SDR Forum Technical Conference 2007

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1 USE OF WAVELET TECHNIQUES IN SPECTRUM HOLES DETECTION IN OPPORTUNISTIC RADIO Shyamale Thlakawardana and Klaus Moessner Moble Communcatons Research Group, CCSR, Unversty of Surrey, Guldford, UK Emal: Correspondng Author: ABSTRACT: Opportunstc Rado (OR) systems make use of the avalablty of spectrum holes n the prmary systems. In OR spectrum hole avalablty needs to be dentfed through spectrum sensng procedures. Apart from the sensng of the spectrum, OR must be capable of detectng the prmary system and move out of the spectrum once the prmary system requres the spectrum usage. Therefore spectrum sensng and detecton needs to be performed effcently for the successful deployment of an OR system. One way of dentfyng the spectrum holes avalablty s dentfyng power spectral densty (PSD) and ther power levels wthn a selected porton of the spectrum. The selected spectrum can be dvded nto multple numbers of spectrum sub bands and power level of each sub band can de determned from the shape of the PSD of the selected spectrum. Accordng to the PSD levels spectrum sub bands can be categorzed as nto black, grey or whte spaces correspondng to hgh, medum and low PSD levels. Whte spaces are usually consdered as spectrum holes that can be pcked by the OR system for opportunstc spectrum usage. In the case of Opportunstc Rado spectrum sensng s n the nterest of spectrum dentfcaton than the detaled spectrum shape over the entre wdeband or the selected porton of the spectrum. The entre wdeband can be consdered as a tran of consecutve frequency sub bands, where the power spectral characterstcs s smooth wthn each sub band but exhbts a dscontnuous change between adjacent sub bands. Such changes are rregulartes n PSD, whch carry key nformaton on the locatons and ntenstes of spectrum holes. Therefore the detecton of the edges of the spectrum sub bands determnes the number of avalable spectrum sub bands. The PSD level n each sub band clarfes the black, grey and whte areas of the spectrum sub bands. Ths dentfes the amount of spectrum holes wthn the spectrum wde band of nterest. In ths work Contnuous Wavelet Transform (CWT) technques are used for the detecton of the sub band edges. The Contnuous Wavelet Transform (CWT) s a two-parameter expanson of a sgnal n terms of a partcular wavelet bass functon. Wavelets have scale aspects and tme aspects. To clarfy them somewhat arbtrarly, scale aspect can be presented as an dea around the noton of local regularty where as tme aspects can be presented as a lst of domans. In ths work PSD sgnal dscontnuty has been detected usng dfferent knd of wavelets. It s mportant to select the approprate wavelet and ts scale when dentfyng dscontnuty of a sgnal. The results are based on a selecton of Gaussan wavelets bass functon at varyng scales. 1. WAVELET TRANSFORM The wavelet theory s based on analyzng sgnals to ther components by usng a set of bass functons [1]. The orgnal wavelet functon, known as mother wavelet functon s used to generate all the bass functons. A very essental characterstc of the wavelet functons s that they are related to each other by smple scalng and translaton. It s mportant to create a mother functon whch provdes an effcent and useful descrpton of the sgnal of nterest. It s not easy to do so, but based on several general characterstcs of the wavelet functons t s possble to determne the most sutable wavelet for a specfc applcaton. A wavelet s a small wave wth fnte energy whch s concentrated n tme or space. The mportant ssue s how to dvde the sgnal nto many parts and then analyze the parts separately. To overcome the sgnal-cuttng problem wavelet analyss uses fully scalable modulated wndow. Ths wndow s shfted along the sgnal of nterest and the spectrum s calculated for every poston. Ths process s repeated many tmes wth a smaller or bgger SDR Forum Techncal Conference 007 Proceedng of the SDR 07 Techncal Conference and Product Exposton. Copyrght 007 SDR Forum. All Rghts Reserved

2 wndow and the end result s a collecton of tme-frequency representaton of the sgnal, all wth dfferent resolutons. Instead of usual tmefrequency representaton wavelet transforms generates tme-scale representaton. Fgure 1. Wavelet transform [] In other words wavelet transform s the breakng of a sgnal nto shfted and scaled versons of the orgnal sgnal. Ths provdes the ablty to perform local analyss, to analyze a localzed area of a larger sgnal. Ths paper nvestgates the use of Contnuous Wavelet Transform (CWT) technques for the detecton of the sub band edges n a wde spectrum band of concern. The focus s on the dentfcaton of the frequency locatons of the non-overlappng spectrum sub bands of a PSD sgnal. Each PSD sgnal s analyzed usng large number of dfferent wavelets to dentfy the best possble wavelets for sub band dentfcaton.. WIDEBAND SPECTRUM HOLE DETECTION IN OR The objectve n OR s to dentfy the spectrum hole n the wde band of spectrum concern. Dependng on the spectrum usage wthn each sub band spectrum holes can be assgned for OR communcaton. Therefore the objectve n OR s to dentfy the frequency locatons of non overlappng spectrum sub bands and categorze them nto whte areas correspondng to the power spectral densty (PSD) level beng low. Whte spaces are usually consdered as spectrum holes that can be pcked by the OR user for opportunstc use. Evdently n OR spectrum sensng s n the nterest of spectrum dentfcaton than the detaled spectrum shape over the entre wdeband. The entre wdeband can be consdered as a tran of consecutve frequency sub bands, where the power spectral characterstcs s smooth wthn each sub band but exhbts a dscontnuous change between adjacent sub bands [Fgure ]. Such changes are rregulartes n PSD, whch carry key nformaton on the locatons and ntenstes of spectrum holes. In [4] suggested the use of wavelet transforms as powerful mathematcal tool for analyzng sngulartes and rregular structures, whch can characterze the local regulartes of sgnals. The sgnal spectrum over a wde frequency band can be decomposed nto elementary buldng blocks of sub bands that are well characterzed by local rregulartes n frequency. In lterature [3] proposed a method of wavelet transforms to detect and estmate the local spectrum rregular structure. Local spectrum rregulartes present mportant nformaton on the frequency locatons and power spectral denstes (PSD) of the sub band. In [3] use of 1 st and nd order dervatves of the wavelet transforms of the PSD are used to dentfy local maxma and thus locatng the frequency boundares of each sub band. Compared to [3] work our approach s based on use of wavelet transforms technque on detecton of edges of the PSD and thus locatng the frequency boundares of each sub band. In our approach we drectly use the CWT for edge detecton of the bandwdth rregulartes for the detecton of spectrum holes. Apart from ths the use of the most sutable wavelet famles needs to be nvestgated aganst each sgnal of concern. The Contnuous Wavelet Transform (CWT) s a two-parameter expanson of a sgnal n terms of a partcular wavelet bass functon. Let the functon f s (x) whch s the wavelet bass functon denotes the dlaton of f(x) by the scale factor s, 1 x (1 ) f s ( x) = f s s For dyadc scales, s takng the values from powers of (.e., s =, where = 1,,,I; where I s the hghest nteger selected) and lettng * denotes the convoluton, the contnuous wavelet transform (CWT) of a functon ψ(x) s defned by Wψ ( s, x) = ψ * fs( x) ( ) The total avalable B Hz bandwdth for a wdeband wreless network can be dvded nto N spectrum sub-bands denotng n the frequency range [f 1 to f n ]. Suppose the spectrum sub-bands le wthn [f 1 to f n ] consecutvely wth ther frequency boundares located at f 1 <f < <f n. The PSD structure of such a wdeband sgnal s llustrated n [Fgure ]. SDR Forum Techncal Conference 007 Proceedng of the SDR 07 Techncal Conference and Product Exposton. Copyrght 007 SDR Forum. All Rghts Reserved

3 regulartes PSD Fgure. PSD of N spectrum sub-bands. Based on [3] the PSD of the observed sgnal y(t) by an OR recever can be wrtten as, N (3 ) S ( f ) = α S ( f ) + S ( f ) y f1 f f3 fx-1 fc,x fx fn = 1 Where α denotes the sgnal power densty of wthn the n th spectrum sub-band and the addtve nose comp onent wth PSD S w ( f ). In ths case the PSD n each spectrum sub-band BBx s assumed as smooth and almost flat, exhbtng dscontnutes from ts neghbourng sub-bands x-1 B and BBx+1. Therefore r n PSD appear at the edges of the N sub-bands. Ths result n wdeband spectrum sensng can be seen as an edge detecton problem of a sgnal presented by the PSD S y (f) as n (3 ). Edges n the sgnal dentfy the locaton of frequency dscontnutes whch dentfes each sub-band. Use of wavelet transform can effectvely characterze these dscontnutes presented n the sngular structure of the PSD. Once the OR user receves the PSD of the above format (3 ) wthn a known wde spectrum of bandwdth B, the objectve s to fnd the number of spectrum sub-bands (N), ther edge frequences (f 1 to f n ) and the value of α for = 1 to N. Once the boundares of the sub-bands are found the estmated value of PSD n each subband determnes the avalablty of whte, black or grey spectrum spaces dependng on low, hgh and medum sgnal power densty wthn each spectrum band. w 3. EDGE DETECTION USING WAVELET TRANSFORMS The frst step n dentfyng spectrum holes s to determne the edge frequency of each sub band. CWT s consdered as a very strong canddate for dentfyng edge detecton n contnuous sgnals. Bx f In our approach the boundares or edge frequences of each spectrum sub bands are dentfed by applyng wavelet transforms to the orgnal sgnal. In the resultng wavelet t ransforms the frequency edges are presented as sudden sharp ncrease or decrease of the ampltude representaton n y axs. Therefore the locaton of these sharp changes n the wavelet transform dentfes the dscontnutes n the PSD. Selected wavelets wth varyng scalng factors can be used to detect the dscontnutes of the PSD accurately. 3.1 Contnuous Wavelet Transform (CWT) The contnuous wavelet transform (CWT) s an alternatve approach to the short tme Fourer transforms (STFT) and t was developed n order to overcome the resoluton problem. The wavelet analyss s done n a smlar way to the STFT. More specfc the sgnal s multpled wth a functon (the wavelet) and the transform s computed separately for dfferent segments of the tme-doman sgnal. The man dfference between the CWT and the STFT s that the wdth of the wndow s changed as the transform s computed for every sngle spectral component, whch s probably the most sgnfcant characterstc of the wavelet transform [6]. The CWT can be defned by the followng formula: ψ ψ 1 t τ CWTx ( τ, s) = Ψx ( τ, s) = x( t) ψ * dt (4) s s Where (τ, s) are translaton and scale parameters respectvely. ψ(t) s the transformng functon and also called the mother wavelet. Accordng to (4), the transformed sgnal s a functon of the varables τ and s. Also we can observe that n CWT there s no frequency (f) parameter, nstead there s a scale parameter (s), whch s defned as (1/f). 3. Computaton of CWT Ths secton explans (4), whch defnes the CWT. Let x(t) denote the sgnal that we want to analyze. Frst of all we need to choose the mother wavelet, whch wll act as a prototype for all the wndows n the processes. All the wndows that are used are dlated and shfted versons of the mother wavelet. There are many wavelet famles such as Gaussan, Morlet, Daubeches, Mexcan hat, whch are dlated and shfted versons of the mother wavelet. As soon as the mother wavelet s chosen the computaton starts wth s=1 and the CWT s computed for the values of s, smaller and larger SDR Forum Techncal Conference 007 Proceedng of the SDR 07 Techncal Conference and Product Exposton. Copyrght 007 SDR Forum. All Rghts Reserved

4 than 1. Usually the startng value of s s 1 (for convenence), but ths s not necessary. Then the procedure contnues for ncreasng values of s,.e. the analyss starts from hgh frequences and then proceeds to low frequences. The frst value of s corresponds to the most compressed wavelet and as the values of s are ncreased, the wavelet wll be dlated. Accordng to [3] the PSD ( α for = 1 to N) of each spectrum sub-band can be deduced from a smple estmator as below. α = β N 0 / (for =1 to n) (4 ) f n 1 where β = S y ( f ) df fn fn 1 f n 1 The nose PSD N 0 / s the mnmum nose of all the sub-bands and can be measured offlne or n an empty sub-band. Therefore the estmated nose s the smallest possble value of β. Therefore for an OR recever whch receves a sgnal of the shape PSD wthn a known wde band of spectrum wth the use of CWT t can be deduced the number of spectrum sub-bands (N), the bound ares of each sub-band (f, for =1 to n) and the PSD of each spectrum sub-band ( α, for =1 to n). Ths can be used to detect the avalablty of spectrum holes n each spectrum sub-band dependng on the PSD levels of n each power categorzng nto hgh, medum and low or black, grey or whte spectrum spaces. 4. CWT WAVELET ANALYSIS RESULTS AND DISCUSSION The MATLAB Wavelet transform toolbox s used to evaluate wavelet transform functons of dfferent PSD varatons. In general t s possble to determne whch wavelet s more sutable for a gven applcaton. CWT wavelets used ntally are the Gaussan wavelets. Gaussan wavelets are obtaned from dervatves of the Gaussan functon. The followng secton ntroduces dfferent sgnals nvestgatng the use of wavelet transforms for spectrum sub band edge detecton. These sgnals have the same bandwdth (00MHz) but they dffer n the shape of the PSD. More specfc they dffer n the number of sub bands, the number of the spectrum holes and the frequency range. Our goal s to nvestgate sgnals wth dfferent characterstcs n order to have better and more accurate results. The characterstcs of each sgnal are descrbed n the followng subsecton. Fgure (3a) Observed Sgnal PSD Fgure (3b) Wavelet transform of the sgnal Gaussan Wavelet at scale = 1 Fgure (3c) Wavelet transform of the sgnal Gaussan Wavelet at scale = 100 [Fgure 3a], [Fgure 3b] and [Fgure 3c] present the results based on spectrum holes detecton based on wavelet transform technque. The SDR Forum Techncal Conference 007 Proceedng of the SDR 07 Techncal Conference and Product Exposton. Copyrght 007 SDR Forum. All Rghts Reserved

5 consdered wde band for spectrum hole dentfcaton s n the range of [50, 50] MHz. the followng presents the PSD S y(f) observed by the opportunstc rado (OR).user. The nose floor of the PSD s consdered as S w (f) = 150. Durng the observed burst of transmssons there are a total of N = 8 sub bands {BBx} wth 8 frequency boundares at { f n} n= 0 = [50, 70, 100, 10, 130, 135, 150, 00, 50]. Among these bands a, c and e have relatvely hgh sgnal PSD at levels 100, 150 and 50 respectvely, whle d and g has low sgnal PSD at a level of 50 and 40, all wth reference S w (f) = 150. The rest three bands b, f and h are not occuped and thus spectrum holes. Gaussan wavelets wth two dfferent scales are used to for edge detecton of PSD. As the scale factor ncreases (from 1 to 100) the wavelet transforms becomes smoother wthn each frequency band thus clearly dentfyng the edges n the PSD. The spectral densty estmaton scheme proposed n equaton (4) s used to estmate nose and the sgnal PSD levels. The estmated values are 8 { α } = 0 = [98.86, 1.43, , 54.46, 18, 6.74, 39.07, 0] correspondng to a true sgnal PSD values of [100, 0, 150, 50, 00, 0, 40, 0] respectvely and the estmated nose floor s correspondng to the true nose floor of 150. In the second example a wdeband of nterest n the range of [0,00] MHz s consdered. The PSD S r ( f ) that s observed by a CR s llustrated n [Fgure 4] wth the nose floor at S w ( f ) =00. Durng the transmssons there are 6 bands (N=6) wth frequency boundares at { f } 6 n = [ ] MHz. n= 0 The bands B 1, B 3 and B 5 have relatvely hgh sgnal PSD at levels 4 30 and 36, whle B 6 has low sgnal PSD at a level of 3, all wth reference to S w ( f ) =00. The sub bands B and B 4 can be consdered as spectrum holes. As can be seen n the [Fgure 5], [Fgure 6] and [Fgure 7] the wavelet transform of the sgnal wth respect to dfferent wavelet famles are nvestgated. It s evdent n all Haar, Daubeches and Borthogonal wavelet famles the wavelet coeffcents lnes, clearly dentfes the edges n the PSD detectng the sub band edges. Therefore these wavelet famles can be effectvely used for capturng the edges thus resultng n dentfcaton of spectrum holes n OR. For comparson purposes the same values (-60, 60) were used for the y axs, n order to able to compare the effects of the dfferent wavelets to the sgnal. After nvestgatng under varyng wavelet famles n the MATLAB wavelet toolbox the best wavelets correspond to those that can gve us a very accurate llustraton of the edges at the begnnng and at the end of the bands, and the worst to those that we can hardly understand where the dfferent sub bands are. Fgure 4 Observed PSD sgnal nd Example Fgure 5 Haar Wavelet at scale 1 Fgure 6 Daubeches wavelet at scale 1 SDR Forum Techncal Conference 007 Proceedng of the SDR 07 Techncal Conference and Product Exposton. Copyrght 007 SDR Forum. All Rghts Reserved

6 Fgure 7 Borthogonal at scale 1 (Reconstraucton factor = 1, Decomposton factor = 3) Accordng to (4) the estmated nose and the sgnal PSD values are as follows; { a ˆ n } = [4.17, 0, 9.7,0, 35.3, 3.4], whch corresponds to the true PSD values [4, 0, 30, 0, 36, 3] respectvely, of the orgnal sgnal and Sˆ w ( f ) = correspondng to the true nose PSD value 00 of the orgnal sgnal. [ Fgure 5] to [Fgure 7] captures the edges of the non-overlappng spectrum bands of consdered PSD sgnal. The edges of the spectrum sub bands ha ve been clearly dentfed and have been estmated the PSD levels of each one of them. The next step s to categorze these sub bands accordng to ther PSD levels. As t was mentoned above PSD sgnal PSD has 6 sub bands, whose estmated PSD levels are [4.17, 0, 9.7, 0, 35.3, 3.4] respectvely. Therefore bands and 4 are characterzed as gray or whte spaces due to ther low PSD levels, whle bands 1, 3, and 5 are characterzed as black spaces due to ther hgh PSD levels. Band 6 has medum PSD level, so s characterzed as gray space. 5. CONCLUSIONS AND FURTHERWORK OR networks are developed n order to solve current wreless network problems whch result from the lmted avalable spectrum and the neffcency n the spectrum usage by explotng the exstng wreless spectrum n an opportunstc manner. OR networks, usng the capabltes of the cogntve rado, wll provde an ultmate communcaton paradgm n wreless communcatons, whch s spectrum-aware. The cogntve spectrum dentfcaton task s formulated as an edge detecton problem. In ths work the wavelet edge detecton approach s consdered for sub band dentfcaton of wdeband channels. A soluton based on the coeffcents lnes of the contnuous wavelet transform s derved and tested for dfferent sgnals. The proposed scheme s able to scan over a wde bandwdth n order to dentfy smultaneously all the pecewse smooth sub bands, wthout any pror knowledge of the number of the sub bands, wthn the frequency range of our nterest. Ths study dentfes wavelet transforms as a strong canddate for the detecton of the non overlappng sub band edges. Manly Haar, Daubeches and Borthogonal wavelet famles are capable of detectng these frequency transtons and thus detectng edges. These wavelet famles have been desgned by researchers, n the past, for many dfferent applcatons. Therefore n order to have better results t would be a challengng task to desgn more specfc wavelet famles sutable for spectrum holes detecton n OR envronment. These wavelets need to be based on the characterstcs of the sgnal PSDs that needs to be nvestgated and analyzed. ACKNOWLEDGEMENT Ths work s supported by the 6 th European Framework Programme, wth the contract number: IST and name ORACLE, whch stands for Opportunstc RAdo Communcatons n unlcensed Envronments, for further nformaton vst org. REFERENCES [1] Al M, Spre Lab, UWM, Wavelet characterstcs, What Wavelet Should I Use, October 1999 WHITE PAPER. [] MATLAB Wavelet Toolbox 006 [3] Z. Tan and G. B. Gannaks, ``A Wavelet Approach to Wdeband Spectrum Sensng for Cogntve Rados,'' CROWN Com 006, Greece. [4] S. Mallat, W. Hwang, Sngularty detecton & processng wth wavelets, IEEE Trans. [5] J. Mtolla III, Cogntve rado for flexble moble multmeda communcaton, IEEE DySPAn, November 005. [6] R. Polkar, The Wavelet Tutoral, Ttutoral.html SDR Forum Techncal Conference 007 Proceedng of the SDR 07 Techncal Conference and Product Exposton. Copyrght 007 SDR Forum. All Rghts Reserved