Analysis of Oscillator Phase-Noise Effects on Self-Interference Cancellation in Full-Duplex OFDM Radio Transceivers

Transcription

1 Revied manucript for IEEE Tranaction on Wirele Communication 1 Analyi of Ocillator hae-oie Effect on Self-Interference Cancellation in Full-Duplex OFDM Radio Tranceiver Ville Syrjälä, Memer, IEEE, Mio Valama, Memer, IEEE, Lauri Anttila, Memer, IEEE, Taneli Riihonen, Student Memer, IEEE and Dani Korpi Atract Thi paper addree the analyi of ocillator phaenoie effect on the elf-interference cancellation capaility of fullduplex direct-converion radio tranceiver. Cloed-form olution are derived for the power of the reidual elf-interference temming from phae noie in two alternative cae of having either independent ocillator or the ame ocillator at the tranmitter and receiver chain of the full-duplex tranceiver. The reult how that phae noie ha a evere effect on elf-interference cancellation in oth of the conidered cae, and that y uing the common ocillator in upconverion and downconverion reult in clearly lower reidual elf-interference level. The reult alo how that it i in general vital to ue high quality ocillator in full-duplex tranceiver, or have ome mean for phae noie etimation and mitigation in order to uppre it effect. One of the main finding i that in practical cenario the ucarrier-wie phae-noie pread of the multipath component of the elf-interference channel caue mot of the reidual phae-noie effect when high amount of elfinterference cancellation i deired. Index Term Full-duplex radio, intercarrier interference, interference cancellation, ocillator phae noie, elf-interference F I. ITRODUCTIO ULL-DULEX radio technology i aed on a fairly old idea of tranmitting and receiving ignal imultaneouly at the ame center-frequency. However, due to maive elfinterference (SI) caued y direct coupling of trong tranmit ignal to the enitive receiver chain, practical implementation of uch radio have not een availale until Manucript received July 1, 013 and revied ovemer 9, 013. Thi wor wa upported in part y the Academy of Finland (under the project In-Band Full-Duplex MIMO Tranmiion: A Breathrough to High- Speed Low-Latency Moile etwor ), the Finnih Funding Agency for Technology and Innovation (Tee, under the project Full-Duplex Cognitive Radio ), the Linz Center of Mechatronic (LCM) in the framewor of the Autrian COMET-K programme, Japan Society for the romotion of Science (JSS) under the otdoctoral Fellowhip program and KAKEHI Grant numer , and Emil Aaltonen Foundation. V. Syrjälä, M. Valama, L. Anttila, and D. Korpi are with the Department of Electronic and Communication Engineering, Tampere Univerity of Technology,.O. Box 69, Tampere, Finland. T. Riihonen i with the Department of Signal roceing and Acoutic, Aalto Univerity School of Electrical Engineering,.O. Box 13000, Aalto, Finland. Correponding author i V. Syrjälä, ville.yrjala@tut.fi. recently [1], [], [3], [4], [5]. Such full-duplex radio technology ha many enefit over the conventional timediviion duplexing (TDD) and frequency-diviion duplexing (FDD) aed communication. When tranmiion and reception happen at the ame time and at the ame frequency, pectral efficiency i oviouly increaing, and can in theory even e douled compared to TDD and FDD, given that the SI prolem can e olved [1]. Furthermore, from wirele networ perpective, the frequency planning get impler, ince only a ingle frequency i needed and i hared etween uplin and downlin. Another poile advantage i that if the device in a wirele networ have full-duplex capaility, they can alo ene the traffic in the networ during their own tranmiion. Thi can lower the amount of needed medium acce and radio lin control ignalling in the networ, therefore improving the maximum throughput of networ, a well a ignificantly lowering the networ delay [3]. Depite of the variou enefit, there are, however, till many practical implementation related iue in uilding commercial mall handheld or portale radio device utilizing full-duplex technology, epecially with low-cot deepumicron integrated circuit technologie. The igget challenge i the elf-interference phenomenon [1], [], [3], [4], temming from the imperfect electromagnetic iolation of the tranmitter and receiver part in the overall tranceiver. Thi iolation can e partially aited y having phyically eparate tranmit and receive antenna, a reported e.g. in [1], [] and [3], which, depending on the center-frequency and phyical eparation, yield typical iolation in the order of 0-40 db or o [1], []. The other central element in elfinterference uppreion i active cancellation, at oth RF/analog and digital part of the receiver chain, uing the tranmit ignal a the reference [1], [], [3], [4], [6], [7]. The mot common analog cancellation approach, lie reported, e.g., in [1], [3], [8] and [9], i aed on utracting the actual tranmit RF waveform, properly aligned in time, amplitude and phae, from the receiver input. Thi reult in fairly low intrumentation complexity, ut can only uppre the dominant SI component while the poile multipath

2 Revied manucript for IEEE Tranaction on Wirele Communication component are then proceed in the digital cancellation phae. A an alternative, ome recent wor [10], [11], [15] have alo reported multipath analog/rf cancellation, which increae the RF intrumentation complexity ut can in principle then uppre the overall SI, including multipath component, more accurately. Yet another, very intereting alternative i to deploy an additional reference tranmitter ranch, from digital aeand up to RF, uch that an accurate RF cancellation ignal can e regenerated. Such wor are reported, e.g., in [] and [5], and can alo upport multipath cancellation already at RF tage. Such tructure doe, however, require the additional tranmit chain, increaing the overall tranceiver complexity. Furthermore, ince a eparate tranmitter chain i ued for the RF cancellation ignal regeneration, uppreing, e.g., the power amplifier nonlinear ditortion occurring in the main tranmit path get potentially more complicated compared to the tructure where the main tranmit path RF ignal i ued a reference [1], [3]. While coniderale progre in antenna development a well a in analog and digital SI cancellation ha een reported in the recent year, the current technology i not yet mature enough, e.g., for full-duplex uer equipment (UE) tranceiver in 3G Long Term Evolution (LTE) networ 1 [16], [17]. Furthermore, when conidering low-cot ma-product commercial device and underlying deep-umicron integrated electronic, all the circuit imperfection related prolem, lie the phae noie iue conidered in thi article, are not even fully recognized yet, a the topic i relatively freh and ha een receiving coniderale reearch interet only over the lat 3-5 year. Exiting wor, uch a [1], [], [3], [5] and [11], can e conidered tate-of-the-art achievement in laoratory cale implementation, ut a hown for example in [18] and [19], all the practical implementation limitation are not yet fully undertood when commercial low-cot integrated electronic are to e ued. In thi article, we addre in detail the ocillator phae-noie phenomenon a one of the performance limiting factor in low-cot full-duplex direct-converion tranceiver. In the exiting literature, phae noie ha een tudied in cae of fullduplex relay in [18], and for general full-duplex tranceiver in [19] and in it very recent extenion [0]. However, the analyi in [19] and [0] i motly limited to narrow-and ignal cenario and a claical mall phae-noie aumption i ued in the analyi. The wor i alo motly temming and motivated through the finding in elected experimental 1 A a concrete example, we conider ower Cla 3 LTE UE with nominal maximum tranmit power of 3 dbm [16]. ow, if the UE antenna eparation i, e.g., 30 db, and analog and digital SI cancellation capailitie are ay 30 db and 50 db, repectively, which repreent fairly optimitic value [3], then the remaining elf-interference power i till around 87 dbm, when referenced ac to the receiver input. Thi i far from the 3G LTE UE receiver reference enitivity level of 110 dbm, which include the thermal noie level, interference margin and receiver noie figure utilizing a ingle reource loc mode [16], [17]. laoratory equipment, which add nice connection to practical oervation ut alo partially limit the general applicaility of the analyi. Moreover, and perhap mot importantly, the main part of the analyi wor in [19] and [0] i focuing on the cenario where the tranmitter and receiver ide have eparate ocillator and thu alo eparate phae noie procee. Thi may e a valid cenario in relay type device, where the receive and tranmit entitie can e located even on different ide of a uilding, and hence have completely eparate receiver and tranmitter hardware. However, in compact full-duplex tranceiver of two-way communication ytem, haring the ame ocillator etween tranmitter and receiver of the device i the realitic cenario, epecially ince the full-duplex device tranmit and receive on a ingle frequency. Thi i alo then the cenario which thi article i motly focuing on, ut for generality and comparion purpoe, we cover oth cae of (i) two independent ocillator and (ii) common hared ocillator. Furthermore, in the analyi of thi paper, no mall phae noie aumption i made which add to the generality of the analyi. Furthermore, no aumption of narrowand ignal i made either, ut we pecifically focu on modern wideand orthogonal frequency diviion multiplexing (OFDM) aed waveform forming the ai of phyical layer of all emerging radio communication ytem. Furthermore, the derivation in thi article do not have any limitation et y any pecific experimental etup. The analyi alo include explicitly the effect of multipath propagation etween the tranmit and receive antenna, which i hown to have ignificant contriution to the overall remaining SI due to phae noie, after realitic analog and digital SI cancellation. Alo, the ucarrier level interference tructure and pectral roadening in the reidual elf-interference, caued y phae noie [1], i explored in detail a the final demodulation and detection of OFDM waveform i done in a ucarrier-wie manner. Hence thi i emphaized alo in the analyi. All the analyi reult are alo verified with extenive computer imulation in variou cae, and the imulation reult are carefully analyed. The ret of thi paper i organized a follow. Section II decrie in detail the full-duplex elf-interference coupling channel etween the tranmitter and receiver part of the tranceiver, including the effect of antenna iolation, multipath propagation, tranmitter and receiver phae noie, and analog and digital SI cancellation. In Section III, temming from the previou modelling, ucarrier-wie power of the SI i analyed in OFDM-aed full-duplex radio at different tage of the receiver path. In Section IV, the derived analytical reult are compared with the imulated one, and the reult are analyed. Finally, Section V conclude the wor. In the Appendix, detail of derivation for the power of the comined frequency-domain phae-noie effect of the tranmitter and receiver phae noie procee are given.

3 Revied manucript for IEEE Tranaction on Wirele Communication 3 t () gain = S gain = A 1 t () Splitter A S xt () A DAC x n TX Multipath Channel t () Tunale Attenuation and Delay ALC j t () t c t e e j t () t c r DLC Tapped Delay Line Bandpa Filter LA rt () yt () Lowpa Filter ADC y n u n RX Fig. 1. rincipal illutration of the tranmitter and receiver analog front-end of direct-converion architecture aed full-duplex tranceiver, including alo tranmitter and receiver phae noie procee. ALC and DLC refer to analog and digital linear cancellation, repectively. II. FULL-DULEX TRASCEIVER RICILE, HASE OISE AD SELF-ITERFERECE In thi ection, the full-duplex tranceiver principle i firt hortly reviewed, epecially from the SI prolem point of view. Then, a fundamental ignal model i given for the reulting SI with tranmitter and receiver ocillator phaenoie procee, including the effect of the multipath channel, antenna iolation, and analog and digital SI cancellation. A. Full-Duplex Tranceiver rinciple A principal illutration of a generic full-duplex tranceiver analog front-end, deploying the direct-converion radio architecture [3], i given in Fig. 1. A the figure illutrate, eparate tranmit and receive antenna are deployed, a, e.g., in [1], [], [3], and hence alo aumed in thi paper. Analog linear cancellation (ALC) i deployed at the very firt tage of the receiver input, to prevent the trong elf-interference aturating the whole receiver chain. The needed attenuation and delay of the ALC depend on the characteritic of the main propagation path lining the tranmitter and receiver antenna, and on the ued tranceiver component. Typical reported antenna iolation and ALC numer are in the order of 0-40 db and db, repectively [1], [], [3]. Lie wa already identified in the Introduction, the ALC principle depicted in Fig. 1 i only one of the many alternative, ut i aumed in thi wor to facilitate low-cot RF circuit implementation. Further uppreion of the SI i then otained y digital linear cancellation (DLC) inide the tranceiver digital front-end. In the DLC, the goal i to etimate the whole SI coupling channel including the multipath component (which are typically ignored in the ALC tage), and then uppre the remaining SI, aed on accurate channel etimate and nown tranmit data ( x n in Fig. 1) [], [3]. Thi i done y feeding the digital ample at the tranmitter efore digital-to-analog converion (DAC) to a tuneale tapped delay line, which i tuned aed on the SIchannel etimate. Thee ample are then utracted, properly ynchronized, from the ignal at the receiver after the analogto-digital converion (ADC). In general, motly linear cancellation olution have een reported o far in the literature for oth ALC and DLC proceing interface, while recently [8], [11], [1], [13], [14], alo nonlinear digital cancellation ha een demontrated. B. Self-Interference Model in Full-Duplex Radio after Analog and Digital Cancellation ow, let u aume that the power amplifier (A) with amplification factor of A i relatively linear, the plitter gain (attenuation) factor i, and let u denote S the complex aeand waveform efore the I/Q upconverion at the tranmitter y xt (). ractical A are typically nonlinear component, ut the aumption of linear A i made here ince the focu i on the phae noie induced effect intead of A. Then, we can write the carriermodulated RF waveform at the tranmitter output a t () () Re xte c t () j t t. A S Here, f i the angular ocillator (carrier) frequency c c and () t i the phae noie of the ocillator of the tranmitter t ide. In the individual formula, time-origin reference i et at the upconverting I/Q mixer interface and the delay in ignal propagation and coupling toward receiver ide, including the multipath component, are referenced to that. Furthermore, for implicity and without lo of generality, mixer are aumed unit-gain component. ext, we aume that the low-noie amplifier (LA) at the receiver ide i relatively linear, and that the total gain and delay etween the ignal plitter at the tranmitter and the ALC cominer element at the receiver, including alo the iolation etween the tranmitter and the receiver antenna (refer to Fig. 1), are and, repectively. Then, the attenuator/delay unit in the ALC proceing hould ideally e tuned o that the total attenuation and delay of the ALC path matche and, repectively. aturally, perfect matching i never poile, o let u denote the realized ALC attenuation and delay y ˆ and ˆ, repectively. Therefore, (1)

4 Revied manucript for IEEE Tranaction on Wirele Communication 4 the remaining SI ignal after ALC proceing in the receiver, including alo the multipath propagation etween the tranmit and receive antenna, can in general e written a L rt () h () t t ( ) ˆ t ( ˆ ) t ( ). B () 1 In the aove, denote convolution, impule repone h () t B model the joint linear filtering effect of the receiver andpa filter and low-noie amplifier, L denote the numer of multipath component etween TX and RX antenna, denote the attenuation of the th multipath component and denote the correponding delay where, a mentioned already earlier, the delay alo model the poile delay effect of the tranmitter and receiver electronic when tranmitter I/Q mixer interface i ued a reference. otice that only the SI ignal i conidered preent in the receiver chain, ecaue the focu in the analyi here i indeed on the SI coupling and cancellation characteritic. Thu, the actual ueful received ignal i omitted for notational convenience. Then, after the I/Q downconverion and lowpa filtering, whoe impule repone i denoted y h () t, the complex L aeand oervation of the SI ignal can e written a j t () t c r yt () h() t rte () L xt ( ) e ˆ xt ( ˆ ) e L 1 j ( t ) ( t) c t r j ˆ ( t ˆ) ( t) c t r j ( t ) ( t) c t r xt ( ) e, where () t i now the ocillator phae noie proce at the r receiver ide. For notational convenience, the repone of the andpa and lowpa filter are aumed ideal, and hence do not appear explicitly in the latter form of (3). otice that for generality, we have denoted the receiver phae noie proce in (3) with different random proce notation, compared to tranmitter ide. Thi later enale u to tudy the two different cenario of (i) independent ocillator where () t t and () t are tatitically independent random procee and r (ii) common hared ocillator where () t () t. r t ext, after ampling the aeand oervation at intant t nt, where T i the ampling interval, and when characterizing the phyical multipath propagation with correponding tapped delay line, we can rewrite (3) a (3) j ( nt ) ( nt ) c t r ( ) ( ) n j ˆ ( nt ˆ) ( nt ) ˆ ( ˆ c t r xnt) e y y nt x nt e j T ( n T ) ( nt ) c t r x( n T ) e. 1 (4) Here, i the maximum delay of the multipath channel in ample and denote the complex coefficient of the th component of the ampled multipath channel model. With utitution zt () xt ( ), we can write (4) then a y y( nt ) z( nt ) e n ˆ znt ( ˆ ) e 1 j ( nt ) ( nt ) c t r j ˆ ( nt ˆ) ( nt ) c t r j T ( n T ) ( nt ) c t r z( n T ) e. ow, with reaonale ALC circuitry, and ˆ can e aumed to e fairly cloe to each other, and auming further that the aeand proceing andwidth i in the range of few ten of MHz, typical to, e.g., moile cellular radio and wirele local area ytem, we can impoe approximation of the form znt ( ˆ ) znt ( ) and ( nt ) ( nt ˆ ). However, in (5), there are alo SI t t term in which and ˆ are eentially multiplied with c which i typically a very high numer (e.g. at 1 GHz). In uch SI term, the mall ALC delay error till ha clear contriution to the overall ignal y. Therefore, we write (5) finally a n y y( nt ) z( nt ) e where n z( n T ) e j ( nt ) ( nt ) c t r j T ( n T ) ( nt ) c t r j T ( n T ) ( nt ) c t r z( n T ) e. (5) (6) jw ˆ c j c e ˆ e e. (7) 0 e Thi model now include the eential effect of the amplitude error ˆ and delay error ˆ in the ALC e e circuitry, phae noie procee of tranmitter and receiver, a well a the multipath propagation etween TX and RX antenna, and i ued in the forthcoming ection for detailed ucarrier-wie SI analyi. Following the notation in Fig. 1, the remaining SI ignal including alo DLC can finally e written a u y h x. (8) n n n, DLC n Here, x are the ample efore tranmitter DAC and h n, i the impule repone of the tapped delay line ued in DLC. ndlc III. SUBCARRIER-WISE SELF-ITERFERECE OWER DUE TO HASE OISE I OFDM FULL-DULEX RADIO In thi ection, the actual ucarrier-wie SI power with phae noie in the full-duplex tranceiver i analyed in cloed form,

5 Revied manucript for IEEE Tranaction on Wirele Communication 5 uing the ignal model derived in the previou ection a the tarting point. The tudy i carried out in two ditinct cae, namely (i) having fully eparate ocillator (thu () t and t () t eing tatitically independent random procee) and r (ii) having a common hared ocillator for TX and RX (thu () t () t ). For oth cae, cloed-form formula for r t ucarrier-wie SI power are derived, and are then ued to, e.g., analye the impact of ALC, multipath propagation and DLC on the reidual SI power. Alo comparion etween the two different ocillator cenario are made. A. Sucarrier-wie Self-Interference ower efore Digital Linear Cancellation A a tarting point, the ampled aeand ignal model for the SI with phae noie, and including ALC, i given in (6). In OFDM ytem, the ignal are dicrete Fourier tranformed (DFT) at the receiver digital front-end for ucarrier level ignal proceing. Therefore, we alo proceed elow with ucarrier-wie ignal model y impoing appropriate locwie DFT operation on the ampled SI ignal. In the following, the amount of ucarrier in a ingle OFDM ymol i denoted y and thi i alo aumed, for implicity, a the DFT ize. Taing now the -ize DFT of ample of y in (6), and auming correct n ynchronization of DFT within cyclic prefix duration, yield Y DFT y : n0,1,, 1 n j 1 / 1 ( ) ( ) c T j t n T r nt j n / Ze e e, 0 n0 where relative ample index n 0 correpond to the firt ample inide a time-domain OFDM ymol. Here, DFT denote the th ample of the DFT of the argument vector, i circular convolution operator and Z i the DFT of znt ( ): n 0,1,,, 1. ext, all the phae noie term can e written with the help of a ingle function n0 (9) 1 1 j ( nt T ) ( nt ) t r j n/ J (, ) e e, (10) where index i the numer of full-ample delay experienced y the tranmitter-induced phae noie. Therefore, we can now rewrite (9) with help of (10) a j T / c Y (, ) Z e J 0 1 j T / c Ze J (, ) l l 0 l0 (11) 1 j j T / c c e Z e J (, ). l l l0 0 Therefore, the power of SI at an aritrary ucarrier at DFT output can e defined a 1 j j T / c c EY E e Z e J (, ). l l l0 0 (1) Here, E denote the tatitical expectation operator. ow with the aumption that : Z are independent of each other, : are independent of each other following the widely ued Bello wide-ene tationary uncorrelated cattering (WSSUS) model [], EZ 0 and E 0, and y denoting E Z and E,, we can rewrite (1) through ome traight-forward manipulation into form 1 j T / E E (, ) c Y e J l l l0 0 1 E J (, ). l, l 0 l0 (13) Cloed-form expreion for E J (, ) are then derived in the Appendix, for oth cae of having independent tranmitter and receiver ocillator and having the ame common ocillator at oth ide. In Appendix, the freerunning ocillator (FRO) model [6] i aumed to implify the analyi. Below, (13) i hown in it final form for oth of the tudied ocillator cae, when the reult of Appendix are deployed. 1) Independent Ocillator Cae: Firt, let u conider the cae where we have independent ocillator at the tranmitter and receiver ide. Then y uing (4) derived in the Appendix, the ucarrier-wie SI power in (13) reduce to the form 1 1 E Y l, 0 l0 1 (14) 4nT ne co ln /. n0 Here, i the 3-dB andwidth of the ued FRO ocillator model. The reult oviouly depend on the phae noie 3-dB andwidth and other eential parameter lie ALC performance, the numer of ucarrier, multipath profile and ucarrier pacing. umerical illutration will e given in Section IV. ) Common Ocillator Cae: In the cae of a common ocillator feeding oth the upconverion and the downconverion, (13) can e, with the help of (5) derived in the Appendix, written a

6 Revied manucript for IEEE Tranaction on Wirele Communication E Y l, 0 l0 4nT ( n) e co ln/ n0 1 4 T 4 ( n) e co ln/. n 1 (15) Again, the expreion i traight-forward depending on the eential ytem parameter and can e eaily evaluated for any aritrary configuration in term of amount of phae noie, coupling propagation and OFDM waveform. B. Sucarrier-wie Self-Interference ower after Digital Linear Cancellation In DLC, the ignal ample at the tranmitter efore DAC are fed to a tuneale tapped delay line or other digital filter that trie to mimic the total SI channel from tranmitter digital front-end to receiver digital front-end. The output ample are then utracted from the ignal at the receiver after ADC. Since all the phae noie impairment tae phyically place efore the DLC, and the reference ignal for the DLC i the pure digital tranmit ignal, phae noie i aically very trouleome in the DLC proce. In general, phae noie ha two-fold effect on OFDM waveform when viewed at ucarrier-level. The firt effect i the o-called commonphae-error (CE) that imply refer to common phae rotation of all ucarrier ignal [3], [4]. otice that in our notation, uch CE can till e included in the effective SI channel, and hence partially mitigated a part of the DLC. How well it i mitigated, depend in general on the performance of DLC, which in turn i directly dependent on the quality of the effective SI channel etimate. Thi will e quantified oon in an explicit manner. The other fundamental impact of phae noie i the o-called intercarrier-interference (ICI) phenomenon [1], [5], [4] which refer to the pread of the ucarrier energy on top of it adjacent ucarrier. In our ignal model in (14) and (15), at a given ucarrier, thi i viile a the term in the inner ummation for all l. Such ucarrier preading in the SI ignal cannot e removed y DLC, or any other linear proceing without ophiticated phae-noie etimation. Thi will thu heavily limit the overall achievale SI uppreion a will e quantified more explicitly elow. In order to quantify the DLC proceing and the reulting SI cancellation performance in detail, we tae next oth the linear channel etimation error a well a the ucarrier preading (ICI) due to phae noie into account. Due to the linear nature of DLC proceing, the aic tructure of ucarrier-level interference power expreion at the output of DLC till follow thoe of (14) and (15), a the ICI i tructurally already included. Due to channel etimation error, even the linear term cannot e, however, uppreed perfectly. Hence, in the power analyi, the joint impact reult into the effective linear channel multipath power, eing replaced with the effective etimation error power, denoted in the following y. Baed on thi, and traightforward manipulation, the ucarrier-wie SI power at the ee DLC output can e now written a and E E 1 1 U l, 0 l0 l 1 4nT ne co ln/ n0 1 4nT ee ne n0 1 1 U l, 0 l0 l 4nT ( n) e co ln/ n0 1 4 T 4 ( n) e co ln/ n T 4 4nT ( ) ee e n e n0 (16), (17) for the cae of independent ocillator and common ocillator, repectively. In thee expreion, the power of the main multipath channel component ha already the,0 antenna eparation and ALC uppreion included in it. Thu the ideal ALC and DLC cae, in our terminology, correpond to 0 and 0. Further inight and detail are given,0 ee in Suection III.C. ext, in order to hortly map the channel etimation error variance to the correponding overall DLC uppreion, a ee imilar approach a in [1], [], [3] i taen. otice that thi mapping i defined for the reference cae of zero phae noie, ince the pectral preading due to phae noie i explicitly already modelled in (16) and (17). Hence, when we want DLC uppreion of d (linear cale amplification/uppreion ( 0d 1) factor) in cae of no phae noie, then the channel etimation error variance for each effective ee channel impule repone tap i ee da, (18) 1 In the aove, a denote ALC uppreion, and it i aumed

7 Revied manucript for IEEE Tranaction on Wirele Communication 7 that the multipath coupling channel ha the main component and other component, and the etimation error variance i aumed identical for all the component for implicity. Here, a in previou literature [1], [], [3], the DLC uppreion d i defined o that it i the extra overall uppreion that DLC offer after ALC ha already een implemented. In the numerical example and illutration in Section IV, for any given ALC and DLC gain, (18) i ued to calculate the channel etimation error variance. otice, again, that in thi terminology, the DLC gain refer to achievale digital SI power uppreion with zero phae, while the impact of phae noie are then explicitly uilt in to (16) and (17) through SI pectral roadening (ICI). C. Further Inight on ALC and Multipath ropagation In the aove derivation, antenna eparation i already taen into account in the definition of in () and the ALC uppreion factor i taen into account in in (7) (o that 0 they do not affect the multipath component). However, it wa till left open what i the exact relationhip etween the amount of antenna eparation c (linear cale amplification/uppreion ( 0 c 1) factor), ALCuppreion factor and the value of 0. Thi i addreed elow. Antenna eparation c i taen into account only in the main multipath component of the channel, ecaue the eparation doe exactly that, namely attenuate the main multipath component, ecaue any reflection coming from further away cannot e eentially attenuated with antenna eparation in mall full-duplex tranceiver. However, uually in the literature [1], [], [3], [4], and thu alo in thi article, the term antenna eparation i ued to denote the iolation of the whole SI ignal with all multipath component included. Therefore, if we aume antenna eparation of c, the uppreion of the main component mut e more than c o that the whole ignal i iolated with the given antenna eparation c when alo multipath component are preent. The ued uppreion factor for the main ignal component i therefore 0 c' c c1, (19), 1 where it i aumed that the main component of the channel ha no attenuation efore the iolation factor c i applied and that the power of the other multipath component,, 1,,, are normalized o that direct lole coupling correpond to unit power. Alo the actual ALC i then modelled y uppreing only the main multipath component of the channel, a already mentioned after (6) and illutrated in Fig. 1. Typically, the ALC uppreion performance i given, imilarly a antenna eparation, a it capaility to uppre the whole SI ignal (including all the multipath component), even though it only uppree the main component. Therefore, if we deire ALC uppreion of a (linear cale amplification/uppreion ( 0 a 1) factor), we actually need to uppre the main component a much a a 1 h,0, 1 h,0 a a '. (0) Here, i the power of the main component of the channel h,0 with antenna eparation taen into account. Thi uppreion factor a ' i needed when uing (14), (15), (16) and (17). For oviou reaon, oth uppreion factor alo need to e non-negative. egative value indicate that the deired c or a are imply not achievale in the conidered multipath coupling channel, and therefore the maximum achievale c and a are logically dependent on the coupling channel a c 1,, 1 1 a, h,0, 1 1,. (1) Thee are the maximum attainale antenna eparation and ALC uppreion factor, repectively. A a final note, we wih to acnowledge again that analog/rf cancellation cheme with more than one path are aically alo poile, and demontrated e.g. in [11]. In thi article, however, a the focu i on low-cot mall commercial device with a imple RF part a poile, the ingle-path ALC concept ha een deployed. It i alo the mot common approach in the exiting literature and demontration. IV. SIMULATIO SCEARIOS, RESULTS AD AALYSIS In thi ection, the validity of the aove analyi reult i verified with full waveform imulation of a complete OFDM full-duplex tranceiver. Firt, the imulator i hortly decried, followed y numerical pecification of the tudied cenario. Then, the imulation reult are given together with the correponding analytical reult. The reult are alo compared, analyed, and dicued in detail. A. Simulator Decription For verification of the analytical reult, the SI lin of the fullduplex tranceiver i imulated a follow. Firt, tranmitter OFDM aeand waveform with 104 ucarrier, of which 300 on the oth ide of the DC-in are active and carry randomly-drawn 16QAM ucarrier data, i created. The ucarrier pacing i 15 Hz. After the aic waveform generation, a cyclic prefix of 63 ample i added to the

8 Revied manucript for IEEE Tranaction on Wirele Communication 8 ignal. The ued ignal reemle cloely the 3G LTE [9] downlin ignal, and it wa thu elected a an example waveform with practical ai and relevance. The given analyi reult are, however, valid for aritrary OFDM ignal. After adding the cyclic prefix, the phae noie in the upconverion i modelled into the ignal y uing the FRO phae-noie model [6]. An RF carrier frequency of GHz i aumed a a practical example of typical cellular radio frequencie. Thee waveform parameter are alo ummarized in Tale I. The ignal i then propagating through a multipath coupling channel that i decried in more detail later. The multipath coupling channel ha alo the eparation etween the tranmit antenna and the receiver antenna included in it, a decried in the previou ection. Then at the receiver, ALC i modelled o that the cae-dependent deired attenuation for the main multipath component i attained y having appropriate amplitude and phae error included in the ALC whoe value depend directly on the aumed ALC uppreion factor. The ALC uppree only the main multipath component, a in the analyi. After ALC modelling, the FRO aed phae noie in the downconverion i modelled. In the common ocillator cae, the ame phae noie realization i ued a in the tranmitter part ut with delay, while in the independent ocillator cae, the two realization are drawn independently. Finally, DLC i modelled o that an appropriate etimation error i aumed in the etimation of the effective multipath coupling channel, a decried in the previou ection. The digital ignal at the tranmitter i then proceed with the coupling channel etimate, with etimation error included, and the output i utracted from the received digital ignal. In the end, the ignal i fed to receiver FFT and the remaining SI power i evaluated numerically. The whole proce i repeated over 1000 independent trial of the underlying data and phae noie realization, to collect reliale tatitic. B. arameter for umerical Reult In all the imulation, the reference ucarrier-level average power at the receiver FFT output i et to 0 db, o the SI power i given in db in relation to that. Therefore the given SI power i alo directly the total ALC+DLC uppreion in the preence of phae noie. We aume a multipath coupling channel with power profile of 30 db, 65 db, 70 db and 75 db for delay of 0, 1, and 4 ample ( 4 ), repectively, which i modified from [7] to fit etter to fullduplex tranceiver cenario. The 30 db attenuation 3 ( c 10 ) of the main tap reult from the 30 db (or db to e exact) antenna eparation, which correpond to a ditance of roughly 0 cm etween the antenna [8]. The correponding delay i Thee are found realitic for mall TABLE I. ARAMETERS OF THE SIMULATED TRASMIT WAVEFORM arameter Value umer of ucarrier 104 umer of active ucarrier 600 Sucarrier modulation Sampling frequency Sucarrier pacing Cyclic prefix length Carrier frequency 16QAM MHz 15 Hz 63 ample GHz handheld/portale device [8]. Thee are alo cloe to the value meaured in [30] for full-duplex relay, ut with a lower, more practical, antenna eparation. To tudy the effect of phae noie on digital and analog SI cancellation, we define two aic cenario. In the o called ractical cae, the uppreion y ALC (with no phae 3 noie) i aumed to e 30 db ( a 10 ) and the uppreion y DLC (with no phae noie) i aumed to e 50 db 5 ( d 10 ), hence the total ALC+DLC uppreion in the phae noie free cae would e 80 db. How much phae noie then impact the total SI uppreion i illutrated in the performance figure. The value of 30 db and 50 db are choen ince they are cloe to the reported achievale value in [3] and [8]. Thi way there i clear connection to recently reported wor, though the value are perhap lightly optimitic due to laoratory cale equipment ued in [3] and [8]. In the other cenario, denoted a the Ideal cae, we ue otherwie the ame parameter ut ALC i now aumed to e ideal, which mean perfect uppreion of the main SI component in the phae noie free cae ( 0 ).,0 Furthermore, in thi Ideal cae, perfect DLC i alo aumed ( ee 0 ), implying that the DLC uppreion, and hence the total SI uppreion, would e db without phae noie. How much phae noie then impact the total SI uppreion i again illutrated in the performance figure. With thi Ideal cae, we can truly puh the limit in the SI cancellation proce et y the phae noie alone. The aic decription of the ractical and Ideal cae are alo hortly ummarized in Tale II. In addition to thee two aic cenario, additional performance tudie are alo carried out where either the ALC or the DLC uppreion i varied. Thee are clearly indicated in the correponding reult figure when applicale. We alo wih to note that even though the FRO model i ued in the analyi and imulation, the reult are fairly generally applicale. Thi i ecaue when the CE i een a part of the linear SI coupling channel, the effective remaining phae noie indeed cloely reemle the practical phae-loced loop (LL) aed

9 Revied manucript for IEEE Tranaction on Wirele Communication 9 TABLE II. ASSUMED REFERECE ALC, DLC AD TOTAL SI SURESSIO VALUES FOR RACTICAL AD IDEAL CASES WITHOUT HASE OISE. I CASES WHERE ALC OR DLC VALUE IS FURTHER VARIED, THE FIXED VALUE I THE TABLE IS RELACED WITH THE VARIED VALUE ractical Cae Ideal Cae Eff. hae oie [degree] ALC uppreion without phae noie DLC uppreion without phae noie 30 db 50 db 80 db Max. attainale, perfect for main SI component db Total uppreion without phae noie db β = 50 Hz β = 10 Hz Time [OFDM ymol] Fig.. Example effective phae noie realization for 50 Hz and 10 Hz phaenoie 3-dB andwidth ( ) with common phae error removed. ocillator when it come to inand effect [1], [5] which i the focu in the full-duplex context. More far away noie floor of practical ocillator contriute in practice, e.g., to adjacent channel interference, ut thi doe not impact the SI cancellation and i thu out of the cope of thi article. Example of the effective phae noie realization are given for reference in Fig. for 50-Hz and 10-Hz phae noie 3-dB andwidth. C. Reult and Analyi 1) rincipal Spectral Illutration: Here, the reult correponding to the previouly given cenario are illutrated and compared with the analytical reult. The firt reult are given in Fig. 3 for the pecified ractical cae with an example FRO 3-dB andwidth of 50 Hz. In the common ocillator cenario, ince mot of the phae noie i cancelled y the downconverting ocillator, the SI level i not far from the level of the SI without phae noie (at 80 db level in ractical cae). In thi example, hae noie caue a noie floor increae of around 4 to 5 db. In the cae of independent ocillator, on the other hand, the phae noie effect i much more evere, a expected intuitively. The SI ignal i only 48 db under it original power. hae noie thu heavily limit the performance of the DLC, and reult in highly prolematic receiver cenario. In general, a the figure illutrate, the analytical and imulated reult match perfectly. Relative Self Interference ower [db] Ind. Simulated Ind. Analytical Com. Simulated Com. Analytical Frequency [Hz] x 10 6 Fig. 3. Relative SI power at DLC output in the ractical cae (defined in Tale II) with either two independent (Ind.) FRO or the common (Com.) FRO with 3-dB andwidth of 50 Hz. Without phae noie, the total SI cancellation would e 80 db. Relative Self Interference ower [db] Ind. Simulated Ind. Analytical Com. Simulated Com. Analytical Frequency [Hz] x 10 6 Fig. 4. Relative SI power at DLC output in the Ideal cae (defined in Tale II) with either two independent (Ind.) FRO or the common (Com.) FRO with 3-dB andwidth of 50 Hz. Without phae noie, the total SI cancellation would e 80 db. In Fig. 4, the correponding reult for the Ideal cae are given for the ame FRO with 50 Hz. A in the ractical cae, in the cae of two independent ocillator, the power of the remaining SI i o high that it ignificantly limit the performance of the DLC, and thu the whole device. On the other hand, in the common ocillator cae, we can ee that the theoretical limit for inand SI uppreion, in term of linear SI channel nowledge, i at around 77 db. Thi how that phae noie caue relatively high performance floor for SI cancellation, depite of perfect linear SI channel nowledge, a in thi Ideal cae, perfect SI cancellation would e otained without phae noie. So, in principle, if very high SI uppreion level are required, while uing low-cot ocillator, it i mot liely vital to have ome mean of phae noie etimation and mitigation implemented in the receiver path. In general, the full pectral illutration with nap-hot

10 Revied manucript for IEEE Tranaction on Wirele Communication 10 parameter value in Fig. 3 and Fig. 4 are given o that the reader can eaily ee that the analytical reult match practically perfectly with the imulated reult ucarrier y ucarrier. In the following, we motly then focu on howing the SI power value a function of variou elementary parameter, intead of pectral illutration. ) Effect of Varying hae oie Level: The reult for average relative remaining inand SI power at DLC output a a function of, ranging from 0 Hz to 1 Hz, are given in Fig. 5 for the ractical and Ideal cae, repectively. In the ractical cae with the independent ocillator, one can ee that the phae noie caue the SI power to increae very fat, and even when i only at a nominal value of around 1 Hz, remaining SI level i already more than 65 db. In the common ocillator cae, the interference due to phae noie tart to rie quite teadily after around 5 Hz (denoted y a vertical dot line in the figure). At 1 Hz the interference ha already caued a 15 db decreae in the achieved SI cancellation. In the Ideal cae, the reult are omewhat different. Uing different ocillator increae the SI level around 30 db compared to the common ocillator cae. In the common ocillator cae, the interference level rie quite fat to 85 db at around 10 Hz. Thi implie that even with mall phae noie, phae noie etimation and mitigation would e very ueful depending on the deired total SI uppreion, if ALC and DLC otherwie wor well. For example, in an LTE UE tranceiver, the required total SI uppreion (including antenna eparation, ALC and DLC) i up to 133 db (from maximum 3 dbm tranmit power to 110 dbm, when referenced to receiver input, including thermal noie level of one reource loc, interference margin and noie figure of UE receiver). In order to have the phae noie degradation taying elow the noie plu interference level, if a practical numer of 30 db antenna eparation i aumed (and therefore the needed ALC+DLC uppreion i around 103 db), effectively only < 0.1 Hz phae noie level are tolerated, even in the common ocillator cae. otice alo the difference in Fig. 5 etween the ractical and Ideal cae with independent ocillator when phae noie rie to high level. The difference i explained y the difference etween the ALC performance, ecaue in that region the ALC performance dictate the overall performance (a heavy phae noie greatly impair the DLC uppreion). In Ideal cae, the ALC perform a it etter (the maximum attainale ALC uppreion i a it higher than the ALC uppreion of the ractical cae). In the ame ocillator cae, the curve are overlapping at high phae noie level, ecaue the ALC and downconverion uppre the phae noie in oth cae evenly. 3) Effect of Varying Multipath ower: In Fig. 6, the reult are given a a function of relative change in the coupling channel multipath profile. The ame channel power profile i Average Inand SI Cancellation [db] ractical Com. Ind. Simulated 110 Ind. Analytical 10 Com. Simulated Ideal 130 Com. Analytical hae oie 3 db Bandwidth [Hz] Fig. 5. Average inand SI cancellation at DLC output in ractical and Ideal cae (defined in Tale II) a a function of 3-dB andwidth of ocillator phae noie generated y either two independent (Ind.) FRO or the common (Com.) FRO. Without phae noie, the total SI cancellation would e 80dB (ractical) or db (Ideal). Vertical dot line mar the phae-noie 3-dB andwidth of 5 Hz for reference. Average Inand SI Cancellation [db] ractical Ideal Com. 80 Ind. Simulated Ind. Analytical 90 Com. Simulated Com. Analytical Relative Channel Change [db] Fig. 6. Average inand SI cancellation at DLC output in ractical and Ideal cae (defined in Tale II) a a function of the relative channel change with fixed phae-noie 3-dB andwidth of 50 Hz generated y either two independent (Ind.) or the common (Com.) FRO. Without phae noie, the total SI cancellation would e 80dB (ractical) or db (Ideal). ued a aove (with antenna eparation of 30 db, and relative to that 1t tap i 0 db, nd tap i 35 db, 3rd tap i 40 db and 5th tap i 45 db for delay of 0, 1, and 4 ample, repectively) a the aeline, ut the power of all the tap other than the firt one are varied according to the amount of deciel denoted y the horizontal axi. Thi model weaening or trengthening the reflecting multipath component y the given db amount. For the Ideal cae, the difference etween the independent and the common ocillator cae remain unchanged even when the channel condition are varied. Thi i ecaue with perfect ALC, the remaining phae noie effect are temming only from the non-main multipath component, and thu changing their relative power change the phae noie impact imilarly in oth of the cae. Ind. Ind.

11 Revied manucript for IEEE Tranaction on Wirele Communication 11 Average Inand SI Cancellation [db] Ideal ractical Ind. Ind. Simulated Ind. Analytical Com. Simulated Com. Analytical Com. Average Inand SI Cancellation [db] Ind. (Ideal and ractical overlapping) Com. Ideal ractical Ind. Simulated Ind. Analytical Com. Simulated Com. Analytical Amount of Digital Cancellation [db] Fig. 7. Average inand SI cancellation at DLC output in ractical and Ideal cae (defined in Tale II) a a function of the amount of digital cancellation with fixed phae-noie 3-dB andwidth of 50 Hz generated y either two independent (Ind.) FRO or the common (Com.) FRO. Without phae noie, the total SI cancellation would e 80dB (ractical) or db (Ideal). In the ractical cae with independent ocillator, the phae noie from the main multipath component limit the performance, o the curve are eentially traight horizontal line. In the correponding curve in the common ocillator cae, one can ee how the tronger multipath component tart to limit the performance already at low relative power level. In the Ideal cae, we can ee a linear increae of the average SI power a the multipath component get relatively tronger. ote that in the ractical cae, curve end at around 3 db relative channel change point, ecaue after that it i not poile to attain the deired 30 db ALC due to too trong multipath component. The curve correponding to the Ideal cae, however, continue forward, ecaue in the Ideal cae the et poile ALC i alway ued independently of it eing le or more than ALC in the ractical cae. 4) Effect of Varying DLC Gain: In Fig. 7, the amount of digital cancellation i varied while ALC performance i fixed. In the Ideal cae, non-ideal DLC i thu now coupled with the ideal ALC. From thee reult, we are ale to ee how the performance of DLC limit the ytem performance. In the Ideal cae, when DLC i non-ideal, the SI level decreae a a linear function of the DLC performance until at ome point it floor to an error floor et y the phae noie of the multipath component. In the cae of different ocillator, the performance tart to clearly deviate from the linear curve at 15 db of DLC. Thi implie that in uch a etup, already relatively low phae noie ( 50 Hz) egin to affect the SI cancellation performance when DLC i et to fairly low level of 15 db. In the common ocillator cae, on the other hand, flooring tart to how at around 40 db of DLC. Thi value i around the et value reported in current literature, ut till very low compared to what i needed in order to implement full-duplex tranceiver that comply with modern moile Amount of Analog Cancellation [db] Fig. 8. Average inand SI cancellation at DLC output in ractical and Ideal cae (defined in Tale II) a a function of the amount of analog cancellation with fixed phae-noie 3-dB andwidth of 50 Hz generated y either two independent (Ind.) FRO or the common (Com.) FRO. Without phae noie, the total SI cancellation would e 80dB (ractical) or db (Ideal). communication tandard, uch a 3G LTE. With the ued coupling channel, the maximum attainale ALC with 0 i around 33.5 db. Thi explain why the Ideal cae,0 curve are o cloe to the ractical cae one, with the exception of the flooring of the independent ocillator cae, where the ALC and therefore the main multipath component limit the SI cancellation performance. 5) Effect of Varying ALC Gain: In Fig. 8 the amount of analog cancellation i in turn varied. In the Ideal cae, a nonideal ALC i thu now coupled with the ideal DLC. One can ee that the non-ideal ALC limit heavily the ytem performance in the cae of independent ocillator, and therefore the curve with independent ocillator linearly decreae a a function of the amount of the ALC. With thee parameter, if ALC i increaed even more, it would alo floor to the noie level een in the curve of the cae with the common ocillator. In the ractical cae, increaing ALC performance increae the SI removal until it at ome point reache the flooring level et y the phae noie. The flooring i caued y the phae noie in the multipath component ince ALC oviouly only affect the main component. The ame i een in the Ideal cae, ut the curve tart from a lightly lower level ecaue of perfect DLC. After certain level of ALC it doe not anymore enefit to have etter DLC, ecaue the phae noie et the performance limit. 6) Effect of Varying TX-RX Delay: The delay that the ignal experience from the upconverting mixer at the tranmitter to the downconverting mixer at the receiver i varied in Fig. 9. The delay i varied from around 0.67 n to around 65 n (delay of one ample). If mapped to correponding ditance, thee correpond to from around 0 cm to around 19.5 m ditance etween the ocillator interface. With higher delay, thi i thu quite a theoretical analyi ecaue the

12 Revied manucript for IEEE Tranaction on Wirele Communication 1 Average Inand SI Cancellation [db] ractical Ideal Simulated Analytical Delay etween TX and RX Ocillator Interface [n] Fig. 9. Average inand SI cancellation at DLC output in ractical and Ideal cae (defined in Tale II) a a function of the delay etween the TX and RX ocillator interface with fixed phae-noie 3-dB andwidth of 50 Hz generated y the common FRO. Without phae noie, the total SI cancellation would e 80dB (ractical) or db (Ideal). varying delay etween ocillator hould alo affect the electrical antenna eparation and iolation, through increaing propagation loe already. However, a the exact mapping of the varying ditance to the varying antenna iolation depend on, e.g., the antenna and other tranceiver implementation detail, we firt ignore thi effect and tudy how the delay alone affect the performance. Thi i in any cae intereting, epecially in the common ocillator cae, a the delay intuitively ha an impact on the phae noie elf-cancellation in the downconverion proce, epecially for the multipath ut alo the main path if ALC i not perfect. More pecifically, in the cae of independent ocillator, the SI power curve v. ditance/delay would jut e traight line ince the delay doe not affect the tatitical propertie of the comined phae noie in any way, a alo implied y (14). That i why the curve correponding to the independent ocillator cae are left out and the numer are imply reported here in the text. In that cae, the average inand SI cancellation level are 48.6 db and 5.1 db for ractical and Ideal cae, repectively. In the common ocillator cae, however, illutrated in Fig. 9, we ee that oth the ractical and the Ideal cae curve logarithmically increae a a function of the delay etween the upconverting and downconverting ocillator. Thee are natural reult a the delay etween the ocillator directly affect the phae noie effect generated y all the multipath component, and in particular the phae noie elf-cancellation in the downconverion proce, i.e., a the delay of the component increae, the phae noie elf-cancellation deteriorate. 7) Effect of Varying TX-RX Ditance: In Fig. 10, the otained reult are given with different ditance etween TX and RX antenna uch that alo the propagation loe are explicitly taen into account. The ame multipath channel cenario, a previouly, i ued a the tarting point, and 30- db antenna eparation i aumed with the default ditance of 0 cm. A the ditance i increaing, exce attenuation i then Average Inand SI Cancellation [db] Ind. Simulated 60 Ind. Analytical Com. Simulated 70 Com. Analytical Ditance etween Antenna [m] Fig. 10. Average inand SI cancellation at DLC output in the Ideal cae (defined in Tale II) a a function of the ditance etween the antenna with fixed phae-noie 3-dB andwidth of 50 Hz generated y the common FRO. Without phae noie, the total SI cancellation would e db (Ideal). modelled to all multipath component, in addition to increaing delay. The exce attenuation i directly calculated y adding extra attenuation to each multipath component according to the widely ued free-pace propagation model for far-field communication [31]. In general, the ued rather imple propagation model i a compromie of eing ale to ae and demontrate the device performance with different ditance and relatively realitic and eaily parameterizale lo model. We alo emphaize that a the ditance increae to 10 to 0 m or o, the power delay profile of the received multipath component already eentially reemle the welletalihed hort-range or mall-cell communication propagation model reported e.g. in [9]. Thi i logical a when the tranmitter-receiver ditance i already in the order of 10-0m, the propagation condition more and more reemle an ordinary radio lin. The otained reult in Fig. 10 are only depicted in the ideal cae. Thi i ecaue the effective multipath channel i varying for varying tranmitter-receiver ditance, and thu the achievale ALC gain alo change with varying ditance and hence fixed ALC gain i not a feaile aumption. The reult in Fig. 10 how that the ditance etween the antenna ha a huge effect on the overall ALC+DLC performance in oth the independent ocillator and the common ocillator cae. In oth cae, the SI cancellation performance degradation i explained y the fact that the main multipath component whoe cancellation i purued in the ALC proceing i getting relatively weaer and weaer compared to the other multipath component a the ditance increae. Since the ALC alway inherently mitigate the phae noie effect from the main multipath component, while the other multipath component get relatively more and more powerful, the overall phae noie effect on the SI cancellation get wore and wore. The performance difference etween the independent ocillator and the common ocillator cae tart from around 6 db at 0 cm ditance and end to around

13 Revied manucript for IEEE Tranaction on Wirele Communication 13 db at around 0 meter ditance (correpond to one ample delay). Thi i natural, ince the inherent phae noie elf-cancellation in the downconverion uffer more and more in the common ocillator cae when the delay increae. The overall performance lo due to phae noie in the SI cancellation i natural when the relative dominance of the main coupling component get maller. However, when the ditance increae, it alo mean that the natural iolation etween the antenna get higher and higher. Therefore, even though the phae noie effect get heavier from the SI cancellation perpective a the ditance increae, the overall full-duplex tranceiver performance i increaing. With the natural iolation y the channel, ALC and DLC all taen into account, the total uppreion of the SI ignal for the independent and the common ocillator cae are 8 db and 108 db, repectively, for 0 cm ditance, and 88 db and 110 db, repectively, for 0 m ditance. Overall, thi tudy how that with higher ditance and epecially delay etween tranmitter and receiver chain, the phae noie effect are emphaized, which thu motivate for either etter ocillator optimization or development of explicit phae noie etimation and uppreion method. The reult alo indicate that epecially with trong multipath and long coupling delay, improving the ALC performance and in particular it capaility to proce multipath component, i eential when operating with practical ocillator with coniderale phae noie. V. COCLUSIOS In thi article, the impact of phae noie in upconverting and downconverting ocillator of full-duplex direct-converion OFDM radio were analyed in detail. The analyi tae into account realitic iolation and multipath propagation etween tranmitting and receiving antenna, analog/rf elfinterference cancellation and digital elf-interference cancellation. Under thee aumption, cloed-form expreion were derived for the remaining ucarrier-wie elf-interference power at the receiver path, covering oth cae of having either independent ocillator or a ingle common ocillator for the upconverion and downconverion. The analyi tae explicitly into account the pectral roadening in the elf-interference ignal, caued y phae noie. A general outcome of the analyi i that phae noie can eriouly compromie the elf-interference cancellation in the receiver path, epecially in the cae of independent ocillator. Hence it can e concluded that in a full duplex tranceiver, it i eneficial to ue the ame common ocillator in the upconverion and downconverion. Furthermore, if high amount of SI cancellation are purued, the ocillator hould e of very high quality, or ome form of phae noie etimation and mitigation hould e uilt into the elfinterference cancellation proceing in the receiver path. It wa alo hown that phae noie limit epecially the performance of the digital cancellation of the elf-interference, even when phae noie level i relatively low, ince the digital cancellation ample do not contain, y default, any reference to phae noie. Another ey oervation i that after the RF/analog cancellation, the phae noie in the elfinterference multipath component ecome a limiting factor in elf-interference cancellation. Hence the cenario with trong reflection and long delay are generally hown to e mot prolematic. AEDIX DERIVATIO OF E J (, ) In thi appendix, we derive the expreion for the power of (, ) J in (10), i.e., E J (, ), following partly the derivation in [33]. Thi i done for the two cae of having either independent ocillator or the common ocillator in the tranmitter and the receiver path. To egin with, we denote the power with and define it a J e 1 1 j ( nt T ) ( nt ) n/ t r E (, ) E n0 1 1 j ( nt T ) ( nt ) n/ E t r e n0 1 j ( nt T ) ( nt ) n/ t r e. n0 () ext, we aume that the phae noie proce i Brownian motion, namely Wiener proce, which on the other hand mean that the phae noie i generated y a free-running ocillator. Thi aumption mae the analyi tractale, ut till alo generally fairly applicale, ecaue previou tudie have hown that free-running ocillator with Brownian motion phae noie give in the end imilar phae noie characteritic a, e.g., phae-loced loop aed ocillator [1], when the common phae error i compenated for, a i done later in the analyi. With uch free-running phae-noie aumption, () can e next written a j ( nt T ) ( nt ' T ) ( nt ' ) ( nt ) n' n/ t t r r E e n0 n' E ( nt ) ( n' T ) ( nt ' ) ( nt ) j n' n/ t t r r e. n0 n' 0 (3) The aove expreion i aed on the fact that the difference etween any two value of a Brownian motion proce, at two different time intant, i alway ormal-ditriuted random-

14 Revied manucript for IEEE Tranaction on Wirele Communication 14 variale with zero mean. For thi ormal ditriuted difference, if 3-dB andwidth i denoted y and the time etween the intant i denoted y, then the variance i 4 [6]; namely () t ( t ) (0,4 ), if () t i Brownian motion with 3-dB andwidth of. The expreion in (3) aove i a general form for the quantity E J (, ). Below, the two cenario of independent ocillator or the common ocillator in the tranmitter and the receiver path are explored further. We conider firt the independent ocillator cae. Then, the phae noie procee (.) and (.) are tatitically t r independent of each other, and (3) can e rewritten a ind n' n T ' / j n n e n0 n' n T j n/ n e (4) n nT ne co n /. n0 The firt form in (4) i aed on the fact that the two phaenoie difference term in (3), namely ( n T ) ( n' T ) and t t ( nt ' ) ( nt), are oth ormal-ditriuted randomvariale with zero-mean, and now mutually independent of r r each other. Therefore, the expectation in (3) yield jut the comined variance of thee two random variale. The econd and final form in (4) follow then from plain algeraic manipulation. The final form i deployed in (14). Q.E.D. ext, we conider the common ocillator cenario etween the tranmitter and the receiver ide, and hence have () t () t () t. A a reult, we can rewrite (3) a t com r E ( nt ) ( n' T ) ( nt ' ) ( nt ) j n' n/ e n0 n' 0 4nT ( n) e co n/ n0 1 4 T4 ( n) e co n/. n (5) Examining the firt line in (5) we can oerve that the tatitical propertie of the random variale inide the expectation operator change a a function of the difference etween the um indice n and n '. Therefore, in the analyi, the indice can e replaced y their eparation when woring toward the final expreion. Then, to progre further require omewhat urdenome ut till traightforward tep-y-tep manipulation where the well-nown propertie of the Wiener proce are exploited. More pecifically, one can eparate the phae noie term inide the expectation in a way that for every n, n ' pair for every value of, the two phae-noie difference are grouped eparately o that they are tatitically independent, i.e., in a way that the two pair of phae noie procee do not overlap in time. Then their comined variance can e calculated eparately and finally ummed together which reult in the two um written in the econd and the final form of (5). Writing out thee intermediate tep i ipped here, for compactne of preentation, and hence the econd form of (5) repreent the final reult, deployed in (15). Q.E.D. REFERECES [1] J. Choi, M. Jain, K. Srinivaan,. Levi, and S. Katti, Achieving ingle channel, full duplex wirele communication, in roc. International Conference on Moile Computing and etworing 010, Chicago, IL, USA, Septemer 010. [] M. Duarte and A. Saharwal, Full-duplex wirele communication uing off-the-helf radio: Feaiility and firt reult, in roc. 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Bello, Characterization of randomly time-variant linear channel, IEEE Tranaction on Communication Sytem, vol. 11, no. 4, pp , Decemer [3]. Roerton and S. Kaier, Analyi of the effect of phae-noie in orthogonal frequency diviion multiplex (OFDM) ytem, in roc. IEEE International Conference on Communication, June 1995, pp , Vol. 3. [4] L. Toma, On the effect on Wiener phae noie in OFDM ytem, IEEE Tranaction on Communication, vol. 46, no. 5, pp , May [5] V. Syrjälä and M. Valama, Analyi and mitigation of phae noie and ampling jitter in OFDM radio receiver, International Journal of Microwave and Wirele Technologie, vol., no., April 010. [6] T. Schen, RF Impairment in Multiple Antenna OFDM: Influence and Mitigation, hd diertation, Techniche Univeriteit Eindhoven, p. [7] K. Haneda, E. Kahra, S. Wyne, C. Icheln, and. Vainiainen, Meaurement of loop-ac interference channel for outdoor-to-indoor full duplex radio relay, in roc. European Conference on Antenna and ropagation 010, Barcelona, Spain, April 010. [8] A. Sahai, G. atel, and A. Saharwal, uhing the limit of full-duplex: Deign and real-time implementation, CoRR, 011, a/ [9] 3G Technical Specification, TS v hyical Channel and Modulation, Releae 8, 009. [30] T. Riihonen, A. Balarihnan, K. Haneda, S. Shurjeel, S. Werner, and R. Wichman, Optimal eigeneamforming for uppreing elf-interference in full-duplex MIMO relay, in roc. Conference on Information Science and Sytem 011, Baltimre, MD, USA, March 011. [31] C. Balani, Antenna Theory, John Wiley & Son, 003. [3] IST WIER II Technilcal Document, D1.1.1 V1.1, Winner Interim Channel Model, Feruary 007. [33] V. Syrjälä, Accurate characterization of ocillator phae-noie corrupted OFDMA-uplin, IEEE Communication Letter, vol. 17, no. 10, Octoer 013. BIOGRAHIES Ville Syrjälä (S 09, M 1) wa orn in Lapua, Finland, in 198. He received the M.Sc. (Tech.) degree in 007 and D.Sc. (Tech.) degree in 01 in communication engineering (CS/EE) from Tampere Univerity of Technology (TUT), Finland. He wa woring a a reearch fellow with the Department of Electronic and Communication Engineering at TUT, Finland, until 013. Currently, he i woring a a potdoctoral fellow of Japan Society for the romotion of Science (JSS) at Kyoto Univerity, Japan. Hi general reearch interet are in full-duplex radio technology, communication ignal proceing, tranceiver impairment, ignal proceing algorithm for flexile radio, tranceiver architecture, direct ampling radio, and multicarrier modulation technique. Mio Valama (S 00, M 0) wa orn in irala, Finland, on ovemer 7, He received the M.Sc. and h.d. degree (oth with honour) in electrical engineering (EE) from Tampere Univerity of Technology (TUT), Finland, in 000 and 001, repectively. In 00 he received the Bet h.d. Thei award y the Finnih Academy of Science and Letter for hi diertation entitled "Advanced I/Q ignal proceing for wideand receiver: Model and algorithm". In 003, he wa woring a a viiting reearcher with the Communication Sytem and Signal roceing Intitute at SDSU, San Diego, CA. Currently, he i a Full rofeor and Department Vice Head at the Department of Electronic and Communication Engineering at TUT, Finland. He ha een involved in organizing conference, lie the IEEE SAWC 07 (ulication Chair) held in Helini, Finland. Hi general reearch interet include communication ignal proceing, etimation and detection technique, ignal proceing algorithm for oftware defined flexile radio, full-duplex radio technology, cognitive radio, digital tranmiion technique uch a different variant of multicarrier modulation method and OFDM, radio localization method, and radio reource management for ad-hoc and moile networ. Lauri Anttila (S 06, M 11) received hi h.d. (with honour) from Tampere Univerity of Technology (TUT), Tampere, Finland, in 011. Currently, he i a Reearch Fellow at the Department of Electronic and Communication Engineering at TUT. Hi current reearch interet include tatitical and adaptive ignal proceing for communication, digital front-end ignal proceing in flexile radio tranceiver, and full-duplex radio ytem. Taneli Riihonen (S 06) received the M.Sc. degree in communication engineering (with ditinction) from Helini Univerity of Technology, Helini, Finland in Feruary 006. During the ummer of 005, he wa an intern at oia Reearch Center, Helini, Finland. Since fall 005, he ha een a reearcher at the Department of Signal roceing and Acoutic, Aalto Univerity School of Electrical Engineering, Helini, Finland, where he i completing hi D.Sc. (Tech.) degree in the near future. He ha alo een a tudent at the Graduate School in Electronic, Telecommunication and Automation (GETA) in Hi reearch activity i focued on phyical-layer OFDM(A), multiantenna and relaying technique. Dani Korpi wa orn in Ilmajoi, Finland, on ovemer 16, He received the B.Sc. degree (with honor) in communication engineering from Tampere Univerity of Technology (TUT), Tampere, Finland, in 01, and i currently puruing the M.Sc. degree in communication engineering at TUT. In 011, he wa a Reearch Aitant with the Department of Signal roceing at TUT. Since 01, he ha een a Reearch Aitant with the Department of Electronic and Communication Engineering, TUT. Hi main reearch interet i the tudy and development of ingle-channel fullduplex radio, with a focu on analying the RF impairment.