PREAMBLE DESIGN FOR THE DIGITAL COMPENSATION OF TX LEAKAGE IN ZERO-IF RECEIVERS. Andreas Frotzscher and Gerhard Fettweis

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1 PREAMBLE DESIG FOR THE DIGITAL COMPESATIO OF TX LEAKAGE I ZERO-IF RECEIVERS Adreas Frotzscher ad Gerhard Fettwes Vodafoe Char Moble Commucatos Systems, Techsche Uverstät Dresde, D-006 Dresde, Germay Emal: {frotzscher, fettwes}@f.et.tu-dresde.de ABSTRACT Trasmtter Leakage has a sgfcat mpact o the system performace moble devces usg zero-if recevers. I cotrast to aalog approaches, dgtal Tx Leakage compesato approaches ca easly be recofgured ad therefore are hghly attractve for future moble devces, usg software defed rados. I ths cotrbuto we preset a dgtal Tx Leakage estmato ad compesatoapproach, usg specfcally desged OFDM preambles, whch are also sutable for the Uplk chael estmato.. ITRODUCTIO I wreless hadset devces operatg the frequecy dvso duplex (FDD) mode, a duplexer coects the trasmt (Tx) ad receve (Rx) cha wth the atea. Sce both chas are operatg smultaeously, the duplexer has to provde a hgh Tx-Rx solato. However, achevg a suffcet Tx-Rx solato s very challegg f low cost mplemetato s targeted. Ths problem becomes eve more serous future FDD trascevers. As a cosequece of the demaded sze ad producto cost reducto, future trascevers wll employ software defed rados, usg frequecy agle duplexers to support several commucato stadards. However, achevg a suffcet Tx-Rx solato wth frequecy agle duplexers s eve more challegg. Due to the suffcet Tx-Rx solato a sgfcat part of the Uplk (UL) sgal s leakg through the duplexer to the Rx cha. Focusg o zero-if recevers, the olearty of the I/Q dow coverter geerates d order termodulato products (IM) of the leakg UL sgal, whch are partly located aroud DC ad thus terfere the dow coverted Dowlk (DL) sgal. Ths Tx Leakage (TxL) becomes a substatal problem dffcult receve codtos (e.g. at cell edges), where t severely deterorates the DL sgal demodulato. I the past several authors proposed TxL mtgato approaches usg a adaptve flter parallel to the duplexer 3 or frot of the I/Q dow coverter 4. Operatg o aalog RF sgals, these approaches have a lmted recofgurablty, complcatg ts employmet software defed rados. Compesatg the TxL dgtally relaxes the requremets o the aalog frot ed, reducg developmet ad producto costs. However, the dgtal TxL compesato etals a olear estmato problem of the TxL chael 5, whch s dffcult to solve f o specfc trag UL sgal ca be used. I ths cotrbuto, we preset a dgtal frequecy doma TxL estmato, based o trasmttg specfc Orthogoal Frequecy Dvso Multplex (OFDM) preambles the UL. The requremets o the preamble desg ad a exemplary preamble set are gve. Sce these preambles are trasmtted the UL, they ca be used for the UL chael estmato as well. However, ths ssue ot the scope of ths work ad therefore s dscussed oly shortly. The outle of the paper s as follows: I Sec. the system model s preseted ad the TxL terferece frequecy doma s derved. Afterwards, Sec. 3 presets the requremets o the preamble desg ad a exemplary preamble set ad explas the TxL estmato approach. The estmato performace of ths approach s umercally evaluated Sec. 4, followed by the coclusos Sec. 5.. SYSTEM MODEL Ths paper focuses o the Tx Leakage (TxL) preset at the moble termal, as depcted Fg.. The dscrete UL sgal DL sgal Duplexer LA Tx Leakage PA LODL TxL CSF IM LOUL DC - ADC DAC yk MRC &CP - η-fft MUX s ULk TxL Est. ad Compesato CSF EQ CP - s cmpk ĥ TxLm TxL Comp. Z TxL Est. DL Demodulator η- IFFT P Plot Ge. UL Modulator Fg.. Block dagram of a FDD zero-if trascever a termal wth plot based estmato of Tx Leakage s UL k results from the tme multplex of the preambles ad the data carryg sgal of the UL modulator. After passg

2 the DAC, the up coverter ad the power amplfer (PA), the UL sgal leaks partly to the Rx cha due to the suffcet Tx-Rx solato. The compoud amplfcato ad flterg of the leakg UL sgal betwee the DAC the Tx cha ad the dow coverter the Rx cha ca be cosdered as a TxL chael. The I/Q dow coverter the Rx cha shfts the receved sgal to basebad, but t also geerates termodulato products d order of the leakg UL sgal (TxL IM). These termodulato products arse partly aroud DC ad thus terfere the dow coverted DL sgal. The dow coverter s followed by the chael select flter (CSF) ad the DC offset cacellato (DC ). The ADC delvers the dgtal basebad sgal yk. I practce the DAC ad ADC operate wth a oversamplg factor η of usually,, 8. Based o the receved UL preambles the TxL chael s estmated. Usg these estmates, the TxL compesato sgal s cmp k s costructed ad subtracted from yk. The reduced, effectve ADC resoluto for the DL sgal due to TxL s ot cosdered here. However, further studes have show, that the SR loss due to the reduced effectve ADC resoluto s db for TxL power levels allowable practce. The receved, dgtal base bad sgal yk ca be modeled as follows : yk = ( ) h CSF h DL s DL k () ak ( jδc) ( h CSF h TxL s UL ) ) kadc wk. bk Term ak () results from the trasmsso of the oversampled DL sgal s DL k over the DL trasmsso chael h DL k ad the chael select flter (CSF), h CSF k. I practce, the chael select flter cossts of two almost detcal aalog low pass flters the I- ad Q-brach. Cosequetly, h CSF k s a real valued mpulse respose, whose legth shall be deoted by L CSF. Furthermore, sce h CSF k ca be measure durg the calbrato of the moble usg aalog test toes, t s assumed to be kow. Term bk () descrbes the DC-free TxL terferece. Due to the uavodable I/Q msmatch of the dow coverter, the TxL IM the I- ad Q brach dffer from each other by the tme varat factor Δc. Beg measured durg the calbrato of the moble, Δc s assumed to be kow as well. The TxL chael s represeted by the mpulse respose h TxL k, whose legth L shall be assumed to be kow. The aalog DC offset compesato troduces the couter sgal value a DC to compesate the TxL IM DC offset. Fally, wk s a complex, addtve whte Gaussa ose sgal (AWG). Focusg o the TxL estmato, the followg we wll cosder oly those tme frames whe preambles are trasmtted the UL. These specfc OFDM preambles, cludg a η-fold oversamplg, are costructed by a sze η IFFT of the frequecy doma sgal P, where deotes the preamble dex. The UL ad DL sgal badwdth s specfed by the commucato stadard. The umber of subcarrers wth ths sgal badwdth s a desg parameter of the TxL estmato ad shall be deoted by. It s mportat to otce, that s depedetly chose from the UL data trasmsso scheme. Sce the TxL estmato the Rx cha uses a sze η-fft, the codto η max(l, L CSF ) must be fulflled. Solvg the equato system based o Eq. (9). demads, that the addtoal codto L s fulflled. I order to prevet dstortos to adjacet chaels, the subcarrers outsde the UL sgal bad must rema at zero, e.g. P =0, / /,/. Therefore the th preamble tme doma s gve by: p k = / η =/ P k jπ η e. () I order to assure a ISI free recepto of the preambles the Rx cha a cyclc prefx of the legth CP s troduced betwee uequal preambles ad betwee preamble ad data blocks, where CP L L CSF s requred. Focusg at the Rx cha, let y k deote the ADC output sgal whe the preamble p k s trasmtted. Due to the TxL I/Q msmatch, the TxL estmato ad compesato block apples a Maxmum Rato Combg (MRC) o the real ad magary part of y k frst, yeldg the sgal: z k = Re{y k} ΔcIm{y k} Δc = ( h CSF h TxL p ) ) kadc w Est k, (3) Sce the DL sgal ad the AWG does ot cota ay formato for the TxL estmato, they are combed to the ose sgal w Est k. Subsequetly, the cyclc prefx s removed from z k, whch s afterwards fed a sze η FFT block, yeldg the frequecy doma (FD) sgal Z : { htxl } Z =H CSF FFT η p k a DC δw Est (4) where δ descrbes the Kroecker delta fucto, represets the crcular covoluto ad W Est deotes the Fourer trasform of w Est k. The CSF trasfer fucto H CSF results from the sze η FFT of h CSF k. A zero forcg equalzer s used, dvdg Z by H CSF, to compesate the CSF ad thus facltate the TxL estmato, yeldg: ( Z = η HTxL P ) ( H P ) TxL B ã DC δ W Est (5) where H TxL = FFT η {h TxL k}. ote that, due to the CSF equalzato W Est s composed of a whte gaussa ose, resultg from wk, ad a arrow bad sgal, resultg from the DL sgal. Due to the bad lmted preambles, term

3 B (5) smplfes to: B = / H TxLmHTxL mpmp m m=,0 / H TxLmH TxL mpmp m,, m= (6) ad B =0otherwse. Sce z k s a real valued sgal, the real ad magary part of Z s a eve ad odd fucto w.r.t., respectvely. Cosequetly, the postve as well as the egatve subcarrers of Z cota all formato about the TxL IM ad thus, the TxL estmato oly eeds to cosder ether the postve or egatve subcarrers. For performace evaluato let γ Est deote the TxL estmato sgal-to-ose rato (SR), descrbg the power rato betwee the TxL terferece ad the combed ose sgal after the CSF equalzato, both excludg DC: γ Est = { } E B { } E WEst (7) 0 Furthermore, let γ descrbe the SR betwee the DL sgal ad the AWG ose wth the DL sgal bad: { γ = E hcsf h DL s DL } k { wk } (8) E /η 3. TX LEAKAGE ESTIMATIO For the TxL chael estmato, / dfferet OFDM preambles are trasmtted the UL B tmes each, to mtgate the DL sgal ad the AWG ose mpact o the estmato. I Sec. 3. the desg of these preambles s explaed. The TxL chael s estmated three steps. Frst, several cross products of TxL chael coeffcets (6), e.g. H TxL HTxL, are estmated, yeldg to Ĥjot, =ĤTxL Ĥ TxL, whch wll be called jot coeffcet. The estmate of H TxL s descrbed by ĤTxL. Secod, the estmated TxL coeffcets ĤTxL are calculated from these jot coeffcets ad fally the estmated TxL mpulse respose ĥtxlk s derved from ĤTxL. Sce the preambles use oly the er subcarrers, we have to estmated H TxL, /,/. Keepg the estmato complexty as low as possble, should be chose as small as possble, accordg to the codtos, gve Sec Estmato of the TxL jot coeffcets Ĥjot, The jot coeffcets are estmated o the base of Z,, /. The TxL terferece o a certa subcarrer s the superposto of several jot coeffcets multpled by the correspodg preamble subcarrers,.e. H TxL H TxL P P (Eq. (6)). Thus, the ma dea of the estmato s as follows: By summg or subtractg Z of dfferet preambles, oe summad (6) ca be aggregated, whle all other summads are caceled out. Thus, the preambles must be desged such, that the sgs of specfc preamble subcarrer products P P dffer betwee certa preambles, whle the magtudes of these products remas costat. Owg to the lmted space, oly a summary of the desg requremets o the / dfferet preambles are gve Fg., where R R\{0, },, are desg parameters. The gray shaded area Fg. emphasze the egatve sg of R. Based o these P P 3 0 R R R R R R R R 3 R R R R R R R R R R R Fg.. Preamble desg requremets desg requremets a exemplary preamble desg s gve Fg. 3, where R = R = cost,. Trasmttg the Subcarrer of the th Preamble, P 3 0 R R R R R R R R R R R R R 3 R R R R R R R R R R R Fg. 3. Preamble desg example used for TxL estmato preamble dex as sde formato to the base stato, these preambles ca be used for the UL chael estmato as well. st terato (g =): Based o the preseted preambles ad (5) ad (6), Ĥ jot, ca be estmated by: R Ĥ jot, = η / R = E { Z } (9) where E{ } deote the expectato operator. The expectato s approxmated by the average over the B receved FD sgals of the correspodg to the cosdered preamble P. d ad followg teratos (g =,, /): I the followg teratos, the jot coeffcets Ĥjot, g ad Ĥjot g, are estmated by: Ĥ jot, g = ( g ) E { Z g } / η (g)r (0) =g E { Z g }

4 ad Ĥ jot g, = η (g)r () ( g ) E { Z g g } / =g 3.. Estmato of FD TxL chael coeffcets E { Z g }. The equatos (9), (0) ad () delver the subset H, H ad H 3 of the estmated jot coeffcets, respectvely. ote that H ad H 3 depeds o ĤTxL ad ĤTxL,respectvely, whle H depeds o both FD coeffcets. Thus, the H represets a lk betwee the two other subsets. Calculatg ĤTxL,, from these subset requres the kowledge of oe ĤTxL start as startg pot. Sce subset lks the two other subsets, start { }, should be chose. Otherwse the estmato approach would suffer from hgher error propagato. Ths problem wll be dscussed more detal at the ed of ths secto. I ths work start = s chose arbtrarly. The commo phase of H TxL does ot affect the TxL terferece (See Eq. (5) ad (6)). Therefore, arg ( Ĥ TxL ) =0s defed arbtrarly. Sce the magtude of H TxL s stll ukow, we frst estmate a scaled verso of H TxL, deoted by H TxL ad defe the startg FD coeffcet as: H TxL start =αh TxL start = () The scalg factor α R wll be estmated later. The scaled coeffcets H TxL are calculated from the estmated jot coeffcets by: ( ) Ĥjot, H H TxL = TxL Ĥ jot, 0. H TxL (3) I case the jot coeffcets are estmated correctly, H TxL relates to H TxL by: H TxL = { αh TxL 0 α H TxL (4) Cosderg H TxL as TxL chael FD coeffcets the expected resultg TxL terferece, STxL,, afterthecsf equalzato ca be calculated accordg to (5) ad (6). The mea dfferece of the subcarrer = betwee the expected ad observed TxL terferece, deoted by Δ Z = E{ Z } S TxL, ca be wrtte as: Δ Z = ( η ( α ) HTxL H TxL ( α ) H TxL H TxL P 0P P ) P 0 (5) Therefore, the scalg factor α ca be estmated by combg Δ Z of dfferet preambles, wth = : =g Δ Z ( )R H TxL H 0 TxL ( ˆα = η (m )Δ Z m m (η (m )Δ Z m m =g Δ Z ( )R H TxL H TxL0 ) ) (6) where m = /. Aalog to (4), the estmated TxL chael FD coeffcets ĤTxL are gve by: { Ĥ TxL = ˆα H TxL 0 ˆα H TxL (7) 3.3. Estmated TxL chael mpulse respose ĥtxlk The estmated TxL mpulse respose ĥtxlk sgvebythe IFFT of ĤTxL: ĥ TxL k = ( ) η η ĤTxLexp jπ k =η η (8) Sce the TxL estmato delvers oly ĤTxL wth,, the remag coeffcets ca be chose arbtrarly. As metoed before, the TxL chael legth L s assumed to be kow. Cosequetly, the requremet ĥtxlk = 0, k L, η has to be fulflled. Therefore, usg (8) the remag TxL chael FD coeffcets ĤTxL, wth η,, η ca be calculated by solvg the lear equato system resultg from the relato: Ĥ TxL e jπ k η = Ĥ TxL e jπ k η (9) for k L, η,where,. Thus, havg estmated all TxL coeffcets, ĥtxlk results from (8). Ths step falzed the TxL estmato ad the compesato sgal ca be calculated usg ĥtxlk, h CSF k ad Δc: s cmp k =(jδc) ( h CSF ĥtxl s UL ) kâdc. (0) The estmated couter sgal value of the DC offset compesato descrbes â DC ad s gve by: â DC = DC m=0 jδc DC ( hcsf ĥtxl s UL ) k () where DC deotes the block legth used for the calculato of the DC offset. The TxL estmato suffers from the combato of the jot coeffcets ad the tally estmated coeffcets Eq. (3), causg a error propagato. Therefore, the estmato performace depeds o the magtude of the TxL chael coeffcets H TxL, besde the ose sgal W Est. Dueto the lmted space a detaled aalyss of ths error propagato ca ot be gve here.

5 4. UMERICAL RESULTS As measure of the TxL estmato performace we defe the compesato ga G C as the power rato: E{ bk } G C = E{ bk s cmp k } () f 0 excludg DC. We used a OFDM FDD smulato cha wth a oversamplg η =ad perfect TxL I/Q match (Δc =). I the DL IEEE 80.a OFDM data symbols wth 6-QAM modulated subcarrers are trasmtted over a AWG chael. Sce the TxL chael s oly weak frequecy selectve 5, t s modeled by h TxL k = e τk e jϕk,k 0,L, where ϕk s uformly dstrbuted over 0, π. Each UL preamble, specfed Sec. 3, s trasmtted B tmes, where the desg parameter s set to L. Afterward several IEEE 80.a OFDM data symbols wth 4-QAM modulated subcarrers are trasmtted the UL. The Rx cha employs a 7-tap CSF flter ad a aalog DC-offset compesato. Mea Compesato ga G c db B =00 B =0 30 L=4 40 L=6 L= γ db Est Fg. 4. Performace of the TxL estmato for dfferet TxL chael legth L ad preamble repettos B (DL SR γ = 0dB, TxL chael: τ =3) I Fg. 4 the estmato performace s plotted for dfferet TxL chael legth L ad preamble repettos B, whle τ =3ad γ =0dB. As expected the compesato ga G C decreases for lower γ Est ad B. However, the error propagato causes a growg addtoal G C loss whe γ Est decreases. Therefore, the curves for L =6ad 8 Fg. 4 exhbt a cocave shape. Furthermore, the error propagato creases whe more TxL chael coeffcets are estmated, reasog the lower estmato performace for larger L. I Fg. 5 the estmato performace s plotted for the DL SR γ =0dB. Due to the chose DL SR, the domat part of the sgal power of the combed ose sgal W Est s located wth the DL sgal bad wdth. Cosequetly, the estmato of the jot coeffcets, usg oly the subcarrers outsde the DL sgal bad wdth, acheves better results. Therefore, the estmato performace preseted creases wth γ, as ca be see Fg. 4 ad 5. Mea Compesato ga G c db B =00 B =0 0 L=4 30 L=6 L= γ Est db Fg. 5. Performace of the TxL estmato for dfferet TxL chael legth L ad preamble repettos B (DL SR γ = 0dB, TxL chael: τ =3) 5. COCLUSIOS We preseted a dgtal approach for the estmato ad compesato of Tx Leakage zero-if recevers usg specfcally desged OFDM preambles the Uplk. Based o the preambles receved by the ow Rx cha, certa cross products of Tx Leakage chael coeffcets are estmated. Afterwards the Tx Leakage chael coeffcets ad the correspodg mpulse respose s calculated from these estmates. Due to the combato of several estmates, the approach suffers from a error propagato. However, the umercal performace evaluato demostrates the good compesato capabltes of ths algorthm. 6. REFERECES Adreas Frotzscher ad Gerhard Fettwes, Basebad Aalyss of Tx Leakage WCDMA Zero-IF Recevers, IEEE ISCCSP 08, March 008, Ivted paper. Adreas Frotzscher, Marco Krodorf, ad Gerhard Fettwes, O the Performace of OFDM dowlk FDD chaels uder Tx Leakage usg zero-if recevers, 3th Iteratoal OFDM-Workshop (IOWo 08), August Shyama Dlruksh Kaagara, Adaptve Duplexer for Software Rado, Ph.D. thess, Vctora Uversty, Melboure, Australa, ovember Vladmr Apar, A ew Method of TX Leakage Cacelato W/CDMA ad GPS Recevers, IEEE Rado Frequecy Itegrated Crcuts Symposum, Jue Adreas Frotzscher ad Gerhard Fettwes, A Stochastc Gradet LMS Algorthm for dgtal Compesato of Tx Leakage zero-if-recevers, IEEE VTC 08, May 008.