wide area networks project the purpose of the work is the theoretical

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Wide Area Networks
Project The purpose of the work is the theoretical and experimental study, using simulation in Matlab,
of the performance of a digital telecommunication system. We consider the following model of
a Digital Telecommunication System
Διαμόρφωση
Πο
Κωδικοποίηση
Καναλιού
Θόρυβος
Κανάλι
Ψηφιακό Σήμα Εισόδου
Πομπός
Απόφαση
Αποδιαμόρφωση
Αποκωδικοποίηση
Καναλιού
Ψηφιακό Σήμα Εξόδου
Δέκτης
A sequence of bits appears at the input of the system. To improve the performance of the
system, based on the criterion of average bit error probability, you will implement a simple
channel coding which is repetition coding. According to it, the same bit of information is
repeated several times. Specifically, each bit arriving at the encoder input is repeated N
times (where N € {1,3,...,}).
The output of the encoder is input to the digital modulator where the input bits are mapped
to the input symbols as follows
Bit
00
Symbol
S1= 1 +j
Σ
01
S 2= − 1 +j
--1
Σ
11
S 3= - 1 +j
√2
10
S4= 1-j
√2
The symbol that is emitted is the x = √Essi,, where Es is the energy of the transmitted
symbols. Gaussian noise modeled as a complex random variable is added to the broadcast
στ
signal which follows the normal distribution with mean value 0 and variance
(for both the real and the imaginary part). The received signal at the receiver is the
=
10-6
r = x+w The receiver makes the decision about which symbol has been sent based on the minimum
distance criterion in this system, the symbol error probability can be calculated as
PR = 2Q
Es
20
1
1
(↓
Es
20
Where Q(.) is the complementary error function defined as
Q(x)
=
1
√✓ 1" exp (-1/7) du
/2π
X
2
Demodulation is then performed where the received symbols are mapped to bits using the
previous table. At the end, the decoding process takes place, according to which in each N
symbols used during encoding, the number of aces and zeroes is counted and a decision is
made in favor of the digit that appears more times. To calculate the average (experimental)
bit error probability (BEP) the relationship can be used
PB
=
P
2
It should be noted that Es=2Eb, where Eb is the average bit energy. For the corresponding
calculation of the average bit error probability using encoding you will use the previous relation in
combination with the fact that a Binomial random variable is created. Specifically, we have a
sequence of N independent Bernoulli trials with a "success" probability in each of them equal to
With PB. The cumulative probability of their occurrence needs to be calculated
¦‚¦ + 1, ..., N
In the end to note
errors bits
(SNR) dB = 10log10
Es
2
Questions
To the under-study telecommunication system we send a gray image. To convert any jpeg
image to grayscale image, as well as to convert the image to bitmap, you can use the
material related to image processing with the help of Matlab and given in eclass.
1. The column table is sent to said digital telecommunication system. Calculate the average bit error probability for different values of (SNR db), [0-10] dB. The results should be
given in a semi-logarithmic graph, with respect to the y-axis. The graphical
representations that should be made concern
a. Theoretical BEP, without repetition coding
b. The experimental BEP, without repetition coding
c. The theoretical BEP, with repetition coding, where N=3
d. The experimental BEP, with repetition coding, where N=3
e. The theoretical BEP, with repetition coding, where N=5
f. The experimental BEP, with repetition coding, where N=5
g. The theoretical BEP, with repetition coding, where N=7
h. The experimental BEP, with repetition coding, where N=7 2. Suppose the symbol mapping had been done in the following way
Bit
00
Symbol
S1= 1 +j
√2
01
S2=
−1 +j
√2
10
S3=- 1+j
√2
11
S 4= 1-j
√2
Give the graphs for the BER
a. The theoretical BEP as a function of (SNR) db, [0-10] dB, without repetition coding and
with the help of the first match
b. The experimental BEP as a function of (SNR) db, [0-10] dB, without repetition coding
and with the help of the first match
c. The theoretical BEP as a function of (SNR )db, [0-10] dB, without repetition coding
and using the second mapping
d. The experimental BEP as a function of (SNR) db, [0-10] dB, without repetition coding
and using the second mapping