WIDEBAND SPECTRUM SENSING FOR COGNITIVE RADIO

Transcription

1 WIDEBAD SPECTRU SESIG FOR COGITIVE RADIO José Viira, Ana aria Tomé and Danil alafaia Univrsidad d Aviro / IEETA Dpartamnto d Elctrónica, Tlcomunicaçõs Informática Aviro, Portugal ABSTRACT In this work w propos a widband spctrum snsing systm basd on hybrid filtr banks Th polyphas implmntation of th digital countrpart of th filtr bank can b modifid to includ a paralllizd vrsion of discrt Fourir transform algorithm FFT) avoiding this way any sampling rat xpandrs In this work w show how to incorporat th FFT block in th structur in ordr to stimat th widband frquncy contnts of th signal Th proposd structur is particularly suitabl for FPGA basd implmntations Indx Trms Hybrid Filtr Banks, FFT, Spctrum Snsing 1 ITRODUCTIO Spctrum Snsing is on of th ky faturs that a Cognitiv Radio CR) must hav In th original concpt prsntd by itola in his highly citd works [1, 2], th CR must b awar of th spctrum availability in ordr to find usag opportunitis and xploit thm to transmit This concpt has gaind spcial attntion during th last yars du to th incrasing dmand for wirlss communications and th lack of fr spctrum to accommodat nw srvics Traditionally, th spctrum has bn allocatd in a rigid way and as svral studis hav shown, most of it is not occupid vn in urban aras [3] On way to solv this problm of spctrum scarcity is to us raltim databass whr usrs can trad spctrum Anothr possibility is to prform spctrum snsing in ral-tim sarching for spctrum hols opportunitis for transmission With this stratgy, th ownrs of th spctrum transmit whnvr thy wish whil scondary scondary usrs transmit whn th channl is fr Th scondary usrs must prform th spctrum snsing in ral-tim in ordr to avoid collision, or at last to minimiz it to accptabl lvls of intrfrnc Svral mthods hav bn proposd to prform spctrum snsing and dal with th problm of th low powr of th rcivd signals quit difficult to dtct in th prsnc of background nois Th proposd mthods gos from basic nrgy This Rsarch Unit is fundd by ational Funds through FCT - Foundation for Scinc and Tchnology, in th contxt of th projct PEst-OE/EEI/UI0127/2014 and also by th FCT projct EXCL/EEI- TEL/0067/2012 dtctors using bandpass filtrs to cyclostationary signal analysis taking advantag of som prior information rgarding transmittd signals [4] Howvr, most of th proposd mthods assum th spctrum is organizd in fixd channls with rlativ narrow bandwith Howvr this stratgy is not usful for a ral-tim widband spctrum snsing as it is cas of th cognitiv radio concpt Som authors rcogniz this problm and proposd compltly nw approachs basd on th Comprssd Snsing concpt such as th analog-to-information convrtr proposd by Tropp t al [5] and th modulatd widband convrtr proposd in [6] Howvr, thos mthods ar only fficint if th spctrum is charactrizd by a fixd lvl of sparsity If th sparsity lvl it is not known a priori, thos mthods can fail orovr, with th xpctd spctrum occupancy by cognitiv radios, th sparsity lvl is xpctd to turn unknown In this papr w propos a diffrnt approach using a Hybrid Filtr Bank HFB) front-nd whr th input RF signal is splittd in diffrnt band-pass channls bfor bing sub-sampld [7] Thn, a digital synthsis filtr bank will prform th signal rconstruction by cancling th amplitud and phas distortion and th aliasing trms introducd by th sub-sampling If th synthsis filtr bank is implmntd using an fficint polyphas structur, w gt at th output signals with a sampling frquncy tims lowr than th yquist frquncy This format is quit convnint to implmnt paralll algorithms for spctrum stimation as w will show in this work This paralllizd structur is wll adaptd to b implmntd in FPGA making possibl to prform ral-tim spctrum stimation for RF signals with a larg bandwidth This charactristic is quit important for Cognitiv Radios to sns th spctrum and find opportunitis in ral-tim This work is organizd as follows, in th nxt sction w will prsnt th HFBs and th rlatd thory and th main rsults On sction 3 w will prsnt th spctrum snsing problm for widband signals W will nd this sction with our mthod that uss a HFB and a paralllizd FFT basd structur Finally w hav th conclusions 2 HYBRID FILTER BAKS Hybrid Filtr Banks ar a kind of multichannl sampling whr th analog input signal is filtrd by a bank of analog

2 filtrs, in our cas, bandpass filtrs In [8] Papoulis hav shown that this multichannl sampling, whr th input signal xt) is filtrd by filtrs H k jω) is quivalnt to th traditional sampling if th dtrminant of a squar matrix dpndnt of th filtrs frquncy rspons and th aliass componnts is diffrnt from zro for all th frquncis Ω radians pr scond) In th Fig 1 w can s th proposd structur whr th filtrs F k z) ar th digital synthsis filtrs From th systm architctur of Fig 1, w can writ xt) H0j ) H1j ) H-1j ) x0t) x1t) x-1t) Ts v0n) v1n) v-1n) y0n) y1n) y-1n) F0z) F1z) F-1z) Fig 1 Gnralizd structur of th Hybrid Filtr Bank th Fourir transform of th output signal X jω) = 1 T s m=0 + p= H m j ω T s j 2πp T s X j ω j 2πp T s T s ) ) F m jω ), with ω th angular frquncy in radians Without loss of gnrality w can assum that th input signal xt) is low-pass with bandwidth B < f s /2, and so w can dfin H m jω ) as th priodic xtnsions of th analog filtrs H m jω) This way w can dfin an all digital quivalnt filtr bank whr th output signal can b writtn as X jω) = 1 X jω 2π p)) T s p=0 m=0 ^ xn) 1) H m jω 2π p)) F m jω ) 2) W can transform th prvious quation on a systm of quations by sampling th quation in th frquncy domain in Q points and gtting f = H Q A) + B, 3) whr H Q is a Q Q matrix function of th analog filtrs, A is a Q L matrix with th discrt Fourir transform trms, B is th dsird frquncy rspons of th systm givn by B jωq) = T s [ jω qd, 0,, 0 ] T, 4) and f is an array with th L cofficints of ach digital synthsis filtr [9] 21 HFB Dsign If th numbr Q of frquncy sampling points is larg, th systm of quations 3 is difficult to solv and som suboptimal algorithms can b usd [10] If th signal xt) has a spars support in th frquncy domain, it is possibl to xploit this to rlax th filtrs F z) by allowing amplitud distortion and aliasing for th frquncis whr th signal xt) is zro or irrlvant In [11] th authors usd a wighting function to improv th rconstruction rsults of th HFB and in [7] th author usd th Papoulis-Grchbrg algorithm to obtain similar rsults 211 Snsitivity to th analog filtrs variation Whn using th mthods basd on a priori masurmnt of th analog filtrs, w nd a prfct charactrization of th frquncy rspons of th analog filtrs in ordr to dsign a digital synthsis filtr bank that can prfctly compnsat th amplitud and phas distortion whil prform th canclation of th aliasing trms du to th subsampling Howvr, as shown in [10] if th frquncy rspons of th filtrs ar masurd off-lin, thn, whn th filtrs ar connctd to th final acquisition systm, th conditions chang and this difrnc can compromis th rconstruction rsults of th signal ˆxn) rsulting in a limitd ffctiv numbr of bits EOB) for th rconstructd digital signal To solv this problm, svral authors [12 14] proposd an adaptiv digital synthsis filtr bank, but all of thm assum that a tim intrlavd vrsions of th signal ˆxn) is availabl to act as th dsird signal, which in ral implmntations can b difficult to obtain Othr authors also proposd som blind tchniqus [15,16] to avoid th gnration of th dsird signal and propos adaptiv tchniqus that only us th output signal from th synthsis filtr bank 212 Jittr snsitivity In a HFB with svral filtrs covring a larg bandwidth, for th filtrs with th highst cntral frquncy, two problms aris, i) th highr quality factor ndd for this filtrs and ii) th highr subsampling ratio ndd maks th sampl and hold opration mor snsitiv th clock jittr In [10] th authors proposd a HFB with two stags that can solv this two problms Howvr th proposd solution is mor complx and nds som furthr dvlopmnts and study 22 Efficint Implmntation of HFB Th structur of th Fig 1 is not fficint bcaus th intrpolators introduc zros into th squncs and simultanously

3 chang th sampling rat by a factor Firstly, th sampling rat xpandrs by a factor bfor th digital filtrs F k z) would b a wast of rsourcs It is wll known that a polyphas structur will b prfrabl Th main advantag of this structur, as w can s in th Fig 2, is that th intrpolators wr movd to th output of th filtr bank Considr th polyphas dcomposition of th m th synthsis filtr F m z) = l=0 z l) R lm z ) 5) xt) H 0j ) H 1j ) H -1j ) x 0t) x 1t) x -1t) Ts v 0n) v 1n) v-1n) Rz) x 0n) x 1n) x-1n) z -1 z -1 ^ xn) that can b writtn in matrix form as [F 0 [ z) F z)] = z ) z 2) 1 ] R 0,0 z ) R 0, z ) R 1,0 z ) R 1, z ) R,0 z ) R, z ) 6) whr w hav now a matrix Rz ) with th 2 polyphas filtrs F m z) This structur is mor fficint but combining all th diffrnt phass x m n) to obtain th signal ˆxn) can b an insuprabl task vn for th high-nd FPGAs Suppos, for xampl, that w hav a systm with = 8 s working at a sampling rat of 100sps Thn, th sampling rat for th signal ˆxn) would b 800sps, which is far abov th maximum that currnt FPGA tchnology can achiv Th main ida and propos of this papr is to show that it is possibl to dirctly us th polyphas signals x i in th algorithms of th rcivr such as spctrum snsing In this work w show that is possibl to avoid th gnration of th signal ˆxn) if th rcption algorithms ar modifid to us dirctly th signals x i n) Doing this, w hav a paralll procssing structur that uss th phass of th signal ˆx from th hybrid filtr bank, making possibl to implmnt this kind of SDR using a FPGA orovr, w will show in th nxt sction how w can modify th FFT algorithm to gt a spctrum analyzr for spctrum snsing with wid bandwidth and a high dynamic rang at th sam tim 3 SPECTRU SESIG WITH HFB On of th ky faturs for a cognitiv radio is th ability to sns th spctrum in ordr to find spctrum hols Howvr, this task must b prformd in ral-tim as th transmission opportunitis can b tmporary Th spctrum analysis must also b prformd for a wid bandwidth In practic, ths two conditions ar difficult to mt Th traditional way to prform spctrum snsing for a larg portion of th spctrum is basd on a htrodyn radio, scanning th spctrum on slic at a tim This tchniqu can not b considrd a ral-tim snsing of th spctrum On of th most promising spctrum snsing tchniqus is th multitapr mthod with Fig 2 Gnralizd structur of th Hybrid Filtr Bank nrgy dtctors at ach frquncy output This mthod dos not nd any a priori information about th input signal and du to this can b considrd as an agnostic spctrum snsing tchniqu In [4] th authors show that similar rsults can b achivd with a proprly dsignd filtr bank To implmnt a filtr bank with a high computational fficincy, w nd an fficint implmntation of a FFT In th nxt sction w will s how to tak advantag of th paralll architctur of th HFB to implmnt a paralll vrsion of th FFT that can fulfill th goals of a ral-tim spctrum snsing for cognitiv radios 31 Widband Spctrum Snsing with HFB From th Fig 2 w can s that th last stag of th polyphas implmntation of th SFB is nothing mor than a to 1 tim multiplxr If w want to prform spctrum snsing of th signal ˆxn) using th spctrogram with nrgy dtction at ach output, th first stp is a srial to paralll opration that is quivalnt to a 1 to dmultiplxr Howvr this structur is not wll suitd for a FPGA implmntation In [17] th author prsnts a dcimatd in frquncy FFT algorithm, whr a -point FFT is dcomposd in 4 /4-point FFTs followd by a 4-points FFT This dcomposition allows th implmntation of a largr FFT with a paralllizd architctur whil taking advantag of th xisting FPGA FFT blocks Howvr, in our cas w nd a diffrnt vrsion of th algorithm whr th input signals ar a polyphas dcomposition of ˆxn) Considr th following dfinition of th discrt Fourir transform DFT) Xk) = 1 xn)w nk 7) with W = j 2π W can dcompos th signal xn) in its phass and th DFT can b writtn as a function of this signals Xk) = / xn + a)w n+a)k, 8)

4 and if w dfin th polyphas signals x a n) = xn + a) with a [0, 1,, 1], thn w can writ Xk) = / x a n)w n+a)k 9) x[n] x[n+1] x[n+2] x[n+-1] /-point FFT /-point FFT /-point FFT /-point FFT -point DFT X[k] X[k+/] X[k+2/] X[k+-1)/] Howvr, w want to transform th -point DFT in / - point DFTs To achiv this w can split th Fourir transform vctor in parts as follows Xl + b/) = / x a n)w n+a)l+b/) 10) whr k = l + b/ with l [0, 1,, / 1] and b [0, 1,, 1] Thn w can simplify to W n+a)l+b/) 11) W nl) / W al) W ab/) 12) whr w hav usd ths two proprtis, W Zl W Zln 10) to with = W ln /Z Xl + b/) = = 1 and with Z an intgr Thn w can simplify X a l) = / X a l)w al W ab/, 13) x a n)w nl /, 14) whr w hav usd th proprty W ab/ = W ab Applying th following chang of variabl X a l) = X a l)w al w can writ 13) as Xl + b/) = X a l)w ab, 15) which can b intrprtd as th -point DFT of th signal X a l) Th prvious quation can b rprsntd graphically as shown in th Fig 3 As w can s, w hav a paralllizd structur that uss /-point FFTs making this structur mor suitabl for a FPGA implmntation Th main rstriction for this kind of implmntation would b th numbr of rsourcs availabl and not th spd of th sampling rat to rprsnt th signals 4 IPLEETATIO RESULTS In this sction w will provid som prliminary rsults of th advantags of th proposd paralllisd structur W will considr two scnarios whit th sam numbr of channls = 8, on whr w considr a FFT with bins Fig 3 Dcomposition of th -point FFT in a paralllizd vrsion and anothr on with 8 FFTs with 4096 bins followd by th procssing showd in th Figur 3 Using Xilinx dsign suit w implmntd th FFT with th LogiCORE IP FFT v80 and w gt th rsults prsntd in Tabl 1 Both FFTs ar Tabl 1 FPGA FFT Rsourcs Siz Latncy ax Frq DSPs mory bins µs Hz 18k BRAS Piplind Straming I/O typ, using 16 bits arithmtic with scald output To th rsults obtaind with th 4096 bins FFT w hav to considr th matriz multiplication which will us 32 DSP slics of th FPGA to prform th 8 8 complx multiplications at a maximum rat of 440 Hz Comparing both implmntations w can s that our paralllisd vrsion nds mor DSPs slics and mmory but prsnts a lowr latncy and can work at highr clock frquncy orovr, for widr bandwidth systms th proposd architctur scals mor asily 5 COCLUSIOS Radio frquncy front-nds basd on hybrid filtr banks ar good candidats for cognitiv radios Thy allow th acquisition and procssing of wid-band signals without using high spd s orovr, th analog filtr bank with svral band-pass filtrs isolat th s from out of band strong nois and allows diffrnt gains for diffrnt bands improving that way th dynamic rang of th whol HFB With th proposd architctur in this work to prform frquncy analysis, w can build a spctrum snsing systm for cognitiv radio with a high bandwidth working in ral-tim This can b usd to find spctrum opportunitis in ral-tim for a wid band spctrum REFERECES [1] J itola and G Q aguir, Cognitiv radio: making softwar radios mor prsonal, I Prsonal Communications, vol 6, no 4, pp 13 18, 1999

5 [2] Josph itola III, Cognitiv Radio An Intgratd Agnt Architctur for Softwar Dfind Radio, Phd, Royal Institut of Tchnology, 2000 [3] Patrick S Ryan, Som Tsts of Spctrum Usag in Brussls, Blgium, Tch Rp, Univrsity of Colorado at Bouldr, 2004 [4] Erik Axll, Grt Lus, Erik Larsson, and H Poor, Spctrum Snsing for Cognitiv Radio : Stat-of-th- Art and Rcnt Advancs, IEEE Signal Procssing agazin, vol 29, no 3, pp , ay 2012 [5] Jol A Tropp, Jason Laska, arco F Duart, Justin K Rombrg, and Richard G Baraniuk, Byond yquist: Efficint Sampling of Spars Bandlimitd Signals, IEEE Transactions on Information Thory, vol 56, no 1, pp , 2010 [6] ishali and YC Eldar, Blind ultiband Signal Rconstruction: Comprssd Snsing for Analog Signals, IEEE Transactions on Signal Procssing, vol 57, no 3, pp , ar 2009 [7] José Pdro agalhãs, Tófilo ontiro, José Viira, Robrto Gómz-Garcia, and uno B Carvalho, Papoulis-Grchbrg Hybrid Filtr Bank Rcivr for Cognitiv-/Softwar Dfind Radio Systms, in IS- CAS2013, Bijing, China, 2013 [8] A Papoulis, Gnralizd sampling xpansion, IEEE Transactions on Circuits and Systms, vol 24, no 11, pp , ov 1977 [9] Davud Asmani, Jacqus Oksman, and Pirr Duhaml, Subband Architctur for Hybrid Filtr Bank {A/D} Convrtrs, IEEE Journal on Slctd Topics in Signal Procssing, vol 2, no 2, pp , 2008 [10] José P agalhãs, José Viira, Robrto Gómz- Garcia, and uno Borgs Carvalho, Bio-Inspird Hybrid Filtr Bank for Sotwar-Dfind Radio Rcivrs, IEEE Transactions on icrowav Thory and Tchniqus, vol 61, no 4, pp , 2013 [11] T Ptrscu, J Oksman, and P Duhaml, Synthsis of hybrid filtr banks by global frquncy domain last squar solving, in IEEE Intrnational Symposium on Circuits and Systms, ISCAS, Kob, Japan, 2005, IEEE, vol 6, pp [12] P Satarzadh, BC Lvy, and PJ Hurst, Adaptiv Smiblind Calibration of Bandwidth ismatch for Two-Channl Tim-Intrlavd s, IEEE Transactions on Circuits and Systms I: Rgular Paprs, vol 56, no 9, pp , Spt 2009 [13] L Fng and W amgoong, An adaptiv maximally dcimatd channlizd UWB rcivr with cyclic prfix, in IEEE Intrnational Confrnc on Communications, 2005 ICC , vol 3, pp , IEEE [14] Zhiguo Song, Carolin Llandais-Prrault, Danil Poulton, and Philipp Bnabs, Adaptiv qualization for calibration of subband hybrid filtr banks A/D convrtrs, in 2009 Europan Confrnc on Circuit Thory and Dsign Aug 2009, pp 45 48, IEEE [15] Davud Asmani, Jacqus Oksman, and Danil Poulton, Digital Estimation of Analog Imprfctions Using Blind Equalization, in 14th Europan Signal Procssing Confrnc, Flornc, Italy, 2006 [16] Damián Edgardo arlli, Kaushik ahata, and inyu Fu, Hybrid Filtrbank s With Blind Filtrbank Estimation, IEEE Transactions on Circuits and Systms I: Rgular Paprs, vol 58, no 10, pp , Oct 2011 [17] Josph Palmr and Brnt lson, A paralll FFT architctur for FPGAs, Fild Programmabl Logic and Application, vol 3203, pp , 2004 [18] Xilinx, LogiCor IP - Fast Fourir Transform v80, 2012