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


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


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]


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


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


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:

7

Estimated energy received from mth transmitter

Estimated noise energy

1

[ ] [ ] [ ]M

m m

m

Y t a t t

m

2


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

8

=

+

+

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


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


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


Proposed Algorithm: Overview

11

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?


Proposed Algorithm: Energy Detection

12

Initialization


Increment

No


Yes

ˆ 1M

Energy Detection

E

'E

'EM

ˆ ˆ,A M

ˆ1 2ˆ ˆ ˆ, ,..., 0,..., 1

MB B B F


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.


Proposed Algorithm: NNMF

13

Initialization


Increment

No


Yes

ˆ 1M

Energy Detection

E

'E

'EM

ˆ ˆ,A M

ˆ1 2ˆ ˆ ˆ, ,..., 0,..., 1

MB B B F


Signal energy shared by all factors

ˆ 4M

Significant signal energy

Noise Band

Reconstructed Factors for


Proposed Algorithm: Detecting Bands

14

Initialization


Increment

No


Yes

ˆ 1M

Energy Detection

E

'E

'EM

ˆ ˆ,A M

ˆ1 2ˆ ˆ ˆ, ,..., 0,..., 1

MB B B F


Signal energy shared by all factors

“Leaked” signal energy

Noise Band

Challenge:


Proposed Algorithm: Detecting Bands

15

Initialization


Increment

No


Yes

ˆ 1M

Energy Detection

E

'E

'EM

ˆ ˆ,A M

ˆ1 2ˆ ˆ ˆ, ,..., 0,..., 1

MB B B F


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


Novel Performance Metrics: Why?

Conventional wideband spectrum sensing metrics are per-bin

– False alarm probability for each bin

– Detection probability for each bin

16

Our Output

Ground Truth

Proposed Metrics:

Number of detected bands

Number of extra bands detected

Relative Errors in Center Frequency and Bandwidth


Novel Performance Metrics: Why?

Conventional wideband spectrum sensing metrics are per-bin

– False alarm probability for each bin

– Detection probability for each bin

17

Our Output

Ground Truth

Challenge

Match each detected band to the corresponding true band, if any


Novel Performance Metrics: How?

18

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


Novel Performance Metrics: How?

19

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


Simulations: Performance vs. Activity

Receiver:

Bandwidth 6MHz

512 length FFT, average of 100 windowed overlapping segments

25 measurements, i.e., ~1ms long

20

Transmitters:

Bandwidth 600kHz each

4-PAM, pulse shaped signals

Shadow fading channels with 6dB variance

Number of Detected Signals Number of Extra Signals


Simulation: Performance vs. Spectral Overlap

21

Number of Detected Signals

Number of Extra Signals

Relative Error in BandwidthRelative Error in Center Frequency


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

22

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


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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