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Project Student
Rock Feller Singh
Russells P
PRK20EC2009
II M.Tech, Communication
systems
IMPLEMENTATION OF WIDE-BAND SPECTRUM
SENSING IN LOW SNR ENVIRONMENT
Project Guide
Dr S.Merlin Gilbert
Raj
Assistant Professor
Outline
 Problem Scenario
 Challenges
 Methodology
 Results
 Conclusions
 References
Problem Scenario
 Why Spectrum Scarcity?
 Increase in wireless devices
 Shortage in spectrum
 Under utilization of spectrum
 Cognitive Radio
 Spectrum Sensing
 Wide-band spectrum sensing
 Low SNR
 Signal fading.
 Practically receiver SNR is very
low.
Challenges
In reality signal is always
not ideal and combined
with unwanted signal that
is considered as noise.
A clean signal will have a
high SNR and a noisy
signal will have a low
SNR.
Goals
 Classify signal and noise
 Achieve high accuracy in
low SNR condition
 Feature extraction
Literature survey
S.NO [REF] AUTHOUR,
YEAR
PAPER TITLE IMPLEMENTAT
ION
ALGORITHM DATASET FREQUENC
Y BAND
PERFORMANCE
METRICS
1 Rhana , Adley -
2019
Implementation
of multi channel
energy detection
SS techniques in
CRnetworks
using LABVIEW
on USRP
NI USRP 2924R
, LABVIEW
ED in
frequency
domain
1000
samples/sec
400MHz -
4.4GHz
Pfa = 0.1
2 Elena, Dobre ,
Alexander -2016
USRP-based
experimental
platform for ED
in CR systems
USRP 2932,
MATLAB
Energy
detection
470MHz-
870MHz
SNR = -9.15dB
Pd = 0.82
Pfa = 0.05
S.NO [REF] AUTHOUR,
YEAR
PAPER TITLE IMPLEMENTA
TION
ALGORITHM DATASET FREQUENCY
BAND
PERFORMANCE
METRICS
3 Mohamoud, Ali
Beydoun, Oussama
Bazzi - 2020
Experimental study
of spectrum sensing
based Energy
detection using
USRP
NI USRP 2901,
MATLAB
Calculation of
energy in time
and frequency
domain
10000
iteration,
1000 samples
915MHz -
925MHz
SNR = -20dB -
0dB
Pfa = 0.1
Pd: 0.690, 0.812,
0.946, 0.950
4 Jayashree, Ishwarya -
2020
Spectrum sensing
based on cascade
approach on
cognitive radio
NI USRP 2920,
MATLAB
Cyclic prefix
autocorrelation
detection
(CPED)
N=1000,
5000
815MHz -
950MHz SNR: -20dB to
-10dB = Pd: 0
SNR: -10dB to
-0dB =Pd:0-0.3
Pfa = 0.2
5 Authu Avinish,
Ramesh Babu - 2019
Enhanced dynamics
noise variance
based energy
sensing for
cognitive radio
using USRP at WiFi
bands
NI USRP 2932 Dynamic noise
variance based
energy sensing
2000/4000/60
00 samples
More than
25MHz
SNR = -20dB
Pd: 80.91
Pfa: 2.69
S.NO [REF] AUTHOUR,
YEAR
PAPER TITLE IMPLEMENTATI
ON
ALGORITHM DATASET FREQUENCY
BAND
PERFORMANCE
METRICS
6 Jacob, Benjamin, Evaluation of real USRP X310 with cognitive 410 test interval 10MHz - 6GHz 45MHz baseband
Anthony - 2020 time Predictive UBX-160 perception-actio to -45MHZ
spectrum sharing n cycle baseband at
for cognitive radio 10MHz interval
Test set dwell
times of 410us,
2.05ms, 4.1ms
7 Chris prema, Covariance and NI USRP, Python Experimental 1000 Monte 93.5MHz SNR: -20dB
Muhammad Eigen value based evaluation of carlo simulation Pfa: 0.1
SS using USRP in covariance and Pd = 0.3
real environment eigen value
based method
8 Daval K. Patel, Artificial neural USRP-N210, Hybrid Training 94MHz SNR:-20dB
Angel network design for MATLAB spectrum samples 100 in Pfa = 0.0440
improved spectrum sensing low SNR Pd = 1
sensing in cognitive technique
radio
S.NO [REF] AUTHOUR,
YEAR
PAPER TITLE IMPLEMENTAT
ION
ALGORITHM DATASET FREQUENCY
BAND
PERFORMANCE
METRICS
9 Anirudh, Ranjan Hardware USRP B210, K-means Testing data/ 70MHz to SNR = -8dB
implementation of MATLAB clustering training data 6GHz Pd = 0.5
K-means clustering approach = 1000x1000 Pfa = 0.1
based spectrum
sensing using USRP
in a cognitive radio
systems
10 Jayesh Patil, PSF-Based Spectrum NI USRP N2922, Pattern-Sequen 400Ms/s 935MHz -
Neeraj Bokde, Occupancy Prediction LABVIEW ce-Based 960MHz
Sudhir Kumar in Cognitive Radio Forecasting
Mishra and Method
Kishore Kulat -
2020
11 Ashwini Kumar Statistical NI USRP, SVM-based SCRSS SVM 810MHz - 815 MHz and 825
Varma and Feature-Based SVM LABVIEW blind sensing Training data 830MHz MHz were used as
Debjani Mitra - Wideband Sensing model = 0.36272 PU signals with 20
2020 Testing data = dB and −10 dB of
0.00196 SNR
VMMA SVM
training data=
0.36390,
testing data=
0.00199
Inference of Literature Survey
0
5000
10000
15000
20000
25000
30000
35000
40000
45000
Statistical…
Machine…
Spatio-…
Hardware…
Generative…
A
Machine…
When
Machine…
IMPLEMENTA…
Practical
Radio…
Spectrum…
Non-…
Spectrum…
Spectrum…
Deep
Learning…
Accuracy
Dataset
SDR Work Bench
 NI USRP-2922
 Transceiver
NI USRP-2922
Methodology
RF DATASET MODELLING
DATA PROCESSING
FEATURE EXTRACTION
(Cross Correlation, Moving
Average)
MACHINE LEARNING
MODELING
SPECTRAL DETECTION
(Pd vs Pfa)
Pd= Pr(Y>𝛌th|H1)
Pfa= Pr(Y>𝛌th| H0)
System Model
 Let the received wideband signal be defines as,
𝑥 𝑚 = 𝑠 𝑚 + 𝑤 𝑚
 𝑋(𝑚) is observed signal, 𝑠(𝑚) is primary wideband
signal and 𝑤(𝑚) is noise
Dataset Modeling
 Machine learning methods learn
from examples.
Dataset Generation
 over-the-air using
 NI USRP-2922 interfaced with
LabVIEW software.
 Using AWGN channel
 Various SNR
 Propagation path
 LoS and NLoS conditions
S.N
o
Parameters Tx(815 MHz) Rx(810MHz-830
MHz)
1. IQ Sampling Rate 1 M 1 M
2. Gain 15 dB 20 dB
3. Active Antenna TX1 RX2
4. PN-Sequence 10 10
5. Frame size 4096 10,000
6. PSK Filter parameter(𝛼) 0.50 0.50
7. PSK Filter length 6 6
8. Samples/ Symbol 8 8
9. Acquisition duration (sec) - 10 m
Experimental
Setup(AWGN Channel)
Specifications
Dataset Modeling
 Machine learning methods learn
from examples.
Wide-band sensed signal at 815MHz
S.N
o
Parameters Tx(815 MHz) Rx(810MHz-830
MHz)
1. IQ Sampling Rate 1 M 1 M
2. Gain 15 dB 20 dB
3. Active Antenna TX1 RX2
4. PN-Sequence 10 10
5. Frame size 4096 10,000
6. PSK Filter parameter(𝛼) 0.50 0.50
7. PSK Filter length 6 6
8. Samples/ Symbol 8 8
9. Acquisition duration (sec) - 10 m
Experimental
Setup(AWGN Channel)
Specifications
Dataset Modeling
S.N
o
Parameters Tx(815 MHz) Rx(810 MHz-
830 MHz)
1. IQ Sampling Rate 1 M 1 M
2. Gain 15 dB 20 dB
3. Active Antenna TX1 RX2
4. PN-Sequence 10 10
5. Frame size 4096 10,000
6. PSK Filter parameter(𝛼) 0.50 0.50
7. PSK Filter length 6 6
8. Samples/ Symbol 8 8
9. Acquisition duration (sec) - 10 m
Experimental Setup
Specifications
Captured data at different receiver location
Features of SVM
 To develop and validate a real-world data efficiently SVM
based blind sensing model uses two statistical features,
 Correlation based feature and
 Moving average based feature
Metrics for various SNR
Detection Probability
 The Pd and Pfa were calculated by
counting the number of TP, TN, FP,
and FN instances.
 𝑃𝑑 =
𝑇𝑃
𝑇𝑃+𝐹𝑁
 𝑃𝑓𝑎 = 1 −
𝑇𝑁
𝑇𝑁+𝐹𝑃
Pd vs SNR using (AWGN Channel)
Pfa vs SNR(AWGN
channel)
Detection Probability
 The Pd and Pfa were calculated by
counting the number of TP, TN, FP,
and FN instances.
 𝑃𝑑 =
𝑇𝑃
𝑇𝑃+𝐹𝑁
 𝑃𝑓𝑎 = 1 −
𝑇𝑁
𝑇𝑁+𝐹𝑃
Pd vs LoS & NLoS condition
Pfa vs LoS & NLoS condition
Measure data location X-axis label
NLoS-1 1
NLoS-2 2
NLoS-3 3
NLoS-4 4
NLoS-5 5
NLoS-6 6
NLoS-7 7
NLoS-8 8
NLoS-9 9
References
[1]Rhana M. Elshishtawy§1 , Adly S. Tag Eldien§2 , Mostafa M. Fouda§3 , and Ahmed H. Eldeib “
Implementation of Multi-Channel Energy Detection Spectrum Sensing Technique in Cognitive Radio
Networks Using LabVIEW on USRP-2942R” 978-1-7281-5146-5/19/$31.00 ©2019 IEEE
[2]Elena Iulia Dobre, Alexandru Martain, Cailin vadeanue “ USRP-based experimental platform for ED in
CR systems “ 971-1-7281-5146-5/19/$31.00 ©2016 IEEE
[3]Dhaval K. Patel1 • Miguel Lo´pez-Benı´tez2,3 • Brijesh Soni1 • A´ ngel F. Garcı´a-Ferna´ndez “ Artificial
neural network design for improved spectrum sensing in cognitive radio” Springer Science+Business
Media, LLC, part of Springer Nature 2020
[4]Jayesh Patil, Neeraj Bokde, Sudhir Kumar Mishra and Kishore Kulat “ PSF-Based Spectrum Occupancy
Prediction in Cognitive Radio” Springer Nature Singapore Pte Ltd. 2020
[5]Mahmoud H. Shehady, Ali Beydoun, and Oussama Bazzi “ Experimental Study of Spectrum Sensing
Based on Energy Detection Using USRP” International Journal of Electronics and Electrical
Engineering Vol. 8, No. 3, September 2020
[6]Avuthu Avinash Reddy, Ramesh Babu Battula, Dinesh Gopalani, Kurra Chaithanya “ DISCERN:
Enhanced Dynamic noISe varianCe based EneRgy sensing for cognitive radio using USRP at Wi-Fi
bands” Int J Commun Syst. 2020;e4550. wileyonlinelibrary.com/journal/dac © 2020 John Wiley & Sons,
Ltd.
[7]Ashwini Kumar Varma and Debjani Mitra “ Statistical Feature-Based SVM Wideband Sensing” IEEE
COMMUNICATIONS LETTERS, VOL. 24, NO. 3, MARCH 2020
[8]Muhammed Althaf C, S Chris Prema “ Covariance and Eigenvalue Based Spectrum Sensing Using
Acknowledgements
Scheme : AICTE
MODROB RF LABORATORY
Thank You
Raw IQ samples for various SNR
SCRSS vi
Feature Vector Z
SNR Z1 Z2 Z3 Z4 Z5 … Z2000
-30dB -0.128 -0.321 -0.404 0.012818 0.013415 … 0.011567
-25dB 0.029375 -0.027233 -0.027016 0.026768 0.026226 … -0.042703
-20dB 0.044988 0.042367 -0.041231 -0.039848 0.040202 … -0.064327
-15dB -0.059949 -0.057947 0.056373 0.053999 0.053237 … 0.070341
-10dB -0.076146 0.07292 -0.071927 -0.069139 0.067452 … -0.083796
0dB -0.093201 -0.089085 0.086845 -0.084683 -0.082549 … 0.097743
5dB -0.109029 0.106073 0.103064 0.099603 0.098101 … -0.111204
10dB 0.126583 0.121899 -0.120048 0.115713 -0.112996 … -0.127064
15dB 0.143136 -0.139441 0.135764 -0.132717 0.129136 … 0.143283
20dB -0.161466 -0.155986 0.153363 -0.148483 -0.146049 … 0.158482
VMMA vi
No. of
samples 1 2 3 4 5 6 7 8 … 10,000
Z 10.92774 0.233207 0.246639 0.144085 0.144016 0.146527 0.143137 0.145822 … 0.132545
SVM_Train
SVM_Test
Project outcome
Conference certificate Badge from NI

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IMPLEMENTATION OF WBSS IN LOW SNR.pptx

  • 1. Project Student Rock Feller Singh Russells P PRK20EC2009 II M.Tech, Communication systems IMPLEMENTATION OF WIDE-BAND SPECTRUM SENSING IN LOW SNR ENVIRONMENT Project Guide Dr S.Merlin Gilbert Raj Assistant Professor
  • 2. Outline  Problem Scenario  Challenges  Methodology  Results  Conclusions  References
  • 3. Problem Scenario  Why Spectrum Scarcity?  Increase in wireless devices  Shortage in spectrum  Under utilization of spectrum  Cognitive Radio  Spectrum Sensing  Wide-band spectrum sensing  Low SNR  Signal fading.  Practically receiver SNR is very low.
  • 4. Challenges In reality signal is always not ideal and combined with unwanted signal that is considered as noise. A clean signal will have a high SNR and a noisy signal will have a low SNR.
  • 5. Goals  Classify signal and noise  Achieve high accuracy in low SNR condition  Feature extraction
  • 6. Literature survey S.NO [REF] AUTHOUR, YEAR PAPER TITLE IMPLEMENTAT ION ALGORITHM DATASET FREQUENC Y BAND PERFORMANCE METRICS 1 Rhana , Adley - 2019 Implementation of multi channel energy detection SS techniques in CRnetworks using LABVIEW on USRP NI USRP 2924R , LABVIEW ED in frequency domain 1000 samples/sec 400MHz - 4.4GHz Pfa = 0.1 2 Elena, Dobre , Alexander -2016 USRP-based experimental platform for ED in CR systems USRP 2932, MATLAB Energy detection 470MHz- 870MHz SNR = -9.15dB Pd = 0.82 Pfa = 0.05
  • 7. S.NO [REF] AUTHOUR, YEAR PAPER TITLE IMPLEMENTA TION ALGORITHM DATASET FREQUENCY BAND PERFORMANCE METRICS 3 Mohamoud, Ali Beydoun, Oussama Bazzi - 2020 Experimental study of spectrum sensing based Energy detection using USRP NI USRP 2901, MATLAB Calculation of energy in time and frequency domain 10000 iteration, 1000 samples 915MHz - 925MHz SNR = -20dB - 0dB Pfa = 0.1 Pd: 0.690, 0.812, 0.946, 0.950 4 Jayashree, Ishwarya - 2020 Spectrum sensing based on cascade approach on cognitive radio NI USRP 2920, MATLAB Cyclic prefix autocorrelation detection (CPED) N=1000, 5000 815MHz - 950MHz SNR: -20dB to -10dB = Pd: 0 SNR: -10dB to -0dB =Pd:0-0.3 Pfa = 0.2 5 Authu Avinish, Ramesh Babu - 2019 Enhanced dynamics noise variance based energy sensing for cognitive radio using USRP at WiFi bands NI USRP 2932 Dynamic noise variance based energy sensing 2000/4000/60 00 samples More than 25MHz SNR = -20dB Pd: 80.91 Pfa: 2.69
  • 8. S.NO [REF] AUTHOUR, YEAR PAPER TITLE IMPLEMENTATI ON ALGORITHM DATASET FREQUENCY BAND PERFORMANCE METRICS 6 Jacob, Benjamin, Evaluation of real USRP X310 with cognitive 410 test interval 10MHz - 6GHz 45MHz baseband Anthony - 2020 time Predictive UBX-160 perception-actio to -45MHZ spectrum sharing n cycle baseband at for cognitive radio 10MHz interval Test set dwell times of 410us, 2.05ms, 4.1ms 7 Chris prema, Covariance and NI USRP, Python Experimental 1000 Monte 93.5MHz SNR: -20dB Muhammad Eigen value based evaluation of carlo simulation Pfa: 0.1 SS using USRP in covariance and Pd = 0.3 real environment eigen value based method 8 Daval K. Patel, Artificial neural USRP-N210, Hybrid Training 94MHz SNR:-20dB Angel network design for MATLAB spectrum samples 100 in Pfa = 0.0440 improved spectrum sensing low SNR Pd = 1 sensing in cognitive technique radio
  • 9. S.NO [REF] AUTHOUR, YEAR PAPER TITLE IMPLEMENTAT ION ALGORITHM DATASET FREQUENCY BAND PERFORMANCE METRICS 9 Anirudh, Ranjan Hardware USRP B210, K-means Testing data/ 70MHz to SNR = -8dB implementation of MATLAB clustering training data 6GHz Pd = 0.5 K-means clustering approach = 1000x1000 Pfa = 0.1 based spectrum sensing using USRP in a cognitive radio systems 10 Jayesh Patil, PSF-Based Spectrum NI USRP N2922, Pattern-Sequen 400Ms/s 935MHz - Neeraj Bokde, Occupancy Prediction LABVIEW ce-Based 960MHz Sudhir Kumar in Cognitive Radio Forecasting Mishra and Method Kishore Kulat - 2020 11 Ashwini Kumar Statistical NI USRP, SVM-based SCRSS SVM 810MHz - 815 MHz and 825 Varma and Feature-Based SVM LABVIEW blind sensing Training data 830MHz MHz were used as Debjani Mitra - Wideband Sensing model = 0.36272 PU signals with 20 2020 Testing data = dB and −10 dB of 0.00196 SNR VMMA SVM training data= 0.36390, testing data= 0.00199
  • 10. Inference of Literature Survey 0 5000 10000 15000 20000 25000 30000 35000 40000 45000 Statistical… Machine… Spatio-… Hardware… Generative… A Machine… When Machine… IMPLEMENTA… Practical Radio… Spectrum… Non-… Spectrum… Spectrum… Deep Learning… Accuracy Dataset
  • 11. SDR Work Bench  NI USRP-2922  Transceiver NI USRP-2922
  • 12. Methodology RF DATASET MODELLING DATA PROCESSING FEATURE EXTRACTION (Cross Correlation, Moving Average) MACHINE LEARNING MODELING SPECTRAL DETECTION (Pd vs Pfa) Pd= Pr(Y>𝛌th|H1) Pfa= Pr(Y>𝛌th| H0)
  • 13. System Model  Let the received wideband signal be defines as, 𝑥 𝑚 = 𝑠 𝑚 + 𝑤 𝑚  𝑋(𝑚) is observed signal, 𝑠(𝑚) is primary wideband signal and 𝑤(𝑚) is noise
  • 14. Dataset Modeling  Machine learning methods learn from examples. Dataset Generation  over-the-air using  NI USRP-2922 interfaced with LabVIEW software.  Using AWGN channel  Various SNR  Propagation path  LoS and NLoS conditions S.N o Parameters Tx(815 MHz) Rx(810MHz-830 MHz) 1. IQ Sampling Rate 1 M 1 M 2. Gain 15 dB 20 dB 3. Active Antenna TX1 RX2 4. PN-Sequence 10 10 5. Frame size 4096 10,000 6. PSK Filter parameter(𝛼) 0.50 0.50 7. PSK Filter length 6 6 8. Samples/ Symbol 8 8 9. Acquisition duration (sec) - 10 m Experimental Setup(AWGN Channel) Specifications
  • 15. Dataset Modeling  Machine learning methods learn from examples. Wide-band sensed signal at 815MHz S.N o Parameters Tx(815 MHz) Rx(810MHz-830 MHz) 1. IQ Sampling Rate 1 M 1 M 2. Gain 15 dB 20 dB 3. Active Antenna TX1 RX2 4. PN-Sequence 10 10 5. Frame size 4096 10,000 6. PSK Filter parameter(𝛼) 0.50 0.50 7. PSK Filter length 6 6 8. Samples/ Symbol 8 8 9. Acquisition duration (sec) - 10 m Experimental Setup(AWGN Channel) Specifications
  • 16. Dataset Modeling S.N o Parameters Tx(815 MHz) Rx(810 MHz- 830 MHz) 1. IQ Sampling Rate 1 M 1 M 2. Gain 15 dB 20 dB 3. Active Antenna TX1 RX2 4. PN-Sequence 10 10 5. Frame size 4096 10,000 6. PSK Filter parameter(𝛼) 0.50 0.50 7. PSK Filter length 6 6 8. Samples/ Symbol 8 8 9. Acquisition duration (sec) - 10 m Experimental Setup Specifications Captured data at different receiver location
  • 17. Features of SVM  To develop and validate a real-world data efficiently SVM based blind sensing model uses two statistical features,  Correlation based feature and  Moving average based feature
  • 19. Detection Probability  The Pd and Pfa were calculated by counting the number of TP, TN, FP, and FN instances.  𝑃𝑑 = 𝑇𝑃 𝑇𝑃+𝐹𝑁  𝑃𝑓𝑎 = 1 − 𝑇𝑁 𝑇𝑁+𝐹𝑃 Pd vs SNR using (AWGN Channel) Pfa vs SNR(AWGN channel)
  • 20. Detection Probability  The Pd and Pfa were calculated by counting the number of TP, TN, FP, and FN instances.  𝑃𝑑 = 𝑇𝑃 𝑇𝑃+𝐹𝑁  𝑃𝑓𝑎 = 1 − 𝑇𝑁 𝑇𝑁+𝐹𝑃 Pd vs LoS & NLoS condition Pfa vs LoS & NLoS condition Measure data location X-axis label NLoS-1 1 NLoS-2 2 NLoS-3 3 NLoS-4 4 NLoS-5 5 NLoS-6 6 NLoS-7 7 NLoS-8 8 NLoS-9 9
  • 21. References [1]Rhana M. Elshishtawy§1 , Adly S. Tag Eldien§2 , Mostafa M. Fouda§3 , and Ahmed H. Eldeib “ Implementation of Multi-Channel Energy Detection Spectrum Sensing Technique in Cognitive Radio Networks Using LabVIEW on USRP-2942R” 978-1-7281-5146-5/19/$31.00 ©2019 IEEE [2]Elena Iulia Dobre, Alexandru Martain, Cailin vadeanue “ USRP-based experimental platform for ED in CR systems “ 971-1-7281-5146-5/19/$31.00 ©2016 IEEE [3]Dhaval K. Patel1 • Miguel Lo´pez-Benı´tez2,3 • Brijesh Soni1 • A´ ngel F. Garcı´a-Ferna´ndez “ Artificial neural network design for improved spectrum sensing in cognitive radio” Springer Science+Business Media, LLC, part of Springer Nature 2020 [4]Jayesh Patil, Neeraj Bokde, Sudhir Kumar Mishra and Kishore Kulat “ PSF-Based Spectrum Occupancy Prediction in Cognitive Radio” Springer Nature Singapore Pte Ltd. 2020 [5]Mahmoud H. Shehady, Ali Beydoun, and Oussama Bazzi “ Experimental Study of Spectrum Sensing Based on Energy Detection Using USRP” International Journal of Electronics and Electrical Engineering Vol. 8, No. 3, September 2020 [6]Avuthu Avinash Reddy, Ramesh Babu Battula, Dinesh Gopalani, Kurra Chaithanya “ DISCERN: Enhanced Dynamic noISe varianCe based EneRgy sensing for cognitive radio using USRP at Wi-Fi bands” Int J Commun Syst. 2020;e4550. wileyonlinelibrary.com/journal/dac © 2020 John Wiley & Sons, Ltd. [7]Ashwini Kumar Varma and Debjani Mitra “ Statistical Feature-Based SVM Wideband Sensing” IEEE COMMUNICATIONS LETTERS, VOL. 24, NO. 3, MARCH 2020 [8]Muhammed Althaf C, S Chris Prema “ Covariance and Eigenvalue Based Spectrum Sensing Using
  • 24. Raw IQ samples for various SNR
  • 26. Feature Vector Z SNR Z1 Z2 Z3 Z4 Z5 … Z2000 -30dB -0.128 -0.321 -0.404 0.012818 0.013415 … 0.011567 -25dB 0.029375 -0.027233 -0.027016 0.026768 0.026226 … -0.042703 -20dB 0.044988 0.042367 -0.041231 -0.039848 0.040202 … -0.064327 -15dB -0.059949 -0.057947 0.056373 0.053999 0.053237 … 0.070341 -10dB -0.076146 0.07292 -0.071927 -0.069139 0.067452 … -0.083796 0dB -0.093201 -0.089085 0.086845 -0.084683 -0.082549 … 0.097743 5dB -0.109029 0.106073 0.103064 0.099603 0.098101 … -0.111204 10dB 0.126583 0.121899 -0.120048 0.115713 -0.112996 … -0.127064 15dB 0.143136 -0.139441 0.135764 -0.132717 0.129136 … 0.143283 20dB -0.161466 -0.155986 0.153363 -0.148483 -0.146049 … 0.158482
  • 27. VMMA vi No. of samples 1 2 3 4 5 6 7 8 … 10,000 Z 10.92774 0.233207 0.246639 0.144085 0.144016 0.146527 0.143137 0.145822 … 0.132545