Frequency Selective IQ Phase and IQ Amplitude Imbalance Adjustments for OFDM Direct Conversion Transmitters

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1 Frequency Selectve IQ Phase and IQ Ampltude Imbalance Adjustments for OFDM Drect Converson ransmtters Edmund Coersmeer, Ernst Zelnsk Noka, Meesmannstrasse 103, Bochum, Germany Abstract Low power and low cost analog front-end archtectures are requred to provde compettve applcatons based on e.g. the IEEE802.11a Wreless LAN standard. Drect converson analog front-end archtectures can fulfll these demands but may ntroduce unwanted mperfectons lke IQ ampltude and IQ phase errors. hs paper presents a fully dgtal soluton to elmnate frequency selectve IQ phase and IQ ampltude mbalance errors caused by the analog modulator n conjuncton wth low cost analog base-band flters. hs paper covers addtonally the relevant hardware and software parttonng of the related error detecton and error correcton blocks. Index erms OFDM, drect converson, frequency selectve IQ phase mbalance, frequency selectve IQ ampltude mbalance I. Introducton Fully dgtal compensaton technques for IQ phase and IQ ampltude mbalance errors provde advantages, because they offer a cheap soluton wth regards to the overall rado archtecture. he IQ mbalance errors can appear n the case of a drect converson analog frontend archtecture. hese archtectures are recommendable f the rado applcaton requres a low cost soluton. hs s very often true for portable or wreless devces such as IEEE802.11a Wreless LAN applcatons. o provde anyhow the requred hgh sgnal accuracy one has to guarantee that the analog drect converson front-end IQ mperfectons wll be elmnated satsfactory. he use of cheap analog front-end components mght ntroduce analog flter ampltude rpple and group delay, whch make the IQ mbalance errors frequency selectve. he frequency selectvty can be removed successfully by employng frequency selectve IQ phase and frequency selectve IQ ampltude adjustment algorthms. he here presented tme doman adjustment technques employ a decson drected IQ ampltude and flter pre-equalzer. he non-decson aded IQ phase adjustment provdes a pre-equalzer-lke archtecture and processes a certan amount of tme doman coeffcents, too. Both mperfectons, the frequency selectve IQ ampltude and IQ phase mbalance errors, can be assumed to vary very slowly over a certan perod of tme. Hence the IQ error detectons are requred durng the trackng phase relatvely seldom. In contrast to that the IQ error correctons are needed all the tme to correct all outgong samples contnuously. Hence t s possble to mplement the IQ error detecton algorthms va software on a Dgtal-Sgnal-Processor (DSP) and the IQ error correctons va hardware n an ASIC or FPGA. Based on an example for a drect converson OFDM transmtter ths paper wll present the mathematcal equatons for an IQ phase and IQ ampltude mbalance error generaton and the correspondng frequency selectve IQ phase and IQ ampltude error adjustments. For both algorthms there wll be gven an mplementaton overvew and smulaton results provde vsual comparablty. II. Drect Converson Front-End A possble drect converson analog front end for an IEEE802.11a OFDM transmtter s gven by fgure 1). Startng from the left upper corner n fgure 1) the dgtal IQ symbols are generated and the IFF block converts them from the frequency doman to the tme doman. he next block takes care about correctng the IQ ampltude and analog flter mperfectons va a preequalzer. he IQ phase error s pre-compensated by the IQ phase pre-equalzer. Both blocks operate on the deal ncomng tme doman symbols and pre-modfy these wth the correspondng correcton values.

2 After the IQ pre-processng has been fnshed the dgtal sgnal s handed over to the analog doman, where the analog low-pass flters mght nsert flter ampltude rpple and group delay. he analog base-band I-branch and the analog Q-branch dffer physcally and hence the analog flters most probably do not equal exactly. Hence the frequency selectve I- and Q-mperfectons n both branches dffer and the correctng pre-equalzers operate as real-number devces n both branches ndependently. Complex-number pre-equalzers would not be able to provde the requred correctons. BPSK, QPSK, QAM IFF RF Adaptve Flter + IQ Ampltude Pre-Equalzer 5-6 GHz IQ Ampltude Error Detecton Sgnal Measurement Adaptve IQ Phase-Equalzer IQ Phase Error Detecton IQ Estmaton Baseband Fg. 1. Example of an IEEE802.11a wreless LAN drect converson analog front-end. he analog IQ modulator wll add the IQ phase mbalance mperfectons. Fnally the outgong sgnal wll be measured at the antenna nput port. An analog envelope measurement s fed back to the dgtal baseband transmtter doman. he envelope can act as the sgnal source to fnd out the requred nformaton about the IQ mperfectons. A dgtal base-band block provdes estmates of the vrtual analog I- and Q-values at the antenna nput port wthout a down-modulaton process. Because the RF sgnal s real and not complex, one can only estmate base-band equvalent I- and Q- branch samples. In case of possble estmaton errors t can be assumed that the wrong values are neglgble durng the loops trackng phase. Durng the acquston mode the IQ estmaton n conjuncton wth the IQ feedback loops provde relable estmates, too. Durng that tme wrong estmates wll be low-pass fltered through the feedback loop archtecture. After the analog I- and Q-symbol estmaton has been calculated successfully, the frequency selectve IQ phase and IQ ampltude error detecton take place. he IQ phase error detecton s a blnd algorthm and requres only the IQ symbol nput from the estmaton block. he IQ ampltude and flter error detecton algorthm needs both, the analog IQ estmates and the correspondng deal IQ symbols. All nformaton s necessary, because the IQ ampltude and flter preequalzer s decson aded. After all errors have been calculated and the correcton coeffcents for both preequalzers have been provded, the feedback loops close wth the IQ correcton blocks. he next sectons wll provde mathematcal descrptons, block and mplementaton dagrams for the IQ phase and IQ ampltude error generaton and the error adjustments. III. IQ Phase Imbalance Error For the analog mxng process two sgnals, a sne- and a cosne-sgnal, have to be provded. Because of techncal reasons precse orthogonal functons cannot be guaranteed and hence an addtonal offset angle ϕ 0 wll be measurable between the sne- and cosnefunctons. hs phenomenon wll be called nonfrequency selectve IQ phase mbalance error. Addtonally the analog base-band components lke low-pass flters mght add frequency selectve mperfectons lke ampltude rpple or group delay. Hence the non-frequency selectve IQ phase mbalance mperfectons wll result n frequency selectve IQ phase mbalance naccuraces. he non-frequency IQ phase mbalance error s formulated n equaton (1). s'(t) = I'(t) + j Q(t) = I(t) + Q(t) sn( ϕ) + j Q(t) (1) One can see, that a certan part of the Q-branch, whch s proportonal to sn(ϕ), has been added to the I- branch. Hence the deal, un-correlated I- and Q- branches wll be correlated after an IQ phase error has been nserted. Before the IQ phase error nserton n equaton (1) takes place mperfect analog flters mght ntroduce frequency selectvty. Hence at the antenna nput port t s not possble anymore to dvde between the IQ phase mbalance and the analog flter effects. Hence dgtal pre-compensaton technques need to employ a pre-correctng sgnal that provdes frequency selectvty. hs can be acheved by a pre-equalzer-lke compensaton archtecture, whch wll be presented n ths paper. he IQ phase error nserton normally ntroduces at the same tme a small IQ ampltude error. hs addtonal IQ ampltude error has been neglected n equaton (1). IV. IQ Ampltude Imbalance Error he IQ ampltude mbalance error s formulated n equaton (2).

3 s' (t) = I'(t) + j Q '(t) = a I(t) + j b Q(t) (2) Each of the two branches can have an own amplfcaton factor, because analog I-branch and Q- branch components mght dffer n terms of ther amplfcaton. Because the analog flters wll ntroduce ampltude rpple n the pass-band the IQ mbalance errors mght become frequency dependent. A tme doman pre-equalzer handles the frequency selectve mperfectons [4]. he followng two sectons ntroduce the frequency selectve IQ phase and the frequency selectve IQ ampltude adjustment loops. V. Frequency Selectve IQ Phase Imbalance Adjustment In ths secton t s assumed that one or both analog base-band flters provde mperfectons. hese mperfectons could be one or more tems lke ampltude rpple or non-lnear flter phase behavor. Because of these addtonal mperfectons a nonfrequency selectve IQ phase mbalance adjustment loop locks to a wrong error value. Hence t s necessary to mplement an IQ phase mbalance error detector, whch s frequency selectve and able to cover analog flter mperfectons. he I and Q syntax defnes I and Q samples whch are afflcted by the frequency selectvty of the analog flters. Equaton (3) descrbes the mathematcal operatons for the error detecton e. N dfferent IQ phase errors are calculated. e [ n] = I [ n ( N 1) / 2] Q[ n ( 1) ] (3) = 1,2,, N In ths paper t s assumed that N s an odd number. Fgure 2) presents a possble mplementaton setup. he center-tap (N-1)/2 of the I-branch wll be multpled wth N dfferent values from the Q-branch. Equaton (4) shows that each error value e wll be low-pass fltered by ts own ntegrator. n [ n] = µ e [ k] c, = 1, k= 0, N (4) he constant µ descrbes the step wdth of the adaptaton loop. he fnal frequency selectve IQ phase mbalance error correcton wll be done by equaton (5) and fgure 3). I' [ n ( N 1) / 2] = 1,2,, N = I [ n ( N 1) / 2] N = 1 c and m > 0 [ n m] Q[ n ( 1) ] (5) he varable m descrbes the mplemented loop latency. Smlar to a normal pre-equalzer the Q-branch values from the tap-delay lne are multpled wth the correspondng correcton coeffcents c and are summed up. hs result s subtracted from the perfect I- branch center tap. Hence the dgtal I-branch values start to provde a frequency selectve IQ phase mbalance error, whch wll be compensated after the analog IQ phase mbalance error has been nserted. Frequency selectvty s needed to pass the analog baseband flters correctly. I Q I'[n-(N-1)/2] + - I'[n-(N-1)/2] I I[n-(N-1)/2] c 1 c 2 c 3 c 4 c N Q Q[n-(N-1)] Fg. 3) Frequency selectve IQ phase correcton. N=5. e 1 e 2 e 3 e 4 e N Fg. 2) Frequency selectve IQ phase mbalance error detector. N = 5. VI. Frequency Selectve IQ Ampltude Imbalance Adjustment In ths secton there wll be ntroduced an LMS based equalzer [4], whch does not operate wth complex coeffcents, but wth real ones. hs s unusual but makes t possble to handle I-branch and Q-branch mperfectons ndependently. he I-branch and Q-

4 branch flter mperfectons are generated by the analog base-band flters, whch are two real flters. he IQ ampltude error detecton wll be done va equaton (6). e I [ n] = I[ n] I[ n] (6) e n = Q n Q n Q [ ] [ ] [ ] From the deal transmtted symbols there wll be subtracted the mperfect estmated symbols. he calculated errors of both branches need not to be the same values. Hence there have to be calculated for both branches ndependent correcton coeffcents. hs s descrbed by equaton (7). he new coeffcents at the tme n+1 wll be calculated from the current coeffcents at the tme n and an addtonal addend. # [ n 1] = c [ n] + e [ n] D [ n] [ n] c + µ (7) I, Q I,Q I,Q I,Q h I,Q he addend conssts out of four factors. Frst the constant µ descrbes the step wdth. he step wdth defnes the loop accuracy, loop adaptaton speed or loop bandwdth. Because the expected IQ ampltude mbalance errors wll not change over a very long perod of tme the loop bandwdth needs not to be large and hence the loop accuracy can be hgh. he second factor s the calculated error from equaton (6). After that the product of the deal nput data matrx D and an approxmaton h # [3] of the analog flters h I,Q follows. he approxmatons of both analog flters wll be smple tap-delay lnes, provdng the same latency as the analog flters contan. After the update of the coeffcent vectors the correcton takes place n programmable FIR flters. VII. HW and SW Parttonng o enable a flexble rado desgn t s useful to mplement some functonalty va software and not only hardware. he advantage s that software code can be optmsed n an exstng rado envronment. A dsadvantage mght be that a Dgtal-Sgnal-Processor (DSP) has not enough processng power to calculate hgh data rate functons n tme. Both new adjustment loops requre three dfferent steps. he frst one takes care about the IQ sample estmaton from the envelope. he second provdes the error detecton of the IQ phase and IQ ampltude mperfectons. he last step handles the error correctons. Assumng that the IQ mperfectons are stable over a long perod of tme and they wll not change ther values rapdly t s possble to employ for the IQ sample estmaton and the IQ error detecton algorthms a DSP-based software approach. hs s possble because the low rate of error value changes does requre only a low rate of error detecton updates and a low rate of the IQ sample estmatons. Hence a DSP, whch mght not handle the same operatons on symbol rate n tme, wll be able to process now a lmted number of operatons based on a lower sample rate. Assumng that the DSP processng power s not enough to handle the symbol rate based error correctons t s stll necessary to employ hardware for both IQ correcton blocks. Fgure 4) provdes a hardwaresoftware parttonng overvew. hree blocks from fgure 1) have been replaced by the DSP. In ths new archtecture the envelope measurement results and deal IQ samples wll be transferred through the data bus to the processor. he nstructon memory provdes the software-based algorthms and the correcton values wll be transferred by the data bus to the IQ correcton blocks. he advantage of the software-based approach s the chance to change the IQ sample estmaton and error detecton after the overall system mplementaton has been fnalzed. he success of the IQ compensatons s strongly dependng on the algorthm development based on the modellng qualty of the analog components. Mght the analog components change wth regards to the used smulaton models, t s an advantage to be able to change the IQ sample estmaton and IQ error detecton, too. Changes of the analog components mght appear because of techncal or commercal reasons. BPSK, QPSK, QAM IFF Sgnal Measurement RF Fg. 4) DSP-based IQ estmaton and error detecton. VIII. Smulaton Results Adaptve Flter + IQ Ampltude Pre-Equalzer 5-6 GHz Adaptve IQ Phase-Equalzer Baseband Fgures 5)-8) show dfferent IQ dagrams n an IEEE802.11a OFDM envronment. Fgure 5) provdes the mperfect IQ symbols after deal down-modulaton. he mperfectons were caused by IQ phase and IQ ampltude errors. Frequency selectvty has been added by mperfect analog base-band flters. Both base-band flters have slghtly dfferent transferfunctons. DSP Data Bus Data & Instructon Memory

5 Fgure 8) provdes the requred accuracy. Both adjustment loops employ 19-coeffcents for each correcton loop. he constellaton ponts provde the requred accuracy. Fg. 5) Imperfect IQ dagram.ϕ = -10.a = 0.7,b = 1.0. Fgure 6) provdes the frst corrected results. A 19- coeffcent flter pre-equalzer and a non-frequency selectve IQ phase adjustment do not provde full IQ compensaton. Fg. 8) 19-coeffcent IQ phase adj., 19-coeffcent IQ ampltude adjustment. ϕ = -10. a = 0.7, b = 1.0. he remanng phase shft of about -10 has been generated by the IQ phase error and wll not be compensated. Fg. 6) 1-coeffcent IQ phase adj., 19-coeffcent IQ ampltude adjustment. ϕ = -10. a = 0.7, b = 1.0. Fgure 7) dffers from fgure 6) only because the IQ phase pre-equalzer coeffcent number equals 3. IX. Concluson hs paper provdes two dfferent tme-doman algorthms to handle frequency selectve IQ phase and IQ ampltude mbalance errors n an OFDM transmtter. By parttonng the algorthms nto hardware and software t s possble to adapt crtcal parts of the dgtal algorthm based on new realzatons of the analog components. In the case of a software-based approach t s mportant to consder the loop update rate. he smulaton results show that the algorthms wll provde sgnfcant mprovements to the IQ samples n case of frequency selectve IQ mperfectons. References [1] A Novel IQ Imbalance Compensaton Scheme for the Recepton of OFDM Sgnals, A. Schuchert, R. Hasholzner, IEEE rans. on Consumer Elec., Vol. 47 Is. 3, Aug. 01 [2] Frequency Selectve IQ Phase Imbalance Adjustment n OFDM Drect Converson Recevers, E. Coersmeer, IEEE ISCE 02, Erfurt, Germany [3] Comparson Between Dfferent Adaptve Pre-Equalzaton Approaches For WLAN, E. Coersmeer, E. Zelnsk, IEEE PIMRC 2002, Lsabon, Portugal [4] Adaptve Flter heory, Smon Haykn, Prentce Hall hrd Edton, 1996 Fg. 7) 3-coeffcent IQ phase adj., 19-coeffcent IQ ampltude adjustment. ϕ = -10. a = 0.7, b = 1.0.

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