Exam
GENERAL Final METHODOLOGIES
In my implementation, I adopted a step-by-step method, which makes implementation
and debugging much easier. First I implemented following functions:
1. Matlab function awgn.m adds additive white Gaussian noise to input signal.
2. Matlab function awgn_complex.m adds complex additive white Gaussian noise to
input signal.
3. Matlab function bingen.m generates random +1/-1 sequence with independent
identically distributed symbols.
4. Matlab function fade.m generates Rayleigh fading.
5. Matlab function fade_fs.m generates frequency selective Rayleigh fading.
6. Matlab function fade_diversity.m generates two channels of Rayleigh fading.
7. Matlab function fh.m generates orthogonal complex exponential matrix for slow
FH-MA scheme.
8. Matlab function ds_mod.m do DS-SS modulation.
9. Matlab function ds_demod.m do DS-SS demodulation.
10. Based on the above functions, I implemented all corresponding programs for each
problem in the final exam.
Detailed information about each problem in the final exam is presented on the following
pages.
1
Final Exam
Problem 1
In this problem, I implemented the corresponding programs to simulate the performance
of a DS-SS/BPSK communication system in the following scenarios:
1. In the AWGN channel
2. In the presence of pulsed noise jamming and AWGN
The average BER obtained by simulation is attached.
Discussion
1. From the simulation, we find that the performance curves are very close to the
theoretical results.
2. We also find that the performance curves are similar for different code lengths.
3. Averaging over more experiments and using a larger symbol size will produce
results closer to the theoretical results. The symbol size used in my simulation is
10,000.
Extra Credit Work
1. Besides implementing all the required simulations, I also tried to use errorcorrecting codes to reduce the average BER. The code used in my experiment is
binary BCH code with code word length and message length equal to 15 and 5,
respectively. The experimental result is attached.
2. I also simulated the performance of the system in barrage noise jamming and
AWGN. The experimental result is attached.
Discussion
1. From the experiment, we find that using error-correcting codes reduces the
average BER obviously, especially when bit energy to noise ratio is relatively
large.
2. The performance of the system in barrage noise jamming and AWGN
environment is very close to the theoretical results.
2
Final Exam
Problem 2
In this problem, I implemented the corresponding programs to simulate the average BER
in:
1. Rayleigh fading and AWGN
2. Frequency selective Rayleigh fading and AWGN
The average BER obtained by simulation is attached.
Discussion
1. From the simulation, we find that the performance curves are very close to the
theoretical results.
2. We also find that the performance curves are similar for different code lengths.
3. Averaging over more experiments and using a larger symbol size will produce
results closer to the theoretical results. The symbol size used in my simulation is
10,000.
Extra Credit Work
Besides implementing all the required simulations, I also implemented a pre-detection
selective combining diversity receiver to reduce the average BER. In my experiment, I
used two branches (channels) to transmit signals. The experimental result is attached.
Discussion
From the experiment, we find that using pre-detection selective combining diversity
receiver reduces the average BER obviously, especially when bit energy to noise ratio is
relatively large.
3
Final Exam
Problem 3
In this problem, I implemented the corresponding programs to simulate the average BER
versus Eb/N0 of K users transmitting BPSK symbols at an equal power lever using DSCDMA and slow FH-MA schemes in the following two scenarios:
1. Perfect synchronism and orthogonal codes in AWGN
2. A random asynchronism between the users, uniformly distributed between 0 and 5
samples, plus AWGN
The average BER obtained by simulation is attached.
Discussion
1. From the simulation, we find that the performance curves are very close to the
theoretical results.
2. Averaging over more experiments and using a larger symbol size will produce
results closer to the theoretical results. The symbol size used in my simulation is
10,000.
3. For the second part of the problem, when the number of users is equal to 4 and 8,
we should use a very large symbol size in the simulation in order to get accurate
results for large bit energy to noise ratio.
4. Although it takes me lots of time to do the simulation, I learn a lot and understand
the theories better by doing it.
5. At last, want I to say that I really like this course. It has lots of fun and makes me
like communications more.
4
Final Exam
Attachments
Attached are the running results of my programs. Also, the source codes of my programs
are attached. Below is a list of my programs and supporting functions.
Programs
Final11.m:
Final12.m:
Final11_extra.m
Final12_extra.m
the first part of problem 1
the second part of problem 1
simulation with binary BCH code
simulation in barrage noise jamming and AWGN
Final21.m:
Final22.m:
Final21_extra.m
the first part of problem 2
the second part of problem 2
simulates a pre-detection selective combining diversity receiver for
Rayleigh fading channels
Final31.m:
Final32.m:
Final31_fh.m:
Final32_fh.m:
the first part of problem 3 using DS-CDMA
the second part of problem 3 using DS-CDMA
the first part of problem 3 using slow FH-MA
the second part of problem 3 using slow FH-MA
Functions
Awgn.m:
Awgn_complex.m:
Bingen.m:
Fade.m:
Fade_fs.m:
Fade_diversity.m:
Fh.m:
Ds_mod.m:
Ds_demod.m:
adds additive white Guassian noise to signal
adds complex additive white Gaussian noise to input signal
generates random +1/-1 sequence
generates Rayleigh fading
generates frequency selective Rayleigh fading.
generates two channels of Rayleigh fading.
generates orthogonal complex exponential matrix for slow FH-MA
DS_SS modulation
DS_SS demodulation
5
Final Exam
Simulation Results for Problem 1
6
BER versus Eb/No in the AWGN channel
0
10
1
10
2
BER
10
3
10
4
10
5
10
6
10
20
AWGNTHEORY
N=16
N=32
N=64
15
10
5
Eb/No (dB)
0
5
10
0
BER versus 10log10[(P/J)(W/R)] in pulsed noise jamming and AWGN
10
1
10
2
BER
10
3
10
4
10
5
10
6
10
20
=1
=0.4
=0.2
THEORY
15
10
5
10log10[(P/J)(W/R)] (dB)
0
5
10
BER versus 10log10[(P/J)(W/R)] in barrage noise jamming and AWGN
0
10
Eb/No=2dB
Eb/No=4dB
Eb/No=6dB
THEORY
1
BER
10
2
10
3
10
0
5
10
15
20
25
30
10log10[(P/J)(W/R)] (dB)
35
40
45
50
0
BER versus Eb/No with binary BCH code in the AWGN channel
BER
10
1
10
2
10
20
AWGNTHEORY
with BCH code
15
10
5
Eb/No (dB)
0
5
Final Exam
Simulation Results for Problem 2
7
HISTOGRAM OF ENVELOPE
3000
2500
2000
1500
1000
500
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
HISTOGRAM OF PHASE
1200
1000
800
600
400
200
0
4
3
2
1
0
Rayleigh fading
1
2
3
4
BER versus Eb/No in Rayleigh fading and AWGN
0
10
1
10
2
BER
10
3
10
4
10
5
10
6
10
20
Rayleigh fading
Frequency selective Rayleigh fading
FADETHEORY
AWGNTHEORY
15
10
5
0
5
Eb/No (dB)
10
15
20
25
30
BER versus Eb/No in Rayleigh fading and AWGN
0
10
1
10
2
BER
10
3
10
4
10
5
10
30
Predetection selective combining receiver (PSCR)
Rayleigh fading
PSCRTHEORY
FADETHEORY
20
10
0
Eb/No (dB)
10
20
30
Final Exam
Simulation Results for Problem 3
8
0
BER versus Eb/No using DSCDMA: perfect synchronism between users
10
1
10
2
BER
10
3
10
4
10
5
10
6
10
20
K=4
K=8
K=16
THEORY
15
10
5
Eb/No (dB)
0
5
10
0
BER versus Eb/No using slow FHMA: perfect synchronism between users
10
1
10
2
BER
10
3
10
4
10
5
10
6
10
20
K=4
K=8
K=16
THEORY
15
10
5
Eb/No (dB)
0
5
10
0
BER versus Eb/No using DSCDMA: a random asynchronism between users
10
K=4
K=8
K=16
K=32
1
10
2
BER
10
3
10
4
10
5
10
20
10
0
10
20
Eb/No (dB)
30
40
50
0
BER versus Eb/No using slow FHMA: a random asynchronism between users
10
K=4
K=8
K=16
K=32
1
BER
10
2
10
3
10
4
10
20
10
0
10
20
Eb/No (dB)
30
40
50
Final Exam
Source Codes for Final Exam
9
Final Exam
Programs
Final11.m: the first part of problem 1
Final12.m: the second part of problem 1
Final11_extra.m simulation with binary BCH code
Final12_extra.m simulation in barrage noise jamming and AWGN
Final21.m: the first part of problem 2
Final22.m: the second part of problem 2
Final21_extra.m simulates a pre-detection selective combining diversity receiver for
Rayleigh fading channels
Final31.m: the first part of problem 3 using DS-CDMA
Final32.m: the second part of problem 3 using DS-CDMA
Final31_fh.m: the first part of problem 3 using slow FH-MA
Final32_fh.m: the second part of problem 3 using slow FH-MA
Functions
Awgn.m: adds additive white Guassian noise to signal
Awgn_complex.m: adds complex additive white Gaussian noise to input signal
Bingen.m: generates random +1/-1 sequence
Fade.m: generates Rayleigh fading
Fade_fs.m: generates frequency selective Rayleigh fading.
Fade_diversity.m: generates two channels of Rayleigh fading.
Fh.m: generates orthogonal complex exponential matrix for slow FH-MA
Ds_mod.m: DS_SS modulation
Ds_demod.m: DS_SS demodulation
10