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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

1Kathmandu University, Nepal 2Politecnico di Torino, Italy 3Fraunhofer HHI, Berlin, Germany 4CSP - 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: H0 : y[n] = w[n]

• nly noise

H1 : 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(Pd) and probability of false alarm (Pfa) as a function of the signal-to-noise ratio (SNR): Pd = P(T > θ | H1) Pfa = P(T > θ | H0)

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 V = ⇒ K × N random noise matrix Y =   y11 . . . . . . y1N . . . . . . . . . . . . yK1 . . . . . . yKN   = ⇒ K × N

Chosen values

N = 80 K = 4 Sample covariance matrix: R 1 N Y Y H Finally we compute the eigenvalues λ1 ≥ . . . ≥ λK 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 TRLRT = λ1 σ2

v

for performance comparison we also considered Energy Detection defined as: TED = 1 KNσ2

v K

• k=1

N

• n=1

|yk(n)|2

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 H0 by the algorithm. THRLRT1,2 = λ1 ˆ σ2

v1,2(S)

THED1,2 = 1 KNˆ σ2

v1,2(S) K

• k=1

N

• n=1

|yk(n)|2

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 H0 by the algorithm. THRLRT1,2 = λ1 ˆ σ2

v1,2(S)

THED1,2 = 1 KNˆ σ2

v1,2(S) K

• k=1

N

• n=1

|yk(n)|2

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 H0 by the algorithm. THRLRT1,2 = λ1 ˆ σ2

v1,2(S)

THED1,2 = 1 KNˆ σ2

v1,2(S) K

• k=1

N

• n=1

|yk(n)|2

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 ˆ σ2

v1(S) =

1 KSN

S

• s=1

K

• k=1

N

• n=1

|vk(n)|2 HRLRT2 ˆ σ2

v2(S) =

Ss

• s=1

K

• k=1

N

• n=1

|hks(n) + v(n)|2 +

SN

• s=1

K

• k=1

N

• n=1

|vk(n)|2

• KSN

PS: signal plus noise probability Pd: RLRT detection probability SS = SPS (1 − Pd): misdetected slots SN = S − SS: 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 f0(θ) = 1 2ξ

• D

π +∞

−∞

|x|fTW 2 xθ − µ ξ

• exp
• −D

4 (x − 1)2

• dx

HRLRT2 f0(θ) = 1 ξσ2

1

√ 2π +∞

−∞

|x|fTW 2 xθ − µ ξ

• exp
• − 1

2σ2

1

(x − µ1)2

• dx

µ = K N 1

2

+ 1 2 ξ = N−2/3 K N 1

2

+ 1 K N − 1

2

+ 1 1/3 µ1 = S + SS S D = 2KNS σ2

1 = S + 2ρSS + ρ2KSS

KNS2 Pfa = 1 − F0(θ)

Daniel Riviello Politecnico di Torino, CSP - ICT Innovation Impact of noise estimation on eigenvalue based spectrum sensing in cognitive radio systems 11 / 16

Introduction System model Test statistics Results Conclusions and future works

Analytical expressions: detection probability

HRLRT1 Pd = Q   θ − µx

• 2θ2

D + σ2 x

  HRLRT2 Pd = Q     θ − µx/µ1

• θ2σ2

1+σ2 x

µ2

1

    provided that the signal-to-noise-ratio ρ > ρcrit, where ρcrit = 1 √ KN µx = (1 + Kρ)

• 1 + K − 1

NKρ

• σ2

x = 1

N (Kρ + 1)2

• 1 − K − 1

NK 2ρ2

• µ1 = S + SS

S D = 2KNS σ2

1 = S + 2ρSS + ρ2KSS

KNS2

Daniel Riviello Politecnico di Torino, CSP - ICT Innovation Impact of noise estimation on eigenvalue based spectrum sensing in cognitive radio systems 12 / 16

Introduction System model Test statistics Results Conclusions and future works

Comparison HRLRT1 vs. HED1, ROC curve

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.2 0.4 0.6 0.8 1 Pr[False Alarm] Pr[Detection] ED (Known Variance) HED1 (S = 2) HED1 (S = 8) HRLRT1 (S = 2) HRLRT1 (S = 8) RLRT (Known Variance)

SNR = -10 dB. Faster convergence for HRLRT1 w.r.t. HED1 with the same increase

• f noise variance

estimation slots S.

Daniel Riviello Politecnico di Torino, CSP - ICT Innovation Impact of noise estimation on eigenvalue based spectrum sensing in cognitive radio systems 13 / 16

Introduction System model Test statistics Results Conclusions and future works

Comparision HRLRT1 vs. HRLRT2, Pd vs. SNR

−12 −11 −10 −9 −8 −7 −6 −5 −4 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 SNR [dB] Pr[Detection] HRLRT2 (S = 2) HRLRT2 (S = 15) HRLRT1 (S = 2) HRLRT1 (S = 15) RLRT (Known variance)

Pfa = 0.05. HRLRT2 slightly lower than HRLRT1. No visible difference in extreme high or low SNR values. Both approximate RLRT with large number of slots S.

Daniel Riviello Politecnico di Torino, CSP - ICT Innovation Impact of noise estimation on eigenvalue based spectrum sensing in cognitive radio systems 14 / 16

Introduction System model Test statistics Results Conclusions and future works

Noise variance estimation uncertainty, RLRT vs. ED

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.2 0.4 0.6 0.8 1 Pr[False Alarm] Pr[Detection] ED (known variance) ED (wrong variance) RLRT (known variance) RLRT (wrong variance)

N = 100, K = 4. Var(ˆ σ2

v) = 0.0032

(-25 dB). σ2

v = 1.

Gap between exact and wrong variance curve is larger for ED as compared to RLRT.

Daniel Riviello Politecnico di Torino, CSP - ICT Innovation Impact of noise estimation on eigenvalue based spectrum sensing in cognitive radio systems 15 / 16

Introduction System model Test statistics Results Conclusions and future works

Conclusions and future works

Analytical expressions for Pd and Pfa verified by Monte Carlo simulations. Impact of noise estimation is severe in case of small number of auxiliary slots S used for estimation, with large S both hybrid approaches tend to ideal performance. Work in progress Focus on the implementation of EBD algorithms in a software-defined radio framework (GNU Radio) and testing with software radio equipment (USRP), K as oversampling factor (single sensor). Definition of an SNR wall expression for RLRT.

Daniel Riviello Politecnico di Torino, CSP - ICT Innovation Impact of noise estimation on eigenvalue based spectrum sensing in cognitive radio systems 16 / 16

Introduction System model Test statistics Results Conclusions and future works

Conclusions and future works

Analytical expressions for Pd and Pfa verified by Monte Carlo simulations. Impact of noise estimation is severe in case of small number of auxiliary slots S used for estimation, with large S both hybrid approaches tend to ideal performance. Work in progress Focus on the implementation of EBD algorithms in a software-defined radio framework (GNU Radio) and testing with software radio equipment (USRP), K as oversampling factor (single sensor). Definition of an SNR wall expression for RLRT.

Daniel Riviello Politecnico di Torino, CSP - ICT Innovation Impact of noise estimation on eigenvalue based spectrum sensing in cognitive radio systems 16 / 16