Performance Study of OFDMA vs. OFDM/SDMA

Transcription

1 Performance Study of OFDA vs. OFD/SDA Zhua Guo and Wenwu Zhu crosoft Research, Asa 3F, Beng Sgma Center, No. 49, Zhchun Road adan Dstrct, Beng 00080, P. R. Chna {zhguo, Abstract: In ths paper, we frst consder the OFD/SDA system whch admts several OFD users smultaneously by reusng the same frequency band. Wth the lnear nmum ean Squared Error (SE recever, t has been shown that such a system can mprove the system capacty sgnfcantly compared to the sngle antenna OFD system. owever, the number of requred lnear flters s huge. hus, n ths paper, we propose two reduced-complexty SE recevers for OFD/SDA system; namely, nterpolated SE and partal SE. We demonstrate that both methods perform much better than the prevously proposed reduced-complexty recever. Other than OFD/SDA, an alternatve to support multple users wth hgh spectrum effcency s to use Orthogonal Frequency Dvson ultple Access (OFDA wth hgh-level modulaton. Wth both theoretcal analyss and smulaton, we fnd that the relatve BER performance of these two systems depends on the recever desgn of OFD/SDA. In partcular, when the SE recever s used, OFD/SDA s usually worse than or comparable to OFDA. owever, the former has the potental to outperform the latter because when the optmal (and the most complcated L detector s used, t s superor to the latter. On the other hand, OFDA has the advantage of smple recever structure. I. INRODUCION In recent years, there has been substantal research nterest n applyng Orthogonal Frequency Dvson ultplexng (OFD to hgh-speed wreless communcatons due to ts advantage n mtgatng the severe effects of frequencyselectve fadng []. It ncreases the symbol duraton by dvdng the entre channel nto many narrow orthogonal subchannels and transmttng data n parallel. At the same tme, to ncrease the system capacty and cancel the cochannel nterference, wreless communcatons wth antenna dversty have been studed wdely []. In partcular, Space Dvson ultple Access (SDA whch employs a recever antenna array can mprove the spectrum effcency sgnfcantly by allowng several users to reuse the same spectrum. It separates the users wth ther spatal sgnature. An array wth P recever antennas essentally can support P smultaneous users wth approxmate dversty order of. In ths paper, we frst consder the combned SDA and OFD system. On the recever sde of such a system, a lnear SE flter operatng on the sgnals n P antennas s usually used to suppress the mult-user nterference (UI and estmate each user s data for each subcarrer [-4]. owever, the SE flter needs drect matrx nverson (DI and the DI s done for all the K subcarrers. hs makes the OFD/SDA recever very complcated. In order to decrease the complexty of the SE recever, n [3, 4], a reduced-complexty grouped SE was proposed. owever, we wll show that t saturates quckly and ts performance degradaton s too much compared to DI-SE. In ths paper, two other reduced-complexty recevers: nterpolated SE and partal SE wll be presented. It s demonstrated that our proposed nterpolated flter sgnfcantly outperforms the prevous grouped approach. owever, t stll saturates at hgh SNR. On the other hand, the partal SE s very effectve n reducng complexty and mantanng good performance wthout saturaton. Other than OFD/SDA, an alternatve to support multple users wth hgh spectrum effcency s to use OFDA [6] wth hgh-level sgnal constellaton. For nstance, wth 4 receve antennas, up to 4 users can reuse all the K subcarrers wth BPSK n OFD/SDA. hese users wth the same throughput can also be supported n OFDA wth 6QA by allocatng K/4 subcarrers to each user. In ths sense, there s no multple access nterference (AI between users and every user can make full use of the antenna dversty wth an order of 4. eanwhle, the demodulaton of OFDA sgnal n each antenna s very smple by takng only the N-pont FF, whch s much smpler than the OFD/SDA recever as we mentoned above. he sgnal n every antenna branch s then combned wth axmum Rato Combnng (RC. A queston now mmedately arses: s the performance of OFDA comparable to that of OFD/SDA? In ths paper, we wll address ths queston. By both analyss and smulaton, t s shown that OFD/SDA has the potental to outperform OFDA because when the optmal or the most complcated L detector s used, t s superor to OFDA. owever, when the DI-SE s used, SDA s usually worse than or comparable to OFDA. he rest of the paper s organzed as follows. In Secton II, the OFD/SDA and OFDA system models are gven. In Secton III, the recever structure for OFD/SDA and OFDA are presented and compared. Fnally, the conclusons are drawn n Secton IV. II. SIGNAL ODEL Assume that there are N moble statons wth sngle antenna and recevng antennas n the base staton. he channel between the -th user and -th recever s assumed to be a L- path channel, whch s gven by

2 L h ( t = β ( l δ ( t τ ( l = ( l ( l β ( and τ are the complex path gan and delay l of the l-th path. he path gan β ( l between dfferent antennas and paths s assumed to be ndependently and L dentcally dstrbuted (..d and E β ( l. Now, l = = assume that the entre channel for an OFD system s dvded nto K subcarrers. It follows that the gan of the k-th subcarrers between the -th user and -th recever s gven by: L ( l ( k = β ( l exp( π ( k f sτ l = = w ( k, h f s s the bandwdth of the subcarrer. ( k w = e... ( ( L π ( k f sτ, π ( k f sτ, [ β... ( ] = ( β L e ( h. (3 hroughout ths paper, we assume that the recever knows the channel state nformaton. he receved sgnal [ ] y [ k ] = y [ k ]... y [ k ] n the antennas for the k-th subcarrer s gven by: y [ k ] = [ k ] x[ k ] + n[ k ] (4 [ ] x [ k ] = x [ k ]... x N [ k ] s the N users sgnals n the k-th subcarrer. For smplcty, we have normalzed the transmtted sgnal so that x ( k =. Lkewse, [ n [ k ]... n ] [ k n [ k ] = ] s the complex nose vector wth varance σ =N 0 / per dmenson for each element. Fnally, [ k ] = [, ( k ] =,..., N, =,..., s the channel between the N users and the recevng antennas for the k-th subcarrer. We now nvestgate the statstc characterstcs of the subchannel gan. From (, t s easy to see that, ( k s the summaton of L..d rotated complex Gaussan random varables. hus,, ( k s stll Gaussan and, ( k s stll wth Raylegh dstrbuton (hence,, ( k s stll exponentally dstrbuted wth E ( ( k, var( ( k, =. (5, = For OFDA system, each user s assgned a set of nonoverlapped subcarrers. herefore, the users sgnals are separated and no AI s presented for each subcarrer. hs results n the conventonal smple OFD recever n the base staton. he sgnals from antennas wll be RC combned. In order to acheve frequency dversty and nterference dversty, the assgned subcarrer set to a specfc user may be vared n both the tme doman and the frequency doman [5]. At the same tme, n order to get the same throughput as SDA, a hgher-level modulaton scheme must be used. III. PERFORANCE COPARISON A. SE Recever for OFD/SDA DI-SE In order to recover the sgnal n the recever (base staton, the lnear SE flter s usually appled [,3]. Because the subcarrer of OFD s fully parallel, thus, the SE flter s appled n a per-carrer fashon. Assume the flter for the k-th subcarrer s gven by A[. hat s, the SE estmaton of the transmtted sgnal x[ s gven by x [ = A [ y[ (6 yy A[ = R R and yx [ yy ] = [ [ + σ Ix R yy = E (7 wth I x denotng the x dentty matrx. Lkewse, [ yx [ ] [ R = E =. (8 yx From (7, we can see that the SE n each subcarrer requres a drect matrx nverson (DI wth dmenson x. Note that the complexty of the matrx nverson s O(m 3, m s the dmenson of the matrx. herefore, we can see that the complexty of the DI-SE recever s very hgh. Grouped SE In order to decrease the recever complexty, there has been some work reported. In [3, 4], a reduced-complexty grouped SE recever was proposed. It dvdes the K subcarrers nto G groups. In each group, a flter s obtaned by mnmzng the summed SE of all the subcarrers wthn ths group and apples ths flter to all the N/G subcarrers wthn ths group. hat s, the flter s to mnmze K G + E / x [ k k + 0 ] A y[ 0 ] (9 = k 0 + s the ndex of the frst subcarrer wthn ths group. It s easy to see that A s now gven by K / G K G = + Nσ I / + + x A [ k0 ] [ k0 ] [ k0 + ] = G = (0 For ths grouped SE recever, ts performance depends heavly on the smlarty of the gans of the subchannels wthn ths group. hus, the performance wll degrade severely and saturate quckly when the frequency dversty s rch, as we wll show n the followng.

3 3 Interpolated SE In order to overcome the drawbacks of the grouped SE, we propose usng the lnear nterpolated SE flter. hat s, we calculate one DI-SE flter for each group. he flters between two successve DI-SE flters are obtaned by nterpolaton. he Interpolaton can be lnear or nonlnear. herefore, we can see that ths approach also utlzes the frequency correlaton between OFD subcarrers. Both the grouped SE and the nterpolated SE roughly reduce the complexty by a factor of G. In contrast to the grouped SE, we wll show that the nterpolated SE s more robust than the grouped SE. owever, as shown n Fg., the nterpolated SE stll saturate n the hgh SNR regon and performs much worse than the DI- SE. 4 Partal SE From above dscusson, we can see that both the grouped and nterpolated SE s not robust to the frequency dversty. In order to reduce complexty and mantan the good performance, we here propose the partal SE recever. Note that most of the complexty of DI-SE comes from the nverse of the matrx wth dmenson. herefore, n our approach, nstead of process the sgnals n the receved antennas smultaneously, we dvde the antennas nto some small overlappng or non-overlappng sets. hen, the SE flter s calculated for each set. Wthout loss of generalty, let =5 and they are dvded nto two sets. hey consst of antennas,,3 and antennas 3,4,5, respectvely. Now, we can obtan two SE estmates for x[, namely, x [k,] and x [k,]. hey are gven by x [ k,] = A y[ k,] x [ k,] = A y[ k,] ( y k,] = [ y [, y [, y [ ] [ 3 y k,] = [ y [, y [, y [ ]. [ A and A can be obtaned as n (7-(8 smlarly. he fnal SE estmate of x[ s gven by x[ = x[ k,] + x[ k,]. ( Recall that the complexty of matrx nverse s O(m 3. hus, for ths example, the complexty of partal SE s approxmately /3 of the DI-SE flter. he complexty reducton wll be even larger when more recevng antennas are employed. For example, wth =6 and two small sets wth 3 antennas n each set, the complexty wll be reduced to /4. Note that the SE flter corresponds to the RC combnng []. herefore, wth the dvson nto small sets, the RC combnaton wthn each small group s mantaned, but t may be destroyed between sets. owever, we can magne that the RC coeffcents between sets may not be altered too much compared to DI-SE. In Fg., we show the performance of the above four SE flters. ere, the U channel model s used [6]. here are totally 5 subchannels and each s wth 0k z bandwdth. he number of the recevng antenna s =4 and two users wth QPSK are smulated. he group sze for nterpolated and grouped SE s 8. he number of antennas n the two sets for partal SE s 3 and, respectvely. We can see that our proposed nterpolated SE flter sgnfcantly outperforms the grouped SE flter. But t stll saturates quckly. he partal SE flter performs a lttle worse than the nterpolated SE n the low SNR regon. But the former performs much better than the latter n the hgh SNR regon and t does not saturate. At the same tme, partal SE reduces the complexty by a factor and s db away from the DI-SE flter. Fg. Performance of dfferent SE recevers for OFD/SDA B. he Optmal L Recever for OFD/SDA As a benchmark, we now derve the BER performance of the axmum Lkelhood recever for OFD/SDA. By referrng to (4, we can see that the L recever s gven by: x [ = mn y[ [ x[ (3 [ ] x[ In the followng dervaton, for smplcty, we assume BPSK s used. On occurrng of an error event, the L decoder decdes erroneously n favor of a symbol set for N users e = e[ k ] e [... e N [ assumng that x = x[ k ] x [ k ]... x N [ k ] was transmtted. hen, the probablty of the error decson s gven by (note that the energy of the transmtted sgnal has been normalzed to : P( x e = Q d ( x, e /(N 0 (4 + y Q ( z = z exp( dy π

4 d N (, e = ( k ( x ( k e ( k x. (5 = When there s only one user n error, the product dstance s gven by: d (, e = 4 x ( k (6 From (6, we can see that the L detector s actually the RC of the sgnals from antennas when one user s n error. Recall n (5, we have shown that, ( k s stll exponentally dstrbuted wth unt mean. hat s, the probablty densty functon (p.d.f of, ( k s gven by, ( = e (7 g Wth characterstc functon, t s easy to show that the p.d.f. of the summaton of exponentally dstrbuted random varable s gven by S e f ( S = (8 (! Fnally, the probablty of one error s gven by p = 0 Q( S / N 0 ds (9 (! When there are two users, say, user and user, n errors, the dstance n (5 s now gven by d (, e = 4 ( k + x ( k (0 =, Snce, ( k and, ( k are uncorrelated complex Gaussan, t follows that ther summaton s stll complex Gaussan wth doubled mean power. herefore, the product dstance n (0 has a smlar p.d.f as n (8 scaled by a constant. Fnally, the probablty of two errors s gven by: p = 0 Q( 4S / N 0 ds ( (! Lkewse, we can derve that the probablty of u errors s gven by pu = 0 Q( us / N 0 ds ( (! In summary, the BER of the L detector for an N-user OFD/SDA system can be gven by: N N BER = p (3 N = Because p << p, thus, when the number of antennas s not large, (3 can be approxmated by, BER p. (4 In other words, the BER performance of the optmal L detector s nsenstve to the ncrease of number of users. hs wll be verfed n Fg.. Followng a smlar approach, we can derve the BER when QPSK and Gray code are used (only up to two errors are consdered. N BER Nq + q (5 N q f ( S Q( S / N ds = q 0 f ( S Q( S / N o ds (6 In Fg., we show the performance of the optmal L detector and the DI-SE recever for OFD/SDA. he parameters are smlar to those n Fg. except that BPSK s used. We can see that the SE recever s much worse than the L recever. At the same tme, the performance of the SE recever degrades severely wth the ncrease of the number of the users; whle the performance of the L recever s rather nsenstve to the number of users. In addton, the analytcal results n (3 and (6 agree qute well wth the smulaton results for the L detector, whch are not shown here due to the lmted space. = + Fg. Performance of L detector vs. SE detector for OFD/SDA C. Performance of OFDA In order to have the same throughput as OFD/SDA, n OFDA system, hgher level modulaton scheme must be used. Assume that the constellaton sze for OFD/SDA s Q NQ. hen, the constellaton sze for OFDA s. eanwhle, the symbol energy of OFDA should be N tmes larger than that of OFD/SDA. he sgnals n the antennas are combned wth RC for each user. s [ = ( k x [ k ] + ( k n [ k ] (7 Eqn. (7 s equvalent to ( k n [ k ] s [ = x [ k ] +. (8 ( k

5 Let ( k n [ k ] η [ = (9 ( k It s easy to show that σ E[ η [ ] = 0, var[ η [ k ]] =. (30 ( k herefore, we can see that OFDA corresponds to the RC NQ of the dstorted symbol wth constellaton sze and OFD/SDA (from (6 corresponds to the RC of the Q dstorted symbol wth constellaton sze. Although the symbol energy of OFDA ncreases lnearly wth the ncrease of N compared to OFD/SDA, the symbol dstance n the constellaton decreases almost exponentally. hus, we can magne that the performance of OFDA should be worse than OFD/SDA usng the L detector. Recall that the subchannel power s exponentally dstrbuted. It follows that the BER for OFDA wth Gray code s gven by (assume BPSK s used for OFD/SDA: QPSK: BER + 0 f ( S Q S / N 0 ds + π 8PSK: BER 0 f ( S Q(sn 6 S / N ds (3 In Fg. 3, we show the performance comparson between OFDA and OFD/SDA wth two users. Frst, we apply BPSK to OFD/SDA and both the L and the DI- SE recevers are presented. We can see that the OFDA (QPSK performs much better than OFD/SDA employng the SE recever, and s comparable to OFD/SDA employng the optmal L recever. Next, n Fg. 3, the performance of QPSK modulated OFD/SDA s also shown (note that the x-axs s stll ndexed by E b /No. o mantan the same throughput as OFD/SDA, OFDA should use 6QA nstead. We can see that OFD/SDA wth DI-SE recever performs a ltter better than OFDA n low SNR regon; whle they are smlar n hgh SNR regon. At the same tme, OFD/SDA wth the L detector s much better than OFDA. From above, we can conclude that:. OFD/SDA has the potental to outperform OFDA when the optmal L detector s appled. owever, the L detector s too much complcated.. When the less complcated SE detector s used for OFD/SDA, t s usually worse than or comparable to OFDA. 3. Ether the L or the SE detector for OFD/SDA s much more complex than the recever for OFDA whch only requres RC. 4. OFD/SDA s stll an attractve choce for multuser communcatons f less complcated multuser detector wth performance approachng that of the L detector can be devsed. Fg. 3 OFDA vs. OFD/SDA IV. CONCLUSIONS In ths paper, we analyzed and compared the performance of OFDA and OFD/SDA system under the condton that they have the same throughput. We have shown that wth the L detector, the OFD/SDA system s much better than the OFDA system. owever, f DI-SE s employed n OFD/SDA system, ts performance s usually worse than or comparable to the performance of the OFDA system. Compared wth OFD/SDA, the man advantage of OFDA s ts smple recever structure and reasonable performance. herefore, ths gves us tradeoff between complexty and performance for OFDA and SDA. At the same tme, to reduce the complexty of the SE recever for OFD/SDA, two reduced-complexty recevers, namely, nterpolated SE and partal SE, were proposed n ths paper. REFERENCES:. J. Chuang, and N. Sollenberger, Beyond 3G: wdeband wreless data access based on OFD and dynamc packet assgnment, IEEE Communcatons agazne, Vol. 38, No. 7, pp , July Y. L and N. Sollenberger, Adaptve Antenna Arrays for OFD Systems wth Cochannel Interference, IEEE rans. Commun. Vol. 47, No., pp. 7-9, Feb P. Vandenameele, L. Perre,. Engels, B. Gyselnckx, and. an, A Combned OFD/SDA Approach, IEEE J. Select A. Commun. Vol. 8, No., pp. 3-3, Nov Keller and L. anzo, Blnd-Detecton Asssted Sub-band Adaptve urbo-coded OFD System, Proc. IEEE VC 99, pp , ay, R. Nee and R. Prasad, OFD Wreless ultmeda Communcatons, Artech ouse, Y. L Plot-Symbol-Aded Channel Estmaton for OFD n Wreless Systems, IEEE rans. Veh. echnol. Vol. 49, no. 4, pp. 07-5, July 000.