On the Impact of User Positions on Multiuser Detection in Distributive Antenna Systems Shahid Khattak, Wolfgang Rave, Gerhard Fettweis

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1 On the Impact of User Postons on Multuser Detecton n Dstrbutve Antenna Systems Shahd Khattak Wolfgang Rave Gerhard Fettwes Vodafone Stftungslehrstuhl Moble achrchtensysteme Technsche Unverstät Dresden Dresden Germany {khattakravefettwes}@fn.et.tu-dresden.de Abstract Ths paper nvestgates the effect of user poston on the performance of a near optmal SIC recever n an uplnk- OFDM system. Mult-user detecton s made possble through cooperaton between dfferent access pont jont detecton at a sngle central pont. To reduce computatonal complexty the number of ncomng data streams are decoupled through a lnear pre-flter whch s followed by smple bt-nterleaved coded modulaton (BICM). The user data streams are detected sequentally based on the mutual nformaton n ther code words. The resultng frame error rate curves for dfferent QAM modulatons are plotted as a functon of average SR for dfferent user postons compared aganst the performance of gene PIC. The results show a consderable mprovement n performance at the nner cell edges of the cooperatng cells. The recever behavor s also nvestgated for dfferent power control strateges for varyng cell loads. Fnally to see how these lnk level results would translate nto system level performance gans the average throughput n a cell for a dstrbuted antenna system s calculated by pluggng lnk level smulaton results nto a system level smulator. Index Terms BICM Dstrbuted Antenna Systems Iteratve Detecton og kelhood Rato Throughput. M I. ITRODUCTIO OBIE cellular networks are severely lmted by nterference due to the need to share the lmted spectrum to acheve hgh rate multmeda communcaton. Most of ths nterference wll come from the neghborng cells due to hgher frequency reuse smaller cell sze. Ths nterference from the neghborng cells s called other cell nterference (OCI). One way to deal wth OCI s to form a dstrbuted antenna system (DAS) whch employs jont detecton of dfferent users through cooperaton between neghborng base statons. Access ponts (AP) located at geographcally dfferent postons receve uplnk sgnals from dfferent user equpment (UE) locally perform RF processng. The sgnals are then quantzed sent to a sngle central unt (CU) for jont processng thereby formng a vrtual MIMO system []. The CU of each DAS detects decodes the receved sgnals makes avalable at ts output the transmtted data from each UE. The effect of such an arrangement not only reduces the aggregate transmtted power but also results n much mproved receved SIR. Usng a proper recevng strategy both array dversty gan s obtaned resultng n substantal ncrease n system capacty. In ths paper the uplnk detecton decodng of a DAS system s consdered. Iteratve mult-user detecton [] based on soft symbol feedback s adopted as the receve strategy snce t gves adequately good performance at a lower complexty. The mult-user turbo jont detectors for a DAS employng a lnear pre flter for non Gray mappng are proposed n [] [4]. The proposed labelng maps are however strongly msmatched to the turbo codes teratve detecton does not lead to substantal performance mprovement. Gray mappng s therefore used n conjuncton wth mnmum mean square error (MMSE) based nterference subtracton schemes [5] [6] to get a more relable estmate of the sgnals. The nterference subtracton wll move up the startng pont of the detecton trajectory n the EXIT chart [7] effectvely ncreasng the lkelhood of successful detecton lower error propagaton. The smulaton results have been obtaned by assumng that the UE moves symmetrcally from the common cell edges towards the APs by changng a sngle path loss varable. Ths gves nsght nto recever performance at dfferent user postons. These results are subsequently translated to throughput as a functon of SR whch are eventually used as lookup table n Okumura-ata based path loss model to determne the average throughput n cells under dfferent frequency reuse. Ths paper s organzed n seven sectons. The lnk level system model s presented n secton II. The SIC recever structure s dscussed n secton III. Secton IV dscusses the framework of the system level smulaton. Smulaton results are presented n secton V. Fnally conclusons references are presented n secton VI VII respectvely. II. IK EVE SIMUATIO MODE Throughout ths artcle complex baseb notaton s used. Vectors matrces are wrtten n lower uppercase boldface respectvely. The ermtan transpose of a matrx s denoted by (.) the n th teratve step of an nterference subtracton recever for user s (.) n. The system conssts of an OFDM based dstrbuted antenna system. Each DAS conssts of M transmt antennas receve antennas correspondng to the numbers of UEs APs respectvely. et s be the transmtted symbol vector of length M whose entres are chosen from a complex Q-ary

2 sgnal constellatonc [e.g. 6 QAM]. If q s the number of bts per symbol then there are Q = q possble sgnal ponts. The receved sgnal vector on a gven subcarrer s gven as r = s+ n () where n s zero mean complex Gaussan nose vector wth varance σ = { n n }.Throughout ths paper the SR s E defned as the rato of transmtted sgnal power σ = E s { s s } M to the nose power σ unless otherwse stated. The channel matrx for each subcarrer s gven as a product between frequency samples of a channel transfer functon obtaned accordng to the ITU Vehcular A channel model path loss coeffcents P reflectng user postons (dfferent path losses between dfferent UEs APs) h = p h j j j () wth = j = M. We assume that s known perfectly to the access pont at each recever. Whle relatve user postons path gans are addtonal rom varables n realty we make the smplfyng assumpton that the path loss matrx P can be approxmated usng a sngle parameter ρ whch models the relatve strength of the receve powers at more dstant access ponts wth respect to the closest one. ormalzng ths latter power to one we therefore consder the general form of P gven as ρ ρ ρ ρ P = () M M O M ρ ρ Varyng the off dagonal elements ρ from zero to one can be nterpreted as movng the user equpments towards a certan AP of the DAS whle mantanng power control stayng n a symmetrc poston to the other APs. A block of nformaton bts u m of length K from each user s encoded bt-nterleaved leadng to the sequence x m where m = M. The sequence x m s dvded nto groups of q bts each (x m ) fed to a symbol mapper gvng modulated symbol s m. The transmtted symbol vector s = [s s s M ] T. The vector model n Eq. s therefore used repeatedly to transmt a contnuous stream of data bts separated nto blocks. Subscrpt m s however omtted n the rest of the paper for clarty. III. RECEIVER COMPOETS A successve nterference cancellaton (SIC) based recever structure s shown n Fg.. Dfferent blocks used n teratve recevers are labeled to 5. Some of these may be turned off durng specfc stage of operaton. Each SIC step nvolves nterference subtracton of the prevously detected data streams followed by lnear MMSE flterng detecton decodng. Users are detected sequentally based on ther mutual nformaton [6] [8]. o soft nterference subtracton s performed durng the frst pass snce there are no symbol estmates avalable. From the a posteror probablty for the coded bts at the output of decoder soft symbols resdual nose are calculated. To further mprove the performance Fgure : Mult user teratve Recever wth turbo detecton parallel nterference cancellaton (PIC) s performed once after SIC. A descrpton of varous components of the recever s as follows. A. Soft Interference Canceller () At the begnnng of every teratve stage soft estmates of the detected symbols are subtracted from the receved sgnal vector r resultng n an nterference reduced receved sgnal y. For the n th teratve stage the canceller output for the th data stream s gven as y = r s ˆ (4) n n where sˆn s the vector of soft symbol estmates wth the undetected symbol estmates ncludng the th element smply set equal to zero. To take nto account the relablty of the estmate a resdual nose varance [9] s calculated whch s added to the AWG nose n the unbased MMSE calculatons. The nose varance φ n for n th teratve stage the th data stream s φn = φ + en 44. (5) resdual nose s the element wse squared norm for the channel matrx. Soft Soft Symbol Symbol 4 Resdual Resdual ose ose r Soft y z Demappng R MMSE/SISO Demappng Interference MMSE/SISO near near flter Canceller flter Decodng Decodng e n s a vector of estmated symbol error wth entres for undetected symbols smply set equal to zero so for the frst pass t s an all zero vector. en s evaluated for each user after detecton decodng n each teratve stage(see subsecton.4). φ s the nose varance vector at the receve antennas. B. near Flter () A lnear unbased MMSE flter [0] s employed for the SIC teraton (n=). The flter vector w for the th user s gven as ( = ψ ( ) + dag( )/ σs ) w h φ (6) g where s the channel matrx n whch the columns correspondng to already detected data streams are set to zero. h s the column of correspondng to the data stream to be detected. dag( φ ) s a dagonal matrx obtaned from nose covarance vector n eq.(5). In addton the scalng factor ψ = /[ g h ] causes the desred sgnal power to be exactly equal to the transmtted symbol power. The nose varance at the output of the lnear flter for the th user n the SIC stage are gven as R_c 5

3 σw = σ s. (7) g h In the second teraton PIC wth sngle user detecton s performed as suggested n [5] vector w gven as w = h. (8) The correspondng nose power s σw = σ. h = σ h. (9) j= The flter output z n s gven as the nner product of w n y n z = w y. (0) n n n Snce lnear flterng decouples the sgnals from dfferent users the complexty of M metrc calculaton therefore grows only lnearly wth the number of UE APs. C. Demappng Decodng () The demapper computes the a posteror probablty (APP) based on the receve flter output z n. The APP s usually expressed as a log-lkelhood rato ( values). The a posteror value of the coded bt x k k=0 q condtoned on the fltered channel symbol z n s Px [ k =+ zn ] D ( x k zn ) = ln () Px [ k = zn ] where the logcal bt zero s represented by ampltude level x k = + logcal bt one represented as x k = -. D s denterleaved then fed as A to the channel nput of the MAP decoder operatng accordng to BCJR algorthm. The MAP decoder delvers the a posteror -values of the nformaton bts: Pu [ k =+ A] D ( u k A) = ln () Pu [ k = A ] where u k s the k th nformaton bt for th user stream k=0 K. D. Soft Symbols ts Error Varance Calculaton (4) Coded bt estmates at the decoder output are used to generate soft symbols s ˆn [9]. Q sˆ = E s = s p( s = s ). () n n D k n k D k = 0 en The estmated symbol error soft symbol s gven as Q ˆ n = k n n = k D k = 0 due to the varance about ths e ( s s ) p( s s ). (4) IV. FRAMEWORK FOR SYSTEM EVE SIMUATIOS The system smulator s an uplnk mult-user cellular system employng dstrbuted antenna system wth APs M users n a DAS. There are a total of co-channel UEs n the entre system. Each AP UE employ sngle antenna. The computaton methodology nvolves performng a Monte-Carlo analyss by generatng rom sets of user locatons wthn our observed area assgnng same block of resources (e.g. sub-carrers) to these. For each set of locatons path losses are evaluated based on the azmuth elevaton dstances wth respect to APs. These path losses together wth transmt powers are used to calculate the average receved power of the desred as well as the nterferng sgnals wth n the dstrbuted area network. These sgnal nterference values so obtaned are used to calculate the SIR values for each user n the central DAS as the nose varance s vared. The mean value of receved sgnal to nterference nose rato (SIR) for an th user n a DAS can be wrtten as P ( ) R E ρk hk σs SIR = E = P I + P k = E ρ h σ + σ j= M+ ( ) j= M kj s j n nterference kj kj s j n ρk σs = (5) k = ρ σ + σ where ρ k s the path-loss for the desred lnk between k th receve (AP) th transmt antenna (UE) reflects user postons. Ths nterference term s due to co-channel users located outsde DAS ρ kj s ther correspondng path loss to the receve antenna k. σ s s the transmtted sgnal power for user. If power control mechansm s employed t equals recprocal of the path loss to the closest AP n ts actve set. On the other h when no power control s assumed σ s can be consdered same for all UEs Eq. (5) s further smplfed as ρk SIR =. (6) k = ρ + σ / σ j= M+ kj n s The throughput correspondng to each SIR value s determned based on the lnk level results avalable for dfferent modulaton-codng schemes. It s assumed that transmtter can choose between dfferent modulaton schemes adaptvely thereby maxmzng the throughput. In order to demonstrate the mpact of the statstcal propertes of the channel matrces on the user capacty wthn dstrbuted antenna systems average path losses between user equpments access ponts have been computed accordng to smple path loss model wthn deal cell setup.e. a flat plane Okumura-ata model wth a hexagonal cell setup three-fold sectorzaton. At each smulaton step 0000 dfferent user postons are generated n each of the cells ths process s repeated untl we have enough realzatons TABE I SYSTEM SIMUATIO PARAMETERS Ste to Ste Dstance 500 meter Path loss exponent.5 Total number of cells umber of cell n a DAS 4 Base staton antenna pattern KATREI Base staton antenna heght 0m User equpment eght m Total user realzatons/cell Antenna down tlt 5 degrees Frequency reuse

4 4 to get a smooth SIR dstrbuton. The smulaton parameters have been lsted n the table below Tx- Vrtual 4 Rx MIMO DAS (/ rate pccc) ITU veh A V. SIMUATIO RESUTS ere we provde smulaton results to llustrate the performance of the proposed recever n an uplnk OFDM based DAS wth 4 cells ( = M =4) 4 Mz channel bwdth. The number of symbols n each code word s 5. The quas statc ITU vehcular A fadng channel model s adopted. The recever s assumed to have perfect channel knowledge. A memory two parallel concatenated convolutonal code (pccc) wth generator polynomal G=[75] Gray mappng wth ether QAM modulaton s used n smulatons. A. Recever Algorthm Performance The comparson of dfferent mult user detecton schemes for the cell edge case (ρ = = 0 db) s llustrated n Fg.. All schemes employ MMSE flterng. It can be seen that lnear flterng followed by one PIC stage (labeled as PIC-BICM ) [5] gves reasonable performance mprovement over lnear detecton (labeled near-bicm ) whch can be mproved to wth n db of gene PIC at =0 - by ncreasng the number of teratons to (PIC-BICM(tr)). It s however observed that SIC schemes perform better converge more quckly than PIC. SIC recever (labeled SIC-BICM ) reaches the of 0 - at only 6.5 db SR. The performance of the SIC-BICM recever can be further mproved f a PIC stage s added to t (labeled SIC-PIC-BICM ) reaches the of 0 - at SR of 5.6 db whch s wth n one db of gene PIC. It therefore appears as the most sutable detecton strategy. B. Influence of Pathloss Fg. shows the curves for dfferent order QAM modulatons as the parameter ρ vares from (complete couplng of the lnks) to /0 (partal couplng). The performance as a functon of SR defned accordngly as SR = σ s / σ s presented here wth parameter ρ. We observe that stronger couplng between the users (more equal dstances to the APs) mproves performance due to receve dversty array gan. Interestngly the dfference n SR between completely coupled solated users settles to QAM 6 QAM 64 QAM ρ=0 db ρ=6 db ρ=0 db E s / 0 [db] Fgure. : curves for dfferent QAM modulaton on SIC-PIC-BICM recever. SR =receved power at nearest AP/nose power around 6dB whch s the array gan ndcatng that the resdual nterference of a coupled recever s compensated by ts mproved receve dversty. C. Effect of Cell loadng wthn the Cooperatng cells Fg. 4 shows the effect of cell loads at dfferent transmtter proxmtes on the. For a gven ρ receve dversty stays the same. The shft n the curve by about db for fully loaded case s due to nablty of our recever to completely remove nterference due to other users on the same resource. owever f >M (partally loaded cell e.g. 50% load) the performance mproves greatly s wth n 0. db of gene PIC correspondng to almost complete absence of nterference (5% load case). D. Power Control based on total Receved Power As the jont receve power s exploted by the CU an alternatve SR defnton accordng to σ s ( + ( M ) ρ ) SR = (7) σ s more reasonable n a DAS system reflectng power control based on total receved power. The correspondng performance s shown agan for dfferent ρ values n Fg. 5. For typcal values ( 0 - to 0 - ) fxed SR the Tx-4 Rx DAS (/ rate pccc) ITU Veh A Cell DAS (/ rate pccc) ITU veh A Gene PIC PIC-BICM ( Itr) SIC-PIC-BICM SIC-BICM PIC-BICM ( Itr) near-bicm db E s / 0 [db] Fgure. : curves for dfferent Multuser Algorthms n a 4Tx-4Rx OFDM based dstrbuted antenna system ρ= 0 db 6 QAM modulaton ρ=0 db ρ=6 db 5% load 50% load 00%load E s / 0 [db] Fgure. 4: curves for dfferent cell loads on SIC-PIC-BICM recever. SR =receved power at nearest AP/nose power. 6QAM modulaton

5 Tx-4Rx DAS (/ rate pccc) ITU veh A ρ = (0dB) ρ = / (-db) ρ = /4 (-6dB) ρ = /0 (-0dB) ρ = /00 (-0dB) ρ = 0 (-nf db) Maxmum Spatal Dversty E s / 0 [db] Fgure. 5: performance for dfferent values of ρ on SIC-PIC-BICM recever. SR= total receved power/ nose power. 6 QAM modulaton recever performance does not change consderably f the user moves from the cell border regon towards ts AP (0 ρ 0). Ths fact s expected to be more pronounced n hgh dversty channels where the curves for solated cells ρ=0 would be expected to converge faster. E. Average User Throughput n a three ter Cellular etwork Fg.6 llustrates the average throughput (bts/ resource/user) n a cellular network plotted as a functon of SR. It s assumed that transmtter can choose between QAM modulaton schemes adaptvely thereby maxmzng the throughput. The channel code on the other h s assumed fxed to ½ rate pccc. The SIR data for a 4 cell DAS s generated by system level smulator (secton IV). The SIR values are calculated based on the total receved power on the assumpton that the nterference from the surroundng cells can be consdered Gaussan. Generalzng the result from subsecton D t s assumed that the performance s strongly correlated to SIR value rrespectve of the poston of the user n cell. The lookup table for the throughput calculaton s therefore sgnfcantly smplfed. It s llustrated n Fg. 6 that the maxmum throughput for a reuse three cellular system mproves from. to bts/resource/user as we change from conventonal system to DAS. The mprovement n the case of reuse one s even more substantal. The curve labeled Isolated DAS ndcates the lmtng case of throughput gan n a DAS wth no nterference from out sde hence serves as an upper bound for performance. VI. COCUSIOS o Spatal Dversty Outer cell nterference n the future cellular networks can be suppressed by jont processng n dstrbuted antenna system. In ths paper a SIC-PIC-BICM based teratve detecton technque s proposed whch results n reduced error propagatons outperforms lnear equalzaton PIC schemes wth a performance qute close to that of MAP. The applcaton of a dstrbuted antenna system shows the potental of sgnfcantly better performance compared to non Throughput [bts/resource used/user] ter network 00% oad Power control Isolated DAS Reuse DAS Reuse DAS Reuse SUD Reuse SUD 0.9bts/resource/user 0.6bts/resource/user SR [db] Fgure. 6: Throughput as a functon of SR n hgh reuse cellular network usng DAS or sngle user detecton (SUD). Curve labeled solated cell represents throughput n an nterference free case cooperatng base statons. The effect of the user poston n a DAS has also been studed t s found that the dversty array gan due to several recevers outweghs the error propagaton effects greatly mproves system performance. The throughput data obtaned from lnk level smulaton s appled to a system level smulator so as to see the potental system gans. It s shown that there s a substantal gan n user experence despte the degradaton caused by the nterference from the surroundng cells. VII. REECES [] Sklavos A. Weber T. ''Interference suppresson n mult-user OFDM systems by antenna dversty jont detecton'' n COST 7 TD(0)00 Bologna Oct. 00 [] ee. Byeongs ee Inkyu ee Iteratve detecton decodng wth an mproved V-BAST for MIMO-OFDM systems Selected Areas n Communcatons IEEE Journal on Volume 4 Issue March 006 Page(s):504-5 [] Khattak S. Rave W. Fettwes G. Multuser Turbo Detecton n Dstrbuted Antenna System 5 th IST Moble Wreless Comm. Summt Jun 006 [4] Khattak S. Rave W. Fettwes G. SIC based multuser Turbo Detecton n a Dstrbuted Antenna System for non Gray mappng WPMC San Dego Sep 006 [5] Kühn V.: Combned MMSE-PIC n Coded OFDM-CDMA Systems In IEEE Global Conference on Telecommuncatons (Globecom 00) San Antono USA ovember 00 [6] Wübben D. Böhnke R. Kühn V. Kammeyer K.D.: MMSE Extenson of V-BAST based on Sorted QR Decomposton IEEE Semannual Vehcular Technology Conference (VTC00-Fall) Orlo Florda USA October [7] Ten Brnk S. Convergence Behavor of Iteratvely Decoded Parallel Concatenated Codes IEEE Tran. on Comm.Oct 0. [8] I. oeher P. A. Computaton of symbol-wse mutual nformaton n Transmsson systems wth ogapp decoders applcatons to EXIT Charts ITG Conf. on SCC 004. [9] Cho W. Coff J. M. Iteratve soft nterference cancellaton for multple antenna systems. Wreless Comm. etworkng Conf WCC. IEEE [0] Seethaler Y. Matz G. lawatsch F. An effcent MMSE-based demodulator for MIMO Bt-Interleaved Coded Modulaton IEEE Globecom 004.