Using the Time Dimension to Sense Signals with Partial Spectral Overlap Mihir Laghate and Danijela Cabric 5 th December 2016
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
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
Potential Applications Spectral overlap by design Measurements @ UCLA [1] IEEE 802.11b/g channels in 2.4GHz Image Source: Wikipedia List of WLAN channels Channel bonding in IEEE 802.11n [1] M. Laghate and D. Cabric, Using Multiple Power Spectrum Measurements to Sense Signals with Partial Spectral Overlap, submitted to IEEE DySPAN 2017. Lack of Guard Bands IEEE 802.11n 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. 1 3. LTE Carrier Aggregation [2] D. Markovic / Slide 4 4
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, 2009. Multi-signal Classification 15 10 5 Signal 1: DSSS Signal 2: 4-QAM Signal 3: OFDM 0 0 7.5 15 22.5 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
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
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
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
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
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
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 1 1 2 Mˆ D. Markovic / Slide 11 11
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]: 2 1 1 2 / NQ P fa Bˆ, Bˆ,..., Bˆ 0,..., F 1 1 2 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. 2765 2775, Nov. 2011. D. Markovic / Slide 12 12
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 1 1 2 Mˆ D. Markovic / Slide 13 13
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 1 1 2 Mˆ D. Markovic / Slide 14 14
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
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
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
Novel Performance Metrics: How? Our Output ˆB 1 ˆB 2 ˆB 3 Ground Truth 9 4 6 3 6 10 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
Novel Performance Metrics: How? Our Output ˆB 1 ˆB 2 ˆB 3 Ground Truth 9 4 6 3 6 10 Fully Connected Bipartite Graph Solution: Find the Maximum Weight Matching Edge Weights: B Bˆ B1 B2 1 F Bˆ m, m Bm m 2 1 2 Symmetric Difference D. Markovic / Slide 19 19
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
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
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
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. D. Markovic / Slide 24 24