Self-Interference Cancellation in Full-Duplex Radio Transceivers with Oscillator Phase Noise

Transcription

1 Self-Ierferece Cacellaio i Full-Duplex Radio Trasceivers wih Oscillaor Phase Noise Ville Syrjälä ad Koji Yamamoo Graduae School of Iformaics Kyoo Uiversiy Yoshida-homachi Sakyo-ku Kyoo-shi Kyoo Japa ville.syrjala@u.fi Absrac This paper addresses he problem of phase-oise esimaio ad miigaio i full-duplex radio rasceivers. I has bee show before ha he phase-oise is oe of he mos criical facors limiig he self-ierferece suppressio performace i full-duplex radio rasceivers. I his paper a algorihm is proposed for he phase-oise esimaio ad miigaio. The algorihm has high esimaio qualiy ad low compuaioal complexiy ad i does o require sychroizaio of he useful ad self-ierferece sigals so i is applicable also i log-rage commuicaios. The performace of he algorihm is he evaluaed ad compared o he performace of he sae-of-hear algorihm wih exesive compuer simulaios. Idex Terms Full-duplex radio oscillaor phase oise self ierferece digial sigal processig esimaio miigaio. O I. INTRODUCTION NE of he emergig echologies i he area of wireless commuicaios egieerig is so-called full-duplex radio echology. The idea is very old ad simple: o simulaeously rasmi ad receive radio sigals a he same frequecies wih a sigle rasceiver. Because of he very powerful self-ierferece (SI) sigal due o he powerful rasmied ow sigal a he aea of he receiver fullduplex echology has o bee cosidered feasible uil recely [1] [2] [3]. However he sigal processig echologies of oday have allowed he miigaio of he effecs of he self-ierferece o accepable levels i laboraory codiios [1] [2] [3]. Phase oise is a criical limiig facor i he SI cacellaio i full-duplex rasceivers uilizig orhogoal frequecydivisio muliplexig (OFDM) [4] [5]. Phase-oise miigaio has bee cosidered i full-duplex radios already i [6] where hey give a modified versio of he phase-oise miigaio algorihm preseed for coveioal direc-coversio radios i [7]. They cosidered a case wih separae oscillaors i he Maiscrip submied o 22d of Jauary The work was suppored i par by he Japa Sociey for he Promoio of Sciece (JSPS) uder he Posdocoral Fellowship program ad KAKENHI Gra umber Emil Aaloe Foudaio he Fiish Fudig Agecy for Techology ad Iovaio (i projec Full-Duplex Cogiive Radio ) ad he Academy of Filad (i projec I-Bad Full-Duplex MIMO Trasmissio: A Breakhrough o High-Speed Low-Laecy Mobile Neworks ). I addiio o Kyoo Uiversiy V. Syrjälä is also affiliaed wih he Deparme of Elecroics ad Commuicaios Egieerig Tampere Uiversiy of Techology P.O. Box Tampere Filad. rasmier ad receiver. This is o he bes possible soluio i small devices because usig a shared oscillaor as proposed i [4] gives huge beefis as i iherely miigaes he par of he phase oise effec [4]. However i seups where rasmier ad receiver are forced o be far away from each oher he case of separae oscillaors is sill ieresig. I such a case usig a shared oscillaor bewee he rasmier ad receiver migh be urealisic. I order o clarify he capabiliy of separae oscillaors i his paper we propose ad evaluae aoher phase-oise miigaio scheme ha i erms of performace ad compuaioal complexiy surpasses he exisig algorihm. Oher coribuios of his paper are as follows. Ulike he exisig algorihm i [6] he algorihm is geerally applicable o maer if he OFDM symbols of he SI sigal ad received useful sigal a he receiver are sychroized or o. Furhermore he whole process of phase-oise miigaio is explaied horoughly akig io accou he aalog ad digial self-ierferece cacellaio blocks. The performace of he phase-oise miigaio is also sudied wih exesive performace simulaios cosiderig differe levels of phase oise ad chael esimaio qualiy as well as differe chael codiios. Oher rasceiver impairmes such as amplifier o-lieariy [8] IQ imbalace [9] samplig jier [10] [11] ad quaizaio [8] are o discussed i his paper. This paper is srucured as follows. The Secio II iroduces used full-duplex rasceiver model. Secio III he gives he used sigal model ha is used for he algorihm developme. I Secio IV he proposed phase-oise esimaio ad miigaio algorihm is derived ad is performace alog wih a descripio of he used simulaor is give i Secio V. The work is cocluded i Secio VI. II. USED FULL-DUPLEX TRANSCEIVER MODEL The used full-duplex rasceiver model is depiced i Fig. 1. The model is simplified so ha he o-liear amplificaio ad filerig sages are lef ou ad he effec of he phase oise ca be aalysed separaely. I he full-duplex rasceiver model a direc coversio rasmier ad receiver are used so ha hey ierac wih each oher i order o miigae he SI. As depiced i Fig. 1 sarig from he rasmier ipu he OFDM samples o be rasmied are firs covered o a aalog sigal waveform. The he aalog sigal waveform is upcovered o he radio

2 s () Splier x () DAC x TX Mulipah Chael s () Tuable Aeuaio ad Delay j () c e e j () c r DLC Tapped Delay Lie r () y () ADC y u RX Fig. 1. Illusraio of he used full-duplex radio rasceiver model icludig rasmier (TX) receiver (RX) aalog liear cacellaio () ad digial liear cacellaio (DLC). Double ad sigle lies deoe complex ad real sigals respecively. frequecies (RF) wih a mixer fed by a oisy oscillaor. The RF sigal is he separaed o a sigal o be rasmied ad o a sigal o be used i aalog liear cacellaio () of he SI. The uable aeuaio ad delay compoe ries o mimic he mai mulipah compoe of he rasmissio chael of he SI sigal. Whe he cacellaio sigal is subraced a he receiver i effecively removes mos of he SI sigal from he mai mulipah compoe of he chael. Afer he he received sigal is dowcovered wih a mixer fed by a oisy oscillaor followed by a coversio o digial samples. Digial liear cacellaio (DLC) is he applied o he sigal. This is doe by feedig samples a he rasmier hrough a apped delay lie ha ries o mimic he mulipah chael wih ake io accou i he mai mulipah compoe. I he overall lik aurally also he received useful sigal afer is ravel hrough a mulipah chael is prese as well as addiive whie Gaussia oise afer he receiver ipu. These are icluded i he sigal model i he ex secio. III. TRANSCEIVER SIGNAL MODEL WITH PHASE NOISE I his secio he sigal model used for he phase-oise esimaio algorihm developme is described i deail. Please oe ha all he approximaios are fially verified wih he simulaios where o approximaios are used. Whe aalog sigal x () buil from OFDM sigal samples x is upcovered wih a oisy oscillaor havig phase oise process () he resulig sigal ca be wrie as () () j c s e x () (1) where c is he agular cere frequecy. The afer he sigal goes hrough a mulipah SI chael wih impulse respose h () i ca be wrie as () () () j c r si h e x(). (2) Here deoes he covoluio operaor. This sigal is he received SI sigal. I he receiver ipu his sigal is summed wih he received useful sigal ruseful () which icludes he mulipah chael effecs ad all he disorio he sigal experieced prior leavig he rasmier. I addiio o he received useful sigal he addiive whie Gaussia oise () is modelled o he sigal a his sage. Now he is carried ou meaig ha he received oal sigal ca be wrie as r() r () rˆ () r () (). (3) si si useful Here rˆ si() is he o-be-rasmied sigal s () fed hrough he uable aeuaio ad delay eleme. Whe his sigal is subraced from he received sigal i oly miigaes he firs mulipah compoe of he self-ierferece sigal. I herefore affecs he chael h () so ha he mai mulipah compoe of he remaiig chael is differe. This effecive chael (he effecs of he acual chael ad he combied) is here deoed by h (). I pracice he firs mulipah compoe of h () compared o h () has experieced sigifica aeuaio ad small phase roaio from delay esimaio error depedig o qualiy of. Now by usig h () (3) ca be rewrie as jc() r () h () e x () ruseful () () (4) jc() e h () x() ruseful () () The approximaio from he firs form o he secod form i (4) is relaively accurae because he phase-oise process is very arrowbad process whereas he SI-chael coherece badwidh is relaively high. This approximaio is oly used i he algorihm developme. Afer he he sigal is dowcovered usig a oisy oscillaor wih phase-oise process r (). Afer his sage he sigal ca be wrie as jcr() y () e jc() e h () x() ruseful () () (5) j() r() e h () x() yuseful () () where is used as a muliplicaio sig for emphasis yuseful () is he useful sigal a basebad wih all he RF impairmes icludig he phase oise icluded ad () is he whie Gaussia oise wih he same variace as (). Now whe he sigal i (5) is covered o he digial domai he sampled versio of i ca be wrie as j r y e h x y useful. (6)

3 Here h is he digialized chael impulse respose wih T s ( T s is he samplig ierval) so he remaiig chael effec i he digial domai is modelled usig he widely used Bello s wide-sese saioary ucorrelaed scaerig (WSSUS) model [12]. Therefore : h are idepede of each oher. Also i (6) ( Ts) y useful yuseful ( Ts ) ad ad r are he sampled rasmier ad receiver phase oise processes respecively. A his poi he DLC is applied which wihou he use of ay iformaio abou he phase oise resuls io he form u ˆ y h x j r (7) e h ˆ x y useful h x. Here h ˆ is he chael impulse-respose esimae wih ake io accou. I he followig secio he phaseoise esimaio ad miigaio is proposed based o hese sigal models. Noe ha all he approximaios i his secio are prove o be reasoable wih he exesive simulaios where o such approximaios are used. IV. PHASE-NOISE ESTIMATION AND MITIGATION This secio describes he proposed phase-oise esimaio ad miigaio algorihm. Also he complexiy of he algorihm is shorly discussed ad compared o ha of he exisig algorihm. The basic idea for he proposed phaseoise esimaio algorihm comes from he algorihms preseed i [13] ad [14] for coveioal direc coversio receiver. A. Phase-Noise Esimaio The proposed phase-oise esimaio is based o he sampled sigal i (6) a he receiver. The mehod is simple ad does o require OFDM symbol level sychroizaio i he IFFT operaio because he esimaio is doe prior o he IFFT. The sampled sigal i (6) ca be rewrie as j r y h e x m. (8) where m y useful is he oise i he esimaio process icludig he addiive oise ad he useful sigal. I he receiver prior DLC SI power is sill a much higher level ha he power of he useful sigal is. Therefore he useful sigal ca be coceived as oise from he phase-oise esimaio poi of view. The addiive whie Gaussia oise o he oher had does o have a pracical effec o he esimaio of he phase oise because he sigal-o-oise raio for he useful sigal is ypically order of 10 o 20 db makig he useful sigal he domiaig coribuor of he oise i he esimaio process. Now we ca simply feed he kow samples x from he rasmier hrough a apped delay lie cosisig of he esimaed chael impulse-respose samples h ˆ (akig io accou he effec o he effecive chael.) Afer his he sigal y is sample-by-sample muliplied wih he complex cojugae of he oupu sigal of he apped delay lie resulig i he followig form c ˆ y h x j r e h ˆ x m h x j 2 r e hˆ x e x m ˆ h x where superscrip deoes complex cojugaig ad e is he esimaio error i he elemes of h ˆ. This sigal is very oisy esimae of he phase-oise complex-expoeial where he esimaed samples are weighed wih he received power of he correspodig sample amely heir reliabiliy. This is acually very desirable because i emphasizes he more reliable samples. Now because we kow ha he phase-oise complex-expoeial process is a seep low-pass process we ca filer he samples i (9) wih a selecive low-pass filer whose ampliude respose resembles he oe-sided ampliude specrum of he phase-oise complex-expoeial. However he shape of he ampliude respose is o very sric ad a simple digial lowpass filer desiged wih he well-kow Remez algorihm works also. The filerig removes mos of he oise from he esimae. The improved phase-oise complex-expoeial esimae ca herefore be wrie as LPF c a e j r. (10) Here LPF x is he low-pass filered versio of a sample sream x ad a is he o-uiy ampliude i he phaseoise esimaes. The oher erms of (9) ac as esimaio error ad are herefore lef ou from (10) for clariy. The fial phase-oise esimae is aaied ow by akig he agle of (10). We lose he iformaio of he o-uiy ampliude i his process which is desirable. The fial phase-oise esimae ca herefore be wrie as o r (9) ˆ agle LPF c (11) x akes he a agle of a complex sample x. The resulig phase-oise esimae is o by ay meas perfec bu he performace simulaios will demosrae is accuracy. Where agle B. Phase-Noise Miigaio Afer he above phase-oise esimaio is carried ou he phase-oise miigaio is doe o he received sigal afer samplig y simulaeously wih DLC. Wih he phase-oise miigaio he sigal i (7) ca be isead wrie as jˆ o u ˆ ye h x j ˆ r j o e h x e hˆ x y y. useful useful (12) This is he sigal wih DLC doe wih he kowledge of he phase oise. As deoed i (12) his approximaely gives he useful sigal samples whose qualiy depeds o he qualiy of he chael esimaes ad phase-oise esimaes.

4 C. Complexiy of he algorihm The proposed algorihm provides compuaioally efficie soluio for phase oise esimaio ad miigaio. I he algorihm he complexiy is dicaed by he complexiy of he low-pass filer. There are very efficie ways o impleme a fiie impulse-respose filer. Therefore implemeig order L filer resuls i aroud oal of 3 L real arihmeic operaios per sample. I his algorihm he esimaio qualiy ca be corolled by he filer order. I low-oise cases eve very low order filer (order 10) ca provide very good resuls as is showed i he simulaios secios. I he previously proposed algorihm i [6] he complexiy comes from he fac ha i requires a separae fas Fourier rasform for he phase-oise esimaio if he useful sigal ad he self-ierferece sigal are o sychroized i OFDM-level which hey are o i geeral. For example i 1024 subcarrier case his resuls io aroud oal of 35 real arihmeic operaios per sample. Furhermore he required marix muliplicaios ad iversio adds he oal o aroud 50 whe esimaig 10 frequecy compoes of he phaseoise. Whe he amou of frequecy compoes is icreased he algorihm ges more ad more complex. For example for esimaio of 50 frequecy compoes oe eeds aroud 250 arihmeic operaios per sample. I he phase-oise miigaio par he proposed imedomai algorihm requires sigle complex muliplicaio per sample whereas he algorihm of [6] requires covolvig he useful sigal wih he sigal whose legh is he same as he amou of esimaed phase-oise specral compoes. Overall he proposed algorihm herefore gives relaively compuaioally efficie soluio o he phase oise esimaio problem. The complexiy ca be furher reduced by esimaig oly a par of he samples of he phase oise process ad applyig ierpolaio o he esimaed samples aferwards. This is a viable soluio ad does o resul io sigifica icrease i he esimaio error because he esimaed phase oise is ayway relaively smooh process i ime-domai sice i is low-pass filered. V. SIMULATOR AND ANALYSIS This secio describes shorly he used simulaor ad gives exesive performace aalysis of he performace of he proposed phase-oise esimaio ad miigaio algorihm. A. Used Simulaor The simulaor is buil as follows. The modulaed useful ad SI sigals are geeraed. They are boh OFDM sigals wih 1024 subcarriers whose 300 subcarriers o boh sides of he cere subcarrier carry 16QAM subcarrier modulaed daa ad he oher subcarriers are zero-subcarriers. The used samplig frequecy is MHz. The cyclic prefix legh was seleced o be 256. This seup resembles he LTE-dowlik sigal wih 10-MHz chael-badwidh ad exeded cyclic prefix. This selecio for sigal was made for he pracical coecio i offers. The he rasmier oscillaor phase-oise is modelled ad he sigals are se hrough heir respecive chaels. The useful sigal is se hrough a exeded ITU-R Vehicular A mulipah-chael [15]. Also he aeuaio of he sigal is hadled a he same ime (o ge he useful sigal a a desirable level compared o he SI sigal.) The SI sigal o he oher had is se hrough a chael wih power delay profile of 0 db 65 db 70 db ad 75 db for delays ad 4 samples respecively. This chael is similar o oe described for full-duplex relays i [16] bu modified o beer fi for full-duplex radio rasceiver case. Afer he chael aea separaio is modelled for he SI sigal by aeuaig he mai ap of he SI chael. The mulipah compoes are o aeuaed sice hey are reflecios from far away ad cao be corolled very well wih aea separaio. Afer he chael ad aea separaio modellig he is modelled. I is modelled so ha he rasmied sigal is muliplied by he esimae of he mai mulipah compoe of he SI chael. This sigal is he subraced from he received sigal. The chael esimaio error is modelled by addig whie-gaussia-oise o he used chael ap value so ha he se level is achieved. The modellig is followed by receiver phase-oise modellig. Afer he phase-oise i digial domai he DLC is modelled. I he DLC he samples from he rasmier side prior he rasmier phase-oise modellig are fed hrough he esimaed chael aps ad he resulig sigal is subraced from he sigal afer he receiver phase-oise modellig. Here he chael esimaio error is modelled by addig whie- Gaussia-oise o he perfec chael aps so ha desired DLC level is achieved. Whe alkig abou DLC level i is always he level of DLC ha is aaiable if o phase oise is prese a all. Therefore i is he limi for he SI cacellaio se by he chael esimaio qualiy. Wih he phase oise he acual digial cacellaio is less ad depeds o he phase-oise esimaio qualiy. A his poi he sigal ca be used for phase-oise esimaio ad he phase-oise miigaio is doe he like described i previous secio. I he phase-oise esimaio he used filer is a filer desiged wih Remez algorihm wih varyig order. I he desig he sar ad he sop of he passbad are boh 0 (ui is frequecy ormalized o he Nyquis frequecy or half-of-he samplig frequecy) ad he begiig of he sopbad is a 0.04 ad he ed is a 1. These were cocluded o be good values i [13]. The rasmier ad receiver phase oises are boh modelled wih well-kow Browia moio model. B. Performace Aalysis The simulaio resuls are depiced i Fig. 2 Fig. 3 Fig. 4 ad Fig. 5. I hese simulaio rials he aea separaio is always fixed a 30 db ad is always fixed a 30 db. The followig quaiies are varied i he simulaio case basis bu he defaul values (used if o separaely oherwise meioed) are 45 db for DLC 10-Hz 3-dB badwidh for he rasmier ad receiver phase oises 50 for filer order i phase-oise esimaio ad 60 db for chael aeuaio differece. The chael aeuaio differece is a quaiy ha ells how much is he differece of he average power bewee he SI sigal afer aea separaio ad he useful sigal afer he chael. I herefore gives also he effecive

5 oise level i phase-oise esimaio. Because addiive whie- Gaussia-oise level is usually i order of db below he useful sigal level he useful sigal is he mai oise from he phase-oise esimaio poi of view. The addiive oise does o have ay pracical effec o he phase-oise esimaio from he SI sigal. Therefore he addiive whie-gaussiaoise is lef ou from his simulaio aalysis for simpliciy of he preseaio. The give 3-dB badwidh of he phase oise is he 3-dB badwidh used i boh rasmier ad receiver oscillaors. The used parameers are also give i Table I. I he simulaio resuls Perfec Esimaes refers o he referece case whe perfec phase-oise kowledge is used i he phase-oise miigaio. Oly CPE Esimaio o he oher had gives he performace whe oly he commo phase error (CPE) par [13] of he phase oise is esimaed (his correspods o he case wihou phase-oise esimaio because he chael esimaio also iherely esimaes he CPE sice he effec is oly commo roaio for each subcarrier wihi a OFDM symbol.) Referece Alg. refers o he algorihm give i [6] ad refers o he proposed algorihm of his paper. I he simulaio resuls he achieved SI suppressio is always give as a egaive sum of he achieved aalog ad digial cacellaio; herefore he maximum achievable is always he egaive sum of used ad DLC quaiies. I Fig. 2 he achieved SI cacellaio is give as a fucio of he phase-oise 3-dB badwidh. A very low levels of he phase oise boh of he used algorihms perform worse ha he CPE esimaio oly. This is because i hese cases he phase oise level is so low ha he esimaio error of he referece ad proposed algorihms are higher ha he level of phase oise iself. However afer he phase-oise 3-dB badwidh ges over aroud 0.2 Hz he proposed algorihm sars o show clear gai. The gai over he referece algorihm is clear aroud 7 db uil i a very high phaseoise levels (ha are o-realisic for full-duplex radios ayway) ges smaller. Wih reasoable phase oise levels he performace of he proposed algorihm is oly aroud 4 db from he performace wih he perfec phase oise kowledge. I Fig. 3 he achieved SI suppressio is give as a fucio of chael aeuaio differece. This differece gives basically he oise i he phase-oise esimaio process because he useful sigal is he mai oise coribuor. As ca be see he proposed algorihm gives oce agai solid aroud 7 db gai over he referece algorihm uil a very high separaio (low oise levels) he referece algorihm sars o cach up as we ge earer o he performace of he ideal phase-oise kowledge. I high-oise case esimaig oly he CPE gives beer performace because of he highesimaio errors i more advaced algorihms. However oce agai already afer aroud 42 db chael separaio differece he gai give by he proposed algorihm is clear. Chael separaio differeces below 42 db are quie urealisic if he devices are o very ear o each oher. Achieved SI suppressio give as a fucio of digial cacellaio is give i Fig. 4. Here we ca see ha wih low SI Suppressio [db] Phase oise 3 db Badwidh [Hz] Fig. 2. Achieved SI suppressio give as a fucio of he phase-oise 3-dB badwidh. SI Suppressio [db] Perfec Esimaes Oly CPE Esimaio Referece Alg Chael Aeuaio Differece [db] Fig. 3. Achieved SI suppressio give as a fucio of he chael aeuaio differece. SI Suppressio [db] 80 Perfec Esimaes Oly CPE Esimaio Referece Alg. Perfec Esimaes Oly CPE Esimaio Referece Alg Digial Cacellaio [db] Fig. 4. Achieved SI suppressio give as a fucio of he DLC. TABLE I. THE FIXED AND DEFAULT PARAMETERS USED IN THE SIMULATIONS. Quaiy Value Fixed Values Aea Separaio 30 db 30 db Defaul Values DLC 45 db For Varyig Chael Aeuaio Differece 60 db Quaiies Phase-Noise 3-dB Badwidh 10 Hz Filer Order 50

6 SI Suppressio [db] Fig. 5. Achieved SI suppressio give as a fucio of he filer order for four differe values of chael aeuaio differece (differe levels of oise.) SI Suppressio [db] Cha. Diff. = 40 db Cha. Diff. = 50 db Cha. Diff. = 60 db Cha. Diff. = 70 db Filer Order Perfec Esimaes Oly CPE Esimaio Referece Alg Phase oise 3 db Badwidh [Hz] Fig. 6. Achieved SI suppressio give as a fucio of he phase-oise 3-dB badwidh whe here is o OFDM-symbol level sychroizaio bewee he useful ad self-ierferece sigals. DLC he proposed algorihm gives almos he same performace as he oe wih he perfec phase-oise kowledge. The differece however ges higher as he DLC level icreases. The proposed algorihm gives clearly beer overall performace ha he referece echique. The effec of he used filer order o he phase-oise esimaio is sudied i Fig. 5 for differe levels of oise (differe levels of chael aeuaio differece.) As ca be see i he high-oise case he performace ca be improved by icreasig he filer order as i filers ou he oise beer. I very clea evirome however very low-order filer is sufficie. The order 50 filer is jus a example seleced for he oher simulaio cases o because i would be ayhow opimal as ca be see here. I he begiig he proposed algorihm was moivaed also by he fac ha i requires o sychroizaio bewee he rasmier ad he receiver. The simulaio cases prior his have assumed OFDM-symbol level sychroizaio i he commuicaios lik for fairess for he referece echique ha cao hadle he more realisic case wihou he sychroizaio. I Fig. 6 his fairess is igored. The phase oise esimaes give by he referece echique a he edges of he OFDM symbols are copied o exed over he duraio of he cyclic prefix. Whe comparig Fig. 2 ad Fig. 6 oly he referece echique gives differe performace. This is because he proposed algorihm works eve i he cyclic prefix regios of he OFDM symbol ad does o require OFDM-symbol level sychroizaio bewee he useful ad self-ierferece sigals. Now i he o-sychroized case we see how he performace of he referece echique is eve worse ha before compared o he proposed algorihm. The gai give by he proposed algorihm is ow aroud 8-13 db. VI. CONCLUSION Phase oise is oe of he criical facors limiig he selfierferece cacellaio i full-duplex radio rasceivers. I his paper a algorihm for phase-oise esimaio ad miigaio was proposed. The algorihm gives very high esimaio qualiy wih low compuaioal complexiy. I addiio he algorihm is very widely applicable. I ca be used i log-disace o-sychroized commuicaios ulike he exisig algorihms. The performace of he algorihm was compared o he performace of he exisig algorihm ad he performace of he proposed algorihm was cocluded o be far beer ha ha of he exisig algorihm. REFERENCES [1] J. Choi e al. Achievig sigle chael full duplex wireless commuicaio i Proc. MobiCom 10 Chicago IL Sep [2] M. Jai e al. Pracical real-ime full duplex wireless i Proc. MobiCom 11 Las Vegas NV USA Sepember [3] M. Duare ad A. Sabharwal Full-duplex wireless commuicaios usig off-he-shelf radios: Feasibiliy ad firs resuls i Proc. Asilomar Cof. o Sig. Sys. Comp. Pacific Grove CA Nov [4] V. Syrjälä e al. Effec of oscillaor phase oise o self-ierferece cacellaio i full-duplex OFDM radios IEEE Tras. o Wireless Commu [5] A. Sahai G. Pael C. Dick ad A. Sabharwa O he impac of phase oise o acive cacellaio i wireless full-duplex IEEE Tras. o Veh. Techol. vol. 62 o. 9 Ju [6] E. Ahmed A. Elawil ad A. Sabharwal Self-ierferece cacellaio wih phase oise iduced ICI suppressio for full-duplex sysems i Proc. GLOBECOM 13 Alaa GA USA Dec [7] D. Perovic W. Rave ad G. Feweis Effecs of phase oise o OFDM sysems wih ad wihou PLL: Characerizaio ad compesaio IEEE Tras. o Commu. vol. 55 o. 8 Aug [8] D. Korpi e al. Full-duplex rasceiver sysem calculaios: Aalysis of ADC ad lieariy challeges IEEE Tras. o Wireless Commu [9] D. Korpi e al. Widely-liear digial self-ierferece cacellaio i direc-coversio full-duplex rasceivers IEEE JSAC [10] V. Syrjälä ad K. Yamamoo Is samplig jier a problem i fullduplex radio rasceivers or o? i Proc. IEEE VTC 04-Sprig Seoul Korea May [11] V. Syrjälä ad K. Yamamoo Samplig jier i full-duplex radio rasceivers: Esimaio ad Miigaio i Proc. IEEE ICASSP 04 Florece Ialy May [12] P. Bello Characerizaio of radomly ime-varia liear chaels IEEE Tras. o Commu. Sysems vol. 11 o. 4 Dec [13] V. Syrjälä ad M. Valkama Receiver DSP for OFDM sysem impaired by rasmier ad receiver phase oise i Proc. IEEE ICC 11 Kyoo Japa Jue [14] V. Syrjälä ad M. Valkama Ieraive receiver sigal processig for joi miigaio of rasmier ad receiver phase oise i OFDM-based cogiive radio lik i Proc. CROWNCOM 12 Sockholm Swede Ju [15] T. Sorese P. Mogerse ad F. Frederikse Exesio of he ITU chael models for wideabad (OFDM) sysems i Proc. IEEE VTC 05-Fall Dallas TX Sep [16] K. Haeda e al. Measureme of loop-back ierferece chaels for oudoor-o-idoor full duplex radio relays i Proc. EuCAP 10 Barceloa Spai Apr