Section 1.
Radar and Satellite Navigation (30060)
- MSc assignment 2018-19
The assignment forms 50% of the final mark.
1. In this group assignment, each group should prepare a combined, brief report presented in
a scientific paper format and style on a specific topic of radar systems analysis. The format
of the essay is specified in Section 3 of this document, and all submitted assignments
should have the same structure.
2. Each student within each group will have an individual task, taken from Section 2 of this
document, and should develop a computer model of an appropriate system and
demonstrate the computer simulation results as well as analytical analysis and their
comparison, where appropriate. The essay will clearly identify which student undertook
which task, and each student will be assessed based on their task only and not the
full group report.
3. Aim: Radar system analysis and modelling. It is assumed that a radar system is being
designed for surveillance. As a part of the radar design, computer models for i) target
detection, ii) the ambiguity function of the radar transmit waveform, and iii) outputs of a
matched filter to a target echo at the background of noise should be generated. The outputs
of the computer model should be compared to theoretical expectations, and should include
analyses of simulated vs. predicted results.
Objectives: The aim above is to be fulfilled by developing three different computer models
in MATLAB or/and Simulink, one by each group member, and presenting and analysing the
simulation results. The final simulation results (intermediate ones may be used to
strengthen the quality of the essay, where deemed appropriate) for each task are:
i) Target detection: a graph should be presented, with the probability of detection as the
vertical axis, signal to noise ratio as the horizontal axis, and the probability of false
alarm as a parameter. On the same graph the result of analytical calculations, e.g.
Barton method, could be presented and in the conclusion comparison of modelling and
calculation results should be presented.
ii) Ambiguity function: a surface plot should be presented, showing the magnitude of the
ambiguity function in dB with delay and Doppler as the horizontal/vertical axes. Graphs
showing cross-sections of the ambiguity function at zero range and at zero Doppler
should be presented, and in the conclusion a comparison of the simulated vs
theoretically expected range and Doppler resolutions should be given.
iii) Matched filtering: two graphs should be presented. The first one should show the
magnitude of the matched filter output vs target range as the horizontal axis for a given
target echo in the absence of noise. The second one should be similar to the first, but
for a given signal-to-noise ratio (SNR) at the output at the radar receive antenna
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assuming additive white gaussian noise. In the conclusion, a comparison of the
simulated vs theoretically expected peak-to-sidelobe ratio and a comparison of the
simulated vs theoretically expected SNR at the output of the matched filter should be
presented. To create these graphs you should first emulate an echo signal from a target
at a given distance, for a single transmit signal, and then apply the appropriate matched
filter.
4. The main text of the essay length for each student should be between 2000 (minimum) and
3000 (maximum) words plus tables, figures and, if necessary, appendices according to the
attached template. Appendices should include MATLAB code listings, where possible.
NOTE: It is expected that all results presented by students are the result of their own
MATLAB code. Results directly obtained from the MATLAB Phased Array Toolbox
may be used at the students’ discretion to cross-check their own results, however
they are not acceptable as answers on their own. Therefore, results presented
without accompanying codes will receive a 30% penalty.
5. In the assignment students should:
Demonstrate knowledge in the specific radar system area;
Analyse the main technical challenges and performance limitations;
Develop a MATLAB or/and Simulink system model;
Introduce the simulation results and analyse these results vs analytical results;
Formulate the appropriate conclusions;
Demonstrate scientific communication skills
6. The assessment criteria are detailed on the last page of this document
Plagiarism, which includes, but is not limited to, a failure to acknowledge sources will be
penalised. For further information on plagiarism please see (you may need to log in)
https://intranet.birmingham.ac.uk/as/studentservices/conduct/plagiarism/guidancestudents.aspx
Submission: Assignments should be submitted on Canvas, as .pdf files, by 4
th March 2019, at
14:00. Late submission will be penalised at 5% per day late.
Recommended textbooks: The main recommended textbooks are
"Radar System Analysis and Modeling", by David Barton (any edition);
"Radar Systems Analysis and Design Using MATLAB", by Bassem R. Mahafza (any edition)
“Principles of Modern Radar, vol.1: Basic Principles”, by M. A. Richards, J.A. Scheer, W.A.
Holm
“Bistatic Radar: Principles and Practice”, by M. Cherniakov, as well as lecture notes
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Section 2.
The given radar parameters per student group are:
1. Chun-Luo Chen, Feng Chen, Yu Chen
i) Target detection (Chun-Luo Chen)
Detection probability over one scan D=0.8-0.95
False alarm probability over one scan F=10-3
Number of pulses during the dwell time N=100
The target echo experiences slow fluctuations
The received signal is coherent over the dwell time
ii) Ambiguity function (Feng Chen)
Transmitted signal is the following M-sequence: 10000011, where logic “1” is 1V and logic “0” is -1V
Sequence duration: 1us
iii) Matched filtering (Yu Chen)
Transmitted signal is the following M-sequence: 10000011, where logic “1” is 1V and logic “0” is -1V
Sequence duration= 1us
SNR at the output of the receive antenna = 3 dB
Target is fixed and located 7km away from the radar
2. Sandeep Deb, Lei Fu, Cheng Gao
i) Target detection (Sandeep Deb)
Detection probability over ten scans D=0.8-0.95
False alarm probability over ten scans F=10-3
Number of pulses during the dwell time N=30
The target echo experiences slow fluctuations
The received signal is coherent over the dwell time
ii) Ambiguity function (Lei Fu)
Transmitted signal is the following M-sequence: 10101011, where logic “1” is 2V and logic “0” is -2V
Sequence duration: 1.5us
iii) Matched filtering (Cheng Gao)
Transmitted signal is the following M-sequence: 10101011, where logic “1” is 2V and logic “0” is -2V
Sequence duration: 1.5us
SNR at the output of the receive antenna = 6 dB
Target is fixed and located 7.5km away from the radar
3. Yuqiang Gui, Bohui Jin, Di Kang
i) Target detection (Yuqiang Gui)
Detection probability over one scan D=0.8-0.95
False alarm probability over one scan F=10-3
Number of pulses during the dwell time N=50
The target echo experiences slow fluctuations
The received signal is coherent over 5 pulses reception time
ii) Ambiguity function (Bohui Jin)
Transmitted signal is the following M-sequence: 10001111, where logic “1” is 0.5V and logic “0” is -0.5V
Sequence duration: 2us
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iii) Matched filtering (Di Kang)
Transmitted signal is the following M-sequence: 10001111, where logic “1” is 0.5V and logic “0” is -0.5V
Sequence duration: 2us
SNR at the output of the receive antenna = 7 dB
Target is fixed and located 8km away from the radar
4. Anni Li, Wenyue Li, Yaxuan Li
i) Target detection (Anni Li)
Detection probability over one scan D=0.8-0.95
False alarm probability over one scan F=10-4
Number of pulses during the dwell time N=100
The target echo experiences slow fluctuations
The received signal is coherent over the dwell time
ii) Ambiguity function (Wenyue Li)
Transmitted signal is the following M-sequence: 10111001, where logic “1” is 5V and logic “0” is -5V
Sequence duration: 2.2us
iii) Matched filtering (Yaxuan Li)
Transmitted signal is the following M-sequence: 10111001, where logic “1” is 1V and logic “0” is -1V
Sequence duration= 2.2us
SNR at the output of the receive antenna = 5 dB
Target is fixed and located 8km away from the radar
5. Jiayi Niu, Lianshan Qi , Guanwei Qiu
i) Target detection (Jiayi Niu)
Detection probability over one scan D=0.8-0.95
False alarm probability over one scan F=10-4
Number of pulses during the dwell time N=30
The target echo experiences slow fluctuations
The received signal is coherent over 10 pulses reception time
ii) Ambiguity function (Lianshan Qi)
Transmitted signal is the following M-sequence: 10001001, where logic “1” is 3V and logic “0” is -3V
Sequence duration: 2.2us
iii) Matched filtering (Guanwei Qiu)
Transmitted signal is the following M-sequence: 10001001, where logic “1” is 3V and logic “0” is -3V
Sequence duration= 2.2us
SNR at the output of the receive antenna = 11 dB
Target is fixed and located 8km away from the radar
6. Jingjing Shi, Marcellina Ayudha Titasari , Jingwen Wang
i) Target detection (Jingjing Shi)
Detection probability over one scan D=0.8-0.95
False alarm probability over one scan F=10-4
Number of pulses during the dwell time N=30
The target echo experiences slow fluctuations
The received signal is coherent over 5 pulses reception time
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ii) Ambiguity function (Marcellina Ayudha Titasari)
Transmitted signal is the following M-sequence: 11100101, where logic “1” is 3V and logic “0” is -3V
Sequence duration: 2.5us
iii) Matched filtering (Jingwen Wang)
Transmitted signal is the following M-sequence: 11100101, where logic “1” is 3V and logic “0” is -3V
Sequence duration= 2.5us
SNR at the output of the receive antenna = 10 dB
Target is fixed and located 10km away from the radar
7. Yaoxuan Wang, Zhangya Wang, Hui Yuan
i) Target detection (Yaoxuan Wang)
Detection probability over one scan D=0.8-0.95
False alarm probability over one scan F=10-5
Number of pulses during the dwell time N=60
The target echo experiences slow fluctuations
The received signal is coherent over the dwell time
ii) Ambiguity function (Zhangya Wang)
Transmitted signal is the following M-sequence: 11001011, where logic “1” is 2V and logic “0” is -2V
Sequence duration: 2us
iii) Matched filtering (Hui Yuan)
Transmitted signal is the following M-sequence: 11001011, where logic “1” is 2V and logic “0” is -2V
Sequence duration= 2us
SNR at the output of the receive antenna = 9 dB
Target is fixed and located 10km away from the radar
8. Puteri Zakaria, Xiaokang Zhang, Xin Zhang
i) Target detection (Puteri Zakaria)
Detection probability over one scan D=0.8-0.95
False alarm probability over one scan F=10-5
Number of pulses during the dwell time N=100
The target echo experiences slow fluctuations
The received signal is coherent over 5 pulses reception time
ii) Ambiguity function (Xiaokang Zhang)
Transmitted signal is the following M-sequence: 10100111, where logic “1” is 5V and logic “0” is -5V
Sequence duration: 3us
iii) Matched filtering (Xin Zhang)
Transmitted signal is the following M-sequence: 10100111, where logic “1” is 5V and logic “0” is -5V
Sequence duration= 3us
SNR at the output of the receive antenna = 5 dB
Target is fixed and located 11km away from the radar
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9. Yu Zhang, Rui Zhao, Hongyan Zhu
i) Target detection (Yu Zhang)
Detection probability over one scan D=0.8-0.95
False alarm probability over one scan F=10-5
Number of pulses during the dwell time N=80
The target echo experiences slow fluctuations
The received signal is coherent over 10 pulses reception time
ii) Ambiguity function (Rui Zhao)
Transmitted signal is the following M-sequence: 10010001, where logic “1” is 1V and logic “0” is -1V
Sequence duration: 1.5us
iii) Matched filtering (Hongyan Zhu)
Transmitted signal is the following M-sequence: 10010001, where logic “1” is 1V and logic “0” is -1V
Sequence duration= 1.5us
SNR at the output of the receive antenna = 8 dB
Target is fixed and located 9.5km away from the radar
10. Tongyue Zhu, Xunyu Zuo
i) Target detection (Tongyue Zhu)
Detection probability over one scan D=0.8-0.95
False alarm probability over one scan F=10-5
Number of pulses during the dwell time N=40
The target echo experiences slow fluctuations
The received signal is coherent over the dwell time
ii) Ambiguity function (Xunyu Zuo)
Transmitted signal is the following M-sequence: 11010011, where logic “1” is 5V and logic “0” is -5V
Sequence duration: 4us
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Section 3.
Template: MSc assignment "Radar and Satellite Navigation", corresponds to the template of papers
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S. B. Author, Jr., was with Rice University, Houston, TX 77005 USA. He is now with the Department of Physics, Colorado State University, Fort Collins, CO 80523
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Radar System Design and Analysis
Student names, ID numbers and the date of submission
T
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Table I).
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VII Other Recommendations
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VIII Some Common Mistakes
The word “data” is plural, not singular. The subscript for the permeability of vacuum μ0 is zero, not a lowercase
letter “o.” The term for residual magnetization is “remanence”; the adjective is “remanent”; do not write “remnance”
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“complement” and “compliment,” “discreet” and “discrete,” “principal” (e.g., “principal investigator”) and “principle”
P a g e | 11
(e.g., “principle of measurement”). Do not confuse “imply” and “infer.”
Prefixes such as “non,” “sub,” “micro,” “multi,” and “ultra” are not independent words; they should be joined to the
words they modify, usually without a hyphen. There is no period after the “et” in the Latin abbreviation “et al.” (it is
also italicized). The abbreviation “i.e.,” means “that is,” and the abbreviation “e.g.,” means “for example” (these
abbreviations are not italicized).
An excellent style manual and source of information for science writers is [9]. A general IEEE style guide and an
Information for Authors are both available at http://www.ieee.org/web/publications/authors/transjnl/index.html
IX Publication Principles
The contents of IEEE TRANSACTIONS and JOURNALS are peer-reviewed and archival. The TRANSACTIONS publishes
scholarly articles of archival value as well as tutorial expositions and critical reviews of classical subjects and topics
of current interest.
Authors should consider the following points:
1) Technical papers submitted for publication must advance the state of knowledge and must cite relevant prior work.
2) The length of a submitted paper should be commensurate with the importance, or appropriate to the complexity, of
the work. For example, an obvious extension of previously published work might not be appropriate for publication
or might be adequately treated in just a few pages.
3) Authors must convince both peer reviewers and the editors of the scientific and technical merit of a paper; the
standards of proof are higher when extraordinary or unexpected results are reported.
4) Because replication is required for scientific progress, papers submitted for publication must provide sufficient
information to allow readers to perform similar experiments or calculations and use the reported results. Although
not everything need be disclosed, a paper must contain new, useable, and fully described information. For
example, a specimen’s chemical composition need not be reported if the main purpose of a paper is to introduce a
new measurement technique. Authors should expect to be challenged by reviewers if the results are not supported
by adequate data and critical details.
5) Papers that describe ongoing work or announce the latest technical achievement, which are suitable for
presentation at a professional conference, may not be appropriate for publication in a TRANSACTIONS or JOURNAL.
XConclusion
A conclusion section is not required. Although a conclusion may review the main points of the paper, do not
replicate the abstract as the conclusion. A conclusion might elaborate on the importance of the work or suggest
applications and extensions.
APPENDIX
Appendixes, if needed, appear before the acknowledgment.
ACKNOWLEDGMENT
The preferred spelling of the word “acknowledgment” in American English is without an “e” after the “g.” Use the
singular heading even if you have many acknowledgments. Avoid expressions such as “One of us (S.B.A.) would
like to thank ... .” Instead, write “F. A. Author thanks ... .” Sponsor and financial support acknowledgments are
placed in the unnumbered footnote on the first page, not here.
REFERENCES
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New York: McGraw-Hill, 1964, pp. 15–64.
[2] W.-K. Chen, Linear Networks and Systems (Book style). Belmont, CA: Wadsworth, 1993, pp. 123–135.
[3] H. Poor, An Introduction to Signal Detection and Estimation. New York: Springer-Verlag, 1985, ch. 4.
[4] B. Smith, “An approach to graphs of linear forms (Unpublished work style),” unpublished.
[5] E. H. Miller, “A note on reflector arrays (Periodical style—Accepted for publication),” IEEE Trans. Antennas Propagat., to be published.
[6] J. Wang, “Fundamentals of erbium-doped fiber amplifiers arrays (Periodical style—Submitted for publication),” IEEE J. Quantum Electron.,
submitted for publication.
[7] C. J. Kaufman, Rocky Mountain Research Lab., Boulder, CO, private communication, May 1995.
[8] Y. Yorozu, M. Hirano, K. Oka, and Y. Tagawa, “Electron spectroscopy studies on magneto-optical media and plastic substrate interfaces
(Translation Journals style),” IEEE Transl. J. Magn.Jpn., vol. 2, Aug. 1987, pp. 740–741 [Dig. 9th Annu. Conf. Magnetics Japan, 1982, p. 301].
[9] M. Young, The Technical Writers Handbook. Mill Valley, CA: University Science, 1989.
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[10] J. U. Duncombe, “Infrared navigation—Part I: An assessment of feasibility (Periodical style),” IEEE Trans. Electron Devices, vol. ED-11, pp. 34–
39, Jan. 1959.
[11] S. Chen, B. Mulgrew, and P. M. Grant, “A clustering technique for digital communications channel equalization using radial basis function
networks,” IEEE Trans. Neural Networks, vol. 4, pp. 570–578, Jul. 1993.
[12] R. W. Lucky, “Automatic equalization for digital communication,” Bell Syst. Tech. J., vol. 44, no. 4, pp. 547–588, Apr. 1965.
[13] S. P. Bingulac, “On the compatibility of adaptive controllers (Published Conference Proceedings style),” in Proc. 4th Annu. Allerton Conf. Circuits
and Systems Theory, New York, 1994, pp. 8–16.
[14] G. R. Faulhaber, “Design of service systems with priority reservation,” in Conf. Rec. 1995 IEEE Int. Conf. Communications, pp. 3–8.
[15] W. D. Doyle, “Magnetization reversal in films with biaxial anisotropy,” in 1987 Proc. INTERMAG Conf., pp. 2.2-1–2.2-6.
[16] G. W. Juette and L. E. Zeffanella, “Radio noise currents n short sections on bundle conductors (Presented Conference Paper style),”
presented at the IEEE Summer power Meeting, Dallas, TX, Jun. 22–27, 1990, Paper 90 SM 690-0 PWRS.
[17] J. G. Kreifeldt, “An analysis of surface-detected EMG as an amplitude-modulated noise,” presented at the 1989 Int. Conf. Medicine and
Biological Engineering, Chicago, IL.
[18] J. Williams, “Narrow-band analyzer (Thesis or Dissertation style),” Ph.D. dissertation, Dept. Elect. Eng., Harvard Univ., Cambridge, MA, 1993.
[19] N. Kawasaki, “Parametric study of thermal and chemical nonequilibrium nozzle flow,” M.S. thesis, Dept. Electron. Eng., Osaka Univ., Osaka,
Japan, 1993.
[20] J. P. Wilkinson, “Nonlinear resonant circuit devices (Patent style),” U.S. Patent 3 624 12, July 16, 1990.
[21] IEEE Criteria for Class IE Electric Systems (Standards style), IEEE Standard 308, 1969.
[22] Letter Symbols for Quantities, ANSI Standard Y10.5-1968.
[23] R. E. Haskell and C. T. Case, “Transient signal propagation in lossless isotropic plasmas
(Report style),” USAF Cambridge Res. Lab., Cambridge, MA Rep. ARCRL-66-234 (II), 1994,
vol. 2.
[24] E. E. Reber, R. L. Michell, and C. J. Carter, “Oxygen absorption in the Earth’s atmosphere,”
Aerospace Corp., Los Angeles, CA, Tech. Rep. TR-0200 (420-46)-3, Nov. 1988.
[25] (Handbook style) Transmission Systems for Communications, 3rd ed., Western Electric Co.,
Winston-Salem, NC, 1985, pp. 44–60.
[26] Motorola Semiconductor Data Manual, Motorola Semiconductor Products Inc., Phoenix, AZ,
1989.
[27] (Basic Book/Monograph Online Sources) J. K. Author. (year, month, day). Title (edition) [Type of
medium]. Volume (issue). Available: http://www.(URL)
[28] J. Jones. (1991, May 10). Networks (2nd ed.) [Online]. Available: http://www.atm.com
[29] (Journal Online Sources style) K. Author. (year, month). Title. Journal [Type of medium].
Volume(issue), paging if given. Available: http://www.(URL)
[30] R. J. Vidmar. (1992, August). On the use of atmospheric plasmas as electromagnetic reflectors.
IEEE Trans. Plasma Sci. [Online]. 21(3). pp. 876–880. Available:
http://www.halcyon.com/pub/journals/21ps03-vidmar
First A. Author (M’76–SM’81–F’87) and the other authors may include biographies at the end of regular papers. Biographies are often not
included in conference-related papers. This author became a Member (M) of IEEE in 1976, a Senior Member (SM) in 1981, and a Fellow (F) in
1987. The first paragraph may contain a place and/or date of birth (list place, then date). Next, the author’s educational background is listed.
The degrees should be listed with type of degree in what field, which institution, city, state, and country, and year degree was earned. The
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The second paragraph uses the pronoun of the person (he or she) and not the author’s last name. It lists military and work experience,
including summer and fellowship jobs. Job titles are capitalized. The current job must have a location; previous positions may be listed without
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The third paragraph begins with the author’s title and last name (e.g., Dr. Smith, Prof. Jones, Mr. Kajor, Ms. Hunter). List any memberships in
professional societies other than the IEEE. Finally, list any awards and work for IEEE committees and publications. If a photograph is provided,
the biography will be indented around it. The photograph is placed at the top left of the biography. Personal hobbies will be deleted from the
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PHOTO
The photo is
not
compulsory.
P a g e | 13
30060 Section 5.
Radar and Satellite Navigation
Dr. M. Antoniou, Prof. M. Cherniakov and Prof. M. Gashinova
Student ID: ………………………………. Mark Max
Demonstration of the problem and the concept understanding as a part of the
broad concept of Radar Systems. Creativity of the material presentation, i.e.
original approach, graphs, figures, examples, etc.
Demonstration of computer modelling skills
/ 40
Proper and clear explanation and presentation of the specified problem. Ability to
draw and clearly formulate conclusions.
Technical communication skills, i.e. clarity of the mathematical presentation, the
introduction and conclusion of arguments, correspondence to the recommended
assignment template.
Marker name: Dr. M. Antoniou, Prof. M. Cherniakov, Prof. M. Gashinova /100
Any evidence of plagiarism YES NO
Comments:
Distinct.
Good Practice
Example of a similar assignment, but not for Radar and
Satellite Navigation
This is an example of how the essay shall look like for each
student. The final report for each group will be a compilation
of these essays from each student in the group, with a clear
identification of student name and ID number for each essay
NON-COHERENT BINARY ASK COMMUNICATION SYSTEM
Abstract— This report demonstrates a non-coherent binary amplitude shift keying communication system with a
data rate of 64Kbps. In detailed analysis of binary ASK system is presented followed by the design, simulation and
modelling of the system in MATLAB and Simulink. To observe the effect of variable channel noise in the overall
performance of system, designed model is simulated in the presence of AWGN with an Eb/ No of 1-15dB. Noise analysis
has also been performed to demonstrate the parameters of white Gaussian noise. Comparison between simulation
results and theoretical results show that the designed system performs well in the presence of AWGN noise.
Keywords – binary ASK, non-coherent, BER, AWGN, digital modulation
I. INTRODUCTION
Digital modulation is advantageous over the analog counterpart because of its high noise immunity, high
spectral efficiency, efficient multiplexing, software implementation and greater security.
Basic aim of this research is to demonstrate a binary amplitude shift keying (BASK) communication system in
the medium with an additive white Gaussian noise having various values of Eb/No (Energy per bit to noise power)
thereby, demonstrating the variation in BER with Eb/No as the BASK signal propagates.
BASK is digital modulation technique in which, data communication is performed using two amplitude levels i.e.
1 and 0. The carrier is transmitted when the bit is 1 whereas, no transmission is done for bit 0. As the modulated
signal is transmitted through the medium, the effect of channel noise is introduced in the transmitted signal. BASK
modulation scheme is comparatively simpler in comparison to other digital modulation schemes; therefore, the
effect is channel noise is prominent. Because of this, the bit error rate for a binary amplitude shift keying system is
more in comparison to FSK, PSK, QAM modulation schemes. Due to an intrinsic high bit error rate (BER), when a
BASK system is designed, it is essential to have an efficient detection of the input bits at the receiver due to the
effect of a dominant channel noise.
In the designed system, to pass the required signal bandwidth and to limit the channel noise (AWGN)
bandwidth, a band-pass and a low-pass filter is used in first stage of receiver. BPF suppresses AWGN at the
receiver thereby, improving the overall bit error rate. Whereas the LPF is used for envelop detection. The designed
LPF has a cut off frequency of 5Hz with an out of band rejection of 30dB. If the cutoff frequency is reduced, the
performance of LPF in suppressing the noise enhances. However, there is a practical limitation on the cut off
frequency of a LPF because of which, the frequency cannot be further reduced from 5Hz. Sampling frequency also
P a g e | 15
affects the performance of filter. The higher the sampling frequency, better is the performance of filter in terms of
noise removal. However, there is again a limit up to how much the sampling frequency of filter can be increased.
Higher sampling frequency makes the overall design of communication system complex. In the designed filter for
the BASK system, sampling frequency is set at 100Hz.
Generic block level diagram of ASK communication system in Figure 1 consists of a transmitter where BASK
modulation is performed on the input bit stream, a transmission medium where noise is added to the system and a
receiver where demodulation is performed to retrieve the transmitter bit stream. Comparison of transmitted and
detected bit stream of performed to determine the BER.
II. LITERATURE REVIEW
A. Digital Modulation
Modulation is a process in which the information from source is encoded by up converting it to a band pass
signal with a frequency higher than the baseband signal. Modulation is performed by translating or keying the
amplitude, frequency or phase of the carrier having higher frequency according to the amplitude of baseband
signal. To extract baseband signal from the continuous carrier signal, demodulation is performed.
B. Digital Modulation Schemes
Different types of digital modulation schemes are shown in Figure 2.
C. Maximum Data Rate
The maximum possible data rate in any transmission medium is given by Shannon’s channel capacity equation
[1].
Figure 1: Block Diagram of a generic Binary ASK Communication System
Figure 2: Types of Digital Modulation Schemes
P a g e | 16
(1)
Where,
C= Channel Capacity in bps
B= Signal Bandwidth
S/N= Signal to noise ratio
D. Binary Amplitude Shift Keying
BASK commonly known as on-off keying (OOK) is modulation scheme in which a digital signal is expressed as
carrier amplitude’s variation. It is narrow band modulation in which amplitude of a continuous high frequency carrier
is varied according to amplitude of input binary data.
i. Modulation
In ASK system, baseband information is unipolar binary data with information as 0’s and 1’s. Bit 1 is transmitted
with a high frequency carrier whereas for bit 0 no transmission is done. ASK waveform can be mathematically
represented as:
(2)
The input bit stream with 16 symbols, sinosoidal carrier and ASK modulated signal to be transmitted is shown in
Figure 3.
ii. Transmission Medium
Transmission medium constitutes of various types of noise, which affects the modulated signal. If the strength of
noise if large, received signal is corrupted thereby, giving errors. There are different types of noise as shown below.
? Band limited white noise
Figure 3: Input bit stream, carrier signal and BASK modulated signal
P a g e | 17
The PSD of this noise is constant over the defined bandwidth. The signal is corrupted when noise level is
greater than the decision threshold leading to bit error.
Additive White Gaussian Noise
AWGN replicates the effect of random processes occurring in the medium.
o Additive: Noise is added to the transmitted signal
o White: Flat spectrum for all frequencies
o Gaussian: Noise follows Gaussian probability distribution [2]
(3)
With μ=0 and
iii. Demodulation
Received signal can now be represented as:
Rx = Tx + No (4)
Where,
Rx = Received signal
Tx = Transmitted modulated signal
No = Channel noise
Demodulator reduces the channel corrupted waveform to a series of symbols which estimates the transmitted
data bits. On the basis of a threshold, it maps the received signal to digital bits. Demodulator only needs to
determine the presence or absence of carrier therefore, it’s a simple process. Signal detection is of two main types
[3]:
Coherent Detection (Synchronous Detection)
o Receiver’s carrier and transmitter carrier are phase locked
o Correlation between received noisy signal and locally generated signal detects the transmitted signal
o Expensive and complex carrier recovery required
o Improved BER
Non-coherent Detection (Asynchronous Detection)
o Phase locking not required between transmitter and receiver carrier
o Simpler signal recovery process
o High probability of BER
E. Bit error rate (BER)
It is the ratio of total error bits and the transmitted bits, affected by the following factors:
o Channel noise
o Inter symbol interference
o Distortion
o Bit synchronization
P a g e | 18
o Signal attenuation
o Multi path Fading
BER is expressed as normalized signal to noise ratio or Eb/No. BER vs SNR (Eb/No) curves are plotted to
express the performance of a digital system.
The received signal is represented by:
Y=s1+n : bit 1 transmitted (s1=1)
Y=so+n : bit 1 transmitted (so=0)
The two conditional probabilities for bit detection can be represented by [4]:
(5)
(6)
If magnitude of received signal Y is greater than the threshold, the detected bit is 1 whereas, if the magnitude of
received signal Y is less than threshold, it is expected that the transmitted bit is 0. The amplitude of modulated
symbol is represented as:
Hence,
(7)
(8)
The signal space of binary ASK system is in single dimension.
The distance between two signal points is
represented by:
Therefore, the probability of error is:
P a g e | 19
BER of non-coherent ASK is mathematically represented as [5]:
(9)
BER of coherent ASK is mathematically represented as:
(10)
F. BASK Constellation Diagram
Constellation diagram of an ASK signal can be represented as:
The x-axis is reference for the in phase signal whereas, y-axis
displays the quadrature component. As the quadrature component is
absent in BASK system, so the constellation diagram shows only the inphase
component along x-axis.
G. Power Efficiency
It is the ability of modulation scheme to preserve signal with low power levels and is expressed as [1]:
H. Bandwidth Efficiency
It is the capacity of modulation technique to limit data within a defined band and is represented as:
Where,
Rb: bit rate in bps
B: bandwidth of modulated RF signal
I. Power Spectral Density (PSD)
PSD demonstrates signal’s frequency response by plotting the frequency vs power. It shows the spectral power
of all the frequency contents within a signal.
J. Pulse Shaping
It is performed using specialized pulse shaping filters in the transmitter to decrease the interference between the
signals by increasing the channel bandwidth. It helps to filter out the spectrum’s side lobes as shown in Figure 4.
P a g e | 20
K. Comparison
An efficient modulation technique should exhibit following characteristics:
Low BER at less SNR
Power and bandwidth efficiency
Good performance in the presence of multipath fading
Utilize less bandwidth
Less complex and cost effective
L. Applications of ASK System
The applications of an ASK communication system are mentioned below:
Transmission of digital information in an optical fiber
Short range military communication
Early telephone modem up to 1200bps on voice grade lines
Used in RF systems for the transmission of Morse code
III. BASK SYSTEM
A. Systematic Block Diagram
Figure 4: Signal Spectrum before and after pulse shaping
P a g e | 21
The detailed block diagram is ASK communication system is shown in Figure 5.
B. Signal Modelling
System modelling is performed in Matlab and Simulink. The Matlab code is attached in Appendix A. ASK system
is composed of a transmitter, transmission medium and a receiver described below.
i. Transmitter
Band Pass
Filter
Figure 5: Systematic Block Diagram of ASK Communication System
P a g e | 22
BASK modulation is performed in the transmitter through the steps mentioned below. The ASK modulated
waveform is shown in Figure 3.
a) Signal Generation
Modulating baseband signal is expressed as a series of symbols or bits in the time domain. Each symbol
represents the information of n bits where,
N = log2m bits/symbol (11)
For the ease of representation, 16 symbols are considered in the design with 4000 bits in each symbol to
achieve a data rate of 64Kbps.
b) Carrier Generation
A continuous high frequency sinusoidal carrier is generated. The frequency of carrier should be greater than that
of baseband signal otherwise, the signal detection results in large BER at the receiver.
c) ASK Modulation
ASK modulation can be performed using a switch which only passes the carrier when the input bit is 1. When the
input bit is 0, no carrier is passed. The spectrum of ASK transmitted signal is shown in Figure 6.
ii. Channel
AWGN is added in the transmission medium. The system’s performance is analyzed in three scenarios.
a) No AWGN
When no noise is added to the system the received waveform is exactly like the transmitted waveform.
b) A constant AWGN with Eb/ No or SNR of 10dB
c) A variable AWGN with Eb/ No or SNR of 1-15dB
Figure 6: Spectrum of transmitted ASK waveform before and after AWGN
P a g e | 23
The received waveform after adding the AWGN with SNR of 1-15dB is shown in Figure 7.
iii. Receiver
In the BASK receiver, signal detection is performed to retrieve the transmitter bit information.
a) Band Pass Filtration
Band pass filter is used as the first stage of receiver to reduce the noise effects.
b) Rectification
The input signal to rectifier is multiplied with itself which rectifies the output. Therefore, only the positive side of
waveform is received at the output of rectifier.
c) Filtration
A low pass filter reduces the effect of noise from rectified signal. A least square FIR filter is designed for the
removal of noise. LPF suppresses the higher noise frequency. Rectification and filtration combines to detect the
envelop of received signal.
d) Comparator
The comparator delivers a digital output of the envelop detected signal on the basis of a threshold value. If the
value of signal is below threshold, the output is 0 whereas, the output is 1 is the value of signal is above threshold.
The received bit steam for AWGN with SNR 1-15dB is shown in Figure 8.
Figure 7: Received Signal after adding AWGN from Eb/ No = SNR 1=15dB and
filtration
P a g e | 24
e) BER
The transmitted bit stream is compared with detected bit stream to find the BER. Simulation results are then
plotted against the theoretical bit error rate for a non-coherent BASK system as shown in Figure 9. Analysis has
been done for BER 10-2 and 10-3
.
1.1.Simulink Model
Figure 8: BASK received Bit Stream with AWGN having Eb/ No = SNR 1-15dB
Figure 9: BER analysis for 10 -2 and 10-3 between theoretical and calculated results
P a g e | 25
The system modelling of ASK system is done in Simulink. Threshold for signal detection is set at 0.5. The
Simulink model is presented in Figure 10a whereas, the simulation results are presented in Figure 10b.
C. Noise Modelling
AWGN is represented by a random process with a PDF having a Gaussian distribution and a constant PSD with
a value equivalent to noise power or variance. Noise has a constant mean and covariance is time invariant making
it a wide sense stationary process. The histogram of white noise is plotted to determine its PDF. The PDF is nearly
equal to the theoretical PDF represented by the following equation with a Gaussian distribution [4].
(12)
Figure 10a: Simulink Model of ASK communication system
Figure 10b: Simulation results of ASK system in Simulink
P a g e | 26
Autocorrelation function is a scaled signal with magnitude equal to the variance. MATLAB code for the noise
modelling is attached in Appendix B. Simulation results of noise modelling are shown in Figure 11.
PSD of a white noise shows that it has nearly fixed power in the entire band with a value equal to 6dB. Thereby,
it is confirmed that the generated white noise has a constant PSD.
Power = 10log10 (σ2
) =10log10 (4) =6 dB
IV. DESIGN ANALYSIS
A. BER Comparison
The comparison of BER calculated using theoretical formula in equation 10 and the simulated results is shown
in Table 1. It is found that the BER of designed BASK system is nearly equal to the theoretical results. The results
can also be verified from Figure 9.dB
TABLE I
COMPARISON OF THEORETICAL AND CALCULATED BER FOR SNR 1-15 DB
Eb/ No or
SNR (dB)
BER Theoretical BER Calculated
1 0.331902666542877 0.527366314920639
2 0.278382207307438 0.4330396525850132
3 0.223823897295794 0.353271833286657
4 0.170651194356157 0.258898845230837
Figure 11: Noise Modelling of AGWN in MATLAB showing generated noise, PDF, ACF and PSD of noise
P a g e | 27
5 0.121709824615639 0.180549318689371
6 0.079814667661548 0.111318237100481
7 0.047093102397304 0.06586618958376
8 0.024325941089215 0.034328134289297
9 0.010627897188806 0.015034552398623
10 0.003760324064043 0.005151674628544
11 0.001020091579789 0.001287084315818
12 0.000198042813939 0.000250194125872
13 0.000025228735034 0.000032213359232
14 0.000001890569040 0.000002305326446
15 0.000000072627681 0.000000085308201
It is determined that for SNR from 1-6dB there is more difference between the simulated and theoretical results.
However, if SNR is increased further, the calculated results are almost equal to the theoretical results.
When the value of SNR is less, the signal to noise ratio is less which means that the difference between desired
signal and noise energy is quiet less therefore, it becomes difficult to distinguish the data bits from noise. As a
result of this, the BER is more when SNR is less.
B. BER for Different Modulation Schemes
An ASK system with non-coherent detection has high probability of error as compared to other digital modulation
schemes. Although it is a bandwidth efficient system, but its power efficiency is low resulting in poor noise immunity
thereby, high BER.
Table 2 shows the comparison of E0/ No (dB) values of different digital modulation schemes needed to achieve a
BER of 10-6
[6].
TABLE II
EB/ NO FOR DIGITAL MODULATION TECHNIQUES TO ACHIEVE BER OF 10-6
Modulation
Scheme
Eb/ No (dB)
BPSK 10.6
QPSK 10.6
4-QAM 10.6
D-BPSK 11.2
D-QPSK 12.7
8-PSK 14
BASK 14
16-QAM 14.5
16-PSK 18.3
64-QAM 18.8
P a g e | 28
32-PSK 23.3
C. BASK System
ASK transmitters are simple and efficient since power is not consumed for bit 0. Receiver complexity can be
reduced by using non-coherent detection.
As BER is high with an abrupt change in the amplitude of carrier at bit transition, therefore BASK is not
spectrally efficient and is limited to low or moderate data rates as compared to other digital modulation techniques.
The threshold detection depends upon the received signal’s amplitude, so BASK has poor performance in presence
of fading. This limits the BASK communication range.
D. BASK Spectral Efficiency
The PSD of binary ASK signal is of the form of which has distribution on both sides of the vertical axis.
Therefore, the bandwidth of a binary ASK system is double than the baseband bit stream’s bandwidth. Therefore,
B= =
The bandwidth of BASK system can be verified from the generalized spectrum shown in Figure 12. This is also
called the null to null bandwidth of an ASK modulated signal. As the quadrature component is wasted in an ASK
modulation scheme, therefore the spectral efficiency is half than that of the baseband unipolar signal. The spectrum
is in the form of sinc2
, which is similar to the one obtained for the designed system shown in Figure 6.
Spectrum of ASK modulated signal is centered on the carrier frequency whereas the spectrum of bit stream is
spread along the frequency band.
E. System Limitation
The noncoherent BASK system receiver often uses a band pass filter at the first stage of receiver with a
bandwidth of 2/Tb Hz centered on the carrier frequency fC Hz. However, as the data rate is very high (64Kbps), the
bit duration is quiet low. Therefore, the design of such a band pass filter is a very tedious task for the required
results. An increase in the data rate reduces the symbol’s pulse width thereby, increasing signal bandwidth.
A half wave rectifier together with a LPF forms an envelope detector. The bandwidth of low pass filter is 2/Tb Hz.
This configuration is used to detect bit stream. In the Matlab code, an envelope command is used for half wave
rectification whereas, in the Simulink model, signal is multiplied with itself for rectification. Design of low pass filter is
again a limitation. A higher cutoff frequency is used to design a more practical filter with good results.
Figure 12: Bandwidth of an ASK signal
P a g e | 29
An analog comparator with a specific threshold voltage outputs the estimate of the received binary data. At low
SNR, the received signal has more BER because of the reason that it has high false detections. If the threshold is
increased to reduce the BER for low SNR, the BER of signal with high SNR is affected. Therefore, threshold is
selected to maximize the performance of the system for wide range of SNR values.
This noncoherent BASK demodulator is not optimal because the envelope detector and comparator are not
equivalent to correlation performed in coherent detection.
For Gaussian case Matched Filter detection is optimal because it maximizes the SNR of received signal and
making it apt for detection. Matched filter allows the detection of bits which are below the threshold. But for the
matched filter, the signal that is being detected should be known. Therefore, the coherent detection provides better
BER as compared to non-coherent detection without the use of a matched filter.
F. System Improvement
To enhance the performance of communication system, digital error control codes are often used to detect and
correct the error bits [7]. The system uses complex signal processing techniques like source coding, encryption and
equalization thereby, reducing the bit error rate. This is however out of scope for this research document. The
system can be improved by following techniques:
Increase in SNR by reducing the communication distance
Decrease in data rate
Decrease in bandwidth which reduces the data rate
Use of pulse-shaping filter which reduces the sharp amplitude transition among different bits
Band limiting the transmitted ASK thereby, reducing the bandwidth
G. Advantages and Disadvantages
1. Advantages
Employed in control applications due to simple architecture and cost effectiveness
Less power consumption as the transmitter is practically off during bit 0
Simple transmitter and receiver design
2. Disadvantages
Sharp discontinuities at the transition points between binary 1 and 0
Can be easily corrupted by noise
High BER
Low SNR
Inefficient to use for multiplexing
V. CONCLUSION
A binary ASK communication system with non-coherent detection is designed using MATLAB and Simulink. The
simulation results are presented in the report. It is observed that as the signal in an ASK signal is only transmitted
for half the time if there is a 50% probability for bit 1, therefore, there is a 3dB degradation in BER as compared to
that in BPSK system where the transmission is for complete communication duration.
P a g e | 30
The designed system is analyzed for various values of Eb/No and it is examined that the performance of system
at high Eb/No is nearly similar to the theoretical results. The data rate of assigned task is quiet high for an ASK noncoherent
system therefore, at low bit energy to noise ratio, there are more deviations in the system performance as
compared to the analytical results. This can be improved by using coherent detection and reducing the data rate.
As there are sharp discontinuities in the received ASK waveform, therefore it is implied that the bandwidth is
high. This might increase the BER. However, if a band limiting or pulse shaping of the message signal is done
before modulation, the sharp discontinuities can be avoided.
Noise Analysis performed shows that the PDF and ACF of the generated white noise are in accordance to the
theoretical results with a Gaussian PDF and an even ACF centered about 0. The PSD of noise is constant over the
entire band with a level of 6dB.
ASK systems are preferred in low cost systems with a short communication distance such as RFID. Pulse
shaping by the use of a band limited filter can improve the bit error rate. The side bands in spectrum can be
eliminated by using a pulse shaping filter.
APPENDIX A
Signal modelling m.file
clc; clear all; close all;
%% ----- BASEBAND SIGNAL PARAMETERS -----%%
D_R=64e3; %Data Rate = 64Kbps
P_D=1/D_R; %Pulse duration
%%% TRANSMITTER %%%%
% SIGNAL GENERATION
bits=16;
Input=rand(1,bits)>0.5;
Input=repmat(Input',1,4000)';
Input=Input(:)';
t=linspace(0,bits,numel(Input));
figure('Name','Transmitted Data')
subplot(3,1,1);
plot(t,Input,'r');
title('INPUT BIT STREAM');
xlabel('Samples');
ylabel('Amplitude');
grid on
% CARRIER GENERATION
DC=1/2;
Ao=3;
F=10;
Carrier=Ao.*sin(2*pi*F*t)+DC;
subplot(3,1,2);
plot(t,Carrier,'b');
title('CARRIER');
xlabel('Samples');
ylabel('Amplitude');
grid;
% ASK MODULATION
ModSig=Carrier.*Input;
subplot (3,1,3);
plot(t,ModSig);
title('BASK MODULATED SIGNAL');
xlabel('Samples');
ylabel('Amplitude');
grid;
P a g e | 31
% POWER SPECTRAL DENSITY:
[Pxx,F] = periodogram(ModSig,[],length(ModSig),D_R);
figure;
plot(F,10*log10(Pxx));
xlim ([0 500]);
%%%% TRANSMISSION MEDIUM %%%%
% ZERO NOISE
No=0;
RxSig_1=ModSig+No;
% FIXED AWGN
SNRdB_C=10;
RxSig_2=awgn(ModSig,SNRdB_C,'measured',10);
% MULTIPLE AWGN
for SNRdB_=1:1:15
RxSig_3=awgn(ModSig,SNRdB_,'measured',10);
end
L1=length(RxSig_1); L2=length(RxSig_2); L3=length(RxSig_3);
%%%% RECEIVER %%%%%
% LOW PASS FILTER TO REDUCE THE EFFECT OF NOISE
LPF = fdesign.lowpass('Fp,Fst,Ap,Ast',5,20,1,30,100);
lowpass = design(LPF,'equiripple');
%BAND PASS FILTER
[ A B C D] = butter(10,[1 5]/50);
d=designfilt('bandpassfir'
,'FilterOrder',20, ...
'CutoffFrequency1',1,'CutoffFrequency2',5, ...
'SampleRate',100);
% RECEIVED BIT STREAM WITHOUT NOISE
% RECEIVED SIGNAL
figure ('Name'
,'Received Bit Stream Without AWGN');
subplot (2,1,1);
plot(t,RxSig_1);
title('BASK RECEIVED SIGNAL WITH ZERO NOISE');
xlabel('Samples');
ylabel('Amplitude');
% COMPARATOR
for a=1:1:L1
if RxSig_1(a)==0
R1(a)=0;
else
R1(a)=1;
end
end
subplot(2,1,2)
plot(t,R1);
title('RECEIVED BIT STREAM WITHOUT NOISE');
xlabel('Samples'); ylabel('Amplitude');
% RECEIVED BIT STREAM WITH CONSTANT NOISE
% RECEIVED SIGNAL
figure('Name'
,'Received Bit Stream for Fixed Noise');
subplot (4,1,1);
plot(t,RxSig_2);
legend('Signal with fixed AWGN:SNR=10dB');
title('BASK MODULATED SIGNAL WITH FIXED AWGN OF 10dB');
xlabel('Samples'); ylabel('Amplitude');
% BAND PASS FILTER
R2_F1=filter(d,R2_R);
% RECTIFICATION
R2_R=envelope(R2_F1);
subplot(4,1,2)
plot(t,R2_R);
P a g e | 32
% FILTERATION
R2_F=filter(lowpass,R2_R);
subplot(4,1,3)
plot(t,R2_F);
% COMPARATOR
for b=1:L2
if R2_F(b)>2
R2(b)=1;
else
R2(b)=0;
end
end
subplot(5,1,5)
plot(t,R2);
%RECEIVED BIT STREAM WITH MULTIPLE AWGN: SNR IN dB=1
-15dB
figure('Name'
,'Received Signal After Multiple AWGN');
title('BASK RECEIVED SIGNAL WITH MULTIPLE AWGN');
for SNR_dB=1:1:15
% ADDING NOISE
RxSig3=awgn(ModSig,SNR_dB,'measured',10);
% FILTERATION
R3F1= filter(d,RxSig3);
R3F=filter(lowpass,R3F1);
subplot(4,4,SNR_dB)
plot(t,RxSig3,'g'
,'LineWidth',2);
hold on
;
plot(t,R3F,'b');
title(['SNR: ',num2str(SNR_dB),'dB']);
xlim([0 16]); ylim( [
-8 8]);
xlabel('Samples'); ylabel('Amplitude');
end
legend(
'Signal with AWGN'
,'Signal After Filteration');
h=1; i=1; j=1; k=1; l=1; m=1;
figure('Name'
,'RECEIVED BITS AFTER AWGN: SNR=1
-15dB');
title('BASK RECEIVED BIT STREAM WITH VARIABLE NOISE');
for SNR=1:1:15
snrlin=10.^(SNR./10);
RxSig_3=awgn(ModSig,SNR,'measured',10);
R3_F=filter(lowpass,RxSig_3);
% RECTIFICATION
R3_R=envelope(R3_F);
% COMPARATOR
for Sample=1:L3
if R3_R(Sample)>2
Rx_Bits(Sample)=1;
else
Rx_Bits(Sample)=0;
end
end
subplot(5,3,SNR)
plot(t,Rx_Bits);
title(['SNR: ',num2str(SNR),'dB']);
xlabel('Samples'); ylabel('Amplitude');
xlim( [0 16]);
%%%%% BER %%%%%
error=length(find(Rx_Bits~=Input));
cber(h)=error/64000;
h=h+1;
tber(i) = 0.5*exp(
-0.5*snrlin)+0.5*qfunc(sqrt(snrlin));
snrdb(j)=SNR;
P a g e | 33
j=j+1;
end
legend('BASK Received BITSTREAM with different AWGN');
%Plotting the theoretical and calculated BER
figure ('Name','Comparison B/W Theoretical & Calculated BER');
semilogy(snrdb,cber,'-bo',snrdb,tber,'-mh')
title('BER vs Eb/No or SNR in dB');
xlabel('Signal to noise ratio'); ylabel('Bit error rate');
APPENDIX B
Noise modelling m.file
clear all; clc; close all;
Length = 64000; % Gaussian Noise Signal Length
% WHITE NOISE
n_mean = 0; % Mean
SD = 2; % Standard Deviation
W_Noise = SD * randn (Length,1) + n_mean; %White Noise
figure;
subplot(4,1,1)
plot(W_Noise);
title(['White noise : \mu_x=',num2str(n_mean),' \sigma^2=',num2str(SD^2)])
xlabel('No. of Samples'); ylabel('Sample Value'); xlim ([0 64000]); grid on;
% NOISE PDF
subplot(4,1,2)
n = 200; %Total Histrogram Bins in the noise PDF
[f,x] = hist (W_Noise,n);
Bar (x,f/trapz(x,f)); hold on;
%Theoretical PDF of Gaussian Random Variable
T_PDF_WN = (1/(sqrt(2*pi)*SD)) * exp (-((x-n_mean).^2) / (2*SD^2));
plot (x,T_PDF_WN);hold off; grid on;
title ('Theoretical PDF and Simulated PSD of White Gaussian Noise');
legend ('Histograms','Theoretical PDF'); xlabel ('Histogram'); ylabel ('PDF f_x(x)');
% NOISE ACF
subplot (4,1,3)
ACF_W_N = 1/Length * conv (flipud(W_Noise), W_Noise);
lag = (-Length+1):1:(Length-1);
plot(lag , ACF_W_N);
title('ACF of White Noise'); xlabel('Lag'); ylabel('Auto-Correlation');
xlim ([-200 200]); grid on;
% VERIFICATION OF CONSTANT PSD
n_mean = 0;
SD = 2;
S_L = 1024;
% Random White Gaussian Noise
Avg_Mean = n_mean * ones(1,S_L);
Co_Var = (SD^2) * diag(ones(S_L,1));
Chol_Cov_M = chol(Co_Var);
% Multivariate Gaussian Distribution
z = repmat(Avg_Mean,Length,1) + randn(Length,S_L)* Chol_Cov_M;
S = 1/sqrt(S_L)*fft(z,[],2);
P_Avg = mean(S.*conj(S));
Norm_Freq = [-S_L/2:S_L/2-1]/S_L;
P_Avg = fftshift(P_Avg);
subplot (4,1,4)
P a g e | 34
plot (Norm_Freq,10*log10(P_Avg),'m');
axis ([-0.5 0.5 0 10]); grid on;
ylabel('PSD in dB/Hz'); title('PSD of AWGN');
xlabel ('Normalized Frequency');
ACKNOWLEDGMENT
REFERENCES
[1] “Wireless Communications- Principles and Practice”, T. Rappaport, Prentice Hall, 1996
[2] Athanasios Papoulis, Probability, Random Variables, and Stochastic Processes, 3rd ed. WCB/McGraw-Hill, 1991
[3] “Coherent and Non-coherent Receivers”, Professor Sheng Chen, School of Electronics and Computer Science, University of Southampton.
[4] “Mobile Communication Systems” Professor Z Ghassemlooy Electronics & IT Division Scholl of Engineering, Sheffield Hallam University U.K.
[5] Y. Kim, S.-W. Tam, G.-S. Byun, H. Wu, L. Nan, G. Reinman, J. Cong, and M.-C. F. Chang, “Analysis of noncoherent ASK modulation-based RFinterconnect
for memory interface,” IEEE J. Emerg. Sel. Topics Circuits Syst., vol. 2, no. 2, pp. 200–209, Jun. 2012
[6] “Digital Communications” by John G.Proakis, Chapter 7: Channel Capacity and Coding
[7] “Error Control Techniques and Their Applications”, Chaudhary, Rubal & Gupta, Vrinda, International Journal of Computer Applications in
Engineering Sciences, Vol I, Issue II, June 2011
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