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
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!
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