Antenna Downselection for Co-Channel Interference Mitigation in a Mobile-to-Mobile Channel

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1 Atea Dowelectio fo Co-Chael Itefeece Mitigatio i a Mobile-to-Mobile Chael Bett. Walkehot *, homa G. Patt *, Sudhahu Gau, May A Igam bett.walkehot@gti.gatech.edu * Geogia ech eeach Ititute, Atlata, Geogia itachi Ameica Ltd, Sa Joe, Califoia Geogia Ititute of echology, Atlata, Geogia Abtact he pefomace of multi-atea eceive i cochael itefeece i ivetigated fo aow-bad lik i o-lie-of-ight (NLOS) ad lie-of-ight (LOS) mobile-tomobile chael. A ovel achitectue utilizig atea dowelectio i aalyzed i imulatio ad compaed with the pefomace of a covetioal aay achitectue. Vaiou dowelectio citeia ae popoed ad aalyzed. he imulatio eult how excellet pefomace ehacemet fo a electio algoithm. Seveal othe method ae alo aalyzed ad compaed with pomiig eult uig the imple method of maximum powe electio. eult ae compaed i tem of etimated complemetay cumulative ditibutio fuctio of output igal-to-itefeece-plu-oie atio (SIN) deived fom Mote Calo imulatio. Idex em Wiele commuicatio, adaptive aay, atea dow-electio, co-chael itefeece, mobile-tomobile chael. I. INODUCION he tudy of tamit ad eceive atea electio ha eceived a geat deal of attetio i the cietific liteatue. May of the publihed pape coide electio fo impovig MIMO ytem capacity [-6] ad ome look at itefeece mitigatio fo imple fadig model [7-8]. hi tudy coide eceive atea electio i a itefeece-limited mobile-to-mobile eviomet. he mobile-to-mobile eviomet i expected to become moe impotat with the advet of ad-hoc ad meh etwok. It i diffeet fom the cellula eviomet i eveal way uch a the aumptio of local catteig at both ode ad a pectum that o loge follow the Jake model [9,]. A exteive et of mobile-to-mobile meauemet how ditict diffeece i the eceived pecta of mobile-to-mobile veu tatic eviomet [6]. It i believed that itefeece i wiele ytem i oe of the mot igificat facto that limit the etwok capacity ad calability of wiele meh etwok [7]. he cuet tudy eek to help adde thi poblem. hi tudy i patly baed o the wok doe i [], which develop a model fo the co-chael itefeece poblem ad aalyze the output SIN fo vaiou atea aay cofiguatio. he tudy i [] exteded thi to coide vaiou dowelectio citeia. hi pape futhe exted thee citeia ad develop a time-domai model to allow fo ealitic paamete etimatio. he aalyi i alo exteded to iclude lie-of-ight (LOS) eviomet. II. AAY ACIECUE he popoed atea aay i compoed of N ectoed atea with o-ovelappig beam coveig the etie azimuth plae. he output of thee N atea ae fed to a witch, which elect K of the atea to be ued fo poceig. A peviou tudy howed thi achitectue yielded a ubtatial impovemet i aay pefomace ove a tadad K-elemet ytem uig optimal combiig []. Iceae i ytem complexity ove the covetioal ytem come fom N-K additioal atea, witchig cicuity, ad igal poceig to detemie which atea elemet to chooe i a give ceaio. Both achitectue ue K F chai. he achitectue of the K-elemet ytem (fo K) i how i Figue (left). he othe diagam i the figue illutate the N-elect-K achitectue decibed i thi ectio whee N4 ad K. he imulatio of thi ytem employ the two-ig chael model decibed i [9], which i ued to chaacteize aowbad chael i o-lie-of-ight (NLOS) eviomet. he model wa exteded to iclude a LOS compoet, dicued i Sectio III. Pepaed though collaboative paticipatio i the Commuicatio ad Netwok Cootium pooed by the U. S. Amy eeach Laboatoy ude the Collaboative echology Alliace Pogam, Coopeative Ageemet DAAD9---. he U. S. Govemet i authoized to epoduce ad ditibute epit fo Govemet pupoe otwithtadig ay copyight otatio theeo. III. SIGNAL MODEL AND POCESSING Akki & abe popoed a time-domai fadig model [] fo mobile-to-mobile wiele commuicatio. hi model, adapted fo the pupoe of thi tudy, i give by

2 h Figue. Multi-Atea Achitectue uig ectoed atea howig vayig degee of coveage m ( t) L + l A Ω j( ωt+ φ ) ( ) e θ () whee l coepod to the LOS compoet ad l,,l+ to the L NLOS multipath compoet, A i the amplitude aociated with the l th multipath compoet of the m th igal, Ω i the th eceive atea patte fuctio, θ i the poitio agle of the cattee o the catteig ig aoud the eceive, φ i a adom phae uifomly ditibuted ove (-π,π], ad ω i the Dopple hift give by ω ω θ ω ξ () X ( ) co( ) co + X whee ω X ad ω X ae the maximum Dopple hift aociated with the X ad X velocitie epectively, ad ξ i the agula poitio of the cattee o the catteig ig aoud the m th tamitte. he amplitude ae fixed to yield aveage deied ad itefeece igal powe of. Icopoatig the icea K- facto (K ) to accout fo LOS chael, the amplitude of the deied igal ae give by K A (3) K + fo the LOS compoet ad A l L( K + ) fo l,, L+ (4) fo the L NLOS compoet. he amplitude of the igal fom the M- itefeece ouce (m,, M) ae give by Al A (5) M he eceived igal at the th atea i give by x ( t) Adaptive aay with ectoed atea 8 o 8 o 9 o Optimal Combiig M L+ m l M m A h m () t a () t m j Ω ( θ ) e + ν ( t) ( ωt+ φ ) a () t + ν ( t) m Dowelectio achitectue 9 o 9 o Select Optimal Combiig 9 o (6) whee a m (t) i the m th tamitted igal (a (t) i the deied igal) ad ν (t) i the oie at the th atea. Fo the tamitted igal, we have aumed the deied igal to be QPSK ad the itefee to be white Gauia oie pocee. o poce the eceived igal, we apply a weight vecto w to the data: y( t) w x( t), (7) whee x (t) i the colum vecto give by tackig the K elected atea output ad w i give by w ˆ ˆ (8) he autocoelatio ad co-coelatio etimate ae computed by aveagig ove a taiig peiod of legth c. ˆ ˆ c x c p c c p * ( p ) a ( p ) x ( p ) x ( p ) ad (9) () ee, p epeet the taiig ymbol idex ad i the ymbol peiod. he etimate (9-) ae ued to compute the weight, which ae applied to the data equece. Fo thee imulatio, we have aumed.μ ad c 5μ. Fo each Mote Calo iteatio, SIN value uig optimal combiig fo all poible combiatio of N-chooe-K atea ae computed ad the dowelectio citeia ae ued to elect the appopiate eult. IV. DOWNSELECION CIEIA he mea-quae eo (MSE) of the poceed igal i give by E{ ( w x a )( w x a ) } w w + () ( ) ( ) he above appoximatio i valid aumig the etimate ad ˆ ae faily accuate. Dowelectio ˆ By computig the weight vecto w, the eceive ha all the ifomatio eceay to etimate the MSE. he popoed algoithm fo electig atea o which to pefom optimal combiig i to compute ˆ ˆ ˆ ˆ w () fo all N-chooe-K combiatio ad elect the combiatio that maximize the expeio, theeby miimizig the MSE. Icemetal Atea Selectio A uboptimal appoach equiig le computatio ca be deived by chooig oe atea that maximize the expeio (), the chooig a ecod atea baed o the

3 ame citeio, the a thid, ad o o util all K atea K have bee choe [3]. hi method equie NK N computatio compaed to fo the method. K A ee, the opeato idicate the umbe of uodeed B ubet of ize B that ca be obtaied fom the et {,,,A}. hi i ofte efeed to a A-chooe-B. Uig thi method, the fit atea choe will be the oe with the laget etimated iput SIN. o illutate thi, coide the expeio () whee all of the tem ae cala ice oly oe atea i ivolved. By uig (6), it i eay to how that { ) * E x t a ( t )} h ( ), ( t ad (3) M { () t x () t } h t + σ P + P + σ, E x m( ) d, I, m (4) whee P d,, P I,, ad σ ae the deied igal, itefeece, ad oie powe at the th atea epectively. he expeio (*) the become P, d, d,, + P P I, + P, + σ P I, + σ d,,, SIN, +,, (5) Miimizig (5) ove all i equivalet to maximizig (SIN +), which i equivalet to maximizig SIN. By uig etimate of the autocoelatio ad co-coelatio fuctio, the algoithm will elect the atea with the highet etimated iput SIN. Chooig ubequet atea ivolve moe complicated expeio, but each ca be implemeted by imply uig (). Ad-hoc Dowelectio Method hee othe electio algoithm will be coideed:. Select the two atea with the laget total powe. Select the two atea with the laget igal powe 3. Select the two atea with the laget SIN Boud ad Baelie he imulatio eult of the five electio algoithm above will be compaed with:. the maximum output SIN ove all N-chooe-K combiatio (uppe boud). the miimum output SIN ove all N-chooe-K combiatio (lowe boud) 3. the pefomace of optimal combiig o a K-elemet ectoed ytem (baelie) 4. the pefomace of a adom electio of K atea to compae with the baelie V. ESULS wo atea cofiguatio wee imulated while vayig the peed of the mobile ode, the umbe of itefeece ouce, ad the icea K-facto. Fo implicity, a fouatea olutio wa imulated followed by a ie-atea cofiguatio to illutate additioal gai that ca be deived though highe-ode atea diveity. All of the imulatio aume L cattee pe ouce ad aveage eceive SN ad IN of 4dB. Fou atea achitectue; two elemet poceig Figue how the etimated output SIN ditibutio fo the vaiou dowelectio citeia fo a 4-elect- achitectue i a tatic NLOS eviomet. All of the eult peeted i thi pape ae deived fom, Mote Calo imulatio. Cumulative Pobability elect-; cattee pe ouce; ouce; v.5 maxsinout misinout.4 K-atea.3 icemet. maxpowe. maxsin adom Output SIN (db) Figue. CCDF etimate of output SIN fo 4-elect- achitectue, m/, with itefeece ouce, ad NLOS coditio. he output SIN uig optimal combiig i computed fo all N-chooe-K atea combiatio. he K-elemet ubet of atea that yield the maximum output SIN out of all poible ubet i foud ad eult ae how a the cuve labeled maxsinout, epeetig the uppe boud o ytem pefomace. he eult of alway chooig the atea pai with the miimum output SIN i how a the cuve labeled misinout, ad the baelie cae of a K- elemet aay a K-atea (hee K). he electio decibed i Sectio IV i labeled, the icemetal electio a icemet, the maximum powe citeio a maxpowe, the maximum igal powe citeio a, the maximum SIN citeio a maxsin, ad the adom atea electio a adom. Notice that the electio cheme doe ot achieve the uppe boud. Whe the exact chael tate ifomatio (CSI) i available, the boud i achieved, but i thi cae, the CSI i etimated by aveagig, o the effect of oie ad cochael itefeece degade the auto- ad co-coelatio etimate ad coupt the electio citeio. he algoithm i the bet choice fo thi ceaio ad i ot difficult to compute baed o the aumptio of a taiig peiod. he icemetal appoach i cloe to the pefomace of the max powe ad max igal powe citeia, but pefom lightly bette.

4 Now coide the cae whee the deied igal ha a icea K-facto of db ad the itefeece i NLOS. eult of thi ceaio ae illutated i Figue 3. Cumulative Pobability elect-; cattee pe ouce; ouce; v.5 maxsinout misinout.4 K-atea.3 icemet. maxpowe. maxsin adom Output SIN (db) Figue 3. CCDF etimate of output SIN fo 4-elect- achitectue, m/, with itefeece ouce, ad LOS coditio fo the deied igal. I thi cae, the maximum powe citeio pefom the bet ad i alo the implet to implemet. he othe algoithm uffe elative to the NLOS cae except fo the electio algoithm. It i alo iteetig to ote that the adom atea electio pefom much woe i thi cae tha the baelie K-elemet achitectue. I geeal, the aveage SIN of the two algoithm ae aot idetical ule the deied igal ha a LOS compoet. Whe that happe, the adom algoithm will ofte chooe ecto that do ot cotai the LOS compoet, which eveely educe the SN. he K-elemet achitectue will alway cotai the LOS compoet ad doe ot uffe i thi way. Coide the aveage output SIN fo each of the algoithm a a fuctio of the K-facto of the deied igal. hi eult i how i Figue 4 fo K-facto fom (NLOS) to (3dB). he value o the left ide of Figue 4 (whee K ) coepod to the aveage of the ditibutio how i Figue ad the value o the ight ae aot idetical to the aveage of the cuve how i Figue 3. Somewhee ea K (3dB), the maximum powe algoithm upae the pefomace of the algoithm. I meaued data, much lage K-facto aoud -db wee foud to be commo [4-5], o i a ceaio whee the deied igal i expected to have a LOS compoet, the maximum powe algoithm will likely pefom the bet. Aveage SIN elect-; cattee pe ouce; ouce; v 4 maxsinout 4.5 K-atea 4 icemet 4.5 maxpowe 4 maxsin adom K-facto of deied igal (liea) Figue 4. Aveage output SIN etimate fo 4-elect- achitectue, m/, with itefeece ouce, a a fuctio of deied igal K-facto. Simila eult ae foud fo othe LOS cofiguatio. Fo example, whe the deied igal i NLOS ad the itefeece ha a K-facto of db, the pefomace i vey cloe to that how i Figue except that the maximum powe algoithm doe ot pefom a well, but i till lightly bette tha the cuve. Coide ow the effect of mobility. Let each tamit ode ad the eceive aay be movig at a peed of m/. he eult fo the NLOS cae ae how i Figue 5. Cumulative Pobability elect-; cattee pe ouce; ouce; v.5 maxsinout misinout.4 K-atea.3 icemet. maxpowe. maxsin adom Output SIN (db) Figue 5. CCDF etimate of output SIN fo 4-elect- achitectue, m/, with itefeece ouce, ad NLOS coditio. he oveall pefomace degade omewhat compaed to the tatic cae, but the elative meit of the vaiou dowelectio algoithm emai about the ame. oweve, i thi cae, the pefomace of the ad icemetal algoithm i aot idetical. I geeal, the velocity of the mobile ha miimal impact o the icemetal algoithm, o i a highly mobile NLOS eviomet, the icemetal i likely a good choice fo dowelectio. Coide the LOS cae i a mobile eviomet, illutated i Figue 6. ee, the deied igal expeiece a icea K- facto of db ad the itefeece emai NLOS. Notice oce agai the upeio pefomace of the maximum powe citeio.

5 4-elect-; cattee pe ouce; ouce; v 9-elect-; cattee pe ouce; ouce; v Cumulative Pobability maxsinout misinout.4 K-atea.3 icemet. maxpowe. maxsin adom Output SIN (db) Figue 6. CCDF etimate of output SIN fo 4-elect- achitectue, m/, with itefeece ouce, ad LOS coditio fo the deied igal. Nie atea achitectue; two elemet poceig Coide ow a lage eceive aay with ie ectoed elemet of o-ovelappig beam. By electig two of the ie elemet, the pefomace ca be igificatly impoved elative to the -elemet ectoed aay with optimal combiig. he tatic NLOS cae i how i Figue 7. Cumulative Pobability elect-; cattee pe ouce; ouce; v.5 maxsinout misinout.4 K-atea.3 icemet. maxpowe. maxsin adom Output SIN (db) Figue 7. CCDF etimate of output SIN fo 9-elect- achitectue, m/, with itefeece ouce, ad NLOS coditio. Oce agai, coide the cae whee the deied igal i LOS with a icea K-facto of db, illutated i Figue 8. Cumulative Pobability maxsinout misinout.4 K-atea.3 icemet. maxpowe. maxsin adom Output SIN (db) Figue 8. CCDF etimate of output SIN fo 9-elect- achitectue, m/, with itefeece ouce, ad LOS coditio fo the deied igal. A i the peviou cofiguatio, the maximum powe electio algoithm pefom extemely well i the LOS eviomet. I geeal, if a LOS coditio i expected fo the igal of iteet o the itefeece, the bet techique fo electig atea may be to meaue the powe at each of the N atea with a couple ad diode detecto ad elect the K atea with the laget etimated powe level. hi appoach would ot equie ay poceig of the N-atea igal to detemie the electio choice ad will uually yield vey favoable eult. I a tatic eviomet, thi i aot the equivalet of poitig a diectioal atea at the tamitte, but i a mobile-to-mobile eviomet, the LOS igal would be expected to move fom oe ecto to aothe ove time. VI. CONCLUSION Multiple atea achitectue have bee ivetigated ad thei pefomace evaluated i a wiele mobile-to-mobile chael i the peece of co-chael itefeece. Uig multiple atea with dow-electio at the eceive followed by optimal combiig ha bee foud to outpefom optimal combiig i a covetioal ectoed ytem whee the umbe of atea ued i the adaptive poceig i kept cotat fo compaio. eult fom achitectue uig fou ad ie atea with dow-electio to two atea wee peeted to how the pefomace impovemet aociated with iceaed atea diveity. Five dow-electio algoithm wee popoed i all, oe baed o the etimated MSE, which i typically the bet pefomig fo the NLOS cae. Whe a LOS igal i peet fom eithe the deied igal o itefeece, a imple dowelectio techique baed o powe i foud to pefom vey well, uually outpefomig the algoithm. I a NLOS coditio, the choice of a algoithm will deped o the cotait of the ytem ad the expected eviomet. Cadidate algoithm iclude the, icemetal, ad maximum powe citeia.

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