Effective Throughput: A Unified Benchmark for Pilot-Aided OFDM/SDMA Wireless Communication Systems

Transcription

1 Effetive Thoughput: A Unified Benhmak fo Pilot-Aided OFDM/SDMA Wieless Communiation Systems Dongxu Shen, Zhengang Pan, Kai-Kit Wong, Vito OK Li Depatment of Eletial & Eletoni Engineeing The Univesity of Hong Kong Pokfulam Road, Hong Kong {dxshen, zgpan, kitwong, vli}@eeehkuhk Abstat In this pape, we study the uplink pefomane of an othogonal fequeny division multiplexing (OFDM) wieless system whee multiple antennas ae utilized at the base station (BS) Futhe, apaity an be geatly enhaned though spatial division multiple aess (SDMA), so that seveal uses an tansmit pakets simultaneously to the BS The system pefomane is detemined by vaious tansmission tehniques, inluding methods fo hannel estimation, modulation, as well as hannel oding Conventional paametes suh as paket eo ate (PER) and bit eo ate (BER) ae unable to eflet the atual system pefomane beause no onsideation is given to the oveheads inued by the tansmission tehniques Theefoe, we ae motivated to popose a novel onept alled effetive thoughput to haateize the apaity available to uses by inopoating all these fatos The effetive thoughput fo a use an be viewed as the aveage numbe of suessfully eeived data bits in an OFDM symbol afte exluding eoneously eeived pakets and the oveheads due to hannel estimation and oding It also dietly elates to the tansmission delay of a use paket The system effetive thoughput is the aggegated effetive thoughput of all uses Simulation esults demonstate that effetive thoughput an seve as a useful and moe meaningful benhmak paamete in optimizing system pefomane Keywods Antenna aay, divesity, effetive thoughput, OFDM, SDMA I INTRODUCTION Othogonal fequeny division multiplexing (OFDM) [], [] is an effetive method fo high speed wieless ommuniations In OFDM, data is aied ove a lage numbe of paallel subaies instead of a single aie Thus the data ate on eah subaie is signifiantly edued, whih effetively mitigates the influene of multipath fading Howeve, eah subaie still undegoes flat fading that degades system pefomane, espeially fo high level modulation By using adaptive antenna aay, the pefomane of OFDM an be geatly enhaned though the divesity ahieved fom multiple antenna elements [3] System apaity an be futhe ineased by spatial division multiple aess (SDMA), in whih moe than one use an be aommodated on the same subaie at the same time [4], [5] In this pape, we fous the uplink pefomane haateization of an OFDM/SDMA wieless ommuniation system, whee the base station (BS) is equipped with multiple eeiving antennas, and multiple mobile uses tansmit pakets to the BS though one tansmitting antenna Fo data ommuniations, data is tansmitted in pakets A ommonly used paamete fo haateizing paket level pefomane is the paket eo ate (PER) Given the oding method and paket length, PER is only detemined by bit eo ate (BER) Theefoe, pevious eseah foused on the BER pefomane of OFDM/SDMA systems [5], [6] Unfotunately, PER (o BER) alone is insuffiient fo pefomane haateization; othe impotant fatos, suh as the ovehead fom hannel estimation, modulation and oding sheme, need to be inluded in pefomane analysis In OFDM/SDMA, thee is a tade-off between PER and the ovehead of hannel estimation The opeation of antenna aay equies the knowledge of the hannel, whih is often obtained though the use of pilots [7], [8] A potion of the subaies is seleted fo pilots, and hannel estimation is pefomed based on the eeived signals on pilot subaies [9], [0] The quality of hannel estimation impoves with moe pilots [], whih leads to lowe BER o PER Howeve, sine pilot subaies annot be used fo data, thoughput is edued Evidently, BER (o PER) does not ompletely haateize the pefomane, so that pefomane optimization annot be solely based on (the minimization of) BER Simila tade-offs exist among PER, modulation and oding sheme Fo example, high level modulation aies moe bits on a subaie, but is pone to eo; oding impoves PER, but intodues edundany Clealy, the pefomane of OFDM/SDMA depends on all of the above fatos that ae not enompassed by PER o BER We ae thus motivated to devise a unified measue fo pefomane haateization In ontast to the pevious eseah, we define the notion of effetive thoughput to haateize the pefomane of OFDM/SDMA systems by taking into aount PER, numbe of data subaies in an OFDM symbol, modulation and oding sheme Effetive thoughput fo a use an be viewed as the aveage numbe of suessfully eeived data bits in an OFDM symbol afte exluding eoneously eeived pakets and the ovehead of pilots as well as oding The effetive thoughput fo the whole system is the aggegation of effetive thoughput of all uses Effetive thoughput haateizes system pefomane in a moe patial sense, and the optimization of system pefomane an be ahieved though its maximization Simulation is onduted to demonstate the influene of vaious fatos on effetive thoughput, suh as the impat of pilot spaing in time and fequeny, modulation and hannel signal-to-noise atio (SNR), et This pape is oganized as follows In Setion II, we desibe the system model In Setion III, we define the effetive thoughput of a use and extend the idea fo the system /03/$700 (C) 003 IEEE IEEE INFOCOM 003

2 We disuss how vaious fatos affet effetive thoughput in Setion IV Simulation esults ae pesented in Setion V In Setion VI, we onlude this pape II SYSTEM DESCRIPTION In this pape, we onside the uplink (fom mobile uses to BS) of an OFDM system The baseband system onfiguation of a mobile use fo OFDM tansmission is illustated in Fig Sine the opeation is idential fo evey OFDM symbol, the time index fo OFDM symbols is omitted in all late notations fo oniseness The bit steam of a use u is fist fed into a modulato, whih maps the data bits into modulation symbols Then a blok of N modulated symbols ae onveted fom seial into paallel to podue the symbols S u (i), i =,, N on the oesponding subaies, whee N is the numbe of subaies in an OFDM symbol Next invese fast Fouie tansfom (IFFT) is pefomed to tansfom the fequeny domain epesentation S u (i), i =,, N into time domain seies s u (i), i =,, N whih ae then paallel-to-seial onveted Cyli pefix is then added to pevent inte-symbol intefeene (ISI) We assume that the length of the yli pefix is always longe than the maximal hannel multipath delay spead, so that thee is no ISI Finally, the esulting signal is tansmitted though a single antenna Assuming thee ae A antenna elements at the BS, and U uses ae tansmitting simultaneously to the BS At the antenna element a, the eeived signal is fist sampled at a sampling inteval of t Then a blok of N samples ae onveted fom seial to paallel to podue a (i), i =,, N, and fast Fouie tansfom (FFT) is pefomed to obtain R a (i), the eeived signal at subaie i (see Fig fo details) The eeived signal R a (i) is the supeposition of the faded vesions of the signals tansmitted fom all uses, oupted by additive white Gaussian noise (AWGN), and an be expessed as U R a (i) = H u,a (i)s u (i) + n a (i) u= whee H u,a (i) is the fading oeffiient between use u and the ath antenna element of the BS at subaie i, n a (i) is omplex AWGN, with zeo mean and vaiane N 0 / pe dimension Antenna ombining is pefomed independently on a pe subaie basis, and the tansmitted signal fo use u at subaie i an be estimated by Ŝ u (i) = A Wu,a(i)R a (i) () a= whee W u,a (i) is the omplex weight at the ath antenna element fo use u, and the supesipt is the omplex onjugate opeation Let S(i) = [S (i) S (i) S U (i)] T be the veto of tansmitted signal on subaie i, whee T denotes the tanspose opeation Also, let R(i) = [R (i) R (i) R A (i)] T be the eeived signal veto, and n(i) = [n (i) n (i) n A (i)] T be the noise veto Then an be expessed as R(i) = H(i)S(i) + n(i) (3) whee H(i) is the hannel tansfe matix H, (i) H U, (i) H(i) = (4) H,A (i) H U,A (i) Denoting the antenna weight matix as W, (i) W U, (i) W(i) =, (5) W,A (i) W U,A (i) the tansmitted signal veto S(i) an be expessed as Ŝ(i) = W H (i)r(i) (6) whee H epesents the Hemitian tanspose It is well-known that with hannel state infomation, the optimal weight matix W(i) an be omputed by [] W(i) = [H(i)H H (i) + σ I] H(i) (7) whee I is an A A identity matix Othe assumptions fo the system ae summaized hee The hannels between any antenna pais ae unoelated, and signals fom diffeent uses ae independent Futhemoe, the numbe of simultaneous uses is no geate than the numbe of antenna elements Uses ae assumed to be pefetly synhonized in both time and fequeny A Pefomane Conens III EFFECTIVE THROUGHPUT The pimay fous of this pape is on the pefomane haateization of an OFDM system with antenna divesity Unlike many of the pevious studies with emphasis on BER pefomane [3], [5], [6], we ae inteested in evaluating pefomane of the system when data is tansmitted in pakets A use paket onsists of a blok of bits with a etain amount of ovehead, suh as heade and oding edundany A paket is poteted at least by eo detetion oding, suh as yli edundany hek (CRC) In this pape, we assume all bit eos an be deteted by the CRC In paket tansmission, it is desiable that a paket an be tansmitted in as few OFDM symbols as possible fo small tansmission delay This is equivalent to having as many data bits as possible in an OFDM symbol On the othe hand, pakets should be eeived at an aeptable level of quality Othewise, eoneous pakets ae eithe etansmitted o disaded that wastes tansmission effots To inease thoughput, moe bits should be put on a subaie; howeve, paket eo is moe likely to ou Theefoe, it is neessay to balane the numbe of data bits in an OFDM symbol with eeption quality B Pefomane Related Fatos Befoe pesenting the definition of effetive thoughput, we identify the fatos that ae uial to system pefomane They ae desibed as follows: Paket eo ate, P e : PER seves as an indiato fo eeption quality Wheneve bit eos ae deteted in a paket by CRC, /03/$700 (C) 003 IEEE IEEE INFOCOM 003

3 s u bit steam Modulation Seial to Paallel S u () Su S u IFFT s u s u () Paallel to Seial Add yli pefix Fig System onfiguation fo OFDM tansmission at a mobile use Antenna Sampling seial to paallel () FFT R () R R W, W, W U, ^ S ^ S Antenna Sampling seial to paallel () FFT R () R R W, W, W U, Antenna A Sampling seial to paallel A A A () FFT R A R A () R A W,A W W,A U,A ^ S U Fig System onfiguation fo antenna poessing at the BS The poessing is idential fo all subaies so that only subaie is shown the whole paket is disaded o etansmitted Thus, the potion of tansmission effots wasted due to bit eo is epesented by PER athe than BER The numbe of data subaies in an OFDM symbol, N d : As shown in Setion II, the opeation of OFDM/SDMA equies the knowledge of hannel infomation, whih is usually estimated by using pilots [7], [8] In the pilot-symbol-assisted shemes, some subaies ae devoted as pilot subaies, aying known pilot symbols, and data bits ae aied by the emaining subaies Theefoe, the numbe of OFDM symbols needed to tansmit a paket depends on the numbe of data subaies in an OFDM symbol Modulation index, M I : Modulation index epesents the numbe of bits aied on a data subaie In this pape, we assume all data subaies employ the same modulation sheme Fo a modulation sheme with a onstellation size of M, the modulation index M I is given by M I = log M, whih gives the numbe of bits on a modulated symbol Although highe ode modulation aies moe bits on one data subaie, it is moe suseptible to eo, whih may offset the gain by having moe bits in a subaie Fo example, QPSK (quadatue phase shift keying), 6 QAM (quadatue amplitude modulation) and 64 QAM ay, 4 and 6 bits/symbol espetively, but BER pefomane deteioates fom QPSK to 64 QAM with the same pe bit enegy [] Coding ate, : The level of edundany due to hannel oding an be haateized by the oding ate = R d R, (8) whee R d is the numbe of data bits, and R is the numbe of oded bits /03/$700 (C) 003 IEEE IEEE INFOCOM 003

4 C Definition of Effetive Thoughput The onept of effetive thoughput aims to integate the above fatos to povide a unified pefomane measue fo pilot-assisted OFDM/SDMA wieless ommuniation systems Definition Use Effetive Thoughput: Let P e be the PER, N d the numbe of data subaies in an OFDM symbol, M I the modulation index on data subaies, and the oding ate The effetive thoughput of a use is defined as T u = ( Pe )N d M I (9) The nomalized effetive thoughput is defined as the atio between the use effetive thoughput and the numbe of subaies in an OFDM symbol That is T u = T u N = ( P e)n d M I N (0) Definition System Effetive Thoughput: Let T u be the effetive thoughput fo use u When thee ae U uses tansmitting simultaneously, the system effetive thoughput is defined as U T a = T u () i= The nomalized system effetive thoughput is similaly defined as T U a = T u i= = T a N () The definition of effetive thoughput onsides the influene of PER (P e ), the ovehead intodued by pilots (N d ), modulation index (M I ), and oding edundany ( ) It inopoates both paket eeption quality and the numbe of data bits in an OFDM symbol The eeption quality is epesented by ( P e ), whih is the potion of pakets oetly eeived In an OFDM symbol, only N d out of N subaies ontibute to aying use data On eah data subaie, the numbe of data bits is M I Also, at a oding ate, the numbe of (peoded) bits in an OFDM symbol is N d M I Thus the effetive thoughput ( P e )N d M I epesents the aveage numbe of bits that is available fo tansmitting pakets in an OFDM symbol Coespondingly, the nomalized effetive thoughput gives the aveage numbe of data bits on a subaie The effetive thoughput an be easily tanslated to the aveage delay fo tansmitting a use paket when etansmission is employed Let L d be the paket size befoe hannel oding, o L d / afte hannel oding The numbe of OFDM symbols needed to tansmit a paket is L d / N d M I, (3) whih oesponds to a peiod of ( Ld / N d M I ) T S whee T S is the duation of an OFDM symbol, and is a fixed paamete Assuming that an eoneous paket is always etansmitted until suessfully eeived, and the ouene of a paket eo is independent, identially distibuted (iid) Then the numbe of tansmission attempts is a geometi andom vaiable and the aveage numbe of tansmission attempts is given by P e Aodingly the aveage delay τ D fo tansmitting a data paket is L d τ D = T S ( P e )N d M I = ( Ld T u ) T S (4) Sine T S is a fixed value, at a given paket length, the aveage delay is solely detemined by the effetive thoughput T u Consequently, minimizing the aveage paket delay is equivalent to maximizing the effetive thoughput IV DISCUSSIONS Effetive thoughput is detemined by PER, the numbe of data subaies (o the numbe of pilot subaies), modulation and oding sheme In this setion, we disuss the influene of these fatos on effetive thoughput A Paket Eo Rate By definition, effetive thoughput is popotional to ( P e ) PER elates to BER as P e = ( P b ) L d, (5) whee P b is BER, and L d is the length of a paket When L d P b, P e L d P b (6) Thus if the paket length is fixed, P e is detemined by P b In OFDM, P b is influened by hannel SNR, quality of hannel estimation, modulation and oding sheme With antenna aay, it is also affeted by the numbe of antenna elements and the numbe of simultaneous uses Fom the system viewpoint, the numbe of antenna elements at the BS is fixed Theefoe, P b is influened by the numbe of simultaneous uses U It is known [] that an A-element aay has A degees of feedom The anellation of CCI fo one use osts one degee of feedom When thee ae U uses, U degees of feedom ae dediated fo CCI anellation, and the emaining A U degees of feedom ae fo divesity Appaently, the level of divesity deeases with moe uses With less divesity, P b and oespondingly P e inease This means the effetive thoughput fo a use is always deeasing with moe uses Howeve, system effetive thoughput T a may still inease /03/$700 (C) 003 IEEE IEEE INFOCOM 003

5 B Pilot Subaies In this pape, hannel estimation is obtained though pilots The numbe of pilots detemines the quality of hannel estimation, and hene the PER pefomane Howeve, the use of pilots auses the edution of effetive thoughput With SDMA, we show in this subsetion that the ovehead fom pilots annot be negleted B Aangement of Pilot Subaies In OFDM/SDMA systems, hannel estimation equies the pope aangement of pilots Fo a use u, let S u (p) be the pilot symbol on pilot subaie p, R a (p) be the eeived signal at antenna a Then R a (p) is expessed as R a (p) = H u,a (p)s u (p) + I(p) + n(p), whee H u,a (p) is the hannel esponse on subaie p between use u and eeiving antenna a, I(p) is the CCI fom othe uses, and n(p) is AWGN The hannel esponse H u,a (p) an be estimated by Ĥ u,a (p) = R a(p) S u (p) (7) When I(p) = 0 (ie, no CCI), the quality of hannel estimation fom (7) only depends on the SNR on subaie p If anothe use u tansmits data on a pilot subaie of use u, CCI fom use u an seveely degade the quality of hannel estimation Theefoe, CCI should be avoided on all pilot subaies, whih alls fo the pope aangement of pilots among all uses M f M f pilot subaie M t :4: ;4; :4: ;4; 49 :4: ;4; ;4; use pilot subaie M t <4< =4= <4< =4= 4> 4? <4< =4= 4> 4? =4= 4> 4? A4A 4B A4A 4B 4C A4A 4B 4C 4C D4D E4E D4D E4E D4D E4E E4E 4F 4G 4F 4G 4F 4G 4G 4H 4I 4H 4I 4H 4I 4I null subaie use L4L M4M L4L M4M L4L M4M M4M N4N O4O N4N O4O N4N O4O O4O use use (a) null subaie P4P Q4Q P4P Q4Q P4P Q4Q Q4Q J4J K4K J4J K4K J4J K4K K4K (b) 4R 4S 4R 4S 4R 4S 4S 4T 4U 4T 4U 4T 4U 4U 0 / 0 / 0 ( / 0 ' ( ' ( ' ( ) * ) * " ) *! "! "! " 4\ 4] 4\ 4] ^4^ _4_ 4\ 4] ^4^ _4_ 4] ^4^ _4 4_ 4V 4W 4V 4W `4` a4a 4V 4W `4` a4a 4W `4` a4a a4a data subaie use $ - $ # $ # $ #, +, + &, + & % & % & % data subaie use 3 a subaie an OFDM symbol Z4Z [4[ Z4Z [4[ d4d e4e Z4Z [4[ d4d e4e [4[ d4d e4e e4e X4X Y4Y X4X Y4Y b4b 4 X4X Y4Y b4b 4 Y4Y b4b 4 4 a subaie an OFDM symbol Fig 3 Aangement of pilot subaies using null subaies: (a) pilots of all uses ae in the same OFDM symbol but at diffeent subaies; (b) pilots of all uses ae at the same subaie but in diffeent OFDM symbols To this end, one solution is to ensue the pilot subaies used by one use ae not used as data subaies fo all othe uses As plotted in Fig 3, when a subaie is used by a use as a pilot subaie, othe uses put a null symbol on the subaie (ie, no symbol is aied, neithe pilot no data) We efe to this appoah as the null subaie (NS) method g g g g g g g g³ g³ g³ g g g gµ gµ gµ g g g g g g g g g g g g¹ g¹ g¹ gº gº gº g«g«g«g g g g g g g g g g g g g g g g g g± g± g± g² g² g² g² data subaie ÌgÌ ªgª pilot fo use ËgË ÌgÌ pilot fo use g ªgª pilot fo use 3 gã gã gã gä gä gä gå gå gå gæ gæ gæ gæ gç gç gç gè gè gè gè gé gé gé gê gê gê g» g» g» g¼ g¼ g¼ g¼ g½ g½ g½ g¾ g¾ g¾ g g g gà gà gà gà gá gá gá gâ gâ gâ gâ gh gf gj gj gi gl gl gk gn gm gp gp go g gq gt gt gs gv gv gu gwgw gxgx gzgz gygy gzgz g g g{g{ g g g}g} g~g~ g g gg g g g g g g g g gƒgƒ g g g g g g g g g g gĝˆ gšgš g g gšgš gœgœ g g gœgœ g g gžgž g g g g g g g g g g g g g g g g g g g g g g use use use 3 (a) 33 data subaie pilot fo use 44 pilot fo use ÍÎÍ ÍÎÍ ÍÎÍ ÏÎÏ ÏÎÏ ÏÎÏ ÐÎÐ ÐÎÐ ÐÎÐ ÑÎÑ ÑÎÑ ÑÎÑ ÎÒÎÒ ÎÒÎÒ ÎÒÎÒ ÎÓÎÓ ÎÓÎÓ ÎÓÎÓ ÎÔÎÔ ÎÔÎÔ ÎÔÎÔ ÎÕÎÕ ÎÕÎÕ ÎÕÎÕ ÎÞ ÎÞ ÎÞ Îß Îß Îß Îà Îà Îà Îá Îá Îá Îâ Îâ Îâ Îã Îã Îã Îä Îä Îä Îå Îå Îå '' (( %% && ## $$!! "" '' (( %% && ## $$!! "" ÖÎÖ ÖÎÖ ÖÎÖ Î Î Î ØÎØ ØÎØ ØÎØ ÙÎÙ ÙÎÙ ÙÎÙ ÎÚÎÚ ÎÚÎÚ ÎÚÎÚ ÎÛÎÛ ÎÛÎÛ ÎÛÎÛ ÎÜÎÜ ÎÜÎÜ ÎÜÎÜ ÎÝÎÝ ÎÝÎÝ ÎÝÎÝ use Îæ Îæ Îæ Îç Îç Îç Îè Îè Îè Îé Îé Îé Îê Îê Îê Îë Îë Îë Îì Îì Îì Îí Îí Îí use // ,, )) ** // ,, )) ** (b) Îî Îï Îñ Îó Îõ Îö Î Îù Îû Îý ŸgŸ g g g g g g g g g g g g šgš œgœ g œgœ žgž g žgž pilot fo use 3 use 3 a subaie an OFDM symbol Îþ Îÿ a subaie an OFDM symbol Fig 4 Pilot aangement using othogonal speading sequenes: (a) speading aoss subaies in the same OFDM symbol; (b) speading aoss symbols at the same subaie In [6], two othe pilot aangement methods wee poposed, both based on othogonal speading sequenes In one sheme, as shown in Fig 4 (a), a Walsh speading sequene is used to spead a pilot onto multiple sequential subaies Uses ae assigned with diffeent speading sequenes, while pilots ae spead onto the same goup of subaies Due to the othogonality among Walsh sequenes, no CCI is intodued unde pefet synhonization We all this method fequeny-domain speading (FS) sheme Anothe sheme is to spead a pilot on the same subaie of suessive OFDM symbols by Walsh sequenes, as illustated in Fig 4 (b) We all this time-domain speading (TS) sheme All of the above shemes equie a -D hannel estimation [0], [3] to be pefomed based on the hannel gains obtained at the pilot loations (using (7)) B Compaison of Pilot Aangement Shemes Pilot subaies ae not available fo data, and ae thus oveheads Among the thee pilot aangement shemes intodued peviously, NS is moe favoable than the othe two, beause it has less ovehead, and exhibits potential fo bette hannel esti /03/$700 (C) 003 IEEE IEEE INFOCOM 003

6 mation Fo NS, the ovehead onsists of the pilot subaies and null subaies When thee ae U uses, eah pilot equies one pilot subaie and U null subaies, whih oesponds to U subaies of ovehead fo one pilot We an show that the ovehead of FS and TS is no smalle than that of NS Sine the length of a Walsh sequene is a powe of, the numbe of subaies fo one pilot in the FS and TS shemes is L s = log U (8) whee U is the numbe of uses, and x denotes the smallest intege that is lage than o equal to x Obviously, L s U Thus the ovehead fo FS and TS shemes is always no smalle than that of NS In some ases, the diffeene an be signifiant Fo example, when U = 5, NS needs 5 subaies fo one pilot, while FS and TS need 8 subaies, whih means 60% moe ovehead than NS On the othe hand, FS and TS impliitly assume that the hannel gain emains onstant aoss the subaies o symbols Howeve, hannel esponse vaies in both fequeny due to the hannel delay spead and time due to the Dopple spead Theefoe, the estimation fom the two shemes would be less auate than that fom NS B3 Ovehead of Pilots In OFDM/SDMA, the effetive thoughput edution aused by pilots ould be signifiant We illustate this by the following example Example : OFDM is adopted in wieless loal aea netwoks (LAN) standads suh as IEEE 80a [4] and HIPER- LAN II [5] In these systems, antenna aay is not used at the BS Only one use an ommuniate with the BS at one time Pilots ae aied in evey OFDM symbol In eah OFDM symbol, thee ae 4 pilot subaies and 48 data subaies out of 64 subaies (thee ae null subaies fo spetum shaping) This epesents an ovehead of 4/5 8% In ontast, fo an OFDM/SDMA system, suppose that thee ae 6 antennas at the BS to suppot 5 uses Using the NS method and assuming again 4 pilots in eah OFDM symbol, we need 4 5 = 0 subaies fo pilots and null subaies fo eah use This means 0/5 40% of ovehead in an OFDM symbol This example eveals that ovehead fom pilots an signifiantly edue effetive thoughput in the pesene of multiple simultaneous uses The impliation is that we an hadly affod to have pilots in evey OFDM symbol, and pilots should be dispesed in time As suh, -D hannel estimation [0], [3] is equied The gain due to the edution of pilot density is obvious, and is shown by the next example Example : If pilots ae inseted one in evey 5 OFDM symbols, the ovehead is edued by 5 times to 8% as ompaed to 40% in Example In the definitions of effetive thoughput, N d is the aveage numbe of data subaies in an OFDM symbol Suppose that pilots ae aanged in suh a way that thee ae N P subaies fo pilots (inluding null subaies) in evey blok of B s OFDM symbols Then N d is alulated as B4 Optimizing the Numbe of Pilots N d = N N P /B s (9) Reduing the numbe of pilot subaies an inease the numbe of data subaies Howeve, hannel estimation is less auate with fewe pilots, whih leads to highe BER and PER Thus minimizing pilots should be aefully balaned with PER pefomane The definition of effetive thoughput povides the iteion fo optimizing the numbe of pilot subaies Sine effetive thoughput is popotional to ( P e )N d, (0) obviously the best seletion of pilot density is to maximize the podut in (0) This also eveals that effetive thoughput is a bette paamete fo system pefomane than PER o BER It an automatially balane between PER and pilot density C Modulation Sheme Similaly, the seletion of modulation sheme should maximize ( P e )M I () Fo example, we ompae two modulation shemes, QPSK (M I = ) and 6 QAM (M I = 4) Let P e,4 and P e,6 be the oesponding PER Then 6 QAM is moe pefeable than QPSK only when o ( P e,4 ) < ( P e,6 ), P e,6 < + P e,4 () Without antenna aay, the pefomane of vaious modulation shemes fo OFDM mainly depends on SNR and hannel onditions [], [6] With antenna aay, the pefomane is futhe elated to the level of antenna divesity, and the quality of hannel estimation D Channel Coding The optimal oding sheme should be seleted by maximizing ( P e ) (3) The influene of hannel oding on OFDM has been investigated in [7], [8] without antenna divesity, and in [9], [0] with antenna divesity The impat of oding on effetive thoughput is a non-tivial issue In this pape, we do not onside the use of oding A thoough investigation of this topi equies futhe study in the futue V SIMULATION RESULTS In this setion, we pesent the simulation esults fo an OFDM/SDMA system The influene of vaious fatos on BER and effetive thoughput pefomane is demonstated /03/$700 (C) 003 IEEE IEEE INFOCOM 003

7 A Simulation Paametes The paametes of the simulation ae summaized in Table I The oding ate = beause hannel oding is not employed TABLE I PARAMETERS FOR AN OFDM/SDMA SYSTEM Numbe of antennas A = 6 Caie fequeny f = 54 GHz Bandwidth 0 MHz Numbe of subaies N = 8 Caie spaing f = 0/8 = 65 khz Sampling inteval t = /N f = 005 µs FFT peiod T F = / f = 64 µs Guad inteval T G = 08 µs Symbol inteval T S = T F + T G = 7 µs Paket length L d =500 bytes Modulation QPSK, 6 QAM, 64 QAM Coding ate = Pilot SNR 0 db We assume all uses apply the same opeating paametes so that they have the same pilot patten and modulation sheme The hannels between evey use and the BS ae statistially idential and independent Theefoe, all uses should have statistially the same BER and PER pefomane In what follows, the effetive thoughput of the system is equivalent to the effetive thoughput of a use multiplied by the numbe of uses Thus we only povide the esults of use effetive thoughput B Channel Simulation and Estimation We assume the multipath fading hannel is wide sense stationay with unoelated satteing (WSSUS)The hannel impulse esponse h(τ) is modeled as a tapped delay line with tap spaing t, and is witten as L p h(τ) = h l δ(τ l t), (4) l=0 whee L p is the numbe of paths, h l is the omplex fading oeffiient at path l, δ( ) is the Dia delta funtion L p is alled the hannel length and is detemined fom the maximal delay spead τ max by L p = τmax t (5) We also assume that the maximal delay spead is always smalle than the guad inteval Fom ou simulation paametes, this means L p T G = 6 (6) t Expessing the fading oeffiient as h l = A l e jθ l, we model the fading amplitude A l by a Rayleigh distibuted andom vaiable (v), and the phase θ l by a unifomly distibuted v between 0 and π In addition, the aveage powe of h l follows an exponential deay pofile E{A l } = A 0e l t τms, (7) whee τ ms is the oot mean squae (ms) delay spead, and A 0 is a powe oeffiient In theoy, τ max an be infinitely lage Fom patial onsideations, we limit τ max = 5 τ ms fo onveniene, beause it is easy to alulate that the powe beyond 5 τ ms is less than % of the total powe In the simulation, we use L p as a paamete fo hannel delay spead instead of τ ms o τ max Sine we also equie τ max to be an intege, t (7) an be ewitten as E{A l } = A 0e 5l Lp (8) The Dopple fequeny F d is nomalized with espet to the peiod of an OFDM symbol T S as F d T S In ou simulation, F d T S is between 000 and 00 At T S = 7 µs, these values oespond to F d between 389 Hz and 389 Hz, whih ae equivalent to vehiula speeds of 77 m/s (78 km/h) and 77 m/s (778 km/h) at the aie fequeny of 54 GHz Those values ae high enough fo ou inteests In ou simulation, we adopt the modified Jakes method in [] to geneate Rayleigh faded hannel taes Channel estimation is ahieved though pilots The NS method illustated in Setion IV-B is adopted fo pilot aangement, in whih pilots ae plaed on etangula gid of subaies [3] The sepaation of pilots is M f aoss subaies, and M t aoss OFDM symbols, as illustated in Fig 3 (b) Maximal likelihood (ML) estimation [9] is fist pefomed within the subaies of an OFDM symbol Afte applying ML estimation on two pilot-inseted OFDM symbols (whih ae M t symbols apat), linea intepolation is used to obtain hannel estimation fo the symbols in between [0] The ML method involves matix invesion To have an invetible matix, the ML algoithm equies the numbe of pilots in an OFDM symbol to N be geate than the hannel length, ie, L p Sine we M f onfine L p 6, M f 8 is suffiient fo all values of L p when N = 8 In ou simulation, the hannel SNR on the pilot subaies is always maintained at 0 db fo eliable hannel estimation egadless of the SNR on data subaies C Influene of Channel Conditions We fist pesent simulation esults fo vaious hannel onditions The modulation sheme is QPSK with eeived SNR E b = 0 db, whee E b is the pe bit enegy on an antenna element, and N 0 is noise powe We also set M f = 8 and M t = 5 N 0 The numbe of uses is fixed at U = 3 In Fig 5, BER esults unde vaious hannel onditions ae povided It an be seen that F d T S has little influene on pefomane This shows that M t = 5 is suffiient fo auate hannel estimation fo all F d T S values unde investigation The BER is aound 0 6 when L p Howeve, when L p = 6, BER degades to 0 5 This indiates hannel length has a moe pofound effet on BER pefomane than nomalized Dopple fequeny fo ou simulation paametes In Fig 6, we pesent esults on the nomalized effetive thoughput As defined in (0), the nomalized effetive thoughput has a unit in the numbe bits pe subaie In the subsequent disussions, the effetive thoughput and the no /03/$700 (C) 003 IEEE IEEE INFOCOM 003

8 FdTs=000 FdTs=0005 FdTs=00 FdTs=00 Given ou simulation settings, the esults eveal that the hannel length is moe influential on pefomane than Dopple spead With a modeate M t, fo example M t = 5, vaiation in Dopple spead hadly impats pefomane On the othe hand, long hannel length tends to degade pefomane Fo this eason, we fous ou attention on the wost ase of hannel onditions with L p = 6 and F d T S = 00 BER hannel length Fig 5 BER unde vaious hannel onditions, M f = 8, M t = 5, U = 3 nomalized effetive thoughput (bits pe subaie) FdTs=000 FdTs=0005 FdTs=00 FdTs= hannel length Fig 6 Nomalized effetive thoughput unde vaious hannel onditions, M f = 8, M t = 5, U = 3 malized effetive thoughput ae used intehangeably fo simpliity Note fom Fig 6 that the effetive thoughput is simila fo diffeent values of F d T S When L p, effetive thoughput is aound 85 bits/subaie, whih is lose to the theoetial limit of bits/subaie fo QPSK It an be alulated fom (9) that N d /N = 095, whih oesponds to 85 bits/subaie if thee is no PER This implies that the diffeene (05 bits/subaie) is mainly aused by the ovehead of pilots When L p = 6, effetive thoughput is about 76 bits/subaie Although the BER fo L p = 6 is highe than those fo L p by an ode, the oesponding effetive thoughput is lowe by only 008 bits/subaie Consequently, fo QPSK with M t = 5 and M f = 8, effetive thoughput is vey lose to the maximal allowable level fo all hannel onditions D Influene of Pilot Spaing In this subsetion, we demonstate the influene of pilot spaing on the pefomane fo vaious modulation shemes, inluding QPSK, 6 QAM and 64 QAM In the simulation, we fix L p = 6, F d T S = 00, as pointed out peviously The numbe of uses is 3 To have a fai ompaison between diffeent modulation shemes, we equie all modulation shemes to have the same E b /N 0 = 0 db on a data subaie In addition, we use (M f, M t ) to denote a seletion of pilot spaing in fequeny and time With (M f = 4, M t = 0) (o M f = 8, M t = 0), the ovehead fo pilots is only 375% of total subaies when thee ae 3 uses (see Setion IV-B3) With (M f = 4, M t = 0) (o M f = 8, M = 5)) and (M f = 4, M t = 5), the oveheads ae espetively 75% and 5% BER QAM 64 QAM Mt QPSK Mf=4, QPSK Mf=8, QPSK Mf=4, 6 QAM Mf=8, 6 QAM Mf=4, 64 QAM Mf=8 64 QAM Fig 7 BER fo QPSK, 6 QAM and 64 QAM with diffeent pilot spaing In Fig 7, we plot the BER pefomane with diffeent values of M t and M f Given the same M t, the ases with M f = 4 always outpefom those with M f = 8 This is natual sine moe pilots ae used with M f = 4 than M f = 8 Inteestingly, fo the pilot spaings with the same amount of ovehead (in this example, pilot spaings of (M f = 4, M t = 0) vesus (M f = 8, M t = 5) and (M f = 4, M t = 0) vesus (M f = 8, M t = 0) have the same oveheads), the BER pefomane all favos the ombinations with M f = 4 This shows pilot spaing in the fequeny domain is moe itial than in the time domain The esults fo effetive thoughput ae shown in Fig 8 We notie that the effetive thoughput fo QPSK ineases with fewe pilots, but the impovement is tivially small The eason is that the inease in PER offsets the edution in pilot ovehead It is also lea fom Fig 8 that M t = 0 and M t = 0 ae not viable fo 6 QAM and 64 QAM, sine they an lead to zeo effetive thoughput Theefoe, in late simulations, we always /03/$700 (C) 003 IEEE IEEE INFOCOM 003

9 set M t = 5 nomalized effetive thoughput (bits pe subaie) QAM 6 QAM Mt Mf=4, QPSK Mf=8, QPSK Mf=4, 6 QAM Mf=8, 6 QAM Mf=4, 64 QAM Mf=8, 64 QAM QPSK Fig 8 Nomalized effetive thoughput fo 6 QAM and 64 QAM unde diffeent pilot spaing Fom Fig 8, we also obseve that 6 QAM ahieves the highest effetive thoughput of 3 bits/subaie at (M f = 4, M t = 5) among all expeimental esults It is inteesting to note that although the BER pefomane of QPSK is muh bette than that of 6 QAM, highe effetive thoughput is ahieved with 6 QAM when M t = 5 This obsevation onfims ou pevious laim that BER (o PER) alone is insuffiient to haateize system pefomane E Numbe of Uses We pesent esults on how the system pefomane is affeted by the numbe of uses QPSK is used with E b /N 0 = 0 db and pilot spaing (M f = 8, M t = 5) The Dopple spead is set as F d T S = 00, and hannel length vaies fom 4 to uses has a geat influene on BER and effetive thoughput pefomane Although BER degades by almost an ode of magnitude when the numbe of uses is ineased fom 3 to 4, effetive thoughput is edued slightly Howeve, with 5 uses, effetive thoughput is damatially edued: at hannel length of 6, effetive thoughput even appoahes 0 This is beause the antenna feedom is mostly used fo intefeene anellation so that thee is little divesity gain Theefoe, the addition of a new use should be autioned In the above example, the numbe of use should be no moe than 4, although the theoetial limit is 6 with 6 BS antennas nomalized effetive thoughput (bits pe subaie) hannel length U=3 U=4 U=5 Fig 0 Nomalized effetive thoughput fo diffeent numbe of uses F Influene of SNR The BER and effetive thoughput ae plotted against SNR in Fig and Fig, espetively In the simulation, we have 3 uses, and (M f = 8, M t = 5) Fo a fai ompaison, all modulation shemes have the same SNR 0 4 U=3 U=4 U= antennas, 3 uses, Mf=8, Mt=5 QPSK 6 QAM 64 QAM 0 BER 0 5 BER hannel length Fig 9 BER pefomane with diffeent numbe of uses E b /N 0 The BER pefomane is plotted in Fig 9, and effetive thoughput is plotted in Fig 0 Both BER and effetive thoughput degade with longe hannel length as expeted (see Setion V-C) Moe emakably, the inease in the numbe of Fig BER pefomane with espet to SNR The esults in Fig show that 6 QAM and 64 QAM equie highe powe fo good BER pefomane ompaed to QPSK /03/$700 (C) 003 IEEE IEEE INFOCOM 003

10 To ahieve the same BER pefomane as QPSK, 6 QAM needs about 6 db moe powe, while 64 QAM needs about db moe In ontast, thee is muh less SNR diffeene to ahieve the same effetive thoughput Fom Fig, we obseve that 6 QAM needs about 3 db moe powe than QPSK to ahieve 7 bits/subaie, while 64 QAM needs about 9 db moe This is beause the highe ode modulation has moe bits on a subaie, whih ompensates fo the powe equiement fo BER Note also that the modulation sheme ahieving the best effetive thoughput depends on the value of SNR Fo example, when SNR is lowe than 6 db, QPSK is the only option, sine 6 QAM and 64 QAM delive no effetive thoughput When SNR is between 0 db and 6 db (appoximately), 6 QAM is the best It podues effetive thoughput above bits/subaie, while the effetive thoughput fo QPSK satuates at 9 bits/subaie, and effetive thoughput fo 64 QAM is lowe than that of 6 QAM When SNR is above 6 db, 64 QAM is the best, beause QPSK and 6 QAM satuate at 9 bits/subaie and 37 bits/subaie, espetively nomalized effetive thoughput (bits pe subaie) antennas, 3 uses, Mf=8, Mt=5 QPSK 6 QAM 64 QAM E b /N 0 Fig Nomalized effetive thoughput with espet to SNR As obseved fom Fig, the uve of effetive thoughput an be haateized by thee segments oesponding to two itial SNR tuning points When SNR is below a ut-off value γ, effetive thoughput is almost zeo When SNR is highe than anothe theshold value γ, effetive thoughput beomes satuated Between the two values, the effetive thoughput gows almost linealy with the SNR The above phenomena an be explained as follows When SNR is low (eg, lowe than γ ), P e is lose to so that effetive thoughput is 0 As a ule of thumb, we an set γ as the SNR fo P e = 09 Obviously, a modulation sheme should always opeate above γ On the othe hand, the nomalized effetive thoughput is expessed in (0) as T u = ( P e )N d M I /N, whee N d is the aveage numbe of data subaies in an OFDM symbol Fom ou aangement of pilots, N d an be alulated as N d = N N /M f /M t (9) Thus, when SNR is high (eg, highe than γ ), P e 0, so that T u is lose to the uppe limit N d M I /N (30) Fo this eason, thee is no need to opeate at SNR above γ, sine effetive thoughput will satuate The theshold γ an be intuitively detemined fom the BER as follows We expet effetive thoughput to satuate when P e 0 (o P e 09) Fom (6), P e L d P b With paket length L d = 500 bytes, o 4000 bits, the oesponding BER is appoximately when P e = 0 Thus, the SNR theshold γ should oespond to a BER of G Summay of Simulation Results Fom ou simulation esults, we have the following onlusions: ) Channel delay spead is moe influential than Dopple spead on system pefomane unde ou expeimental settings Consequently, the pilot spaing in the fequeny domain is moe impotant than in the time domain; ) Caution should be taken when detemining the numbe of opeating uses, sine pefomane an be seiously degaded when the numbe of uses is lose to the numbe of antennas; 3) Fo any modulation sheme, the opeating SNR should fall between two utoff SNR values obtained fom the effetive thoughput uve: the effetive thoughput is almost zeo when the SNR is smalle than the lowe theshold, and is satuated when highe the uppe theshold VI CONCLUSION In this pape, effetive thoughput is poposed as a unified pefomane measue fo wieless OFDM/SDMA systems This paamete inopoates PER, numbe of data subaies, modulation index and oding ate System optimization an be ahieved though the maximization of effetive thoughput Though ompute simulations, we have demonstated how system pefomane is influened by vaious opeating paametes Simulation esults have evealed a set of onlusions fo system optimization, whih ae othewise not obtainable without the aid of effetive thoughput Theefoe, it is onfimed that effetive thoughput an seve as a useful pefomane measue fo OFDM/SDMA wieless systems The impat of hannel oding is not onsideed in this pape, whih is to be investigated in futue eseah REFERENCES [] T Kelle, L Hanzo, Adaptive multiaie modulation: A onvenient famewok fo time-fequeny poessing in wieless ommuniations, Po IEEE, vol 88, pp 6-640, May 000 [] R van Nee, R Pasad, OFDM fo Wieless Multimedia Communiations, Ateh House, 000 [3] Y Li, N R Sollenbege, Adaptive antenna aays fo OFDM systems with ohannel intefeene, IEEE Tans Commun, vol 47, no, pp 7-9, Feb 999 [4] K K Wong, R Cheng, K B Letaief, R D Muh, Adaptive antennas at the mobile and base stations in an OFDM/TDMA system, IEEE Tans on Commun, vol 49, pp 95-06, Jan 00 [5] P Vandenameele, L Van De Pee, M Engels, B Gyselinkx, H De Man, A ombined OFDM/SDMA appoah, IEEE J Selet Aeas Commun, vol 8, pp 3-3, Nov 000 [6] C Ganie, M Loosvelt, V Le Thu, Y Delignon, L Clavie, Pefomane of an OFDM-SDMA based system in a time-vaying multi-path hannel, Po VTC 00, Fall, 00, vol 3, /03/$700 (C) 003 IEEE IEEE INFOCOM 003

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