B),coherentASK :
0
Average normalized power at the receiver is (2.25 volts2) (0.25)2 = 0.1406 volts2.
Eb=0.1406 volts2/100,000 bits per second = 1.406 x 10'6 volts2-sec.
Substituting in,
—6
Income.“ = Q
COMMUNICATION SYSTEMS: Analysis and Design
chosen, the carrier will be at the lowest frequency of the modulated signal, which will
be 300 kHz. See solutions to Part b for the magnitude spectrum of the transmitted
signal for both lower sideband and upper s
4.31
4.32
CONHVIUNICATION SYSTEMS: Analysis and Design
1
fl),er Code 2 Z
f. Suppose that the assumption that all errors are to adjacent symbols is not valid.
Translate your results in Part d to probability of bit error assuming that errors to all
symbols
COMMUNICATION SYSTEMS: Analysis and Design
As shown in the textbook on pp. 388, we can write v(t) as
v(t) = 8 sin[200,0007zt + 4 sin(10,0007rt)] = 1m(8e1'2’-”‘v’ejﬂsi“2’-me’ )
where fc=I 00 kHz, ﬂ=4, and fm=5 kHz.
As established in Equation (6.71),
ejﬂ sm
COMMUNICATION SYSTEMS: Analysis and Design
The Fourier series expression for a single angle-modulated sinusoid is
v(t) = A sin(27zfct + ﬂ sin 27ifmt)
= A iJn<ﬂ)sin[2z(nn + fur]
n=—oo
From Parts a and b, we know that fc = 200 kHz and fm = 20 kHz. By Carson
6.18
6.19
COMMUNICATION SYSTEMS: Analysis and Design
A certain symmetry is required for the transfer function of the ﬁlter in an AM—VSB
transmitter. Describe the symmetry and explain why it is required.
T he ﬁlter must have a linear phase response and a r
COMMUNICATION SYSTEMS: Analysis and Design
b. Which amplitude modulation technique uses an envelope detector in its receiver
circuit?
AM—DSB—C. For a detailed description of how an AM—DSB-C signal is demodulated
see the solution to Problem 6.10 and see Se
COMMUNICATION SYSTEMS: Analysis and Design
b. Does AM—VSB use coherent or noncoherent demodulation? Explain your answer.
AM— VSB uses coherent demodulation. The receiver requires a reference signal that is
phase and frequency synchronized to the carrier s
CONHVIUNICATION SYSTEMS: Analysis and Design
7.4 Information bits generated on a continuous basis by three different users are time division
multiplexed and then transmitted over a channel. The ﬁrst user’s data rate is 200 kbit/ sec,
the seconds is 400 kb
COMMUNICATION SYSTEMS: Analysis and Design
6.4 For an AM-DSB-SC system, derive Equation (6.18), which shows the effect on the
6.5
6.6
receiver’s output signal if the transmitter and receiver carriers are not perfectly frequency
synchronized.
Using the blo
COMMUNICATION SYSTEMS: Analysis and Design
The bandwidth of the AM—DSB—SC signal will be 20 kHz (twice the bandwidth of the
information signal) and will be centered at the carrier frequency. Therefore, the
carrier frequency must be 310 kHz. See solutions
CONHVIUNICATION SYSTEMS: Analysis and Design
The larger the value of M the greater the transmission speed but also the greater the
bandwidth (M does not aﬂect spectral eﬂiciency). Larger values of M also require more
equipment in the receiver (but not mor
CONHVIUNICATION SYSTEMS: Analysis and Design
Calculating the autocorrelation will be a little more difficult. We know that at any
particular time the PAM waveform either has a value of A or -A, depending on the data
at the particular time.
Rxqutz) = (A)(A
4.33
CONHVIUNICATION SYSTEMS: Analysis and Design
h. Discuss how you can use the values you obtained in Parts f and g to evaluate a system
Where many, but not all, errors are to adjacent symbols.
In a system where many, but not all, errors are to adjacent
5.15
5.16
COlVﬂVIUNICATION SYSTEMS: Analysis and Design
where 21(in) represents the signal at the input to the threshold comparator if a “I ” was
transmitted and there was no noise at the receiver; and 22(in) represents the signal at
the input to the thre
CONHVIUNICATION SYSTEMS: Analysis and Design
5.4 Each waveform in Figure P5-4 is transmitting data at a rate of 100,000 bits/sec. For each
waveform, state
a. the modulation technique
b. the carrier frequency
0. minimum acceptable channel bandwidth (assume
5.24
CONHVIUNICATION SYSTEMS: Analysis and Design
1 —E /N
3 _ e b a
2
Average normalized power at the receiver is (4.5 volts?) (0.25)2 = 0.28125 volts2.
E1, = 0.28125 volts2/100, 000 bits per second = 2.8125 x 10'6 volts2-sec.
Substituting in,
(5.102R)
Pb
5.34
CONHVIUNICATION SYSTEMS: Analysis and Design
10'6 voltsz/Hz. If the system requires a symbol error rate of 105, what is the
minimum required transmitted signal power?
2
0A) Ts . 2 n Jqoe
sm —
N M
0
})s,coherent M -aiy PSK z [
2
Q[ O'IA TS sinzn] S
CONHVIUNICATION SYSTEMS: Analysis and Design
Give the expression for probability of bit error for each of the three systems.
Expressions for probability of bit error for the three systems are given in Table 5-4 in
the textbook.
If a bit error rate of 10'4
5.26
5.27
COlVﬂVIUNICATION SYSTEMS: Analysis and Design
1 4652/2] —7
0.5 = 0.5 4.65 = 0.5 —e = 8.65 x10
Q{ 1 Q( ) [4.65/2n
Since this second term is more than an order of magnitude smaller than the ﬁrst term,
we can effectively ignore it and use E, > 21.6
CONHVIUNICATION SYSTEMS: Analysis and Design
sources are limited to bandwidths of 5 kHz. In order to minimize interference, commercial
AM stations broadcasting in the same area are not assigned to aajacentfrequency bands.
This has the same ejfect as provi
CONHVIUNICATION SYSTEMS: Analysis and Design
magnitude of the signal (i.e., error as a percentage of the signal ’s magnitude).
Nonuniform quantization requires more complex equipment than uniform quantization.
DPCM is the most complex of the encoding tech
CONHVIUNICATION SYSTEMS: Analysis and Design
thereby providing the most compression but also the greatest vulnerability to error
propagation. B frames also require the most computational complexity, so some of our
older PCs will not be able to process a l
CONHVIUNICATION SYSTEMS: Analysis and Design
an element in the system). A binary system with conventional addition and multiplication
is not as structured as GF(2) and therefore is not as useful in constructing error control
codes.
10.5 Consider the Hammi
CONHVIUNICATION SYSTEMS: Analysis and Design
the number of information bits in the code, an error in any of the information bits is
uniquely identiﬁed. The code can therefore detect and correct any single bit error in
either the parity or information bits