DISTRIBUTED AND SEQUENTIAL SENSING FOR COGNITIVE RADIO NETWORKS Georgios B. Giannakis University of Minnesota [email protected] Outline Cognitive radios (CRs) and spectrum sharing ¾ Motivation and context Collaborative and distributed CR sensing ¾ RF interference spectrum cartography ¾ Channel gain cartography Sequential CR sensing ¾ … if time allows … 2 What is a cognitive radio ? - sensing Fixed radio - learning CR ¾ policy-based: parameters set RX by operators RF TX environment Software-defined radio (SDR) Dynamic - adapting to ¾ programmable: can adjust Resource spectrum parameters to intended link Allocation Cognitive radio (CR) ` Cognizant receiver: sensing ¾ intelligent: can sense the ` Agile transmitter: adaptation environment & learn to adapt ` Intelligent DRA: decision making [Mitola’00] ` radio reconfiguration decisions ` spectrum access decisions 3 Spectrum scarcity problem US FCC / fixed spectrum access policies have useful radio spectrum pre-assigned PSD inefficient occupancy 0 1 2 3 4 5 6GHz 4 Dynamical access under user hierarchy Primary Users (PUs) versus secondary users (SUs/CRs) PU PU PSD 2 PSD 2 PU PU PU 3 3 1 PU1 SU SU noise floor f f Spectrum underlay ¾ restriction on transmit-power levels ¾ operation over ultra wide bandwidths Spectrum overlay ¾ constraints on when and where to transmit ¾ avoid interference to PUs via sensing and adaptive allocation 5 Motivating applications Future pervasive networks: efficient spectrum sharing Licensed networks Secondary markets Cellular, PCS band Public safety band Improved spectrum Voluntary agreements efficiency between licensees and third party Improved capacity Limited QoS Third party access in Unlicensed networks licensed networks ISM, UNII, Ad-hoc TV bands (400-800 MHz) Automatic frequency Non-voluntary third party coordination access Interoperability Licensee sets a protection threshold Co-existence √ more users/services √ higher rates √ better quality √ less interference 6 Efficient sharing requires sensing Multiple CRs jointly detect the spectrum [Ganesan-Li’06 Ghasemi-Sousa’07] Source: Office of Communications (UK) Benefits of cooperation ¾ spatial diversity gain mitigates multipath fading/shadowing ¾ reduced sensing time and local processing ¾ ability to cope with hidden terminal problem Limitation: existing approaches do not exploit spatial dimension 7 Cooperative PSD cartography Idea: collaborate to form a spatial map of the RF spectrum Goal: Find PSD map across space and frequency ¾ Specifications: coarse approx. suffices ¾ Approach: basis expansion of J. A. Bazerque and G. B. Giannakis, “Distributed spectrum sensing for cognitive radio networks by exploiting sparsity,'' IEEE Transactions on Signal Processing, vol. 58, no. 3, pp. 1847-1862, March 2010. 8 Modeling Transmitters Sensing CRs Frequency bases Sensed frequencies ¾ Sparsity present in space and frequency 9 Space-frequency basis expansion Superimposed Tx spectra measured at CR r ¾ Average path-loss ¾ Frequency bases Linear model in 10 Sparse linear regression Seek a sparse to capture the spectrum measured at Lasso ¾ Soft threshold shrinks noisy estimates to zero ¾ Effects sparsity and variable selection ¾ Improves LS performance by incorporating a priori information R. Tibshirani, ``Regression Shrinkage and Selection via the Lasso,“ Journal of the Royal Statistical Society, Series B, vol. 58, no. 1, pp. 267-288, 1996. 11 Distributed recursive implementation Centralized Decentralized Fusion center Ad-hoc Scalability Robustness Lack of infrastructure Consensus-based approach ¾ solve locally Exchange of local Constrained optimization using the estimates alternating-direction method of multipliers (AD-MoM) 12 RF spectrum cartography sources candidate locations, cognitive radios NNLS Lasso As a byproduct, Lasso localizes all sources via variable selection 13 MSE performance Error between estimate and Monte Carlo MSE versus analytical approximations ¾ PA1 with known ¾ PA2 with bounds for 14 Tracking performance Normalized error batch solutions path of distributed one per time-slot online updates time-slot t Non-stationarity: one Tx exits at time-slot t=650 15 Simulation: PSD map estimation Centralized sensing No fading I=25 J=15 transmitters sensors 16 Centralized sensing without fading “true” Tx spectrum BP solution ¾ LS solution yields spurious peaks L1 norm minimization yields a sparse solution 17 Distributed consensus with fading “true” Tx spectrum sensed at the consensus step Starting from a local estimate, sensors reach consensus 18 Spline-based PSD cartography Q: How about shadowing? A1: Basis expansion w/ coefficient-functions : known bases accommodate prior knowledge ¾ overcomplete expansions allow for uncertainty on Tx parameters : unknown dependence on spatial variable x ¾ learn shadowing effects from periodograms at spatially distributed CRs J. A. Bazerque, G. Mateos, and G. B. Giannakis, ``Group-Lasso on Splines for Spectrum Cartography, ‘‘IEEE Transactions on Signal Processing,’’ submitted June 2010. 19 Smooth and sparse coefficient functions Twofold regularization of variational LS estimator (P1) Smoothing penalty sparsity enforcing penalty Proposition: optimal admits kernel expansion parameters 20 Estimating kernel parameters Need Group Lasso on (P1) equivalent ¾ X depends on kernels and bases Case admits closed-form solution not included 21 Simulation: PSD atlas Nr=100 CRs, Nb=90 bases (raised cosines), Ns=5 Tx PUs Frequency bases identified by enforcing sparsity Power distribution across space revealed by promoting smoothness 22 Cartography for CR sensing Power spectral density (PSD) maps ¾ Capture ambient power in space-time-frequency ¾ Can identify “crowded” regions to be avoided Channel gain (CG) maps ¾ Time-freq. channel from any-to-any point ¾ CRs adjust Tx power to min. PU disruption 23 Cooperative CG cartography Wireless CG (in dB) gain path loss shadowing TDMA-based training yields CR-to-CR shadow fading measurements Goal: Given , estimate and for any S.-J. Kim, E. Dall'Anese, and G. B. Giannakis, ``Cooperative Spectrum Sensing for Cognitive Radios using Kriged Kalman Filtering,'' IEEE J. of Selected Topics in Signal Proc., Feb. 2011.24 Dynamic shadow fading model Shadowing in dB is Gaussian distributed Spatial loss field-based shadowing model [Agrawal et al. ’09] Spatio-temporal loss-field evolution [Mardia ’98] [Wikle et at. ’99] : spatio-temporally colored : temporally white and spatially colored : known, captures interaction between and : zero-mean Gaussian, spatially colored, and temporally white K. V. Mardia, C. Goodall, E. J. Redfern, and F. J. Alonso, “The Kriged Kalman filter,” Test, vol. 7, no. 2, pp. 217–285, Dec. 1998. 25 State-space model Basis-expansion representation for and Retain K terms and sample at ¾ state equation Recall loss field model ¾ measurement equation 26 Tracking via Kriged Kalman Filtering Idea: estimate (and hence ) via Kalman filtering (KF) spatially interpolate with Kriging (KKF) to account for ¾ Conditioned on is Gaussian Estimated CG map: 27 Distributed implementation Prediction step locally but correction step collaboratively ( proper sub-matrix of ) : local copy of at CR r Distributed solution via alternating direction method of multipliers (AD-MoM) Kriging can be distributed likewise via AD-MoM and consensus E. Dall’Anese, S.-J. Kim, and G.B. Giannakis, “Channel Gain Map Tracking via Distributed Kriging,” IEEE Trans. on Vehicular Technology, June 2010 (submitted). 28 Simulation: map estimation performance 29 Tracking of PU power and position Given maps , candidate PU positions Estimate sparse power vector Sparse regression for tracking [Kim-Dall’Anese-GG’09] 30 Simulation: PU power tracking Average tracking performance ¾ Power MSE (avg. over all grid points) across time (KKF iterations) ¾ Mean spurious power (avg. over all grid except PU points) vs. time ¾ Area 200m x 200m ¾ Parameters [Kim ’09] ¾ Shadowing: 0-mean, std. dev. 10 dB 31 CG maps for resource allocation After having located the PU at with tx-power (dB); and rx-PU power at any x PU coverage probability: ¾ Coverage region not a disc (due to shadowing) CR interf. probability: ¾ Interference regions not discs either 32 Coverage and interference maps PU PU coverage coverage CR CR Interfer.. Interfer.. Path loss-only KKF-based ¾ disc-shaped and time-invariant ¾ captures spatial macro-diversity and spatio-temporal variations 33 Sequential sensing for multi-channel CRs Extra samples help detection/sensing but lower rate/throughput ¾ Sensing-throughput tradeoff in batch single-channel [Liang et al’08] ¾ Single-channel sequential CR sensing [Chaudhuri et al’09] ¾ Multi-channel (e.g., OFDM) CR sensing [Kim-Giannakis’09] Frame duration (T) 1 … 2 … … … subchannelssubchannels M n (≤ N) Sensing Data tx phase phase 34 Joint sensing-throughput optimization Features ¾ Sense bands in parallel; stop sensing simultaneously (half-duplex constraint) ¾ Throughput-optimal sequential sensing terminates when confident Basic approach: maximize avg. throughput under collision probability constraints to control Tx-CR interference to PUs (due to miss-detection) ¾ Admits a constrained Dynamic Programming (DP) formulation ¾ Reduces to an optimum stopping time problem ¾ Optimum access: LR test w/ thresholds dependent on Lagrange multipliers S.-J. Kim and G. Giannakis, “Sequential and Cooperative Sensing for Multichannel Cognitive Radios,” IEEE Transactions on Signal Processing, 2010. 35 Simulated test case M = 10, N = T = 100, chi-square distributed channel gains Average performance over 20,000 runs per operating SNR 36 Concluding remarks Power spectrum density cartography ¾ Space-time-frequency view of interference temperature ¾ PU/source localization and tracking Channel gain cartography ¾ Space-time-frequency links from any-to-any point ¾ KF for tracking and Kriging for interpolation Parsimony via sparsity and distribution via consensus ¾ Lasso, group Lasso on splines, and method of multipliers Vision: use atlas to enable spatial re-use, hand-off, localization, Tx-power tracking, resource allocation, and routing Acknowledgements: National Science Foundation J.-A. Bazerque, E. Dall’Anese, S.-J. Kim, G. Mateos Thank You! 37.