Using Multiple Power Spectrum Measurements to Sense Signals with Partial Spectral Overlap

Transcription

1 Using Multiple Power Spectrum Measurements to Sense Signals with Partial Spectral Overlap Mihir Laghate and Prof. Danijela Cabric 7 th March 2017 IEEE DySPAN 2017, Baltimore

2 Outline w Goals, Motivation, and Existing Work w System Model Assumptions Time-Frequency Map w Non-Negative Matrix Factorization (NNMF) Challenges with existing algorithms w Proposed Algorithm: Greedy Energy Minimizing NNMF w MATLAB Simulation Results w USRP Measurement Results w Conclusions and Future Work D. Markovic / Slide 2 2

3 Goals Distinguish Signals with Spectral Overlap Estimate noise power spectrum That is, w Count number of signals rcvd w Detect sets of discrete Fourier transform bins occupied by each signal Challenges: Colored noise Spurs and always-on interferers [1] M. Laghate and D. Cabric, Using the Time Dimension to Sense Signals with Partial Spectral Overlap, in IEEE GLOBECOM, Washington, USA, D. Markovic / Slide 3 3

4 Motivating Applications Spectral overlap by design IEEE b/g channels in 2.4GHz UCLA Image Source: Wikipedia List of WLAN channels Channel bonding in IEEE n 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 Existing Work for Distinguishing Signals Single Spectral Detect Blind to Based on Blind Antenna Overlap Bands Channel Transmission protocols [4],[5] û ü ü ü ü Cyclic frequency [7] û ü ü û ü Channel model & location [6] û ü ü û û Angle of Arrival [8] ü û ü û û Random Matrix Theory [9] ü û ü û ü Multiple CRs [10],[11] ü û û ü ü Power Spectrum Threshold [12] ü ü û ü ü Multiple Power Spectrum Measurements ü ü ü ü ü Proposed method and our prior work [1] D. Markovic / Slide 5 5

6 System Model Wideband sensor w Baseband bandwidth W Hz w Additive wide sense stationary Gaussian noise ν t R % & w Welch power spectrum estimator using FFT of length F Incumbent Users w M distinct frequency bands w m th band has U m transmitters with freq. support B m DFT bins Power spectrum received from u th transmitter: X (,* R % & Activity a (,* t 0,1 is fraction of t th measurement that u th transmitter in m th band is active w Received power spectrum: D. Markovic / Slide 6 6

7 Time-Frequency Map: 1 user/band w Time-Freq. map E of received energy: E = [Y[1] Y[2] Y[T]] T w Define matrices: A tm = a m [t], S mf = X m ( f ), and Δ /0 = ν t f Y[t] = M Example: M = 3, F = 512, T = 30 U m m=1 u=1 a m,u [t]x m,u [t]+ν[t] Input: Simulated Power Spectrum E = AS+D Output: Time-Freq of Each Tx A (1) S(1) E Output computed by Non-Negative Matrix Factorization (NNMF) when given M = 3 = + A (2) S(2) + A (3) S(3) D. Markovic / Slide 7 7

8 Non-Negative Matrix Factorization (NNMF) w Let M4 = Estimated number of received signals T w NNMF finds Â! ˆM +, ˆΣ! ˆM F to minimize E 2 -Aˆ Sˆ F Challenges: w Estimating M4 is hard when w Non-convex cost function Þ convergence to global minima not guaranteed w Cost function is not probabilistic Þ Not robust to noise T < F w Non-unique solution and  is not binary Þ Ŝ»S /, i.e., thresholding Ŝ will not detect all occupied DFT bins D. Markovic / Slide 8 8

9 Prior Work: NNMF-based Algorithm Increment ˆM No Initialization M ˆ = 1 E Energy Detection E ' NNMF of with signals Aˆ, Sˆ ˆM Yes E ' Noise band detected? Detect Occupied Bands Reconstructed Factors for Leaked energy Significant signal energy Noise Band ˆ 4 M = Bˆ, Bˆ,..., Bˆ Ì 0,..., F Mˆ { } D. Markovic / Slide 9 9

10 Motivating NNMF Algorithm: Robust XRay E Y[t] a[t] M i.e., cone with received power spectra as extreme rays U m [ ] = a m,u [t]e X m,u [t] m=1 u=1 [ ] + E ν[t] Recursive Algorithm: 1. Choose point with maximum residual as extreme ray 2. Measure residual to all measurements 3. Repeat 1 until all measurements lie within cone Image source: [13] [13] A. Kumar, V. Sindhwani, and P. Kambadur, Fast conical hull algorithms for near-separable non-negative matrix factorization, in International Conference on Machine Learning, D. Markovic / Slide 10 10

11 Separability Assumption E Y[t] a[t] M i.e., cone with received power spectra as extreme rays U m [ ] = a m,u [t]e X m,u [t] m=1 u=1 [ ] + E ν[t] Separability Assumption: Requires at least one measurement of each extreme ray w At least one noise only measurement w For each transmitter, at least one measurement where it is the only active transmitter Image source: [13] [14] D. Donoho and V. Stodden, When Does Non-Negative Matrix Factorization Give a Correct Decomposition into Parts?, in Advances in Neural Information Processing Systems, MIT Press, 2004, pp D. Markovic / Slide 11 11

12 Proposed Greedy Energy Minimizing NNMF Received Signal Welch Power Spectrum Estimator Noise power spectrum learned from data 1. Initialize noise estimate as min. energy measurement 2. Estimate noise as mean of measurements with Mahalanobis distance < t to est. noise distribution 3. Repeat Step 2 until convergence Append to Time Frequency Map E Detect Noise-Only Measurements L Index in 1,, T \L with Lowest Energy labelled as Detected Signal No L Measurements that are linear combinations of Detected Signals L = T? Yes Energy Detection on Detected Signals Ø Center Frequency Ø Bandwidth D. Markovic / Slide 12 12

13 Proposed Greedy Energy Minimizing NNMF Received Signal Welch Power Spectrum Estimator Append to Time Frequency Map E Detect Noise-Only Measurements L Index in 1,, T \L with Lowest Energy labelled as Detected Signal Noise power spectrum learned from data 1. Initialize noise estimate as min. energy measurement 2. Estimate noise as mean of measurements with Mahalanobis distance < t to est. noise distribution 3. Repeat Step 2 until convergence Constrained least squares minimization estimates activity 1. Activity for noise (, 1] 2. Activity for detected signals [0, )» Measurement Detected Signal 1 Detected Signal 2 Noise Estimate No L Measurements that are linear combinations of Detected Signals L = T? Yes Energy Detection on Detected Signals Ø Center Frequency Ø Bandwidth D. Markovic / Slide 13 13

14 Performance Metrics w Number of detected bands w Number of extra bands detected w Relative Errors in Center Frequency and Bandwidth D. Markovic / Slide 14 14

15 Performance Metrics w Number of detected bands w Number of extra bands detected w Relative Errors in Center Frequency and Bandwidth Edge Weights: δ ( B m1, ˆB ) m2 = F B m1! ˆB m2 Our Output ˆB 1 Symmetric Difference ˆB 2 ˆB 3 Ground Truth Fully Connected Bipartite Graph B1 B2 Computed using Maximum Weight Matching D. Markovic / Slide 15 15

16 MATLAB Simulations: Performance vs. T Receiver: w Bandwidth 100 MHz w 512 length FFT, average of 64 windowed overlapping segments w Up to 50 measurements, i.e., 8.32ms w Parameters: P fa = 0.01, τ r = 0.1 Number of Detected Signals g Transmitters: w Each network = 1 AP + 2 STAs w Channels 1, 4, 6, 8, 11 w Saturated uplink and downlink flows w Shadow fading channels with 6dB variance Number of Extra Signals D. Markovic / Slide 16 16

17 Simulation: Performance vs. Spectral Overlap Number of Extra Signals Number of Detected Signals Frequency Error Relative Error in Bandwidth D. Markovic / Slide 17 17

18 USRP Measurements: Example USRP Measurements w Device: USRP N210 with CBX daughtercard w Measurements at GHz w 8-bit 50 MS/s Signals Detected Colored Noise Learnt Black arrows: detected supports Labels: corresponding channels D. Markovic / Slide1818

19 Multiple USRP Measurements w Contour plot of 2D histogram of detected center frequencies and bandwidths w 1000 realizations of 50 MHz GHz at UCLA Android WiFiAnalyzer used to confirm channels 6, 7, 8, and 11 in use D. Markovic / Slide 19 19

20 Conclusions and Future Work w Noise power spectrum can be estimated automatically when sensing communicating incumbent users w Multiple power spectrum measurements can distinguish real world spectrally overlapped signals even in unknown channels w Conventional signal detection and estimation theory may not be sufficient Future Work: w Find structural properties of optimization problem to reduce computational complexity w Estimate time of activity, i.e., Â, for use in traffic estimation D. Markovic / Slide 20 20

21 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

22 Selected References [1] M. Laghate and D. Cabric, Using the Time Dimension to Sense Signals with Partial Spectral Overlap, in IEEE GLOBECOM, Washington, USA, [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 [13] A. Kumar, V. Sindhwani, and P. Kambadur, Fast conical hull algorithms for near-separable non-negative matrix factorization, in International Conference on Machine Learning, [14] D. Donoho and V. Stodden, When Does Non-Negative Matrix Factorization Give a Correct Decomposition into Parts?, in Advances in Neural Information Processing Systems, MIT Press, 2004, pp D. Markovic / Slide 22 22