Performance Comparison of Cyclo-stationary Detectors with Matched Filter and Energy Detector M. SAI SINDHURI 1, S. SRI GOWRI 2

Transcription

1 ISSN Vo.3,Issue.39 November-14, Pages: Performance Comparison of Cyco-stationary Detectors with Matched Fiter and Energy Detector M. SAI SINDHURI 1, S. SRI GOWRI 1 PG Schoar, Dept of ECE, SRK Institute of Technoogy Enikepadu, Vijayawada, AP, India, E-mai: manikondasindhuri@gmai.com. Professor, Dept of ECE, SRK Institute of Technoogy Enikepadu, Vijayawada, AP, India. Abstract: Cognitive Radio (CR) is a promising technoogy that can be used to aeviate the spectrum shortage probem or the barrier to communication in various appication domains. CR has been proposed as a key soution for the probem of efficient usage of spectrum band. Spectrum sensing is one of the most important issues in cognitive radio system. Spectrum sensing invoves in obtaining the usage characteristics across mutipe dimensions such as time, space, frequency, code and what type of signa occupying the spectrum. In spectrum sensing, different method are proposed for identifying the presence of signa transmission a of which are in eary deveopment stage. They are Energy detection based spectrum sensing, Matched fiter based and cycostationary based spectrum sensing. This paper presents the cacuation of probabiity of fase aarm and probabiity detection verses SNR for three detectors, Comparison has been made in terms of receiver operating characteristic curves, Miss Detection probabiity Versus SNR and PSNR for three detectors. Keywords: Cycostationary, SCD, MCS, ED, MFD Detectors. I. INTRODUCTION A Cognitive radio is an inteigent radio that can be programmed and configured dynamicay. The main aim of (CR) in wireess communication is efficient use of spectrum without any interference. The promise of CR to reaize a fexibe spectrum management by impementing agorithms for spectrum awareness and improved spectrum utiization shoud be evauated for security and reiabiity. CR shoud provide the foowing functions: Spectrum Sensing-determine which portions of the spectrum are avaiabe and detect the presence of icensed (primary) Users, when a user operates in a icensed band. Spectrum management-seect the best avaiabe channe for communication. Spectrum sharing- coordinate access to this channe with other users. Spectrum mobiity- vacates the channe when icensed user is detected. Spectrum sensing, agorithm which is used is broady cassified into three types: Energy Detector(ED), Matched fiter Detector (MFD), Cycostationarity Feature Detector. ED based spectrum sensing technique pays major roe because of its ow compexity. Matched Fiter Detector correate receiver signa with the transmitted signa. [1]. Spectrum sensing is we researched topic: This paper presents the probem of testing the hypothesis H (primary signa absent) and H 1 (primary signa present) but CR is modeed by H as additive white Gaussian noise and H 1 as received signa with piot tone signa. SNR wa for energy detection that shows the noise uncertainty which is given by the scientist Named as Tandra and sahai in []. In Cycostationary two different detectors are impemented and proposed Spectra correation density signa estimation Magnitude squared coherence Setting the detector to threshod probabiity detection for SCD,, MFD and ED is determined. In this paper it is found that cycostationarity detector impemented with exhibits better performance. II. CYCLOSTATIONARITY FEATURE DETECTOR Moduated signas are generay couped with sine wave carriers, puse train, repeating, hoping sequences, or cycic prefixes which resuts in buit-in periodicity though the data is stationary random process, then the moduated signa is characterized as cycostationary. In cycostationary two types of detectors are impemented they are spectra correation density function (SCD) and magnitude squared coherence (MCS). A. Spectra Correation Density Function Spectra correation is the way to extract the periodic features of the primary user signa. These signas undergo cycostationarity processes that are periodic in time t. They aso possess a periodic autocorreation function. 14 IJSETR. A rights reserved.

2 When a function is cycic autocorreation then a signa exhibits second- order periodicity. is not for some nonzero frequency α is caed cycic frequency. Fourier transform of cycic autocorreation function is caed Spectra Correation Density (SCD) function. is the cross spectra density of shifted frequency signas[1]. FFT Accumuation method for estimating the SCD: In SCD impementation of FFT accumuation method of estimation is idea of time smoothing using a Fourier transform as shown in Fig.1. The compex demoduates and M.SAI SINDHURI, S.SRI GOWRI (1) () estimated by means of a siding N point FFT., foowed by down shift in frequency to baseband. The vaue of K is chosen as it aows the good compromise between efficiency and minimizing cycic eakage and aiasing. Impementation of FAM bock diagram [1]. defined as. uv f is estimated and obtained by observing the finite interva, and used for signa detection. C. System Mode and Probem CR was first proposed and impemented on TV broadcast service with vestigia side band moduated signa. A strong piot tone signa in the power spectra density is appied in TV transmission. From this spectrum sensing probem is tested under H and H 1.Where Where f is the carrier frequency.θ is the initia phase of the carrier frequency. Signa S (t) is modeed as with f m being with frequency the piot tone in the TV signa and being anaog waveform. Wi be dropped and it effects the incuded in P S which aso modes the transmitted power, path oss, and fading. More over probem anayticay tractabe and mode is simiar to use one existing. In this two effect are not captured they are interference and frequency-seective fading. Whie interference adversey affects the ED and the MFD, Its effect on the cycostationary based detector woud be minima. The effect of frequency-seective fading is ignored [1]. III. STATISTICAL CHARATERISTICS OF CYCLOSTATIONARY DETECTORS A. Statistica characterization of SCD SCD in cycostationary detector is estimated by using FFT Accumuation method is (5) Fig.1. Bock diagram of FFT Accumuation Method. B. Magnitude Squared Coherence The spectra coherence is a statistic that can be used to examine the two signas or data sets. The coherence (sometimes caed as magnitude squared coherence) between two signas is rea vaued functions. Spectra Auto coherence of x (t) at cycic frequency α and spectrum frequency f is defined as [3] The difference SCD and SC is the normaized measure of cross- correation between shifted versions of frequencies. By the definition of SC is identicay zero for a α if and ony if x(t) doesn t contain second order periodicity. Since and and are the power spectra densities of u(t) and v(t). is the power spectra density. Magnitude Squared is (3) (4) (6) Are sampes overapped between adjacent segments is the discrete frequency corresponding to the frequency f. By using centra imit theorem the distribution of is given under H and H 1 CN (, ) is circuar symmetric compex Gaussian noise with mean and variance [1]. The power spectra density evauated at discrete frequency k and k. The decision rue of SCD detector is α S x n, k H 1 τ SCD N' N < H (7) (8) (9) Internationa Journa of Scientific Engineering and Technoogy Research Voume.3, IssueNo.39, November-14, Pages:

3 Performance Comparison of Cyco-stationary Detectors with Matched Fiter and Energy Detector foows Rayeigh distribution under H and under H 1, Rician. Then the corresponding probabiity of fase L-1 p γ L, γ = = L γ (13) aarm and probabiity detection is given by The above function can be derived from density function [16]. Probabiity of fase aarm is, (14) (1) Where Q 1 (a,b) is the Marcum Q function of a and b[4][1].probabiity of fase aarm can be obtained by using genera Gaussian distribution function under mean. B. Statistica characterization of is the second detector in cycostationary based detector. Magnitude squared coherence is nothing but the spectra coherence that examine the signas or datasets.statistica distribution of estimates, severa works have discussed (eg.,[5][6]).in this resuts are appied to derive probabiity of fase aarm and probabiity of detection. is cassified in two they are segmentation without overapping and overapped segmentation. C. Segmentation without Overapping In this and denotes N-ength compex sequences are segmented to L disjoint symbos and, =1,.L, each M=N/L.,, where F is FFT operation and k is the discrete frequency. Then spectra densities are estimated as L L S v k = U k, Svk = v k, =1 =1 L * Suv k = U k V k =1 (11) From this S uv k is estimated. γ uv (k) = S ks u vk For decision rue is given under H 1 and H. H : k 1 UV H : otherwise The cumuative distribution function of conditioned on L and true, from [5], is given as F 1 is the hyper geometric function [4]. The probabiity distribution of H is given by when (1) under Probabiity detection with the threshod from (8) is Internationa Journa of Scientific Engineering and Technoogy Research Voume.3, IssueNo.39, November-14, Pages: is obtained (15) D. Overapped Segmentation In case of overapped segmentation omitted here, it is anayzed using the first deveoped too in [7]. To find the effective number of degrees of freedom in decision statics under H 1 performance with overapped segmentation is discussed in resuts. IV. PERFORMANCE OF ENERGY DETECTOR AND MATCHED FILTER DETECTOR A. Energy Detector Energy detection is the most common way of spectrum sensing because of its ow computationa and impementation compexities. It is a more generic method as the receivers do not need any knowedge on the primary user s signa. The signa is detected by comparing the output of the energy detector with a threshod which depends on the noise foor. Important chaenges in energy detector: Seection of the threshod for detecting the primary users. Inabiity to differentiate from interference from primary users and noise and poor performance under ow signa-to-noise ratio vaes. Probabiity detection and probabiity of fase aarm are the important factors for energy detector based detection which gives the information of the avaiabiity of the spectrum. The decision statistic of the energy detector is given by L-1 Τ ED Δ X = σ W (16) X denotes the FFT output of th M-ength segment. Τ ED is distributed with L degree of freedom under H and non-centraity parameter is under H 1.Probabiity of fase aarm with the threshod is given as P (a,x) is the ower incompete gamma function. Probabiity of detection is given as Is the centra (17) (18) cumuative distribution function of x with v degree of freedom and positive non-centraity parameter δ.

4 PSNR Pmd Pmd M.SAI SINDHURI, S.SRI GOWRI B. Matched Fiter Detector VII. RESULTS AND DISCUSSIONS It is a inear fiter which maximizes the signa to noise 1 ratio. The main advantage of this fiter is that it requires ess time to achieve high gain because of the coherence. Comparison of ED, MFD and detector with noise uncertainty of ±1dB and PFA =.5 Decision statistic of MFD is given by 1-1 (19) 1 - is the deterministic signa of interest. Under () with energy Where probabiity detection and fase aarm detection is given by (1) (), (3) Q(.) is Gaussian compementary distribution function. V. NOISE UNCERTAINTY A the three detectors considered in this paper require the knowedge of the noise variance (under H ) set to the threshod. In this noise uncertainty mode actua noise power is bounded in the interva for some. Worst case fase aarm occurs when. Worst-case detection occurs when. The detection threshod is set corresponding to worst-case of probabiity of fase aarm and probabiity of detection is evauated with the noise variance. VI. PSNR CALCULATION Peak Signa to Noise Ratio is the maximum possibe power of signa and the power of corrupting noise. For improving the performance of detectors we impemented PSNR cacuation. PSNR is mosty easiy defined via the mean squared error (MSE).The mean squared error (MSE) of an estimator measure the average of the squares of errors that is the difference between the estimator and what is estimated. The MSE is the second moment (about the origin) of the error, and thus incorporates both the variance of the estimator and is bias. MAX I is higher and better, Acceptabe vaues for wireess transmission quaity oss are considered to be about db to 5dB Cacuation of PSNR: For three detectors PSNR is cacuated using formua in simuation (4) MFD 1-3 ED no noise uncertainity (75% overap) ED with noise uncertainty MFD(1 sampe sync error) MFD (1.5 sampe sync error) Nomina SNR(db) Fig.. Comparison of ED, MFD and detector with noise uncertainty of ±1dB and P FA = Miss detection probabiity Vs SNR, detector.pfa=.1 a b c 1 - d e f g 1-3 h i j k SNR Fig.3. Miss detection probabiity Vs SNR, for detector P FA =.1. 1 PSNR for three detectors SCD Matched Fiter detector Energy detector No.Of Iterations Fig.4 PSNR performance comparison of various detectors. Resuts are present by using MATLAB simuation.fig. is obtained by considering some specifications in [1] and comparison of ED, MFD and detector with noise uncertainty of ±1dB and P FA =.5.From the figure whie the detector is unaffected. The performance degradation of synchronization error aso iustrated. Fig.3 is obtained Internationa Journa of Scientific Engineering and Technoogy Research Voume.3, IssueNo.39, November-14, Pages:

5 Performance Comparison of Cyco-stationary Detectors with Matched Fiter and Energy Detector for tweve data sets from working group abeed a through (a, b, c, d..).averaged over a the data sets the detector achieves the significant performance improvement at P FA =.1. Fig.4 PSNR for three detectors is cacuated for each detector and potted. Whereas cycostationary detector is the combination of two detectors that is magnitude squared coherence () and spectra correation density function. Cycostationary detector with exhibits better performance. VIII. CONCLUSION This paper presents the probem of detecting a primary transmitter s signa corrupted by additive white Gaussian noise. Probabiity of fase aarm and probabiity detection for SCD,, Energy detector and matched fiter is determined. Comparison is done for ED with MFD and, SCD detector in which we found that is efficient with the noise rejection abiity. We have potted the curves Miss detection probabiity Verses SNR we found some miss detection probabiity. We cacuated PSNR for various detectors and found that cycostationary detector using is more efficient. IX. REFERENCES [1]. Deepa Bhargavi and Chandra R.Murthy, Performance Comparison of Energy, Matched-fiter and Cycostationarity- Based Spectrum Sensing IEEE Conference. Page June 1. []. R.Thandra and A.Sahai, SNR was for signa detection, IEEE J. of Se. Topics in Sig. proc., vo., no.1, pp.4-17, Feb.8. [3]. W.A. Gardner, Expoitation of spectra redundancy in cycostationarysignas, IEEESig.proc. Magazine, pp.14-35, Apr [4]. I. S. Gradshteyn and I. M. Ryzhik, Tabe of Integras, Series and Products, 5 th ed. Press, [5]. G. C. Carter, C. H. Knapp, and A. H. Nutta, Estimation of the magnitude-squared coherence function via overapped fast Fouriertransform processing, IEEE Trans. On Audio and Eectro acoustics, vo.au-1, no.4, pp , Aug [6]. H. Gish and D. Cochran, Invariance of the magnitudesquared coherence estimate with respect to second-channe statistics, IEEE Trans on Acoustics,Speech and Sig.Proc., vo.assp-35, no.1, pp , Dec [7]. R. Lugannani, Distribution of the sampe magnitude squared coherence obtained using overapped Fouriertransforms, Proc of the IEEE ICASSP, vo.6, pp apr Internationa Journa of Scientific Engineering and Technoogy Research Voume.3, IssueNo.39, November-14, Pages: