Using the Time Dimension to Sense Signals with Partial...
Transcript of Using the Time Dimension to Sense Signals with Partial...
Using the Time Dimension to Sense
Signals with Partial Spectral Overlap
Mihir Laghate and Danijela Cabric5th December 2016
D. Markovic / Slide 2
Outline
Goal, Motivation, and Existing Work
System Model
– Assumptions
– Time-Frequency Map
Proposed Algorithm: NNMF-based Algorithm
Novel Performance Metrics: Why and How
Simulation Results
Conclusions and Future Work
2
D. Markovic / Slide 3
Goal
Distinguishing Signals with Spectral Overlap
That is,
Counting number of signals received
Detecting sets of discrete Fourier transform bins occupied by each signal
3
D. Markovic / Slide 4
Potential Applications
– IEEE 802.11n in 5GHz bands
– LTE-Advanced
4
Image Source: Wikipedia “List of WLAN channels”
LTE Carrier Aggregation [2][2] H. J. Wu et al., “A wideband digital pre-distortion platform with 100 MHz
instantaneous bandwidth for LTE-advanced applications,” in 2012 Workshop on
Integrated Nonlinear Microwave and Millimetre-Wave Circuits, 2012, pp. 1–3.
[1] M. Laghate and D. Cabric, “Using Multiple Power Spectrum Measurements to
Sense Signals with Partial Spectral Overlap,” submitted to IEEE DySPAN 2017.
– IEEE 802.11b/g channels in 2.4GHz
– Channel bonding in IEEE 802.11n
Lack of Guard Bands
Spectral overlap by design Measurements @ UCLA [1]
D. Markovic / Slide 5
Motivation
5
[3] Z. Quan, S. Cui, A. H. Sayed, and H. V. Poor, “Optimal
Multiband Joint Detection for Spectrum Sensing in Cognitive
Radio Networks,” IEEE TSP, 2009.
0 7.5 15 22.5
0
5
10
15
Mag
nit
ud
e (d
B)
Frequency (MHz)
Signal 1:DSSS
Signal 2:4-QAM
Signal 3:OFDM
Improved sensing accuracy
Multi-signal Classification
Multichannel TrafficEstimation and Prediction
Ch. 1 Ch. 2 Ch. 3 Ch. 4 Ch. 5
Occupied
Unoccupied
Tim
e
Frequency
D. Markovic / Slide 6
Existing Work
6
Based on BlindSingle
AntennaSpectral Overlap
Detect Bands
Blind to Channel
Transmission protocols [4-5]
Cyclic frequency [7]
Channel model & location [6]
Angle of Arrival [8]
Random Matrix Theory [9]
Multiple CRs [10-11]
Power Spectrum Threshold [12]
Multiple Power SpectrumMeasurements
Proposed method
D. Markovic / Slide 7
System Model
Incumbent Users
M transmitters with center frequency Fm and bandwidth Wm
– Power spectrum received from mth transmitter:
– Activity 𝑎𝑚 𝑡 = 1 if transmitting at time t, 0 otherwise
Wideband sensor
Baseband bandwidth W Hz, known noise power
Welch power spectrum estimator using FFT of length F
can store multiple power spectrum measurements
Received power spectrum:
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Estimated energy received from mth transmitter
Estimated noise energy
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[ ] [ ] [ ]M
m m
m
Y t a t t
m
2
D. Markovic / Slide 8
Time-Frequency Map
Time-Freq. map E of received energy: E = [Y[1] Y[2] … Y[T]]T
Define matrices: Atm= am[t], mf = m( f ), and Δ𝑡𝑓 = 𝜈 𝑡 𝑓
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=
+
+
E A
E
(1) (1)A
Output computed by Non-Negative Matrix Factorization (NNMF)
Input:Power Spectrum measurements
Output: Time-Freq of Each Tx
(2) (2)A
(3) (3)A
Example: M = 3, F = 512, T = 30
D. Markovic / Slide 9
Non-Negative Matrix Factorization (NNMF)
Let 𝑀 = Estimated number of received signals
NNMF finds , to minimize
Challenges:
Estimating 𝑀 is hard when
Non-convex cost function
convergence to global minima not guaranteed
Cost function is not probabilistic
Not robust to noise
Non-unique solution and is not binary
, i.e., thresholding will not detect all occupied DFT bins9
ˆˆ T MA
ˆˆ M F
2
ˆ ˆFE A
T F
A
D. Markovic / Slide 10
Non-Negative Matrix Factorization (NNMF)
Let 𝑀 = Estimated number of received signals
NNMF finds , to minimize
Challenges:
Estimating 𝑀 is hard when
Non-convex cost function
convergence to global minima not guaranteed
Cost function is not probabilistic
Not robust to noise
Non-unique solution and is not binary
, i.e., thresholding will not detect all occupied DFT bins10
ˆˆ T MA
ˆˆ M F
2
ˆ ˆFE A
T F
A
Iteratively increase model size 𝑀
Re-initialize multiple times
Use energy detection to obtain binary time-freq. map
Reconstruct each factor before detection
Our Proposed Solution
D. Markovic / Slide 11
Proposed Algorithm: Overview
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Initialization
NNMF of with signals
Increment
No
Detect Occupied Bands
Yes
ˆ 1M
Energy Detection
E
'E
'EM
ˆ ˆ,A M
ˆ1 2ˆ ˆ ˆ, ,..., 0,..., 1
MB B B F
Noise band detected?
D. Markovic / Slide 12
Proposed Algorithm: Energy Detection
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Initialization
NNMF of with signals
Increment
No
Detect Occupied Bands
Yes
ˆ 1M
Energy Detection
E
'E
'EM
ˆ ˆ,A M
ˆ1 2ˆ ˆ ˆ, ,..., 0,..., 1
MB B B F
Noise band detected?
Threshold [3]:
2 1
fa1 2 / NQ P
E 'E
[3] T.-H. Yu, O. Sekkat, S. Rodriguez-Parera, D. Markovic, and
D. Cabric, “A Wideband Spectrum-Sensing Processor With
Adaptive Detection Threshold and Sensing Time,” IEEE TCAS I,
vol. 58, no. 11, pp. 2765–2775, Nov. 2011.
D. Markovic / Slide 13
Proposed Algorithm: NNMF
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Initialization
NNMF of with signals
Increment
No
Detect Occupied Bands
Yes
ˆ 1M
Energy Detection
E
'E
'EM
ˆ ˆ,A M
ˆ1 2ˆ ˆ ˆ, ,..., 0,..., 1
MB B B F
Noise band detected?
Signal energy shared by all factors
ˆ 4M
Significant signal energy
Noise Band
Reconstructed Factors for
D. Markovic / Slide 14
Proposed Algorithm: Detecting Bands
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Initialization
NNMF of with signals
Increment
No
Detect Occupied Bands
Yes
ˆ 1M
Energy Detection
E
'E
'EM
ˆ ˆ,A M
ˆ1 2ˆ ˆ ˆ, ,..., 0,..., 1
MB B B F
Noise band detected?
Signal energy shared by all factors
“Leaked” signal energy
Noise Band
Challenge:
D. Markovic / Slide 15
Proposed Algorithm: Detecting Bands
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Initialization
NNMF of with signals
Increment
No
Detect Occupied Bands
Yes
ˆ 1M
Energy Detection
E
'E
'EM
ˆ ˆ,A M
ˆ1 2ˆ ˆ ˆ, ,..., 0,..., 1
MB B B F
Noise band detected?
Challenge: and unknown noise
Solution:Reconstruct and threshold peaks:
Active bin ignored if adjacent bins are not active
– Reduces false alarms
Ignore “duplicate” bands
– Similarity quantified by symmetric difference
1, ,
ˆmax 0ˆ .5m m tft T
A
D. Markovic / Slide 16
Novel Performance Metrics: Why?
Conventional wideband spectrum sensing metrics are per-bin
– False alarm probability for each bin
– Detection probability for each bin
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Our Output
Ground Truth
Proposed Metrics:
Number of detected bands
Number of extra bands detected
Relative Errors in Center Frequency and Bandwidth
D. Markovic / Slide 17
Novel Performance Metrics: Why?
Conventional wideband spectrum sensing metrics are per-bin
– False alarm probability for each bin
– Detection probability for each bin
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Our Output
Ground Truth
Challenge
Match each detected band to the corresponding true band, if any
D. Markovic / Slide 18
Novel Performance Metrics: How?
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Our Output
Ground Truth
Edge Weights:
Fully Connected Bipartite Graph
2 211
ˆ ˆ, mm m mF BB BB
9 364 6 10
Symmetric Difference
1B 2B
2B3B
1B
D. Markovic / Slide 19
Novel Performance Metrics: How?
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Our Output
Ground Truth
Fully Connected Bipartite Graph
Solution: Find the Maximum Weight Matching
Edge Weights: 2 211
ˆ ˆ, mm m mF BB BB
Symmetric Difference
1B 2B
2B3B
1B
9 364 6 10
D. Markovic / Slide 20
Simulations: Performance vs. Activity
Receiver:
Bandwidth 6MHz
512 length FFT, average of 100 windowed overlapping segments
25 measurements, i.e., ~1ms long
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Transmitters:
Bandwidth 600kHz each
4-PAM, pulse shaped signals
Shadow fading channels with 6dB variance
Number of Detected Signals Number of Extra Signals
D. Markovic / Slide 21
Simulation: Performance vs. Spectral Overlap
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Number of Detected Signals
Number of Extra Signals
Relative Error in BandwidthRelative Error in Center Frequency
D. Markovic / Slide 22
Conclusions and Future Work
Multiple power spectrum measurements can distinguish spectrally overlapped signals
Conventional signal detection and estimation theory may not be sufficient
Future Work:
Reduce number of extra signals detected
– By improving non-negative matrix factorization methods?
Estimate time of activity, i.e., , for use in traffic estimation
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A
Thank you!
Questions?
This material is based upon work supported by the National Science Foundation under Grant No. 1527026: Dynamic Spectrum Access by Learning Primary Network Topology
D. Markovic / Slide 24
Selected References
[1] M. Laghate and D. Cabric, “Using Multiple Power Spectrum Measurements to Sense Signals with Partial Spectral Overlap,”
submitted to IEEE DySPAN 2017.
[2] H. J. Wu et al., “A wideband digital pre-distortion platform with 100 MHz instantaneous bandwidth for LTE-advanced
applications,” in 2012 Workshop on Integrated Nonlinear Microwave and Millimetre-Wave Circuits, 2012, pp. 1–3.
[3] Z. Quan, S. Cui, A. H. Sayed, and H. V. Poor, “Optimal Multiband Joint Detection for Spectrum Sensing in Cognitive Radio
Networks,” IEEE Transactions on Signal Processing, 2009.
[4] I. Bisio, M. Cerruti, F. Lavagetto, M. Marchese, M. Pastorino, A. Randazzo, and A. Sciarrone, “A Trainingless WiFi Fingerprint
Positioning Approach Over Mobile Devices,” IEEE Antennas Wirel. Propag. Lett., vol. 13, pp. 832–835, 2014.
[5] M. Ibrahim and M. Youssef, “CellSense: An Accurate Energy-Efficient GSM Positioning System,” Veh. Technol. IEEE Trans.
On, vol. 61, no. 1, pp. 286–296, Jan. 2012.
[6] H. Yilmaz, T. Tugcu, F. Alago¨z, and S. Bayhan, “Radio environment map as enabler for practical cognitive radio networks,”
IEEE Commun. Mag., vol. 51, no. 12, pp. 162–169, Dec. 2013.
[7] S. Chaudhari and D. Cabric, “Cyclic weighted centroid localization for spectrally overlapped sources in cognitive radio
networks,” in 2014 IEEE Global Communications Conference (GLOBECOM), Dec. 2014, pp. 935–940.
[8] J. Wang and D. Cabric, “A cooperative DoA-based algorithm for localization of multiple primary-users in cognitive radio
networks,” in IEEE GLOBECOM, Dec. 2012, pp. 1266–1270.
[9] L. Wei, P. Dharmawansa, and O. Tirkkonen, “Multiple Primary User Spectrum Sensing in the Low SNR Regime,” IEEE
Transactions on Communications, vol. 61, no. 5, pp. 1720–1731, May 2013.
[10] M. Laghate and D. Cabric, “Identifying the presence and footprints of multiple incumbent transmitters,” in 2015 49th Asilomar
Conference on Signals, Systems and Computers, 2015, pp. 146–150.
[11] M. Laghate and D. Cabric, “Cooperatively Learning Footprints of Multiple Incumbent Transmitters by Using Cognitive Radio
Networks,” submitted to IEEE Transactions on Cognitive Communications and Networking, Sept. 2015.
[12] T.-H. Yu, O. Sekkat, S. Rodriguez-Parera, D. Markovic, and D. Cabric, “A Wideband Spectrum-Sensing Processor With
Adaptive Detection Threshold and Sensing Time,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 58, no. 11,
pp. 2765–2775, Nov. 2011.
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