Download 22-06-0187-03-0000

doc.: IEEE 802.22-06/0187-02-0000
Updates on the covariance based and
eigenvalue based sensing algorithms
IEEE P802.22 Wireless RANs
Date: 2007-03-21
Authors:
Name
Company
Address
Phone
email
Yonghong Zeng
Institute for
Infocomm Research
Institute for
Infocomm Research
21 Heng Mui Keng
Terrace, Singapore 119613
21 Heng Mui Keng
Terrace, Singapore 119613
65-68748211
[email protected]
65-68748225
[email protected]
Ying-Chang Liang
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>
Submission
Slide 1
Yonghong Zeng, Insitute for Infocomm Research
doc.: IEEE 802.22-06/0187-02-0000
Abstract
• Sensing algorithms using properties of the
sample covariance matrix are presented
• Two statistics are extracted from the received
signals and compared to make a decision
• The methods can be used without knowledge of
the signal, the channel and noise power
• Simulation results based on the captured DTV
signals and wireless microphone signals are
presented
Submission
Slide 2
Yonghong Zeng, Insitute for Infocomm Research
doc.: IEEE 802.22-06/0187-02-0000
Principle of the algorithms
• The statistics of signal is different from
that of noise
• The difference is characterized by the
eigenvalue distributions or non-diagonal
elements of the covariance matrix
Submission
Slide 3
Yonghong Zeng, Insitute for Infocomm Research
doc.: IEEE 802.22-06/0187-02-0000
Flow-chart of the maximum-minimum eigenvalue
(MME) detection
Sample
and filter
the signals
Choose a
smoothing
factor and the
threshold r
Compute the maximum
eigenvalue and
minimum eigenvalue
of the covariance
matrix
Submission
Compute the
sample
covariance
matrix
Transform the
sample
covariance
matrix
Decision: if the maximum
eign >r*minimum eign,
signal exists;
Otherwise, signal not
exists.
Slide 4
Yonghong Zeng, Insitute for Infocomm Research
doc.: IEEE 802.22-06/0187-02-0000
Flow-chart of the energy with minimum eigenvalue
(EME) detection
Sample
and filter
the signals
Choose a
smoothing
factor and the
threshold r
Compute the average
energy and minimum
eigenvalue of the
covariance matrix
Submission
Compute the
sample
covariance
matrix
Transform the
sample
covariance
matrix
Decision: if the energy
>r*minimum eign,
signal exists;
Otherwise, signal not
exists.
Slide 5
Yonghong Zeng, Insitute for Infocomm Research
doc.: IEEE 802.22-06/0187-02-0000
Flow-chart of the covariance absolute value (CAV)
detection
Sample
and filter
the signals
Choose a
smoothing
factor and the
threshold r
Compute the absolute
sum of the matrix, T1,
and the absolute sum of
diagonal elements, T2
Submission
Compute the
sample
covariance
matrix
Transform the
sample
covariance
matrix
Decision: if T1 >r*T2,
signal exists;
Otherwise, signal not
exists.
Slide 6
Yonghong Zeng, Insitute for Infocomm Research
doc.: IEEE 802.22-06/0187-02-0000
Flow-chart of the Covariance Frobenius norm (CFN)
detection
Sample
and filter
the signals
Choose a
smoothing
factor and the
threshold r
Compute the sum of
powers of the matrix
elements, T3, and the
sum of powers of
diagonal elements, T4
Submission
Compute the
sample
covariance
matrix
Transform the
sample
covariance
matrix
Decision: if T3 >r*T4,
signal exists;
Otherwise, signal not
exists.
Slide 7
Yonghong Zeng, Insitute for Infocomm Research
doc.: IEEE 802.22-06/0187-02-0000
Threshold setting
The threshold is set based on the Pfa, number of samples and L by
using the random matrix theory. The threshold is not related to noise
power and signal property. The threshold is fixed for all signals. For
examples, the thresholds for the MME and CAV are set respectively
as follows (where P0 is the required Pfa).

  ( N s ) 
( N s  L )2  ( N s  L )2 / 3 1



1
F1 (1  P0 ) 
1/ 6
2 

(
N
L
)
N
( Ns  L ) 
s
s


1  ( L  1)
 
Submission

2
N s
  ( N s )  1
2
 Q (1  P0 )
1  
Ns
 Ns 
Slide 8
Yonghong Zeng, Insitute for Infocomm Research
doc.: IEEE 802.22-06/0187-02-0000
Advantages of the algorithms
• No signal information is needed (compared to coherent
detection)
• Robust to multipath propagation (compared to
coherent detection)
• No synchronization is needed (compared to coherent
detection)
• No noise uncertainty problem (compared to energy
detection)
• Good performance (can be better than the ideal energy
detection without noise uncertainty)
Submission
Slide 9
Yonghong Zeng, Insitute for Infocomm Research
doc.: IEEE 802.22-06/0187-02-0000
Advantages of the algorithms
• Same detection method for all signals (DTV,
wireless microphone, analog TV, …)
• Same threshold for all signals (the thresholds
is independent on the signal and noise power)
• Can use continuous or discontinuous time
slots for sensing
Submission
Slide 10
Yonghong Zeng, Insitute for Infocomm Research
doc.: IEEE 802.22-06/0187-02-0000
Simulations for wireless microphone signals
t

w(t )  cos 2  ( f c  f  wm ( )) d 
0


FM modulated wireless microphone signal (200 KHz bandwidth)
• The source signal is generated as evenly distributed real number in (-1,1).
We assume that the signal has been down converted to the IF with central
frequency 5.381119 MHz (the same as the captured DTV signal). The
sampling rate is 21.524476 MHz (the same as the captured DTV signal). The
signal and white noise are passed through the same filter. The passband
filter with bandwidth 6 MHz is shown at the next page (provided by Steve
Shellhammer). The smoothing factor is chosen as L=10. The threshold is set
based on the Pfa, number of samples and L (using random matrix theory)
and fixed for all signals. The threshold is not related to noise power and
signal. SNR is measured in 6MHz bandwidth. The central frequency location
of the microphone signal is unknown.
• The MME, CAV and CFN have similar performances and EME is worse. In
the following, only results for CAV are given.
Submission
Slide 11
Yonghong Zeng, Insitute for Infocomm Research
doc.: IEEE 802.22-06/0187-02-0000
The passband filter
(provided by Steve Shellhammer)
Submission
Slide 12
Yonghong Zeng, Insitute for Infocomm Research
doc.: IEEE 802.22-06/0187-02-0000
Probability of misdetection at 4ms sensing
time (wireless microphone signal)
Submission
Slide 13
Yonghong Zeng, Insitute for Infocomm Research
doc.: IEEE 802.22-06/0187-02-0000
Probability of misdetection at 8ms sensing
time (wireless microphone signal)
Submission
Slide 14
Yonghong Zeng, Insitute for Infocomm Research
doc.: IEEE 802.22-06/0187-02-0000
Simulations for captured DTV signals
• The captured DTV signals in [5] are used in the simulations. The
signal and white noise are passed through the same filter. The
filter is shown before (provided by Steve Shellhammer). The
smoothing factor is chosen as L=10. The threshold is set based
on the Pfa, sensing time and L (using random matrix theory) and
fixed for all signals. The threshold is not related to noise power
and signal.
• The MME, CAV and CFN have similar performances and EME is
worse, in the following, only results for CAV are given.
• The time slots can be continuous or discontinuous.
• 12 captured DTV files are tested: WAS-047/48/01, WAS-311/48/01,
WAS-311/35/01, WAS-311/36/01, WAS-086/48/01, WAS-006/34/01,
WAS-003/27/01, WAS-051/35/01, WAS-049/39/01, WAS-032/48/01,
WAS-068/36/01, WAS-049/34/01.
Submission
Slide 15
Yonghong Zeng, Insitute for Infocomm Research
doc.: IEEE 802.22-06/0187-02-0000
Probability of misdetection at 4ms
sensing time
(average over 12 DTV signals)
Submission
Slide 16
Yonghong Zeng, Insitute for Infocomm Research
doc.: IEEE 802.22-06/0187-02-0000
Probability of misdetection at 8ms
sensing time
(average over 12 DTV signals)
Submission
Slide 17
Yonghong Zeng, Insitute for Infocomm Research
doc.: IEEE 802.22-06/0187-02-0000
Probability of misdetection at 16ms
sensing time
(average over 12 DTV signals)
Submission
Slide 18
Yonghong Zeng, Insitute for Infocomm Research
doc.: IEEE 802.22-06/0187-02-0000
Probability of misdetections for 12 DTV
signals at sensing time 16 ms
Submission
Slide 19
Yonghong Zeng, Insitute for Infocomm Research
doc.: IEEE 802.22-06/0187-02-0000
Average probability of misdetection at
sensing time 16 ms
If we fix the Pmd=0.1, Pfa=0.1 and find the
SNRs for the DTV signals to meet this Pmd
and then average on the SNRs, we get the
average SNR=-16dB.
If we first average the Pmd’s of all the DTV
signals at various SNR’s and then find the
SNR to meet Pmd=0.1 and Pfa=0.1, we get
the average SNR=-15dB.
Submission
Slide 20
Yonghong Zeng, Insitute for Infocomm Research
doc.: IEEE 802.22-06/0187-02-0000
Probability of misdetection at 32ms
sensing time
(average over 12 DTV signals)
Submission
Slide 21
Yonghong Zeng, Insitute for Infocomm Research
doc.: IEEE 802.22-06/0187-02-0000
The computational complexity
• Filtering the received signals: (K+1)N multiplications
and additions, where K is the order of filter and N is
the number of samples (if K is large, FFT can be
used to reduce the complexity);
• Computing the covariance matrix of the received
signal: LN multiplications and additions, where L is
the smoothing factor;
• Transforming the covariance matrix: needs 2L^3
multiplications and additions;
• Others: at most L^2 multiplications and additions;
• Total: (K+L+1)N+2L^3+L^2 multiplications and
additions.
Submission
Slide 22
Yonghong Zeng, Insitute for Infocomm Research
doc.: IEEE 802.22-06/0187-02-0000
Conclusions
• The covariance based detections do not need any
information on signal, the channel, the noise level
and SNR
• Same detection method for all signals (DTV,
wireless microphone, …)
• The threshold is set based on sensing time and
Pfa. Same threshold for all signals (the
thresholds is independent on the signal and
noise power)
• Can use continuous or discontinuous time slots
for sensing (same performance), which allows
flexible sensing time slots allocation
Submission
Slide 23
Yonghong Zeng, Insitute for Infocomm Research
doc.: IEEE 802.22-06/0187-02-0000
Conclusions
• Can reach Pfa=0.1 and Pmd=0.1 at SNR=-20dB
and sensing time less than 100ms
• Filter with better conditional number can be
used to improve the performance or reduce
sensing time
Submission
Slide 24
Yonghong Zeng, Insitute for Infocomm Research
doc.: IEEE 802.22-06/0187-02-0000
References
1.
A. Sahai and D. Cabric, “Spectrum sensing: fundamental limits and practical challenges,” in
Dyspan 2005 (available at: www.eecs.berkeley.edu/∼sahai), 2005.
2.
Steve
Shellhammer
et
al.,
“Spectrum
sensing
simulation
model”,
http://grouper.ieee.org/groups/802/22/Meeting_documents/2006_July/22-06-0028-07-0000Spectrum-Sensing-Simulation-Model.doc, July 2006.
3.
Suhas Mathur et al., “Initial signal processing of captured DTV signals for evaluation of
detection
algorithms”,
http://grouper.ieee.org/groups/802/22/Meeting_documents/2006_Oct/22-06-0158-06-0000Intial-Signal-Processing-for-DTV-Signal-Files.doc, Feb. 2007.
4.
I.M. Johnstone, “On the distribution of the largest eigenvalue in principle components
analysis,” The Annals of Statistics, vol. 29, no. 2, pp. 295—327, 2001.
5.
Victor
Tawil,
“51
captured
DTV
signal”,
http://grouper.ieee.org/groups/802/22/Meeting_documents/2006_May/Informal_Documents,
May 2006.
6.
Yonghong Zeng and Ying-Chang Liang, “Eigenvalue based sensing algorithms”,
http://grouper.ieee.org/groups/802/22/Meeting_documents/2006_July/22-06-0118-000000_I2R-sensing.doc
7.
Yonghong Zeng and Ying-Chang Liang, “Performance of eigenvalue based sensing
algorithms
for
detection
of
DTV
and
wireless
microphone
signals”,
http://grouper.ieee.org/groups/802/22/Meeting_documents/2006_Sept/22-06-0186-000000_I2R-sensing-2.doc
Submission
Slide 25
Yonghong Zeng, Insitute for Infocomm Research
doc.: IEEE 802.22-06/0187-02-0000
References
8.
Yonghong Zeng and Ying-Chang Liang, “Performance of eigenvalue based sensing
algorithms
for
detection
of
DTV
and
wireless
microphone
signals”,
http://grouper.ieee.org/groups/802/22/Meeting_documents/2006_Sept/22-06-0187-000000_I2R-sensing-2.ppt
9.
Yonghong Zeng and Ying-Chang Liang, “Covariance based sensing algorithms for
detection
of
DTV
and
wireless
microphone
signals”,
http://grouper.ieee.org/groups/802/22/Meeting_documents/2006_Nov/22-06-0187-010000_I2R-sensing-2.ppt
Submission
Slide 26
Yonghong Zeng, Insitute for Infocomm Research