Introduction System model Test statistics Results Conclusions and future works Impact of noise estimation on eigenvalue based spectrum sensing in cognitive radio systems Pawan Dhakal 1 Roberto Garello 2 Federico Penna 3 Daniel Riviello 2 , 4 1 Kathmandu University, Nepal 2 Politecnico di Torino, Italy 3 Fraunhofer HHI, Berlin, Germany 4 CSP - ICT Innovation, Turin, Italy The 4th Workshop of COST Action IC0902 Rome, October 9-11, 2013 Daniel Riviello Politecnico di Torino, CSP - ICT Innovation Impact of noise estimation on eigenvalue based spectrum sensing in cognitive radio systems 1 / 16
Introduction System model Test statistics Results Conclusions and future works Outline 1 Introduction 2 System model 3 Test statistics and hybrid approaches HRLRT1 HRLRT2 4 Results 5 Conclusions and future works Daniel Riviello Politecnico di Torino, CSP - ICT Innovation Impact of noise estimation on eigenvalue based spectrum sensing in cognitive radio systems 2 / 16
Introduction System model Test statistics Results Conclusions and future works Introduction Semi-blind spectrum sensing algorithms are the optimum spectrum sensing techniques in a known noise power level scenario. In practice No prior knowledge of the noise variance is possible, estimation is needed. Question What is the impact of noise estimation accuracy on Eigenvalue Based Detection (EBD) semi-blind algorithms? Daniel Riviello Politecnico di Torino, CSP - ICT Innovation Impact of noise estimation on eigenvalue based spectrum sensing in cognitive radio systems 3 / 16
Introduction System model Test statistics Results Conclusions and future works Introduction Semi-blind spectrum sensing algorithms are the optimum spectrum sensing techniques in a known noise power level scenario. In practice No prior knowledge of the noise variance is possible, estimation is needed. Question What is the impact of noise estimation accuracy on Eigenvalue Based Detection (EBD) semi-blind algorithms? Daniel Riviello Politecnico di Torino, CSP - ICT Innovation Impact of noise estimation on eigenvalue based spectrum sensing in cognitive radio systems 3 / 16
Introduction System model Test statistics Results Conclusions and future works Introduction Semi-blind spectrum sensing algorithms are the optimum spectrum sensing techniques in a known noise power level scenario. In practice No prior knowledge of the noise variance is possible, estimation is needed. Question What is the impact of noise estimation accuracy on Eigenvalue Based Detection (EBD) semi-blind algorithms? Daniel Riviello Politecnico di Torino, CSP - ICT Innovation Impact of noise estimation on eigenvalue based spectrum sensing in cognitive radio systems 3 / 16
Introduction System model Test statistics Results Conclusions and future works Spectrum sensing Key enabling technology for Cognitive Radio Systems sense and identify spectrum opportunities prevent interference with the licensed primary users (PUs). Decision whether a channel is free or not determined as the result of a binary hypothesis testing experiment: H 0 : y [ n ] = w [ n ] only noise H 1 : y [ n ] = x [ n ] + w [ n ] signal plus noise A detector collects samples y [ n ] , computes a test statistic T and compares it against a predefined threshold θ . The performance of each detector has been assessed in terms of probability of detection( P d ) and probability of false alarm ( P fa ) as a function of the signal-to-noise ratio (SNR): P d = P ( T > θ | H 1 ) P fa = P ( T > θ | H 0 ) Daniel Riviello Politecnico di Torino, CSP - ICT Innovation Impact of noise estimation on eigenvalue based spectrum sensing in cognitive radio systems 4 / 16
Introduction System model Test statistics Results Conclusions and future works System model Detector computes T from K sensors and N samples stored in Y = hs + V where: s = ⇒ 1 × N signal vector h = ⇒ K × 1 complex channel vector Chosen values V = ⇒ K × N random noise matrix N = 80 y 11 y 1 N . . . . . . K = 4 = Y = . . . . . . . . . . . . ⇒ K × N y K 1 y KN . . . . . . Sample covariance matrix: R � 1 N Y Y H Finally we compute the eigenvalues λ 1 ≥ . . . ≥ λ K of R . Daniel Riviello Politecnico di Torino, CSP - ICT Innovation Impact of noise estimation on eigenvalue based spectrum sensing in cognitive radio systems 5 / 16
Introduction System model Test statistics Results Conclusions and future works Test statistics Optimum test algorithm under the semi-blind class of EBD: Roy Largest Root Test T RLRT = λ 1 σ 2 v for performance comparison we also considered Energy Detection defined as: K N 1 � � | y k ( n ) | 2 T ED = KN σ 2 v n = 1 k = 1 Daniel Riviello Politecnico di Torino, CSP - ICT Innovation Impact of noise estimation on eigenvalue based spectrum sensing in cognitive radio systems 6 / 16
Introduction System model Test statistics Results Conclusions and future works Hybrid approaches 2 different approaches: HRLRT1 : offline estimation , noise variance is estimated from S auxiliary noise-only slots in which we are sure that the primary signal is absent. HRLRT2 : online estimation , auxiliary noise-only slots NOT available, noise variance is estimated from the previous slots declared as H 0 by the algorithm. K N 1 λ 1 � � | y k ( n ) | 2 T HRLRT 1 , 2 = T HED 1 , 2 = σ 2 σ 2 ˆ v 1 , 2 ( S ) KN ˆ v 1 , 2 ( S ) n = 1 k = 1 Daniel Riviello Politecnico di Torino, CSP - ICT Innovation Impact of noise estimation on eigenvalue based spectrum sensing in cognitive radio systems 7 / 16
Introduction System model Test statistics Results Conclusions and future works Hybrid approaches 2 different approaches: HRLRT1 : offline estimation , noise variance is estimated from S auxiliary noise-only slots in which we are sure that the primary signal is absent. HRLRT2 : online estimation , auxiliary noise-only slots NOT available, noise variance is estimated from the previous slots declared as H 0 by the algorithm. K N 1 λ 1 � � | y k ( n ) | 2 T HRLRT 1 , 2 = T HED 1 , 2 = σ 2 σ 2 ˆ v 1 , 2 ( S ) KN ˆ v 1 , 2 ( S ) n = 1 k = 1 Daniel Riviello Politecnico di Torino, CSP - ICT Innovation Impact of noise estimation on eigenvalue based spectrum sensing in cognitive radio systems 7 / 16
Introduction System model Test statistics Results Conclusions and future works Hybrid approaches 2 different approaches: HRLRT1 : offline estimation , noise variance is estimated from S auxiliary noise-only slots in which we are sure that the primary signal is absent. HRLRT2 : online estimation , auxiliary noise-only slots NOT available, noise variance is estimated from the previous slots declared as H 0 by the algorithm. K N 1 λ 1 � � | y k ( n ) | 2 T HRLRT 1 , 2 = T HED 1 , 2 = σ 2 σ 2 ˆ v 1 , 2 ( S ) KN ˆ v 1 , 2 ( S ) n = 1 k = 1 Daniel Riviello Politecnico di Torino, CSP - ICT Innovation Impact of noise estimation on eigenvalue based spectrum sensing in cognitive radio systems 7 / 16
Introduction System model Test statistics Results Conclusions and future works HRLRT1 Daniel Riviello Politecnico di Torino, CSP - ICT Innovation Impact of noise estimation on eigenvalue based spectrum sensing in cognitive radio systems 8 / 16
Introduction System model Test statistics Results Conclusions and future works HRLRT2 Daniel Riviello Politecnico di Torino, CSP - ICT Innovation Impact of noise estimation on eigenvalue based spectrum sensing in cognitive radio systems 9 / 16
Introduction System model Test statistics Results Conclusions and future works ML Noise variance estimation HRLRT1 S K N 1 σ 2 � � � | v k ( n ) | 2 ˆ v 1 ( S ) = KSN s = 1 k = 1 n = 1 HRLRT2 � S s S N � K N K N | h k s ( n ) + v ( n ) | 2 + � � � � � � | v k ( n ) | 2 s = 1 n = 1 s = 1 n = 1 σ 2 k = 1 k = 1 ˆ v 2 ( S ) = KSN P S : signal plus noise probability P d : RLRT detection probability S S = SP S ( 1 − P d ) : misdetected slots S N = S − S S : detected slots Daniel Riviello Politecnico di Torino, CSP - ICT Innovation Impact of noise estimation on eigenvalue based spectrum sensing in cognitive radio systems 10 / 16
Introduction System model Test statistics Results Conclusions and future works Analytical expressions: false alarm probability HRLRT1 � + ∞ � f 0 ( θ ) = 1 D � x θ − µ � � − D � 4 ( x − 1 ) 2 | x | f TW 2 exp d x 2 ξ π ξ −∞ HRLRT2 � + ∞ 1 � x θ − µ � � − 1 � ( x − µ 1 ) 2 f 0 ( θ ) = √ | x | f TW 2 exp d x 2 σ 2 ξσ 2 ξ 2 π 1 1 −∞ � 2 � 1 / 3 �� K � 1 �� K � 1 � �� K � − 1 2 2 2 ξ = N − 2 / 3 µ = + 1 + 1 + 1 N N N 1 = S + 2 ρ S S + ρ 2 KS S µ 1 = S + S S σ 2 D = 2 KNS S KNS 2 P fa = 1 − F 0 ( θ ) Daniel Riviello Politecnico di Torino, CSP - ICT Innovation Impact of noise estimation on eigenvalue based spectrum sensing in cognitive radio systems 11 / 16
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