Effect of Tme-Interleaved Analog-to-Dgtal Converter Msmatches on OFDM Performance Vo-Trung-Dung Huynh, Nele Noels, Peter Rombouts 2, Jean Armstrong 3, Hed Steendam Department of Telecommuncatons and Informaton Processng, Ghent Unversty 2 Department of Electroncs and Informaton Systems, Ghent Unversty 3 Department of Electrcal and Computer Systems Engneerng, Monash Unversty {votrungdunghuynh, nelenoels, hedsteendam}@telnugentbe 2 {peterrombouts}@elsugentbe 3 {jeanarmstrong}@monashedu Abstract For the extremely hgh samplng rate and hgh resoluton requred for mult-ggabt orthogonal frequency dvson multplexng (OFDM) communcaton systems, tmenterleaved analog-to-dgtal converters (ADCs) are beng consdered However, n practce, msmatches such as offset msmatch, gan msmatch and tmng msmatch occur between the parallel sub-adcs Ths paper theoretcally analyzes the mpact of the dfferent msmatches on the performance of the OFDM system The theoretcal results are confrmed by smulatons and show that OFDM performance s strongly degraded, even for small msmatches Index Terms OFDM, tme-nterleaved analog-to-dgtal converter, msmatch, performance I INTRODUCTION Orthogonal frequency dvson multplexng (OFDM) s an effcent mult-carrer transmsson technque that s wdely adopted n many wred and wreless standards, thanks to ts hgh spectral effcency, nherent bandwdth management and tolerance aganst channel dsperson In the last decade, t has also been suggested for mult- Ggabt fber-optc communcaton systems [] In such a hgh-speed OFDM system, the trend s to mnmze the number of analog components n favour of dgtal sgnal processng (DSP) As a result, the analog-to-dgtal converter s placed pror to the baseband DSP core, mplyng the ADC needs to operate at an extremely hgh samplng rate Current devces are not able to meet the requrements as they are already operatng close to the physcal lmts of the used technology [2] As a result, the ncrease n speed n the comng years s expected to be rather modest A low cost soluton to ths hardware restrcton s the use of tme-nterleaved ADCs (TI-ADCs) [3] In a TI-ADC archtecture, slow sub-adcs are placed n parallel, as shown n Fg The l th ADC slcer samples the sgnal at nstant CK l, l =,,, where the samplng nstants are shfted n tme Ideally, these samplng nstants are equdstant wth as spacng the samplng tme In ths way, the overall samplng rate s tmes hgher than the samplng rate of each sub-adc However, msmatches between the parallel sub-adcs, such as offset and gan msmatch as well as the tme skew of the used clocks n the sub-adcs, can degrade the performance of the TI-ADC Although there are a few authors that have studed the effects of TI-ADC msmatches on hgh-rate OFDM systems, ther results are based on smulatons only [2], [4] There s also some closely related work on the effect of tmng jtter n OFDM systems [5], [6] In ths paper, we evaluate the effects of these msmatches n an analytcal way The theoretcal results, whch are n agreement wth our smulaton results, can be used for dervng calbraton methods for TI-ADCs used n hghspeed OFDM-based systems The paper s organzed as follows In Secton II, we descrbe the system model, ncludng the model of the OFDM transcever and the model of the TI-ADC wth the offset, gan and tmng msmatch In order to assess the bt error rate () performance of the OFDM system, a theoretcal analyss of the effect of these msmatches on the spectrum of the sampled OFDM sgnal and on the output of the dscrete Fourer transform (DFT) unt that s used to demodulate the resultng samples s presented n Secton III and Secton IV, respectvely In Secton V, we frst valdate the accuracy of the derved expressons by comparng the theoretcal results wth the smulaton results, and then we numercally assess the effects of the TI-ADC msmatches on the performance of the system Fnally, our concluson s gven n Secton VI II SYSTEM MODE In ths secton, we descrbe the consdered OFDM transcever model, of whch the system block dagram s provded n Fg 2 The recever s assumed to employ a TI-ADC archtecture n whch the dfferent sub-adcs experence dfferent offset, gan and tmng msmatches The model of the l th sub-adc of the TI-ADC, wth offset (do l ), gan (dg l ) and tmng (dt l ) msmatch s llustrated n Fg [7] Snce the msmatch parameters vary slowly over tme, we can model them as constants over the duraton of an OFDM symbol perod In an OFDM-based system wth N sub-carrers, a hghrate data stream s dvded nto N parallel low-rate data streams, whch are modulated on the dfferent sub-carrers
Input s h (t) D M U X CK CK Tme shft dt l CK - ADC CK ADC CK ADC - CK - The model of the l th sub-adc x + +dg l do l M U X m + l Output r l [m] Fg Block dagram of the TI-ADC and the model of the msmatches n the l th sub-adcs bts s h (t) Fg 2 Receve Flter TI-ADC Mappng r[m] X[a] Cyclc Prefx Removal OFDM Modulaton + nose Channel OFDM Demodulaton Cyclc Prefx Inserton s[k] Downconverter Upconverter R DFT [n] DAC Transmt flter Data Detector Block dagram of a OFDM system wth a TI-ADC at recever wth an nverse dscrete Fourer transform (IDFT) et the vector X denote the nput of the IDFT Then, the vector X conssts of N complex-valued symbols (e, X = (X[], X[],, X[N-]) t, where the superscrpt t denotes transpose), whch are taken from an M-ary Phase Shft Keyng (PSK) or Quadrature Ampltude Modulaton (QAM) constellaton wth each constellaton symbol correspondng to a sequence of log 2 (M) bts The IDFT converts the data symbols to the tme doman Because of channel dsperson, the pulses assgned to the tme-doman samples wll be spread n tme In order to avod ntersymbol nterference (ISI) at the recever, whch causes a performance degradaton, adjacent OFDM symbols are separated by a guard nterval In ths paper, the guard nterval conssts of a cyclc prefx (CP), where the last samples of each OFDM symbol are coped and placed n front of the samples generated by the IDFT The tmedoman samples of an OFDM symbol after CP nserton are gven by: s[k] = N a= ak j2π X[a]e N, NCP k N, () bts where N CP s the number of cyclc prefx samples The dgtal-to-analog converter (DAC) converts the dscretetme OFDM sequence () to a contnuous-tme sgnal by usng pulses spaced by an nterval The resultng sgnal s shaped by the transmt flter, and up-converted from the baseband to the hgh frequency of the carrer, n order to transmt the sgnal over the channel At the recever, the receved waveform s downconverted, passed through a receve flter and sampled at Nyqust rate by a TI-ADC The sgnal s h (t), whch s the nput of the TI-ADC, can be expressed as: s h (t) = k= s[k]h eq (t k ) + nose, (2) where s[k] s defned by () and h eq (t) s the equvalent mpulse response of the cascade of the transmt flter, the channel and the receve flter It s assumed that the duraton of h eq (t) s restrcted to the nterval [, N CP ] such that no ISI occurs To smplfy the notatons, we consder the transmsson of only one OFDM symbol and neglect other OFDM symbols transmtted n dfferent tme ntervals In that case, the output of the TI-ADC gven n Fg, can be wrtten as: r[m] = q= δ[m q l] (( + dg l ) s h [m dt l ] + do l ) + nose, m = N CP,, N, (3) where r[m] denotes the m th sample, s h [] s defned as s h [m] = s h (m ) and δ[] denotes the dscrete drac functon After removng the cyclc prefx, the samples r[m], m =,, N, from (3) are appled to a dscrete Fourer transform (DFT) The sgnal at the output of the DFT unt can be wrtten as: N mn j2π r[m]e N, n =,,, N R DF T [n] = N m= (4) The quanttes R DF T [n] are used to perform symbol detecton, after whch estmates of the nformaton bts are computed by eg applyng the nverse of the mappng rule To smplfy the notatonal complexty n our analyss, we assume that the number of sub-adcs s a power of two However, the extenson to other values of s straghtforward III ANAYSIS OF MISMATCH EFFECTS ON OFDM SPECTRUM In the lterature, the effect of the TI-ADC msmatches on (sngle-carrer) communcaton systems s commonly nvestgated by evaluatng the spectral behavor after the TI-ADC Therefore, n ths secton, we consder the effect of the msmatches on the spectrum of the OFDM sgnal To ths end, we consder the power spectral densty (PSD) after the TI-ADC, but n front of the DFT The PSD s approxmated by takng the averaged modulo-square
of the frequency response of the sgnal Neglectng the presence of the nose, the frequency response of r[m], m =,, N defned n (3), s found to be: N R jont (f) = r[m] e j2πfm m= N CP = ( ( + dgl ) S h (f) e j2πfdt l D l (f) ) + do l D l (f), where denotes convoluton, S h (f) s the frequency response of s h [m] gven by: S h (f) = N (5) m= N CP s h [m] e j2πfm, (6) and D l (f) s the frequency response of an nfnte sum of drac functons defned as: D l (f) = N m= N CP q= = δ(f = δ[m q l] e j2πfm 2π j ) e l Substtutng (7) nto (5), the frequency response of the output of the TI-ADC ncludng all msmatches s gven by: R jont (f) = + = + + = DGT (f) S h (f DO δ(f where DGT (f) and DO are gven by: DGT (f) = ), ) (7) (8) ( + dg l ) e j2π(f Ts )dtl 2π j e l, DO = (9) 2π j do l e l () Next, we separately consder the effect of the dfferent msmatches on the PSD to clearly solate the nfluence of each msmatch Offset Msmatch: In ths case, we consder the effect caused by the offset msmatch do l only The other msmatches are neglected, e, dg l = and dt l = The frequency response of r[m] n (3) becomes: R offset (f) = = S h (f )+ = DO δ(f where we used: { 2π j e l, f = s nteger, else ), () (2) Gan Msmatch: Smlarly, f the offset and tmng msmatch are gnored, e, do l = and dt l =, the frequency response of r[m] n the presence of the gan msmatch dg l s gven by: R gan (f) = = where DG s gven by: S h (f )+ DG = = DG S h (f ), (3) 2π j dg l e l (4) Tmng Msmatch: In ths case, only the tmng msmatch dt l s present and the other msmatches are not taken nto account The frequency response of r[m] can be expressed as: R tmng (f) = = where DT (f) s gven by: DT (f) = DT (f) S h (f e j2π(f Ts )dtl e ), (5) j 2π l (6) From (), t can be observed that offset msmatch causes the ntroducton of data-ndependent tones at frequences n the spectrum, whereas (3) ndcates that the gan msmatch produces replcas of the man OFDM spectrum, weghted by DG and shfted by Furthermore, from (5), t follows that the tmng msmatch has a smlar effect on the OFDM spectrum as the gan msmatch, but addtonally, the man spectrum and replca spectra are dstorted due to the frequency-dependent phase shft DT (f) caused by the tmng skew, as ndcated n (6) IV ANAYSIS OF MISMATCH EFFECTS ON DFT OUTPUT In the secton wth the numercal results, we wll show that the performance of the OFDM system n the presence of the msmatches s dffcult to evaluate based on the spectrum only Therefore, n ths secton, we evaluate the mpact of the msmatches caused by the TI-ADC on the OFDM sgnal at the DFT output n order to assess the nfluence of these msmatches on the performance Substtutng (3) nto (4) and neglectng the presence of the nose, we obtan: N R DFT jont [n] = N δ[m q l] ( m= q= ) ( + dg l ) + h eq [k]s[m k dt l ] + do l k= mn j2π e N, n =,,, N (7) et us defne H eq [] as the channel frequency response: H eq [a] = k= ka j2π h eq [k] e N, a =,,, N (8)
Takng nto account (8) and (), the DFT output (7) can be wrtten as: R DFT jont [n] = = ( ) N +dgl H eq [a] X[a] e j2π adt l N δ [ a n + N] a= + = = = + = do l 2π e j l δ [ n N] DGT ( n N ) H eq [n N] X[n N] DO δ[n N], n =,,, N, (9) where DGT () and DO are defned n (9) and (), respectvely To better understand the effect of each msmatch on the performance, we wll separately dscuss the nfluence of each msmatch on the DFT output requred to detect the data symbols Offset Msmatch: In ths case, the offset msmatch do l s present and the other msmatches are neglected The DFT output can be expressed as: R DFT offset [n] = 2π e j l H eq [n N] X[n N] = + DO δ[n N], n =,,, N = (2) Substtutng (2) nto (2), the DFT output becomes: R DFT offset [n] = H eq [n]x [n] + = DO δ[n N], n =,,, N, (2) where DO s defned n () Gan Msmatch: Smlarly, the DFT output wth the nfluence of the gan msmatch dg l can be expressed as: R DFT gan [n] = H eq [n]x[n] + DG H eq [n N]X[n N], = n =,,, N, (22) where DG s defned n (4) Tmng Msmatch: In the presence of the tmng msmatch dt l, the DFT output s gven by: R DFT tmng [n] = DT ( n N )H eq [n N]X[n N], = n =,,, N, (23) where DT () s defned n (6) As expected from Secton III, the offset msmatch ntroduces complex-valued data-ndependent peaks to the sub-carrers at postons N and a real-valued peak at frequency (see (2) and ()) Takng nto account that the data symbol transmtted on these sub-carrers are complex-valued, both the real and magnary part of these data symbols are affected by the offset msmatch Hence, for large sgnal-to-nose ratos (SNR) and suffcently large values of the offset msmatch, we expect an error floor n the performance Ths error floor can be approxmated by: offset Pr[no peak] [no peak] + Pr[peak] [peak], (24) where Pr[peak] = Pr[no peak] and Pr[peak] = N s the probablty that a sub-carrer s affected by a peak ntroduced by the offset msmatch, wth s the number of peaks occurrng n the data-bearng part of the DFT output The probablty [no peak] corresponds to the of the OFDM system as f no msmatch s present, whle [peak] s the probablty of a bt error f the carrer s affected by the offset msmatch In the worst case, when ths offset s large, on average half of the bts of the data symbols wll be erroneous Hence, [peak] can be approxmated by 2 for the sub-carrers N ( ) and 4 for =, where only the real part of the symbol s affected Ths results n the : offset ( N ) no msmatch + 2N + 4N (25) A smlar analyss for the gan msmatch and the tmng msmatch turns out to be more complex However, (22) and (23) ndcate that all sub-carrers are affected by the gan and tmng msmatch, whch could also be expected from the spectral contents gven n (3) and (5) Takng nto account that all sub-carrers are dsturbed by an nterference term, whch orgnates from other data symbols and s proportonal to the number of sub-adcs and the levels of the msmatches, t s expected that the wll sgnfcantly ncrease wth the number of sub- ADCs Furthermore, f the nterference term becomes the domnatng contrbuton, the wll show an error floor, whch wll become apparent at large SNR V NUMERICA RESUTS In ths secton, we frst nvestgate the valdty of the proposed expressons for the spectral behavor by comparng the theoretcal approxmatons for the PSD wth smulatons To llustrate the results, we use the European Dgtal Vdeo Broadcastng-Terrestral (DVB-T) 2k mode standard [8] as the PHY protocol We consder an OFDM sgnal contanng 75 data carrers and 343 unused carrers for the guard band; each of the data carrers s modulated wth symbols drawn from the 4- QAM constellaton The transmt and receve flter are a 3 th -order Butterworth lowpass flter wth a roll-off factor of 4 In the followng, we assume that the values of the msmatches are fxed To obtan these reference values, we selected them unformly n the ntervals [ A o ; A o ] for the offset msmatch and [ ; ] for the gan and tmng In case not all sub-carrers are modulated, some of the peaks occurrng n the spectrum at postons N wll not concde wth a data-bearng sub-carrer Hence, the number of sub-carrers affected by a peak s upper bounded by
msmatch, respectvely Here, A corresponds to the rootmean-square (RMS) ampltude value of the TI-ADC nput s h (t), defned as: A o = lm T (s h (t)) 2 dt (26) T T These ntervals correspond to % of the sgnal ampltude (for the offset and gan msmatch) and the Nyqust samplng rate (for the tmng msmatch), respectvely The selected reference values used throughout ths secton are gven n Table I Msmatches Offset ( do l A ) Gan (dg l ) Tmng (dt l ) TABE I MISMATCH PARAMETERS Reference values [6, 2, -59, -2, 3, -66, 4, -94] [33, -24, -95, -73, 485, -923, -59, 2] [-2,2, 5, -, 44, 39, -5, 62, 6] To solate the effect of the TI-ADC msmatches on the OFDM spectrum, we consder an deal channel Fg 3 llustrates the theoretcal spectra from Secton III as well as the smulated spectra based on Welch s perodogram [9] It s assumed that the number of sub-adcs s equal to 4 The msmatch values are fxed and gven by the frst four values for each msmatch ndcated n Table I Fg 3 shows that the smulaton results closely approach the theoretcal results, whch demonstrates the accuracy of the derved expressons From Fg 3, as expected, t can be seen that the offset msmatch causes peaks n the OFDM spectrum at frequences wth = [- 2,-,,,2] Furthermore, at frst sght, the effect of the gan msmatch on the spectrum s small The addton of the replcas of the man spectrum, centered around the frequences wth = [-2,-,,,2] and weghted by DG (4), only ntroduces small varatons n the spectrum compared to the case of no msmatch Although the effect of the tmng msmatch s smlar to that of the gan msmatch, e copes of the man spectrum centered around the frequences, and addtonally dstorted by DT (f) (6), the effect of the tmng msmatch s better vsble n the spectrum, especally n the center of the frequency band Combnng all three effects, n Fg 3d, manly the effects of the offset msmatch and the tmng msmatch are vsble However, although at frst sght, the gan msmatch and tmng msmatch have only small effect on the spectrum of OFDM at the output of the TI-ADC, we wll see later n ths secton, when evaluatng the outputs of the DFT and the correspondng curves, that the gan and tmng msmatch wll have a larger nfluence on the OFDM performance than the offset msmatch, manly because more sub-carrers are affected Hence, the spectrum at the TI-ADC output, whch s commonly used n the lterature to evaluate the effect of the msmatches, turns out to be not effectve n OFDM applcatons Therefore, we wll have to resort to the analyss of the DFT output and the results Fg 4 compares the real and magnary part of the DFT output obtaned wth the expressons (9)-(23) and through smulatons Agan, Fg 4 shows that the smulaton results are close to the theoretcal results, whch llustrates the accuracy of the proposed expressons As expected, the offset msmatch causes complex-valued peaks at the N-ndex sub-carrers ( ) and a realvalued peak at the th sub-carrer For large offsets, we ponted out n Secton IV that the offset msmatch would lead to an error floor n the curve at hgh SNR In our example, where = 3, the error floor from (25) s expected to be approxmately 74x 4 Furthermore, n Fg 4b and Fg 4c, t can be observed that the gan and tmng msmatch equally affects the real and magnary parts of the DFT output, although n the case of the gan msmatch, manly the outer sub-carrers, whle for the tmng msmatch more the central sub-carrers are dsturbed Nevertheless, both results demonstrate that a much larger part of the sub-carrers s dstorted by the nterference component ntroduced by the gan and tmng msmatch, compared to the case of the offset msmatch Hence, when ths nterference component becomes the domnatng contrbuton, whch wll happen f the number of sub-adcs ncreases, or when the level of the msmatches ncreases, we expect that t wll ntroduce a floor that s much hgher than that for the offset msmatch Next, we present the nfluence of the msmatches on the performance The results from Fg 5 are obtaned by transmttng 4-QAM modulated data symbols n 2 OFDM symbols over an AWGN channel The dfferent curves n each of the sub-graphs correspond to = 2, 4 and 8 sub-adcs The msmatches consdered for the producton of the graphs are selected as the frst 2, 4 or 8 values for each msmatch n Table I, respectvely As expected, n the case of the offset msmatch, the curves from Fg 5a show error floors Based on (25), the expected values for these error floors are approxmated by 5x 4 for 2 sub-adcs ( = ), 74x 4 for 4 sub-adcs ( = 3) and 9x 3 for 8 sub-adcs ( = 7), respectvely As can be observed from Fg 5a, the error floors of the smulated curves are close to these theoretcal approxmatons Hence, (25) can easly be used to predct the performance of the OFDM system n the presence of a suffcently large offset msmatch Furthermore, the effects of the gan msmatch and the tmng msmatch on the performance are presented n Fg 5b and Fg 5c, respectvely As can be observed, no error floor occurs for 2 sub-adcs, although the performance s strongly degraded by the presence of the gan and tmng msmatch, but when the number of sub-adcs ncreases, a large part of the DFT outputs wll be affected by an nterference term, resultng n the error floor observed n the fgure Comparng Fg 5b and Fg 5c, the effect of the tmng msmatch s larger than that of the gan msmatch Ths could also be observed n Fg 4 where the level of the nterference contrbuton s larger for the tmng msmatch than for the gan msmatch For both cases, the level of the error floor s much hgher than
a) -5-6 b) -5-6 PSD (db/hz) c) PSD (db/hz) -7-8 -9 - - -5-4 -3-2 - 2 3 4 5 Normalzed Frequency -5-6 -7-8 -9 - Msmatch by smulaton Msmatch by theory Msmatch by smulaton Msmatch by theory - -5-4 -3-2 - 2 3 4 5 Normalzed Frequency PSD (db/hz) d) PSD (db/hz) -7-8 -9 - - -5-4 -3-2 - 2 3 4 5 Normalzed Frequency -5-6 -7-8 -9 - Msmatch by smulaton Msmatch by theory Msmatch by smulaton Msmatch by theory - -5-4 -3-2 - 2 3 4 5 Normalzed Frequency Fg 3 The OFDM spectrum of the TI-ADC output wth frequency normalzed to msmatch, b) Gan msmatch, c) Tmng msmatch, d) Jont msmatch and % msmatch level, n the presence of: a) Offset a) Ampltude (db) b) Ampltude (db) c) Ampltude (db) d) Ampltude (db) 2 8 6 4 2-2 2 - -2 2 - -2 2 8 6 4 2-2 The real part Normalzed Frequency Normalzed Frequency Normalzed Frequency Normalzed Frequency The magnary part Msmatch by smulaton Msmatch by theory Normalzed Frequency Msmatch by smulaton Msmatch by theory Normalzed Frequency Msmatch by smulaton Msmatch by theory Normalzed Frequency Msmatch by smulaton Msmatch by theory Normalzed Frequency Fg 4 The real part and the magnary part of the DFT output wth frequency normalzed to and % msmatch level, n the presence of: a) Offset msmatch, b) Gan msmatch, c) Tmng msmatch, d) Jont Msmatch
a) b) c) E-3 E-4 E-5 E-6 5 5 2 25 9x -3 74x -4 5x -4 Msmatch by 2 sub-adcs Msmatch by 4 sub-adcs Msmatch by 8 sub-adcs d) E-3 E-4 E-5 E-6 Msmatch by 2 sub-adcs Msmatch by 4 sub-adcs Msmatch by 8 sub-adcs 5 5 2 25 E-3 E-4 E-3 E-4 E-5 E-6 Msmatch by 2 sub-adcs Msmatch by 4 sub-adcs Msmatch by 8 sub-adcs 5 5 2 25 E-5 E-6 Msmatch by 2 sub-adcs Msmatch by 4 sub-adcs Msmatch by 8 sub-adcs 5 5 2 25 Fg 5 versus Eb/No wth % msmatch level, n the case of: a) Offset msmatch, b) Gan msmatch, c) Tmng msmatch, d) Jont msmatch The numbers n Fg 5a are the theoretcal error floor values obtaned wth (25) for the offset msmatch Ths can be explaned as a larger part of the DFT outputs wll be affected by nterference, although for the offset msmatch, the few sub-carrers that are affected by the offset msmatch experence a hgher nterference level, as can be seen n Fg 4d Furthermore, for all msmatches, we observe that the degradaton ncreases when the number of sub-adcs ncreases The domnatng effect s the tmng msmatch, as can be seen from Fg 5d Up to now, we have evaluated the effect of the dfferent msmatches for a fxed level of the msmatches, correspondng to % of the sgnal ampltude (for the offset and gan msmatch) and % of the samplng rate (for the tmng msmatch) Next, we wll consder the effect of the level of the msmatches on the performance Fg 6 shows the performance for the jont msmatch effect n the case of 4 sub-adcs wth three msmatch settngs of %, 5% and % For these later two cases, we smply scale the reference values n Table I by a factor 2 and, respectvely As can be observed n Fg 6, the cases of % msmatch and 5% msmatch do not exhbt an error floor Ths ndcates that the offset msmatch ntroduces an nterference term that s suffcently small to not nduce the error floor gven n (25) In addton, also the nterference terms caused by gan and tmng msmatch do not cause an nterference that gves rse to an error floor, n contrast wth the case of the % msmatch level However, even for the case of a % msmatch level, the performance wll be strongly degraded by the presence of the msmatches, ndcatng that even small msmatches cannot be tolerated n an OFDM system E-3 E-4 E-5 E-6 E-7 E-8 E-9 % msmatch 5% msmatch % msmatch 5 5 2 25 Fg 6 versus Eb/No n the presence of the jont msmatch for 4 sub-adcs wth the dfferent msmatch levels
VI CONCUSIONS Hgh-speed samplng ADCs are consdered as the bottleneck of mult-ggabt OFDM-based systems due to the hardware lmtatons of current technology An effcent approach to overcome ths problem s the use of multple parallel ADCs n a tme-nterleaved archtecture However, msmatches between the parallel sub-adcs, such as offset, gan and tmng msmatch can sgnfcantly degrade the system performance In ths paper, we analytcally studed the nfluence of the TI-ADC msmatches on the spectrum and the DFT output of the OFDM system It turns out that the evaluaton of the spectrum, whch s commonly used n the lterature to descrbe the effects of the msmatches on snusodal sgnals, s not effectve to study ther nfluence on OFDM sgnals Therefore, we consdered the output of the DFT and the correspondng performance to evaluate the effects of these msmatches The analytcal expressons for the spectrum and the DFT output were compared wth smulaton results, and we found that our theoretcal expressons are hghly accurate Hence, these expressons can be used for further nvestgatons on the TI-ADC usage for hgh-speed OFDM systems In the case of the offset msmatch, we showed that only a few sub-carrers are affected by an nterference term, that could lead to an error floor n the performance f the level of the msmatch s suffcently hgh A smple way to overcome ths senstvty of the OFDM system to the offset msmatch s to not modulate the sub-carrers where a peak ntroduced by the offset msmatch occurs However, especally when the number of sub-adcs further ncreases, such that more sub-carrers are affected by peaks, ths would lead to a strong reducton n the throughput effcency For the gan and tmng msmatches, such a smple soluton as for the offset msmatch s not avalable, as a much larger number of carrers s affected by an nterference term Hence, the degradaton s much larger than for the offset msmatch When all msmatches are present, we showed that the degradaton ncreases wth both the levels of the msmatches and the number of sub-adcs, and even n the presence of a very small level of the msmatches, the performance strongly degrades Hence, to overcome ths problem, we wll need to compensate the effects of the msmatches, ether by usng hardware-compensated TI-ADCs, resultng n very expensve TI-ADCs, or by estmatng and compensatng the msmatches through DSP, whch would allow the usage of low-cost TI-ADCs REFERENCES [] W Sheh et al, Orthogonal Frequency Dvson Multplexng for Optcal Communcatons, Academc Press, USA, 29 [2] S Ponnuru et al, Jont Msmatch and Channel Compensaton for Hgh-Speed OFDM Recevers wth Tme-Interleaved ADCs, IEEE Transacton on Communcatons, vol 58, no 8, 2 [3] Ken Poulton, Tme-Interleaved ADCs, Past and Future, IEEE Internatonal Sold State Crcuts Conference, February, 29 [4] Y Zheng et al, DC Offset Msmatch Calbraton for Tme- Interleaved ADCs n Hgh-Speed OFDM Recevers, CCIS 337, Sprnger, pp 22-23, 23 [5] Yang et al, Oversamplng to Reduce the Effect of Tmng Jtter on Hgh Speed OFDM Systems, IEEE Communcatons etters, vol 4, no 3, March 2 [6] K N Manoj et al, The effect of samplng jtter n OFDM systems, IEEE Internatonal Conference on Communcatons, vol 3, pp 26-265, May 23 [7] J Elbornsson et al, Analyss of Msmatch Effects n a Randomly Interleaved A/D Converter System, IEEE Transactons on Crcut and Systems, vol 52, no 3, 25 [8] ETS 3 744, Dgtal broadcastng systems for televson, sound and data servces; framng structure, channel codng, and modulaton for dgtal terrestral televson, European Telecommuncatons Standard, DOC 3 744, 779 [9] P D Welch, The Use of Fast Fourer Transform for The Estmaton of Power Spectra: A Method Based on Tme Averagng Over Short, Modfed Perodograms, IEEE Transactons on Audo and Electroacoustcs, vol AU-5, pp 7-73, 967 VII ACKNOWEDGEMENT The frst author gratefully acknowledges the European Commsson for hs Erasmus Mundus scholarshp Ths research has been funded by the Interunversty Attracton Poles Programme ntated by the Belgan Scence Polcy Offce The authors would lke to thank Prof Ken Poulton for the helpful dscussons