Behaviors of MIMO UWB-IR Transceiver with Statistical Models

Transcription

1 Behaviors of MIMO UWB-IR rasceiver wih Saisica Modes Xu Huag ad Dharedra Shara Absrac I is we kow ha ui-aea-based ui-ipu ui-oupu (MIMO) couicaios becoe he ex revouio i wireess daa couicaios. MIMO has goe hrough he adopio curve for coercia wireess syses o he oday s siuaio, a high hroughpu coercia sadards, i.e. WiMax, Wi-Fi, ceuar, ec., have adoped MIMO as par of he opioa. his paper is o prese our ivesigaios of he behaviors of he MIMO Ura-Wide-Bad-Ipuse Radio (UWB-IR) syses, which wi coribue o opia desigs for he ow-power high-speed daa couicaio over uicesed badwidh spaig severa GHz, such as IEEE faiies. We have deveoped ad aayzed hree o cohere rasceiver odes wihou requirig ay chae esiaio procedure. he assive siuaios are ade based o he esabished odes. Our ivesigaios show ha he Poisso disribuio of he pah arrivig wi affec he siga-oise raio (SR) ad ha for he akagai disribued uipah fadig chae he facor, ogeher wih receiver uber, wi ipac o he SR of he MIMO UWB-IR syses. Idex ers MIMO, WiMax, UWB-IR, Poisso disribuio, akagai disribuio. I. IRODUCIO I is recaed ha ui-aea-based ui-ipu ui-oupu (MIMO) couicaios firs occurred i he id-1990s whe researchers a Be Labs ad Saford were ookig for ways o icrease syse hroughpu wihou icreasig badwidh. Afer ha housads of research papers have bee wrie o he opic deaig wih boh physica ayer ad ework ayer raificaios of he echoogy. I fac a high hroughpu coercia sadards, such as WiMax, Wi-Fi, ceuar, ec., have adoped MIMO as par of he opioa. he adopio of MIMO io iiary wireess couicaios syses has payed ipora roe as we as i he coercia area. Ura Wide Bad Ipuse Radio (UWB-IR) is a eergig wireess echoogy, proposed for ow power high speed daa couicaio over uicesed badwidh. his echoogy has bee drawig grea aeios fro he researchers [1-9]. Currey he rasceiver archiecures have bee showig he edecy of exedig his echoogy o ex geeraio WLA copia operaig scearios. herefore, expoiig boh spaia ad epora diversiy ad cobig he MIMO echoogy wih he UWB-IR becoe ieviabe, which becoes our oivaio o his curre paper. I is we kow ha he desig of a MIMO couicaio syse depeds o he degree of kowedge of he chae sae iforaio (CSI), which is oray very expesive. I his paper, as ora way did, i is based o he UWB-IR saisica chae odes. We ake he ocohere rasceiver [7, 16-18] ad focus o wireess hree odes, aey Gaussia, akagai ad og-ora disribuio chaes. We, i paricuary, exeded he previous research resus [13-15] o ivesigae how he akagai facor ipacs o he siga o oise raio (S/) i he saisica chae ode. he siuaios uder various codiios have bee doe i his paper, our siuaios preseed he foowig suggesios: (a) if we ake so caed sige-cuser Poisso ode [7], aey he rado ieger vaued uber, he he ea of his rado ieger vaued uber wi ipac o he MIMO S/ regardess which of hree odes (Gaussia, akagai ad og-ora disribuio chaes) ad (b) for he akagai disribuio chae, as we expeced ha he facor wi ipac o he MIMO S/. I he ex secio he MIMO UWB-IR saisica chaes are o be ivesigaed. he, he odes for hose discussed saisica chae wi be esabished i secio 3. I secio 4 siuaios wi be give for he ivesigaed odes i secio 3. I he fia secio he cocusios are preseed. o iser iages i Word, posiio he cursor a he iserio poi ad eiher use Iser Picure Fro Fie or copy he iage o he Widows cipboard ad he Edi Pase Specia Picure (wih Foa over ex uchecked). IMECS 006 reserves he righ o do he fia foraig of your paper. II. MIMO UWB-IR SAISICAL CHAELS he basebad poi o poi (PP), show i Figure 1, is coposed by rasi ad r receive aeas workig o a UWB-IR MIMO chae. A he sigaig period s secod he source of Figure 1 geeraes a L-ary (L ) iforaio sybo b, i.e. b {0, 1,, L -1}. he ui-aea rasier aps b oo M-ary basebad sigas of ie duraio iied by s. I is oed ha he USB basebad puse is iied o puse ie, p, ad repeaed f ies over each sigaig period, s, here f is he uber of fraes ad he ie for fraes of duraio deoed by f. I order o avoid ier-frae ierferece (IFI), we us have f > μ, where μ is he UWB chae deay spread ie. Xu Huag is wih he Facuy of Iforaio Scieces ad Egieerig, Uiversiy of Caberra, Ausraia (e-ai: Xu.Huag@caberra.edu.au). Dharedra Shara is wih he Facuy of Iforaio Scieces ad Egieerig, Uiversiy of Caberra, Ausraia (e-ai: Dharedra.Shara@caberra.edu.au).

2 Figure 1: he MIMO poi o poi UWB-IR syse wih rasi ad r receive aeas. he MIMO UWB-IR chae is affeced by uipah fadig ha is described by r basebad ipuse chae resposes. I is we kow ha we have sige ipu sige oupu (SISO) UWB-IR chae by IEEE If we ake he ipuse chae resposes i Figure 1 as h ji (), 0 j, 0 j r ), we ay coec hese ipuse resposes io he correspodig ( r ) arix H() []. herefore, as IEEE recoed ha each SISO ipuse respose h ji () i Figure 1 is odeed as he superposiio of severa pah cusers, wih boh ier-cuser ad ira-cuser ier-arriva ies beig expoeiay disribued. Hece, we have [1, 7]: h ji = = = 0 = 0 h here, 1 i ( j, δ ( τ ) β ( j, α ( j, δ ) τ ),1 j I is oed he ieger vaued uber of received pahs over a sigaig period s is a Poisso disribued rado variabe wih ea vaue E{} = λ s, where λ is rae i (s) -1, τ is he o-egaive arriva ie of he h pah, i s. We use h (j, for he h pah gai of SISO ik goig fro he ih rasi aea o he jh receive oe. he rado variabe (r.v.) β (j, {-1,1} ad he o-egaive r.v. α (j, are he correspodig phase ad apiude, respecivey. As he previous refereces [1, 7, , 15 19] show ha he saisic of he fadig affecig rich-scaered ediu-rage quasi-los UWB-IR iks ay be we odeed by resorig o he akagai disribuio, og-ora disribued chae apiudes, α (j, ay be suiabe for ess scaered LOS shor-rage idoor propagaio eviroes ad he og-ora disribuio is recoeded by IEEE workgroups for WPA ad sesor appicaios [1-]. he cera ii heore [, 0] uderpi he fac ha zero-ea Gaussia disribued chae coefficies we ode highy scaered oudoor LOS propagaio eviroes. For he space-ie orhogoa PPM (OPPM) oduaed he size M of he epoyed OPPM fora equaes L ad cous of he -h arix codeword are cosiued by he ui-vecors of R M wih idex i ragig fro i = o ((+1) )-1, i.e. = [ e( )... e(( + 1) 1)], 0 L 1 () Because of orhogoa ad uiary we have: r (1) = 0, for (3) = I, for ay We aso have he reaio bewee Bi-Error-Probabiiy P (b) E ad he correspodig Word Error Probabiiy P E [7] as show beow: ( b) L P E = ( ) PE (3) ( L 1) As he geera equaio we have he decisio saisics se {z } ca be expressed by ML = arg ax{ z } (4) 0 L 1 ow we ca ake z as differe saisics for he hree chaes we discussed above, aey akagai disribuio, og-ora disribuio ad Gaussia disribuio. he odes for hose chaes wi be ivesigaed i he ex secio. III. MODELS OF MIMO UWB-IR OF DIFFERE SAISIC CHAELS We firs ivesigae how does he r.v. paraeer,, ipac o he S/ i he above hree differe saisic chaes? For he akagai disribuio uipah fadig chae, we have [7]: z r = = 0 j= 1 i 1 {cosh[φ( y ( ) where, = 0..., L 1 ad φ is defeded as cμ ϕ = βe, = 0,..., ad c = μ = E{ α (j,}. j e ( ))]} 1 0 i (10), Aso as he Appedix of [7] eioed, we have he word error probabiiy (WEP): σ β (1 + ) 4e Γ() r ( + 1) PE ( L 1)( ). [ ] Γ( ) = 0 σ β (1 + ) (6) Here G(.) is he Gaa fucio [11, 13-15], i is oed ha if r.v. is arge eough equaio (5) ca be sipified furher fora. We ow cosider he siuaio of og-ora disribued uipah fadig, i.e. he fadig apiudes {α (j,} is og-ora disribuio wih 0.5, we have[16]: P E ( L 1)( [ + ) π exp{ ( + 1) r βφ e = 0 μ c exp{ c r (5) σ }} d] r r

3 (7) Fiay e s have a coser ook a he Gaussia disribuio, we have [16]: (1 + σ β ) r / PE ( L 1) [ ] (8) 1 = 0 (1 + σ β ) I is oed ha he siuaio siiar o equaio (6) ad ha whe r.v. is arger ha ui we ca sipify equaio (8). he foowig secio we sha prese a uber of siuaios uder differe codiios o expore he behaviors of MIMO UWB-IR of differe saisic chaes. Le s have a ook a Figures 6 ad 7, which show he differe disribuios. he disribuio becoes zero ea Gaussia disribuio, which odes highy-scaered oudoor LOS propagaio eviroes. I is ideed, as we observed, he ore drops uder he sae codiios = 4 = 5 = 1 = = 3 I. SIMULAIOS OF MIMO UWB-IR OF DIFFERE SAISIC CHAELS Our arge is, based above iduced resus, o ivesigae wo siuaios ha ead he opia desigs for MIMO UWB-IR couicaios, aey (a) because we do wa o have expesive chae sae iforaio (CSI), we ake he sige cuser Poisso Mode for capurig he behavior of each h ji (). herefore, quesio occurs: how does he r.v. ipac o he S/ of he MIMO UWB-IR rasceiver chaes? (b) As akagai disribuio is of ipora wireess couicaio disribuios ad he ajor paraeer,, wi ipac o he akagai disribuios. Hece, he secod quesio occurs: how does he facor of he akagai disribuio ipac o he S/ of he MIMO UWB-IR rasceiver chaes? I he foowig secio, he assive siuaios, based o above heories, are ade for hose wo quesios. For he firs quesio wihou oss geeraiy we ake sipe case, L =, ad he correspodig SISO ipuse resposes {h j, i ()}i equaio (1) have bee geeraed accordig o he CM 6 UWB-IR chae ode, i.e. IEEE wih λ = 1.13 (1/s), μ = 15.9 (s), γ = 9.3 (s), f = 8, ad he specra efficiecy of 1/00 (bi/sec/hz). he siuaios firs ake r = 1 ad he e = 1,, 3,4, aey ivesigaig he MISO siuaios. Uder he above codiios, Figures, ad 3 show he = 5, 15 wih akagai disribuio uipah chaes. I is ceary o show ha uder he sae saisic disribuio he rado variabe has ipaced o he S/ uder he sae. For exape, for he argeed, 10-5, whe he = here are 1.6 db draped ad i geera case i is obviousy ha wih icreasig he S/ wi sigificay dropped (Figures ad 3). Figures 4 ad 5 preseed he aos siiar siuaios as ha i Figures ad 3 excep for he disribuio chaged fro akagai disribuio o og-ora disribuio. Eve hough he disribuios are chaged fro he akagai- o og-ora- disribuios, he siuaio cocusios are highy siiar, which ca be evideced by he observaios fro Figures 4 ad 5. However, i is oed ha uder he siiar codiios og-ora disribuio wi cause ore S/ drops if we copare he siuaio resus obaied fro Figure wih ha fro Figure 4. his is o surprised as he sapes icreased hose wo disribuios approach he coo aure S/ Figure : akagai disribuio uipah chae wih r =1 ad = 1,, 3, ad 4 he S/ is i db = 4 =15 = 3 = = S/ Figure 3: akagai disribuio uipah chae wih r =1 ad = 1,, 3, ad 4 he S/ is i db = 4 = 3 = 5.0 = = S/ Figure 4: Log-ora disribuio uipah chae wih r =1 ad = 1,, 3, ad 4 he S/ is i db = 4 = = 1 = 3 = S/ Figure 5: Log-ora disribuio uipah chae wih r =1 ad = 1,, 3, ad 4 he S/ is i db.

4 = 5 = 15 & = = 4 = 3 = 10 0 = 1 = S/ Figure 6: Gaussia disribuio uipah chae wih r =1 ad = 1,, 3, ad 4 he S/ is i db. = 15 = 4 = 3 = S/ Figure 11: akagai disribuio wih =0.9 = 15 he res paraeers are he sae as ha i previous figures. =15 & = 0.6 & r = = 4 = 3 = = S/ Figure 7: Gaussia disribuio uipah chae wih r =1 ad = 1,, 3, ad 4 he S/ is i db. = 5 & = = 4 = 3 = 1 = S/ Figure 1: vs. S/ wih he sae codiio as eioed above ad r =1, =0.6, =15 for he akagai disribuios. = 15 & = 0.6 & r = = 4 = 3 =1 = = 1 =4 =3 = S/ Figure 8: akagai disribuio wih =0.6 = 5 he res paraeers are he sae as ha i previous figures. = 15 & = S/ Figure 13: vs. S/ wih he sae codiio as eioed above ad r =, =0.6 ad = 15 akagai disribuios. = 15 & = 0.6 & r = = 4 = 3 = = = 3 = = S/ Figure 9: akagai disribuio wih =0.6 = 15 he res paraeers are he sae as ha i previous figures = 4 = 3 = 5 & = 0.9 = = S/ Figure 10: akagai disribuio wih =0.9 = 5 he res paraeers are he sae as ha i previous figures. = S/ Figure 14: vs. S/ wih he sae codiio as eioed above ad r =3, =0.6 ad = 15 akagai disribuios he observaios fro Figures 6 ad 7 preseed ha as he couicaios is odeig for he ou door he eviroea siuaios are copeed i ers of oises he ipacs o he SR woud be sroger as expeced. I order o ivesigae how does he facor affec he akagai disribuio as he above secod quesio described, we have ake he facor = 0.6 ad 0.9 ad he rado variabe = 5 ad 15 ad he siuaios are show i figures 8, 9 10 ad 11. For exape, for he argeed 10-5 whe = uder he sae codiios excep for = 0.6 ad = 0.9 he forer S/ dropped 1.9 db i copariso wih aer (referrig Figures 9 ad 11). Aso fro Figures 8 ad 10 for = 3, a

5 he argeed 10-5, we have S/ dropped abou db fro = 0.6 o = 0.9 wih he sae r.v. vaues. Figures 1, 13 ad 14 show he sae vs. S/ wih he coparabe paraeers bu for receiver uber, r = 1, ad 3. Fro hose siuaios we ca observe ha as he receiver uber icreasig, for he akagai disribuio uipah couicaio chaes, he S/ wi drop because of his ode (akagai disribuio) focus o he case ha he couicaio chae approaches o quasi-los, which is ow deviaig fro he assupios whe he r becoes ager. If you are usig Word, use eiher he Microsof Equaio Edior or he Mahype add-o (hp:// for equaios i your paper (Iser Objec Creae ew Microsof Equaio or Mahype Equaio). Foa over ex shoud o be seeced.. COCLUSIOS I his paper, i order o have opia desigs for MIMO UWB-IR rasceiver uipah couicaio chaes, i paricuary, uder he codiio of ha here is o expesive CSI we have esabished saisic odes for hree ajor siuaios i MIMO UWB-IR couicaios. hey are akagai disribuio, og-ora disribuio, ad Gaussia disribuio. Our paper focuses o (a) how does he rado variabe affec MIMO UWB-IR uipah couicaio chaes? (b) If we sick wih geera LOS case, akagai fadig chae, how does he ajor facor affec he MIMO UWB-IR couicaio chaes? Our have preseed assive siuaios, based o heoreicay ivesig, which show he aswers for above quesios we cocered. he siuaio resus aso offer beer iforaio for he opia desigs for MIMO UWB-IR rasceiver uipah couicaio chaes. Fiay we aso ivesigae how he receiver uber affecs he MIMO UWB-IR S/. A hose resus wi give he opia desigs for MIMO UWB-IR rasceiver uipah couicaio chaes. [8] Sahapor Prowog, Waaru Haiach, Ju-ichi akada, Pichaya Supaa Koo ad Praki agisao, Measuree ad Aaysis of UWB-IR Aea Perforace for WPAs, haasa I. J. Sc. ech. o. 8, o.4, Oc-Dec 003, pp56-6. [9] Sau Rodriguez Dueas, Xizhog Do, Sezi Yaac, Mohaed Lsai ad Li-Rog Zheg, CMOS UWB IR o-cohere Receiver for RF-ID Appicaios, Appicaios, Circuis ad Syses, 006 IEEE pp [10] Xu He, Xiaoyog Peg, Yue Xiao, ad Shaoqia Li, A ove ie ad Frequecy Sychroizaio echique for MIMO-OFDM, he fourh advaced ieraioa coferece o eecouicaios 008, pp [11] J. Proakis, Digia Couicaios, Ed. 4 McGrawHi, 001. [1] L. Yag, G. B. Giaakis, Aaog Space-ie Codig for Muiaea Ura-Widebad rasissios, IEEE ras. O Co. oi.5, o.3, 004 pp [13] X. Huag ad A. C. Madoc, Iage Mui-oise Reova via Levy Process Aaysis, Lecure oes i Coipuer Sciece. Sprig Beri/ Heideberg, vo 3684/005, pp-5. [14] Xu Huag, oise Reova for Iage i akagai Fadig Chaes by Wavee-based Bayesia Esiaor, IEEE Ieraioa Coferece o Muiedia & Expo 008, Jue 3-6, 008 Geray, pp1-4. [15] X. Huag ad A. C. Madoc, Iage ad Is oise reova i akagai Fadig Chaes, IEEE 8 h Ieraioa Coferece o Advaced Couicaio echoogy, Phoeix Park, Repubic of Korea, Proceedig Par I, pp [16] E. Baccarei, M. Biagi, C. Peizzoi, ad. Cordeschi, o-cohere rasceiverrs for Muipah-affeced MIMO UWB-IR Couicaios for uipah affeced MIMO UWB-IR Couicaios, hp://ifoco.uiroa1.i/~pecris/ech.1.pdf [17]..S agesh Pou, B. G. Copis, B. R. Peerso, Sybo-waveegh MMSE gai i a ui-aea UWB syse, IEEE Proc. Of he 4-h Aua Couicaio eworks as Service Research Coferece (CSR 06), pp [18]. Ezaki,. Ohsuki, Perforace Evauaio of Space Hoppig Ura Widebad Ipuse Radio (SH-UWB-IR) Syse, IEEE Ier. Cof. o Co. 004 (ICC 04), vo.6, pp [19] H. Liu, C. Qiu, ad Z. ia, Error Perforace of Pause-Based Ura-Widebad MIMO Syses Over Idoor Wireess Chaes, IEEE ras. O Wireess Co., vo.4 o.6, pp , ov.005. [0] C. Preie, D. Cheug, L. Rusch, ad M. Ho, Spaia Correaio i a Hoe Eviroe, IEEE Cof. o Ura Widebad Sys. Ad ech., May 00, pp I. REFERECES [1] Jeffrey Hugh Reed, A Iroducio o Ura Widebad Couicaio Syses, Preice Ha PR, 005. [] A. F. Moishch, D. Cassio, e Aii, A Coprehesive Sadardized Mode for Urawidebad Propagaio Chaes, IEEE r. O Aeas ad Propagaio, vo. 54, o. 11, pp , 006. [3]. Ohsuki, Space-ie reis Codig for UWB-IR, ehicuar echoogy Coferece, C 004, Sprig 004 IEEE 59 h o., pp [4] akahiro Ezaki ad ooaki Ohsuki, Rake Perforace for UWB-IR Syse wih SISO ad MISO, IEICE rasacios o Couicaios 005 E88-B(10) pp [5] Richard J. Baro ad Divya Rao, Perforace Capabiiies of Log-Rage UWB-IR DOA Locaizaio Syses, EURASIP Joura o Advaces i Siga Processig o.008, pp1-17. [6] Sag-Heo Lee, a-sug Ki, Heau-Jo Kag ad Soo-Goh Ki, perforace Iproree of Ieige UWB-IR Couicaio Syse i Muipah Chae, ICIC 006, Sprig-erag Beri Heideberg 006, pp [7] J. H. Reed, Ezo Baccarei, Mauro Biagi, Crisia Peizzoi, ad icoa Cordeschi, Opia MIMO UWB-IR rasceiver for akagai-fadig ad Poisso-Arrivas, Joura of Couicaios, o. 3, o. 1, Jauary 008 pp7-40.