Using the Time Dimension to Sense Signals with Partial Spectral Overlap. Mihir Laghate and Danijela Cabric 5 th December 2016

Transcription

1 Using the Time Dimension to Sense Signals with Partial Spectral Overlap Mihir Laghate and Danijela Cabric 5 th December 2016

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 D. Markovic / Slide 2 2

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 D. Markovic / Slide 3 3

4 Potential Applications Spectral overlap by design UCLA [1] IEEE b/g channels in 2.4GHz Image Source: Wikipedia List of WLAN channels Channel bonding in IEEE n [1] M. Laghate and D. Cabric, Using Multiple Power Spectrum Measurements to Sense Signals with Partial Spectral Overlap, submitted to IEEE DySPAN Lack of Guard Bands IEEE n in 5GHz bands LTE-Advanced [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 LTE Carrier Aggregation [2] D. Markovic / Slide 4 4

5 Motivation Time Magnitude (db) Improved sensing accuracy [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, Multi-signal Classification Signal 1: DSSS Signal 2: 4-QAM Signal 3: OFDM Frequency (MHz) Frequency Multichannel Traffic Estimation and Prediction Ch. 1 Ch. 2 Ch. 3 Ch. 4 Ch. 5 Occupied Unoccupied D. Markovic / Slide 5 5

6 Existing Work Single Spectral Detect Blind to Based on Blind Antenna Overlap Bands 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 Spectrum Measurements Proposed method D. Markovic / Slide 6 6

7 System Model Incumbent Users M transmitters with center frequency F m and bandwidth W m Power spectrum received from m th transmitter: m Activity a m t = 1 if transmitting at time t, 0 otherwise Wideband sensor Baseband bandwidth W Hz, known noise power 2 Welch power spectrum estimator using FFT of length F can store multiple power spectrum measurements Received power spectrum: M Y[ t] a [ t] [ t] m1 m m Estimated energy received from m th transmitter Estimated noise energy D. Markovic / Slide 7 7

8 Time-Frequency Map Time-Freq. map E of received energy: E = [Y[1] Y[2] Y[T]] T Define matrices: A tm = a m [t], mf = m ( f ), and Δ tf = ν t f E A Example: M = 3, F = 512, T = 30 Output: Time-Freq of Each Tx Input: Power Spectrum measurements E Output computed by Non-Negative Matrix Factorization (NNMF) = A(1) (1) + A(2) (2) + A(3) (3) D. Markovic / Slide 8 8

9 Non-Negative Matrix Factorization (NNMF) Let M = Estimated number of received signals ˆ NNMF finds ˆ TM A, ˆ M ˆ F to minimize E 2 Aˆ ˆ F 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 T F Non-unique solution and  is not binary ˆ, i.e., thresholding ˆ will not detect all occupied DFT bins D. Markovic / Slide 9 9

10 Non-Negative Matrix Factorization (NNMF) Let M = Estimated number of received signals ˆ NNMF finds ˆ TM A, ˆ M ˆ F to minimize E 2 Aˆ ˆ F Challenges: Estimating M is hard when T Non-convex cost function Re-initialize multiple times convergence to global minima not guaranteed F Our Proposed Solution Iteratively increase model size M Cost function is not probabilistic Not robust to noise Use energy detection to obtain binary time-freq. map Reconstruct each factor Non-unique solution and  is not binary before detection ˆ, i.e., thresholding ˆ will not detect all occupied DFT bins D. Markovic / Slide 10 10

11 Proposed Algorithm: Overview Increment ˆM Initialization Mˆ 1 E Energy Detection E ' E ' NNMF of with signals Aˆ, ˆ ˆM No Noise band detected? Yes Detect Occupied Bands Bˆ, Bˆ,..., Bˆ 0,..., F Mˆ D. Markovic / Slide 11 11

12 Proposed Algorithm: Energy Detection Increment ˆM No Initialization Mˆ 1 E Energy Detection E ' NNMF of with signals Aˆ, ˆ ˆM Yes E ' Noise band detected? Detect Occupied Bands E E ' Threshold [3]: / NQ P fa Bˆ, Bˆ,..., Bˆ 0,..., F Mˆ [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 , Nov D. Markovic / Slide 12 12

13 Proposed Algorithm: NNMF Increment ˆM No Initialization Mˆ 1 E Energy Detection E ' NNMF of with signals Aˆ, ˆ ˆM Yes E ' Noise band detected? Detect Occupied Bands Reconstructed Factors for Signal energy shared by all factors Significant signal energy Noise Band ˆ 4 M Bˆ, Bˆ,..., Bˆ 0,..., F Mˆ D. Markovic / Slide 13 13

14 Proposed Algorithm: Detecting Bands Increment ˆM No Initialization Mˆ 1 E Energy Detection E ' NNMF of with signals Aˆ, ˆ ˆM Yes E ' Noise band detected? Detect Occupied Bands Challenge: ˆ Signal energy shared by all factors Leaked signal energy Noise Band Bˆ, Bˆ,..., Bˆ 0,..., F Mˆ D. Markovic / Slide 14 14

15 Proposed Algorithm: Detecting Bands Increment ˆM No Initialization Mˆ 1 E Energy Detection E ' E ' NNMF of with signals Aˆ, ˆ ˆM Noise band detected? Challenge: ˆ and unknown noise Solution: Reconstruct and threshold peaks: max Aˆ ˆ 0.5 t m m tf 1,, T Active bin ignored if adjacent bins are not active Reduces false alarms 1 2 Yes Detect Occupied Bands Bˆ, Bˆ,..., Bˆ 0,..., F 1 Mˆ Ignore duplicate bands Similarity quantified by symmetric difference D. Markovic / Slide 15 15

16 Novel Performance Metrics: Why? Conventional wideband spectrum sensing metrics are per-bin False alarm probability for each bin Detection probability for each bin 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 16 16

17 Novel Performance Metrics: Why? Conventional wideband spectrum sensing metrics are per-bin False alarm probability for each bin Detection probability for each bin Our Output Ground Truth Challenge Match each detected band to the corresponding true band, if any D. Markovic / Slide 17 17

18 Novel Performance Metrics: How? Our Output ˆB 1 ˆB 2 ˆB 3 Ground Truth B1 B2 Fully Connected Bipartite Graph Edge Weights: B 1 Bˆ F B Bˆ 2 2 m, m m m 1 Symmetric Difference D. Markovic / Slide 18 18

19 Novel Performance Metrics: How? Our Output ˆB 1 ˆB 2 ˆB 3 Ground Truth Fully Connected Bipartite Graph Solution: Find the Maximum Weight Matching Edge Weights: B Bˆ B1 B2 1 F Bˆ m, m Bm m Symmetric Difference D. Markovic / Slide 19 19

20 Simulations: Performance vs. Activity Receiver: Bandwidth 6MHz 512 length FFT, average of 100 windowed overlapping segments 25 measurements, i.e., ~1ms long 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 20 20

21 Simulation: Performance vs. Spectral Overlap Number of Extra Signals Number of Detected Signals Relative Error in Center Frequency Relative Error in Bandwidth D. Markovic / Slide 21 21

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., Â, for use in traffic estimation D. Markovic / Slide 22 22

23 Thank you! Questions? This material is based upon work supported by the National Science Foundation under Grant No : Dynamic Spectrum Access by Learning Primary Network Topology

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 [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 [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, [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 , [5] M. Ibrahim and M. Youssef, CellSense: An Accurate Energy-Efficient GSM Positioning System, Veh. Technol. IEEE Trans. On, vol. 61, no. 1, pp , Jan [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 , Dec [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 [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 [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 , May [10] M. Laghate and D. Cabric, Identifying the presence and footprints of multiple incumbent transmitters, in th Asilomar Conference on Signals, Systems and Computers, 2015, pp [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 [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 , Nov D. Markovic / Slide 24 24