Noise Uncertainty in Cognitive RadioAnalytical Modeling and Detection Performance             Marwan A. Hammouda          ...
Outlines    Motivation    Introduction         Cognitive Radio         Primary Sensing    Noise Uncertainty NU    System M...
Motivation    Methods for primary user detection in cognitive radio may be severely    impaired by noise uncertainty (NU) ...
IntroductionCognitive Radio      Cognitive Radio is an interesting emerging paradigm for radio networks.      Basically ai...
IntroductionPrimary Sensing      Usually treated using classical detection theory.      The decision is made among two hyp...
Noise Uncertainty    Given a perfect noise information, detection is possible at any SNR with    energy detector.    Pract...
Noise UncertaintySo, the main idea behind this work is to find out a good statistical model for theNU and investigate if we...
System ModelGeneral Assumptions     Define random noise parameter α = 1/σ, where σ2 is the variance.     Assume noise/signa...
System ModelNoise Uncertainty Model      Popular Log Normal Model:                                  1        1            ...
System ModelNoise Uncertainty ModelLog Normal vs. Gaussian Approximation                                                  ...
Detection with NUCase I: Uncorrelated Signal Samples                               2      In (4), see that p = ∑n xn suffic...
Detection with NUCase I: Uncorrelated Signal Samples      Using the Gaussian model for f (α), we can derive the closed-for...
Detection with NUCase I: Uncorrelated Signal SamplesExample Detection Performance      Parameters: SNR=0 dB, NU=1 dB, N = ...
Detection with NUCase II: Correlated Signal Samples      Assume a correlated primary user signal with a covariance matrix ...
Detection with NUCase II: Correlated Signal Samples      Now, consider the following:            Make integration for the ...
Detection with NUCase II: Correlated Signal Samples      Continue ..          B0 = 1 ∑N=1 yn and B1 = 1 ∑N=1 λan yn       ...
Detection with NUCase II: Correlated Signal Samples      Assuming a covariance matrix with an exponential correlation mode...
Detection with NUCase II: Correlated Signal SamplesAt this point, I don’t have clear results to show for the next steps. I...
Noise Calibration MeasurmentSince most of the noise in a true receiver comes from the front-end LNA, asimple architecture ...
Noise Calibration Measurment   Parameters: f = 2.55GHz , BW = 20MHz , Ns = 100, L = 110dB , M =   800Realizations, (SNR = ...
Conclusion   Noise uncertainty limits robust detection at low SNR.   SNR can be relaxed by simple NU modeling.   Experimen...
Future Work   More analysis on the detector in case of a correlated signal   Study the importance of signal energy and cor...
Published Work   Hammouda, M. and Wallace, J., ”Noise uncertainty in cognitive radio sensing:   analytical modeling and de...
References   Mitola, J., III and Maguire, G. Q., Jr., ”Cognitive radio: Making software radios   more personal,”, IEEE Per...
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Noise Uncertainty in Cognitive Radio Analytical Modeling and Detection Performance

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Noise Uncertainty in Cognitive Radio Analytical Modeling and Detection Performance

  1. 1. Noise Uncertainty in Cognitive RadioAnalytical Modeling and Detection Performance Marwan A. Hammouda Supervisor: Prof. Jon Wallace Jacobs University Bremen June 19, 2012 Marwan A. Hammouda Noise Uncertainty in Cognitive Radio
  2. 2. Outlines Motivation Introduction Cognitive Radio Primary Sensing Noise Uncertainty NU System Model General Assumptions Noise Uncertainty Model. Detection with NU Case 1: Uncorrelated Signals Case 1: Correlated Signals Noise Calibration Measurments Conclusion Future Works Published Work References Marwan A. Hammouda Noise Uncertainty in Cognitive Radio
  3. 3. Motivation Methods for primary user detection in cognitive radio may be severely impaired by noise uncertainty (NU) and the associated SNR wall phenomenon. Propose the ability to avoid the SNR wall by detailed statistical modeling of the noise process when NU is present. Derive closed-form pdfs of signal and energy under NU, allowing an optimal Neyman-Pearson detector to be employed when NU is present. Explore energy detector at low SNR in a practical system. Marwan A. Hammouda Noise Uncertainty in Cognitive Radio
  4. 4. IntroductionCognitive Radio Cognitive Radio is an interesting emerging paradigm for radio networks. Basically aims at improving the spectrum utilization where radios can sense and exploit unused spectrum Allow networks to operate in a more decentralized fashion. Challenge: Require low missed detection at low SNR Marwan A. Hammouda Noise Uncertainty in Cognitive Radio
  5. 5. IntroductionPrimary Sensing Usually treated using classical detection theory. The decision is made among two hypothesis: H0 : xn = wn , n = 1, 2, . . . , N (1) H1 : xn = wn + sn , n = 1, 2, . . . , N Neyman-Pearson (N-P) test statistic: fH1 (x ) L (x ) = , (2) fH0 (x ) where fH (x ) is the joint pdf of the observed samples for hypothesis H Provides optimal detection if pdfs in (2) are known. Some famous detectors: Energy detector, Cyclostationary detectors, CAV detectors, Corrsum, and others. Marwan A. Hammouda Noise Uncertainty in Cognitive Radio
  6. 6. Noise Uncertainty Given a perfect noise information, detection is possible at any SNR with energy detector. Practical systems will only have a estimate of the noise variance σ2 . This imperfect knowledge is refereed to as noise uncertainty (NU). The NU concept was identified and studied in detail in [2]. In [2], σ2 is assumed to be confined in the interval [σ2 , σ2 ], but otherwise lo hi unknown. Worst-case detector assumes σ2 under H0 σ2 = hi σ2 lo under H1 For some value of SNR, the detector exhibits Pd < Pfa , regardless of the number of samples ⇒ SNR wall Below SNR wall, no useful detection is possible for the model above. Marwan A. Hammouda Noise Uncertainty in Cognitive Radio
  7. 7. Noise UncertaintySo, the main idea behind this work is to find out a good statistical model for theNU and investigate if we can avoid the SNR wall be detailed statisticalmodeling. Marwan A. Hammouda Noise Uncertainty in Cognitive Radio
  8. 8. System ModelGeneral Assumptions Define random noise parameter α = 1/σ, where σ2 is the variance. Assume noise/signal Gaussian α f (xn |α) = √ exp{−α2 xn /2}, 2 (3) 2π Assuming i.i.d. process, the marginal pdf of sample vector x is N 1 ∞ α2 f (x ) = f (α)αN exp − ∑ xn2 d α, (4) (2π)N /2 0 2 n =1 where f (α) is the distribution of the noise parameter α Marwan A. Hammouda Noise Uncertainty in Cognitive Radio
  9. 9. System ModelNoise Uncertainty Model Popular Log Normal Model: 1 1 fLN (α) = √ exp − (log α + µLN )2 /σ2 LN (5) ασLN 2π 2 Fit to truncated Gaussian with µ = E {α} = exp{−µLN + σ2 /2}, LN (6) 2 2 σ = Std{α} = [exp(σLN ) − 1] exp(−2µLN + σLN ), (7) Marwan A. Hammouda Noise Uncertainty in Cognitive Radio
  10. 10. System ModelNoise Uncertainty ModelLog Normal vs. Gaussian Approximation LogNorm 6 NU = 0.5 dB Gauss f (α) 4 2 0 0.7 0.8 0.9 1 1.1 1.2 1.3 α NU = 1.0 dB LogNorm 3 Gauss f (α) 2 1 0 0.6 0.8 1 1.2 1.4 1.6 α Marwan A. Hammouda Noise Uncertainty in Cognitive Radio
  11. 11. Detection with NUCase I: Uncorrelated Signal Samples 2 In (4), see that p = ∑n xn sufficient statistic. Pdf of p conditioned on noise parameter α2 f (p|α) = (α2 p)N /2−1 exp{−α2 p/2}, (8) 2N /2 Γ(N /2) Required marginal distribution on p only: 1 ∞ α2 p f (p)= f (α)α2 (α2 p)N /2−1 exp{− } d α. (9) 2N /2 Γ(N /2) 0 2 Marwan A. Hammouda Noise Uncertainty in Cognitive Radio
  12. 12. Detection with NUCase I: Uncorrelated Signal Samples Using the Gaussian model for f (α), we can derive the closed-form f (p) as follows: c0 e−c3 N N k c2 f (p)= ∑ L Γ(Lk ) 1+(−1)N −k Γ Lk , c1 c2 2 (10) 2 k =0 k c1 k where Lk = (N + 1 − k )/2 and pN /2−1 p 1 c0 = √ c1 = + 2N /2 Γ(N /2) 2πσα 2 2σ2 1 µ2 1 c2 = µα /(σ2 p + 1) α c3 = α 2 1− 2 2 σα σα p + 1 Marwan A. Hammouda Noise Uncertainty in Cognitive Radio
  13. 13. Detection with NUCase I: Uncorrelated Signal SamplesExample Detection Performance Parameters: SNR=0 dB, NU=1 dB, N = 20 samples Proposed detector knows σα but not realizations of α For robust (worst-case) detector let α ∈ [µα − 1.5σα , µα + 1.5σα ] 1 0.9 0.8 0.7 0.6 Pd 0.5 0.4 0.3 0.2 Modeled NU 0.1 Worst Case NU 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Pfa Marwan A. Hammouda Noise Uncertainty in Cognitive Radio
  14. 14. Detection with NUCase II: Correlated Signal Samples Assume a correlated primary user signal with a covariance matrix Σs . Consider the following assumptions: s ´ Σs = σ2 .Σs , where σ2 is the signal variance. s σ2 = σ2 .γ, where σ2 is the noise variance and γ is the SNR. s SNR is constant, one can think about it to be the worst SNR. Then, the marginal pdfs of the received signal for both hypothesis are: H0 1 ∞ α2 f (x ) = f (α)αN exp − XT X d α, (11) ´ (2π)N /2 |Σs + I | 1/ 2 0 2 H1 1 ∞ α2 f (x ) = f (α)αN exp − XT (Σs + I )−1 X d α, ´ ´ (2π)N /2 |Σs + I| 1/ 2 0 2 (12) Marwan A. Hammouda Noise Uncertainty in Cognitive Radio
  15. 15. Detection with NUCase II: Correlated Signal Samples Now, consider the following: Make integration for the exponential parts since they assume to have the most effect. Take the Eigendecomposition of the signal covariance matrix. Then, the N-P detector can be derived as follow: µ2 2 2 erfc − α 2σ2 (1+σ2 B1 ) µα B0 µα B1 1 + 2σ2 B α 0 α α L(Y) = exp − 1 + 2σ2 B0 α 1 + 2σ2 B1 α 1 + 2σ2 B1 α µ2 erfc − α 2σ2 (1+σ2 B0 ) α α (13) where Y is the uncorrelated version of the received signal X with σ2 I for H0 Σy = σ2 (γΛ + I ) for H1 ´ where Λ = diag (λ1 ...λN ) and λn is the nth eigenvalue of Σs Marwan A. Hammouda Noise Uncertainty in Cognitive Radio
  16. 16. Detection with NUCase II: Correlated Signal Samples Continue .. B0 = 1 ∑N=1 yn and B1 = 1 ∑N=1 λan yn 2 n 2 2 n 2 ´ where λan is the nth eigenvalue of the matrix A = (γΣs + I )−1 Using the identity (Q + ρM)−1 Q − ρQ−1 MQ−1 , we have ´ A I − γ.Σs . Note this identity is used for small values of γ Then, B1 B0 − 2 γ. ∑N=1 λn yn = B0 − R 1 n 2 Note B0 represents the signal energy, where R is seen to be a correlation-based value. Taking the logarithm of the NP detector in (13), rewriting it in terms of B0 and R and considering only the exponential term: µ 2 B0 α µ2 B0 − µ2 R α α l (y ) = − (14) 1 + 2σ2 B0 1 + 2σ2 B0 − 2σ2 R α α α Marwan A. Hammouda Noise Uncertainty in Cognitive Radio
  17. 17. Detection with NUCase II: Correlated Signal Samples Assuming a covariance matrix with an exponential correlation model, as follows: 1 for i = j cov (xi , xj ) = σ2 .γ. ρ|i −j | for i = j i , j = 1, 2, .., N and ρ is the correlation coefficientThe inverse of the covariance matrix is then known to be tridiagonal matrix,and the a closed form for the eigenvalues of this tridiagoal matrix can beobtained. Then, a closed form for the eigenvalue λn could be as follows: γ.(1 − ρ2 ) λn = (15) 1 + ρ2 + 2ρ cos( Nπn1 ) + Marwan A. Hammouda Noise Uncertainty in Cognitive Radio
  18. 18. Detection with NUCase II: Correlated Signal SamplesAt this point, I don’t have clear results to show for the next steps. I trying tostudy more the detector in (14) by applying Taylor series expansion andperforming sensitivity analysis to investigate how dominant B0 and R are forwith respect to the number of samples, NU level and SNR Marwan A. Hammouda Noise Uncertainty in Cognitive Radio
  19. 19. Noise Calibration MeasurmentSince most of the noise in a true receiver comes from the front-end LNA, asimple architecture depicted below can be used for noise calibration Marwan A. Hammouda Noise Uncertainty in Cognitive Radio
  20. 20. Noise Calibration Measurment Parameters: f = 2.55GHz , BW = 20MHz , Ns = 100, L = 110dB , M = 800Realizations, (SNR = −6dB ) 2 1 TX1 RX1 800 6400 TX0 RX1 TX1 RX0 0.8 1.5 Prob. Density TX0 RX0 0.6 Ns =100 Pd 1 0.4 0.5 0.2 0 0 0 0.5 1 1.5 2 2.5 3 0 0.2 0.4 0.6 0.8 1 Norm. Energy Pfa Parameters: f = 2.55GHz , BW = 20MHz , Ns = 6400, L = 120dB , M = 600Realizations, (SNR = −16dB ) 1 16 0.8 Prob. Density 12 6400 0.6 800 Pd 8 Ns =100 0.4 4 0.2 0 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 0 0.2 0.4 0.6 0.8 1 Norm. Energy Pfa Marwan A. Hammouda Noise Uncertainty in Cognitive Radio
  21. 21. Conclusion Noise uncertainty limits robust detection at low SNR. SNR can be relaxed by simple NU modeling. Experiment demonstrates useful detection to -16 dB Marwan A. Hammouda Noise Uncertainty in Cognitive Radio
  22. 22. Future Work More analysis on the detector in case of a correlated signal Study the importance of signal energy and correlation-based value on the detection in case of a correlated signal. Make more measurements with longer integration times and lower grade amplifiers. Marwan A. Hammouda Noise Uncertainty in Cognitive Radio
  23. 23. Published Work Hammouda, M. and Wallace, J., ”Noise uncertainty in cognitive radio sensing: analytical modeling and detection performance,”, the 16th International ITG Workshop on Smart Antennas WSA,2012 Marwan A. Hammouda Noise Uncertainty in Cognitive Radio
  24. 24. References Mitola, J., III and Maguire, G. Q., Jr., ”Cognitive radio: Making software radios more personal,”, IEEE Personal Commun. Magazine, vol. 6, pp. 1318, Aug. 1999. R. Tandra and A. Sahai, ”SNR walls for signal detection,”, IEEE J. Selected Topics Signal Processing, vol. 2, pp. 417, Feb. 2008. 1318, Aug. 1999. S. M. Kay, ”Fundamentals of Statistical Signal Processing: Detection Theory,”, Prentice Hall PTR, 1998. F. Heliot, X. Chu, and R. Hoshyar, ”A Tight closed-form approximation of the Log-Normal fading channel capacity,”, IEEE Transaction on Eireless Communications, vol. 8, No. 6 , June. 2009. 1318, Aug. 1999. Marwan A. Hammouda Noise Uncertainty in Cognitive Radio

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