Journal of Engineering Science and Technology Review 6 (5) (2013) Research Article

Transcription

1 Jestr Journl of Engineering Science nd Technology Review 6 (5) (3) 76-8 Reserch Article JOURNAL OF Engineering Science nd Technology Review An Improved Three-dimensionl MIMO chnnel Model bsed on GBSBEM Ming LI* nd Yun-fei GUO Ntionl Digitl Switching System Engineering &Technologicl Reserch Center, Zhengzhou,Henn province, 45,Chin Received June 3; Accepted 3 December 3 Abstrct Geometriclly bsed single-bounce ellipticl model (GBSBEM) does not consider the impct of time dely nd pitch ngle, nd cnnot response the correltion between MIMO ntenns. In order to solve these problems, n improved threedimensionl MIMO chnnel model bsed on GBSBEM is presented. By introducing sptil distnce nd pitch ngle, this model trnsformed the D GBSBEM to 3D GBSBEM, which includes spce distnce, direction of rrivl (AOA) nd multipth time dely. And the probbility density functions of the AOA, time dely nd their joint re lso derived. Wht s more, by building 3D GBSBEM between multi-ntenns, 3D MIMO GBSBEM is presented. For illustrtion, MATLAB simultion is utilized to show the fesibility nd pplicbility of this 3D MIMO GBSBEM. The nlysis results show tht the improved model is not only comptible with the originl model, but lso improve the ccurcy of the ltter, nd extend the scope of its ppliction. The improved model is more suitble for nlyzing the signl reception performnce of MIMO communiction systems. Keywords: MIMO chnnel model, GBSBEM, AOA, Pitch ngle. Introduction In MIMO wireless fding chnnel, the direction of wve propgtion is directionl nd non-uniformity. However, the wider ppliction of MIMO chnnel model bsed on the direction nd ngle geometric sttisticl properties re built under n idel condition thttrnsmitting ntenns nd receiving ntennsre locted in the sme horizontl plne. Therefore, geometriclly bsed sctter (GBS) model is not fit for estblishing MIMO chnnel models. GBS model cn relize concise description of the rdio chnnel, nd does not require extensive nd time-consuming mesurement for nlyzing the chnnel chrcteristics, such s geometriclly bsed single-bounce ellipticl model (GBSBEM) [] nd geometriclly bsed single-bounce circle model (GBSBCM) []. In order to me the GBS model suitble for MIMO chnnel modeling, lot of literture reserch MIMO chnnel of GBS models. In literture[3],lee modelssumed sctters uniformly distributed in ring round the mobile sttion. Literture [4] ssumed tht N scttering bodies in the rnge of the ngle of AOA. All of these litertures used different functions to describe the distribution of the chnnel ngel nd scttering bodies. However, these models did not consider the impct of time dely. For this reson, the spce time frequency correltion function of MIMO chnnel cnnot be expressed. Literture [5] hs confirmed tht the scttering signls in rdio chnnel hve lrge pitch ngels. So reserches for * E-mil ddress: dingdllm@gmil.com ISSN: Kvl Institute of Technology. All rights reserved. MIMO chnnel must consider the influences of pitch ngel nd time dely, nd need to crete three-dimensionl model. Literture [6], referring [5], built 3D GBS model, but ssumed tht received signls t the receiver were evenly distributed in the rnge of ngulr spred. Literture [7] creted three-dimensionl chnnel model for different receiver rrys, considering the influence of pitch ngle, but ssuming the horizontl ngle nd the pitch ngle were uniformly distributed. To solve this problem, n improved 3D-MIMO- GBSBEM is presented in this reserch. This model introduces spce distnce vector, AOA nd time dely s the model prmeters, nd derive the probbility density functions of the AOA, nd the spce time frequency correltion function of MIMO chnnel. MATLAB simultion results show tht the improved 3D-MIMO- GBSBEM model is not only comptible with the trditionl GBSBEM, but lso overcome the limittions of the ltter. This model cn be used more widely in MIMO chnnel modeling by selecting pproprite prmeter settings.. The Improved 3D-GBSBEM. model of 3D-GBSBEM As shown in Fig., Tx, Rx, re the trnsmitting ntenn nd receiving ntenn respectively. Mny ellipses with different lengths chrcteristics cn be obtined using Tx nd Rx s focus. A,B nd Cre rndom scttering points in these ellipses. Ellipticl model depicted in this mnner hs two chrcteristics:

2 Ming LI nd Yun-fei GUO/Journl of Engineering Science nd Technology Review 6 (5) (3) 76-8 () lthough the distnce between A nd Rx is different to the distnce between B nd Rx, A nd B hve the sme ngle of rrivl. So they hve sme Doppler frequency; () ccording to the nture of ellipse, A nd C re in the sme ellipse, nd they hve thesme pth length. So they hve the sme propgtion dely. Tx B ' d A ' φ ʹ 3 ʹ ʹ Rx experienced only one reflection, nd scttering bodies re uniformly distributed in the ellipsoid. Its cross-sectionl view is shown in Fig. : Fig.. sectionl view of the 3D- GBSBEM C Fig.. n GBSBEM chnnel model x Elliptic equtions is defined s: y + () b Where c i / b f f d / C is speed of light, nd i is time dely. Bsed on the GBSBEM, AOA s probbility density function on the stndrd time dely is defined s: 3/ ( i ) ( i icosφ+ ) 3 π(i )( i cos φ) f ( φ ) π < φ < π () i It cn be seen tht originl GBSBEM does not consider the pitch ngle formed by the trnsmitting ntenn, receiving ntenn nd the horizontl plne. When communiction distnce is fr wy, the pitch ngle is very smll, nd the time dely is long. While communiction is ten plce between the high-rise buildings in n urbn environment, the pitch ngle is lrger, nd the time dely is smller compred with long distnce communiction. In this wy, originl twodimensionl GBSBEM estblished under the horizontl will no longer be ble to gurntee its ccurcy. In order to me up for the deficiencies of the originl D-GBSBEM, new improved ellipsoid modelis constructed within three-dimensionl coordinte system. This model mes the trnsmitting ntenn nd the receiving ntenn s the ellipsoid s focuses. Wht s more, it ssumes tht the scttering signls reched the receiving ntenn hve Where d is the distnce between trnsmitting ntenn Tx nd receiving ntenn Rx. is the smllest bsolute dely, d / c θ is the pitch ngle formed by the trnsmitting ntenn, receiving ntenn nd the horizontl surfce. A is ssumed s n rbitrry point on the ellipticl boundry, which it s time dely is. φ AR T. φ is AOA, nd x x ri is stndrd dely, nd i i i r /. The PDF of AOA According to the nture of ellipsoid, three-dimensionl elliptic equtions is built s follows: ( z z) x y + + (3) b b Where, z is n offset in the Z-xis of ellipse. In order to fcilitte the nlysis, this 3D-GBSBEM model is mpped to horizontl plne. The mpped eqution is: ( x f ) y + (4) b f b This eqution s prmetersre defined s follows: sin sin b θ + b b θ + b cos cos θ b b cosθ sin θ + b cos θ θ 77

3 Ming LI nd Yun-fei GUO/Journl of Engineering Science nd Technology Review 6 (5) (3) 76-8 According to this mpped eqution,the reltionship between the AOA nd the mpped stndrd time dely in horizontl plne cn be obtined. The reltion ship is shown s: r φ rccos r i i Where ri is ssumed the stndrd time dely in horizontl plne, ri ri /cosθ. In order to generte the probbility density function of AOA, this reserch uses the distribution function method, nd obtins the AOA s conditionl probbility density function ccording to the formul (3), (4) nd (5), shown s follows: ( r r cosφcosθ + cos θ)( r cos θ) (6) f( φ r), π < φ < π i 3/ i i i 3 π(ri cos θ)( ri cosφcos θ).3 The PDF of stndrd time dely It ws found tht the dely cn be pproximted by n exponentil distribution [8] in distnce environment, such s the close scttering bodies, tll buildings nd mountins, by nlyzing the mesured environmentl in literture [8] nd [9]. Therefore, the 3D-GBSBEM proposed in this study, lso believes tht scttering bodies obey the uniform distribution on the ellipse in the sme dely. At the sme time, these scttering bodies obey exponentil distribution on the ellipse in the different dely. Under this condition, the probbility density function of the stndrd time dely is ( r/cosθ ) σ fr() r e,< r < r (7) m σ For ech scttering body, the ngulr distribution nd the distnce distribution re independent, so ccording to the formul (6) nd (7), the joint probbility density function of AOA nd stndrd time dely cn be expressed s: f( φ, r) f( φ r) f( r) i i i ( r r cosφcosθ + cos θ)( r cos θ) 3/ ( r cos θ ) i i i σcosθ e 3 πσ (ri cos θ )( ri cosφ cos θ ) 3. The 3D-MIMO-GBSBEM 3. chnnel model bsed on 3D-MIMO-GBSBEM Bsed on the 3D-GBSBEM, 3D-MIMO-GBSBEM is presented in this chpter. In Fig.3, we show the model of 3D-MIMO-GBSBEM. Where p, q re trnsmitting ntenns. S pq is the distnce between them. The m, n re receiving ntenns. S mn is the distnce between them. The is rndom sctter in φ ellipsoid. Bsed on the, pm, is the DOA between the trnsmitting ntenn p nd the receiving ntenn n. D is the horizontl distnce between the trnsmitting nd receiving ntenns. (5) (8) q ht p D φ pm, θ m φ qn, Fig. 3. MIMO model bsed on 3D-MIMO-GBSBEM Assuming there is no line of sight between the trnsmitting ntenn nd receiving ntenn, the chnnel impulse response between the trnsmitting ntenn p nd the receiving ntenn m is expressed s follow: NR NT K L NLOS ij i j pm, l p m K i j l h (, t ) lim g ( d d ) hr n wpthloss / π i j ij exp[ jφl j ( dp + dm)] δ( l ) w ij Where pthloss is the fctor of pth loss. l is the lth pth time dely,which derived by the wve going throughing the sctter. g, φ re the rndom gin nd rndom phse introduced by rndom sctter. Wht s more, { } g ij (9) cn be seen s independent nd identiclly distributed rndom vribles. And it s normlized form is shown s follow: NR NT K ij lim E[( g ) ] K K i j () 3. spce time frequency correltion function Wireless fding chnnel second-order sttisticl properties cn reflect the bsic chrcteristics of the chnnel. It is necessry to nlyze the MIMO chnnel sptil correltion properties in the time domin nd frequency domin. The literture [3] improved the GBSBEM, but filed to give effective expression of spce-time-frequency correltion function. By ting the corros-correltion of the ntenns Tp-Rm nd Tq-Rn shown in Fig. 3 s exmple, the spcetime-frequency correltion function of 3D-MIMO-GBSBEM is derived nd nlyzed in this pper. Spce-time-frequency correltion function is defined s: ρ pm, qn Eh th t (, t ) * [ pm( ) qn( )] pm qn () Where ()* mens solving complex conjugte. Assuming the wves received by different ntenns hve, nd the rice the sme verge power, pm qn fctors on different chnnels re the sme, 78

4 Ming LI nd Yun-fei GUO/Journl of Engineering Science nd Technology Review 6 (5) (3) 76-8 K K K. Bsed on the formul (9), nd (), pm qn Rice Spce time frequency correltion function of 3D-MIMO- GBSBEM is obtined: density, verge dely nd dely spred cn be derived. The solving eqution cn be written s follows. () The verge dely: NR NT K L NLOS ij pm, qn ( tt,,, Δ ) lim E[( gl ) ] + K K Rice i j l ρ ζ ζ ζ i j wpthloss / i j wpthloss / p m q n ( d d ) ( d d ) π i j i j ij exp[ j( φpm φqn) j ( dp + dm dq dn )] δ( l ) δ( Δζ) () B () S ( ) d S ( ) d (5) When K, K L E[( gl ) ] cn be KL l pproximted s f( φ r) f( r) dφ dr, which is obtined in formul(8). Then the formul() cn be simplified s follow: NLOS ρpm, qn(, tt, ζ, ζ Δ ζ) f( φ ) f( ) + K i j wpthloss / i j wpthloss / p m q n ( d d ) ( d d ) π exp[ j( φpm φqn) j ( dp + dm dq dn )] δ( Δζ) dφd S (, ζδ )( Δζ) h Rice (3) Where Sh(, ζ) is the dely power spectrum density function. is pth dely, nd ζ is time difference. According to the chrcteristics of GBSBEM, the received wves trnsmit distnce cn be written s: d + d d d ( ) c ζ c p m q n pm qn Since the trmsmit nd receive ntenns distnce is much lrger thn the ntenn spce, the pth loss cn be equivlent to the form: i j wpthloss / i j wpthloss / wpthloss p m q n t r ( d d ) ( d d ) ( d d ) In this wy, the dely power spectrum density function cn be simplified s follow: w S (, ) ( ) () ( ) pthloss h ζ f φ f dt dr + K (4) Rice exp[ j π fζ ] δ( ζ ζ ) dφd According to the chnnel fetures under the condition of wide sense sttionry uncorrelted scttering (WSSUS) [4], mny other MIMO chnnel prmeters cn lso be derived. For exmple, when ζ, the dely power spectrum density function, Sh(, ζ ), cn lso be clled the dely power spectrl density S (),which determines the verge power of the scttered components ssocited with the propgtion dely. It cn be seen tht the dely power spectrl density is proportionl to the probbility density function of propgtion dely. By the dely power spectrl The verge dely is the sttisticl verge dely of crrier signls trnsmitted in multipth fding chnnel, nd is determined by first-order of S (). (b) The dely spred: B () () ( ) ( ) B S d S () d (6) The dely spred, which is determined by the secondorder of S (), cn be used to mesure the time dely of pulse going through the multipth fding chnnel. Since the time-frequency correltion function cn be expressed s the fourier trnsform of dely power spectrum density function, the time-frequency correltion function is derived s follow: NLOS R (, f) S (, ζ)exp( j π fζ) dζ h f( φ ) f( )( dt dr ) + K Rice wpthloss π exp[ j ζ c j π f ζ ] δ ( ζ ζ ) d φ d d ζ 4. The simultion (7) In order to prove the fesibility nd pplicbility of the 3D- MIMO-GBSBEM proposed in this study, MATLAB simultion is utilized. In this study s preliminry experiment, we set d 5m, σ 5µ s. Assuming MIMO chnnel bndwidth of the input signl is MHz. The coefficients of cross-correltion function re obtined by AR model. The chnnel simultion is chived by tpped dely line model. The number of tps is 5, nd the order of AR model is 5. In Fig. 4, we show the AOA s PDFs of the GBSBEM nd the improved 3D-GBSBEM model in different pitch ngle cses. Seen from Fig. 4, the improved AOA s PDF hs the sme distribution with the GBSBEM, when the pitch ngle is zero, i.e. the trnsmitting ntenn nd the receiving ntenn is locted in the sme horizontl plne. And the vlues mostly concentrte in the smll ngle region. When there is smller pitch ngle( φ < π /)between the 79

5 Ming LI nd Yun-fei GUO/Journl of Engineering Science nd Technology Review 6 (5) (3) 76-8 receiving ntenn nd the trnsmitting ntenn, the distribution of PDF becomes flt. Fig. 6. the dely profile for 3D-MIMO-GBSBEM Fig. 4. the PDF of AOA for 3D-GBSBEM In Fig. 5, we show the reltionship between the improved AOA distribution nd the time dely in the cse of sme pitch ngle. Seen from Fig. 5, the ngle of rrivl is minly distributed in region with smll dely. As the time dely increses, the distribution of the AOA grdully spred. To the ntenn element for exmple, this pper simulted the spce time correltion function( R( )) of 3D- MIMO-GBSBEM. The simultion prmeter defined s: crrier frequency (fc) is GHz, height of trnsmitting ntenns is h h, nd the height of receiving p q h h. The distnce between ntenns is 5 m n trnsmitting ntenn nd receiving ntenns is m. In Fig. 7, we show the comprison between the correltion vlue of 3D-MIMO-GBSBEM obtined by theoreticl nlysis nd the relted chrcteristics obtined by simultion. L is the number of pths. It cn be seen tht, the greter of L, the more similr the theoreticl curve nd the simultion curve. It cn be seen from the simultion of 3D-GBSBEM, there is close reltionship mong the time dely, rrivl ngle nd sptil distnce between trnsmitting ntenns nd receiving ntenns. For receiver, the reception will be better, if the time dely is smller nd the concentrtion of AOA is higher. Therefore suitble compromise between the height nd distnce of the receiver is needed. Fig. 5. The PDFof stndrd time dely for 3D-GBSBEM In order to verify the performnce of the 3D-MIMO- GBSBEM model under frequency selective environment, this pper simulted the model s dely profile, nd compre the dely profile with the mesurement results in literture [7]. Literture [7] mesured the dely profile under the condition of low bse sttion ntenns. In order to pproximte the mesured environment, the simultion prmeter defined s: w.5, Dm, θ 5 pthloss o The dely profile simultion result is shown in Fig.6. It cn be seen from Fig.6 tht the dely profile of 3D-MIMO- GBSBEM simulted in MATLAB is consistent with the mesurement results of Literture [7]. It mens tht the 3D- MIMO-GBSBEM cn ccurtely describe the chrcteristics of the frequency selective multipth fding chnnel. Fig. 7. The spce time correltion function for 3D-MIMO-GBSBEM In ddition, the dely profile nd spce time correltion function of 3D-MIMO-GBSBEM cn more ccurtely describe the frequency-selective multipth fding chnnel correltion properties compred with mesurement. Therefore, this improved model cn provide theoreticl bsis for the performnce nlysis of receiver to chieve optimum reception. 8

6 Ming LI nd Yun-fei GUO/Journl of Engineering Science nd Technology Review 6 (5) (3) Conclusion This study nlyzes the limittions of trditionl GBSBEM, nd proposes n improvement 3D-MIMO-GBSBEM. The probbility density function of the ngle of rrived, spce time frequency correltion function, nd dely power spectrum density function re derived. Compred with the trditionl GBSBEM, this improved model hs the following chrcteristics: () There is degree of freedom to describe the cellulr spce environment. Selecting pproprite chrcteriztion of the trnsceiver ntenn spce distnce, the model is pplied to city buildings nd rurl communiction environment. () It is more intuitive nd resonble to explin the physicl chrcteristics of wireless fding propgtion. The simultion results show tht the trditionl GBSBEM cn be regrded s subset of the improved model in the idel environment. The proposed model is not only comptible with the trditionl GBSBEM, but lso effective to overcome the limittions of the ltter to me the model more suitble for the ctul environment needs. References. Liberti J C, Rppport T S., A geometriclly bsed model for lineof-sight multipth rdio Chnnels, IEEE 46th Vehiculr Technology Conference[C]. Atlnt: IEEE, 996, pp Ertel R B, Reed J H, Angle nd time of rrivl sttistics for circulr nd ellipticl scttering models, IEEE Journl on Selected Ares in Communictions, 7(), 999, pp Lee. W C Y, Mobile Communictions Engineering, New Yor: McGrw Hill Publictions, Aszetly D (996), On Antenn Arry in Mobile Communiction Systems: Fst fding nd GSM Bse Sttion Receiver Algorithm, Royl Instituted of Technology Ph.D. 5. Lee W C Y, Brndt R H, The elevtion ngle of mobile rdio signl rrivl, IEEE Trnsctions on Communictions,, pp Leong S-Y, Zheng Y R, Xio C, Spce-time fding correltion functions of 3-DMIMOchnnelModel, In:4 IEEE Wireless CommunictionsndNetworingConference,4.WCNC, pp Yong S K, Thompson J S, Three-dimensionl sptil fding correltion models for compct MIMO receivers, Wireless Communictions, IEEE Trnsctions, 4(6),5, pp Yong S K, Thompson J S, A three-dimensionl sptil fding correltion model for uniform rectngulr rrys, IEEE Antenns nd Wireless Propgtion Letters,, 3. pp Ml Umr Mustph Bur, Geometriclly bsed MIMO mobile-to-mobile chnnel model, Beijing: Beijing University of Posts nd Telecommunictions, 3(), pp B. S. Reddy, N. J. Krishn, J.S. Kumr nd K.V.K. Reddy, Prediction of Surgce Roughness in End Milling of P MouldSteel Using Artificil Neurl Networs, 5(),,pp Sh. Mirseidov, A. Inoue, L. Atymtyev, Evluton of Fir Mret Price of Resources In Oil And Gs Industry Using Fuzzy Sets And Logics,6(),,pp