Adaptive self-calibrating image rejection receiver.

Transcription

1 Univsiy of Wsmins Epins hp://pins.wmin.ac.uk Adapiv slf-calibaing imag cion civ. Ediz Cin Izz Kal Richad Moling Cavndish School of Compu Scinc Copyigh [4 IEEE. Rpind fom 4 IEEE Innaional Confnc on Communicaions (ICC 4), pp This maial is posd h wih pmission of h IEEE. Such pmission of h IEEE dos no in any way imply IEEE ndosmn of any of h Univsiy of Wsmins's poducs o svics. Innal o psonal us of his maial is pmid. Howv, pmission o pin/publish his maial fo advising o pomoional puposs o fo caing nw collciv woks fo sal o disibuion mus b obaind fom h IEEE by wiing o pubs-pmissions@i.og. By choosing o viw his documn, you ag o all povisions of h copyigh laws pocing i. Th Epins svic a h Univsiy of Wsmins aims o mak h sach oupu of h Univsiy availabl o a wid audinc. Copyigh and Moal Righs main wih h auhos and/o copyigh owns. Uss a pmid o download and/o pin on copy fo non-commcial piva sudy o sach. Fuh disibuion and any us of maial fom wihin his achiv fo pofi-making npiss o fo commcial gain is sicly fobiddn. Whils fuh disibuion of spcific maials fom wihin his achiv is fobiddn, you may fly disibu h URL of h Univsiy of Wsmins Epins (hp://pins.wmin.ac.uk). In cas of abus o copyigh appaing wihou pmission -mail wasn@wmin.ac.uk.

2 ADAPTIVE SELF-CALIBRATING IMAGE REJECTION RECEIVER Ediz Çin, İzz Kal and Richad C. S. Moling Dpamn of Elconic Sysms, Applid DSP and VLSI Rsach Goup, Univsiy of Wsmins London, Unid Kingdom Absac An adapiv slf-calibaing imag cion civ is dscibd, conaining a modifid Wav imag cion mix and a Digial Imag Rcion Pocsso (DIRP). Th blind souc-spaaion-basd DIRP liminas h I/Q os impoving h Imag Rcion Raio () wihou h nd fo imming o us of pow-hungy disc componns. Hadwa complxiy is minimal, quiing only wo complx cofficins; hnc i can b asily ingad ino h signal pocssing pah of any civ. Simulaion suls show ha h poposd appoach achivs db of. Kywods- Imag-cion-civ, Adapiv I/Q-cocion, Phas and gain mismach,unsupvisd/blind signal pocssing. I. INTRODUCTION Imag cion civs uiliz in-phas and quadau (I/Q) signal pocssing in pocssing of bandpass signals. Howv, analog implmnaions of I/Q signal pocssing is vulnabl o phas and gain mismachs bwn h I and Q banchs of h civ. This suls in impfc imag cion, which is no sufficin fo communicaions applicaions lading o sv pfomanc dgadaion. Thfo, digial chniqus which will nhanc his imag cion and allvia h I and Q channl mismachs play an impoan ol in simplifying h analog fon-nds in fuu high pfomanc highly-ingad singl-chip wilss civs. Convnional imag cion achicus a implmnd by analog cicui chniqus [ [4. Howv, hybid and digial soluions hav also bn pod in h liau ying o impov [5 - [7. In his pap w popos digial slf-calibaing imag cion civ achicu o ovcom h pfomanc dgadaion du o analog fon-nd nonlinaiis. Th poposd chniqu uss unsupvisd/blind digial signal pocssing chniqus o sima nonlinaiis and compnsa fo hm in al-im duing h nomal opaion of h civ. Th civ can adap is configuaion o h nvionmn, a mao faco fo mainaining pfomanc und almos all cicumsancs. Wha is mo, h algoihm can b asily ingad ino h sandad digial signal pocssing pah fo any civ wih a minimal hadwa ovhad. Th pap is oganizd as follows: Scion II dfins h achicu of h adapiv imag cion civ. Scion III dscibs h pfomanc analysis and h simulaion suls, whil concluding maks a givn in Scion IV. II. ADAPTIVE IMAGE REJECTION RECEIVER ARCHITECTURE This scion dscibs h slf-calibaing adapiv imag cion civ achicu, block diagam of which is shown in Fig.. In his achicu, a Radio Fquncy (RF) signal is civd by an annna and passd hough an RF fon-nd o poduc a bandpass signal. This signal is hn digiisd and sn o an imag-cion civ o suppss h imag signal incasing h imag cion ha can b achivd. Th slf-calibaing adapiv imag cion civ can b dividd ino wo pas. Fis pa is h modifid Wav imag cion mix, and h scond pa is h Digial Imag Rcion Pocsso (DIRP). Th modifid Wav imag cion mix gnas wo complx digial oupu signals, and, wh h signal mphasizs h dsid signal and mphasizs h imag signal. Th DIRP uilizs boh signals and o achiv incasd dg of imag cion. ~ RF-Fil LNA Poposd Achicu c I Imag Rcion Mix Q Digial Imag Rcion Pocsso Figu. Imag cion civ sysm. c Basband DSP In h following wo subscions w fis dscib h imag cion mix. Thn w inoduc h DIRP. A. Imag Rcion Mix Th block diagam of h modifid Wav imag cion mix is shown in Fig.. Th incoming signal, s(, consiss of h wand signal u( a f RF and unwand imag signal a f IMG wh f IMG = f RF f IF. Hnc, h incoming signal s( can b xpssd as: { } { } π f RF π f IMG u( s( = R R () IEEE Communicaions Sociy 73

3 (f) f IF RF Inpu spcum s(f) Inf -f RF -f img f img f RF Lakd Wand Signal f ϕ cos(πf ε ) α ε α - ε ϕ -sin(πf - ε ) Phas o Analog Phas o Gain o I Q IF spcum IF (f) ADC ADC Digial cos(πf II IQ -sin(πf cos(πf QI QQ -sin(πf I Q I Q dc (f) dc f -f IF f IF f Figu. Imag Rcion Mix. wh u( and a h complx nvlops of h wand and imag signals spcivly. To simplify h analysis, whol phas and gain imbalancs bwn h I and Q channls a modlld as an unbalancd quadau downconv [8. Th onous complx signal, x (= I Q, is givn as: x πf ( = ( g ) ( g g πf ) () wh g =(α ε ), g =(-α ε ) and ϕ ε is h phas and α ε is h gain mismach bwn h I and Q channls. As shown in Fig., h civd signal s( is quadau mixd wih h non-idal signal, x, and low-pass fild suling in an IF signal IF (= I Q, which can b xpssd as: [ i ( ( g ) πf πf IF ( g g ) πf IF IF IF ( = [ u( ( g g ) u ( ( g ) (3) πf IF wh h dsid signal u( is coupd by h imag lakd in-band du o analog mismachs. Th is also a lakag fom h dsid signal ino h imag channl. A fquncy domain illusaion, IF ( f ), of his is givn Fig.. In a fully balancd sysm, howv, h wand signal and h inf a downconvd o opposi fquncis f IF and f IF. Signals I and Q a hn convd ino h digial domain. Following his, anoh mix sag aks ca of h final downconvsion fom IF o basband. As his convsion sag aks plac in h digial domain, h I and Q channls a machd hnc, idal mixing is assumd lading o h following s of fou signals: II = g [ u( IQ = g [ u( QQ = g [ u( QI = g [ u( u ( u ( u ( u ( i ( i ( i ( i ( Th I and Q signals of h dsid channl coupd by h imag signal du o h phas and gain os can b xpssd as: (4) I Q = II QQ ( g ( g = IQ QI = [ u( ( g g g ) u ) i ( ( g ( ( g ) u ( g ) i ( ( g Combining hm as I Q yilds: ( ( g g g ) ) ) g ) i ( ( g ) ) ( g (6) This conains h dsid signal coupd by h imag signal scald by h, supimposd du o h phas and gain os. This is dmonsad in h fquncy domain in h op-igh con of Fig.. Th Wav achicu is fuh xndd, a h xpns of xa adds, o povid anoh channl,, which conains h imag signal infd by h dsid signal du o I/Q os ( makd as on Fig. ). Th I and Q signals of can b xpssd as: I Q = II QQ ( g ( g = IQ QI = [ u( ( g g g ) u ( ( g ) i ( ( g g ) u ( g g ) i ( ( g Combining hm as I Q yilds: g ( ( g g h g ) ) ) ) ( g ) i ( ( g ) h wh h imag signal is coupd by dsid signal scald by h. Th fquncy domain psnaion of is givn in h boom-igh con of Fig.. I can b obsvd fom (7) and (8) ha h mixing cofficins h and h can b xpssd as: (5) (7) (8) IEEE Communicaions Sociy 73

4 Hnc, xpanding (9) yilds: h = h = ( g ) (9) h = ε cos ε ( ϕ ) sin(. ϕ ) h = α 5 () Signals and fom h wo inpus of h DIRP. To xamin h pfomanc of h mix, w dfin h Imag- Rcion Raio () as h aio bwn h dsid signal o imag signal. This as a funcion of phas and gain os (α ε, ϕ ε ) is givn in dcibls as: ε - w w - LMS cofficin upda c c cos α ε ( cos ) ( α ϕ = ε, ε ) log () cos α ε ( cos ) This is visually dpicd in Fig. 3. In od o achiv an of 6 db, phas and gain os mus b. db and. spcivly, valing vy singn, maching quimns. In pacic, analog mismachs limi h o 5 4 db [7. Gain Mismach α ε db 5 db db 5 db db 5 db 3 db 35 db 4 db 45 db 5 db 55 db 6 db Imag Rcion Rspons - - Phas Mismach φ ε dg Figu 3. as a funcion of phas and gain os. B. Digial Imag-Rcion-Pocsso (DIRP) To nhanc h pfomanc of h modifid Wav imag cion mix, h mismaching ffcs in h analog dvics mus b compnsad digially. In h DIRP, w compnsa fo h mismachs by liminaing h imag signal componn in h oupu signal c. Th block diagam of h fd-fowad implmnaion of h DIRP is shown in Fig. 4. This pocsso conains wo complx muliplis and complx LMS upda hadwa. Fo claiy, w dfin: u( and as soucs. and as availabl obsvaions. Expssd by (6) and (8). c and c as covd soucs. c is h dsid channl ha w a insd in. w and w a boh complx. Th souc simas, c ( and c (, bcom: c ( = ( wh ) u( ( h w ) c ( = ( h w ) u( ( w h ) () Whn h fils convg, i.. w = h and w = h hn h souc simas bcom: c( = ( hh ) u( c ( = ( h h ) (3) Figu 4. DIRP, fd-fowad sucu. As i can b sn fom (3) h soucs hav bn spaad. Also, (-h h ) and can b safly ignod. An alnaiv implmnaion fo h spaaion sucu is found by simply placing h fils in h fdback loop [8. Th Las-Man- Squas (LMS) algoihm [9 is usd o upda fil cofficins. Th upda quaions a givn as: w w ( k ) ( k ) ( m) = w ( n) = w ( m) µ c ( k m) ( n) µ c ( k n) m =... L n =... L (4) wh, L and L a h fil ods. In his cas boh w and w hav complx singl ap cofficins. III. PERFORMANCE ANALYSIS A. Simulaion Sup Th pfomanc of h poposd sucu is analysd considing QPSK, 8/3-PSK and 6/3/56-QAM signals wih idal symbol a sampling. Fo all simulaions, infing signal is assumd o b db song han h dsid on. AWGN and Mulipah Rayligh Fading channls w assumd. Th pfomanc of h adapiv algoihm is chaacizd by h modlling-o [8. This givs a global figu fo h qualiy of h idnificaion of h coupling cofficins h and h by w and w. I is dfind as h squad nom of h diffnc of h valus bwn h oiginal cofficins usd in h mixu and h simad cofficins, laiv o h squad nom of h mixu cofficins. Anoh pfomanc masu usd is h dscid in (). B. Tacking Capabiliis Anoh pfomanc masu is h capabiliy of h adapiv algoihm in acking non-saionay nvionmns, i.. im vaying phas and gain os. In od o show h obusnss of h poposd appoach w sa by adaping h fils o 5 (ϕ ε = 8 ad) phas and db (α ε = ) of gain o. Af 6 fams, h ampliud imbalanc is changd linaly fom db o db. (α ε = ). Af fuh 4 fams, an abup chang fom db o 3 db (α ε = 4) is mad and h phas o is abuply changd o 3 (ϕ ε = 36 ad). 4 fams la, h phas o is changd linaly fom 3 o ach 4 (ϕ ε = 98 ad) fo h nx fams. Fig. 5 dpics h acking capabiliy of h poposd algoihm (a) fo QPSK modulaion and (b) fo 6- QAM modulaion schms in h psnc of AWGN channl wih SNR of db. IEEE Communicaions Sociy 733

5 Modlling Eo. sp gain and phas chang slow gain chang slow phas chang W W Modlling Eo. sp gain and phas chang slow gain chang slow phas chang W W Rcivd Signal Pow Rcivd Signal Pow Fams (a) x 4 Wi Wi Fams x 4 (b) Wi Wi Fams x 4 (a) Fams x 4 Figu 6. Channl pofils fo (a) slow fading and (b) fas fading, mulipah Rayligh Channl. (b) Modlling Eo.. slow gain chang sp gain and phas chang slow phas chang Fams x 4 (c) Modlling Eo.. slow gain chang sp gain and phas chang slow phas chang Fams x 4 Figu 5. Tacking capabiliis of h poposd algoihm, (a), (c) QPSK and (b), (d) 6-QAM cas. As can b sn fom Fig. 5, a suddn chang in h mixu cofficins, and phas and gain os, dos no caus h algoihm o divg and h algoihm acks h changs apidly and h modlling o is zod. In addiion, h compnsao pfomanc is no affcd by im-vaian phas and gain os. This indicas ha h poposd mhod is also capabl of acking im-vaying imbalancs. As can b obsvd fom Fig. 5 (c) and (d), as xpcd, gain chang has no affcd h modlling o sinc w i and w i a dpndn only on h phas chang (cf. ()). On h oh hand, w and w boh dpnd on h phas and gain os. This can b obsvd fom Fig. 5 (a) and (b). C. Muli-Pah and Fading Channls Anoh pfomanc masu is h capabiliy of h adapiv algoihm o pfom und fading and muli-pah nvionmns. Th obusnss of h poposd appoach in a mo alisic nvionmn han h AWGN channl is dmonsad using a Rayligh Fading channl wih mulipah. Fig. 6 dpics h channl pofils, civd signal pow ov im fo (a) slow fading and (b) fas fading wih a mulipah Rayligh channl. Fig. 7 shows h simulaion suls. As can b sn fom Fig. 7, h poposd algoihm is abl o wok und boh slow and fas fading mulipah channls and h modlling o is ffcivly zod. Tabl I dpics h suling ap simas w and w, sidual gain and phas os and h sady-sa fo QPSK and 6-QAM modulad signals in slow and fas fading mulipah nvionmns. Fuh simulaion suls a givn in Figs. 8- fo vaying phas and gain os spcivly. As wll as vaying boh a h sam im. W can obsv fom Fig., on avag 7 db impovmn in af compnsaion is achivd. (d) Modlling Eo Modlling Eo Fams (a) Fams (c) W W W W Modlling Eo Modlling Eo Fams (b) W W Fams Figu 7. Modlling o fo (a), (c) QPSK and (b), (d) 6-QAM cas fo slow and fas fading spcivly. TABLE I. Modulaion yp Slow Fading Fas Fading RESULTS FOR SW AND FAST FADING RAYLEIGH MULTIPATH ENVIRONMENTS. Bfo Cocion α ε ϕ ε α ε (d) Af Cocion ϕ ε QPSK QAM QPSK QAM D. Diffn Modulaion Fomas and Low SNR Th pfomanc of h poposd algoihm und low SNR valus and diffn modulaion fomas and consllaion sizs is shown in Tabl II. Th SNR quid o achiv - BER is compud fo 8-PSK and 3-PSK as wll as 3-QAM and 56- QAM cass. As can b obsvd fom Tabl II, h algoihm is abl o limina h phas and gain os. in h od of db af DIRP was shown o b achivabl. This is much mo han h quid amoun. W W IEEE Communicaions Sociy 734

6 Modulaion yp Gain Eo Phas Eo (dg) TABLE II. PARAMETER VALUES FOR BER OF -. Bfo Cocion h = h Gain Eo Phas Eo (dg) Af Cocion w w 8-PSK SNR= Eb/No= PSK SNR= Eb/No= QAM SNR= Eb/No= QAM SNR= Eb/No= Af compnsaion bfo compnsaion Phas Eo (dg) Figu 8. bfo and af compnsaion fo vaying phas o Af compnsaion bfo compnsaion Gain Eo Figu 9. bfo and af compnsaion fo vaying gain o Phas Eo (dg) Af compnsaion Bfo compnsaion 3 Gain Eo Figu. 3-D visualisaion of bfo and af compnsaion, vaying boh phas and gain os. IV. CONCLUDING REMARKS Adapiv slf-calibaing imag cion achicu capabl of achiving valus fom db af compnsaing has bn dscibd. Th algoihm is vy simpl o implmn consising of wo, singl-ap-complx adapiv FIR fils wih LMS cofficin upda hadwa. Th algoihm nabls fas and vy accua I/Q imbalanc compnsaion in h whol civ chain a low cos. Algoihm is abl o wok und mulipah and Rayligh fading nvionmns as wll as und low SNR. I woks on-h-fly and is abl o ack im-vaying os. I woks wih any yp of modulaion fomas and consllaion sizs. Th poposd sucu galy laxs h analogfonnd spcificaion nabling high lvls of ingaion and lading a pah o singl chip adio civ. Nx phas of h sach is o pooyp his sucu on FPGA and un i in al-im and compa h pfomanc ha can b achivd wih h simulaion suls. REFERENCES [ M. D. McDonald, A.5GHz BiCMOS imag-c fon-nd, ISSCC Dig. of Tch. Paps, pp , Fb [ W. Baumbg, A singl-chip imag cing civ fo h.44 GHz band using commcial GaAs-MESFET-chnology IEEE Jounal of Solid-Sa Cicuis,, vol. 9 issu., pp , Oc [3 Pach, D.; Founi, J.M.; Billio, G.; Snn, P.; An impovd 3 V GHz BiCMOS imag c mix IC IEEE Cusom Ingad Cicuis Confnc, pp , May 995. [4 Maligogos, J.P.; Long, J.R., A low-volag GHz imagc civ wih wid dynamic ang ; IEEE Jounal of Solid- Sa Cicuis, vol. 35, issu:, pp , Dc. [5 F. Ehbahani, Y. Ishigami, J. L and A.A. Abidi, CMOS mixs and polyphas fils fo lag imag cion IEEE Jounal of Solid-Sa Cicuis, vol. 36, pp , Jun. [6 L. D, B. Razavi, -GHz CMOS imag-c civ wih LMS calibaion IEEE Jounal of Solid-Sa Cicuis,, vol. 38 pp , Fb. 3. [7 C. C. Chn, C. C. Huang, On h achicu and pfomanc of a hybid imag cion civ, IEEE Jounal on Slcd Aas in Communicaions, vol. 9, pp. 9-4, Jun. [8 Cin, E.; Kal, I.; Moling, R.C.S., Adapiv digial civs fo analog fon-nd mismach cocion, IEEE VTS 54 h Vhicula Tchnology Confnc (VTC Fall), vol: 4, pp. 59 5,. [9 Widow B. and S.D. Sans, Adapiv Signal Pocssing, Pnic Hall, 985, ISBN: IEEE Communicaions Sociy 735