Multi-Sector Beamforming with MMSE Receiver for Spatially Correlated Channel

Transcription

1 Mult-Sector Beamformng th Recever for Spatally Correlated Channel Jae-Heung Yeom and Yong-Han Lee School of lectrcal ngneerng and NMC Seoul Natonal Unversty Seoul, Korea e-mal: Abstract The use of statstcal egen-beamformng s effectve n spatally correlated fadng envronments, but t may suffer from nterference near the sector boundary hen appled to the donln th unversal frequency reuse. Ths nterference effect may not suffcently be handled by a mnmum mean square error ( recever unless a suffcent number of receve antennas are employed. n ths paper, e consder the use of mult-sector beamformng that cooperates th a neghborng sector n the same cell to mtgate ths nterference problem. By explotng long-term channel state nformaton (CS, the proposed scheme can obtan transmt array gan thout the use of nstantaneous CS, hle avodng nterference from the adjacent cooperatng sector. The performance of the proposed scheme s analyed th combned use of an recever and verfed by computer smulaton. Keyords-beamformng; nterference; mult-sector; correlaton. NTROUCTON emand for hgher throughput has motvated advanced reless systems such as the 3GPP LT and moble-wmax to employ mult-cell confguraton th unversal frequency reuse [], []. Varous measurement results sho that multantenna channels are often spatally correlated n real envronments [3]. The use of egen-beamformng s qute effectve th lo feedbac sgnalng overhead n spatally correlated channel [4], [5]. Hoever, t may cause users near the cell boundary to experence serous nter-cell nterference n unversal frequency reuse envronments [6]. n partcular, hen the cell s dvded nto a number of sectors, users near the sector boundary may experence ea receved sgnal strength (RSS from the servng sector due to sector antenna pattern as ell as nterference from adjacent sectors [], [7]. Advanced reless systems consder the use of multple receve antennas n the moble staton (MS [], [8], enablng the use of a mnmum mean square error (-type recever to suppress nterference hle reducng the fadng effect [9]. Hoever, hen the number of strong nterferers s larger than the number of receve antennas mnus one, the output sgnal-tonterference-plus-nose poer rato (SNR of the recever may sgnfcantly deterorate []. To mprove the performance of users near the sector/cell boundary, the use of base staton (BS coordnaton has recently been consdered, here the BSs share the channel state nformaton (CS to mnme the nterference effect [], []. Hoever, ths BS cooperaton may ncur sgnalng overhead ncreasng n exponetally proportonal to the number of coordnatng BSs and suffer from performance degradaton due to the sgnalng delay. Recently, null beamformng technque has been ntroduced, here the nterference to other co-channel cells s removed by exchangng nstantaneous nter-cell CS [3]. Hoever, t requres a consderable amount of nstantaneous CS and cannot cancel out the nterference due to the use of a sngle receve antenna. t s qute practcal and easy to cooperate among sectors n the same cell, because nformaton beteen these sectors can be exchanged thout sgnalng overhead [8]. The performance near the sector boundary can also be mproved thout the exchange of nter-cell nformaton th the ad of softer handover, macro dversty handover or fast sector selecton (FSS th mutng [8], [4]. n the macrodversty handover, users can demodulate the sgnal thout nterferng th each other, hle obtanng frequency dversty gan. The FSS th mutng allos only one sector n better condton to transmt data sgnal th doubled transmt poer, hle mang the other sector, called muted sector, sleep to avod mutual nterference. Hoever, these schemes do not consder the use of multple transmt antennas and spatal correlaton. n ths paper, e desgn a mult-sector beamformng scheme that cooperates th an adjacent sector n the same cell. The proposed scheme can avod nterference from the adjacent sector n the same cell, hle enhancng the transmt array gan usng long-term statstcs of the channel. t does not requre addtonal sgnalng overhead compared to conventonal snglesector beamformng schemes. When appled to the use of an recever, the performance s analyed n the presence of arbtrary-poer nterferers. Follong ntroducton, Secton descrbes the system model n consderaton. Secton presents the proposed multsector beamformng and analyes ts performance. The performance of the proposed scheme s verfed by computer smulaton n Secton V. Fnally, conclusons are gven n Secton V.. SYSTM MOL Consder the donln of a cellular system that comprses N hexagonal cells each of hch comprses S sectors (.e., a

2 total of S N sectors. For ease of descrpton, t s assumed that each sector uses M transmt antennas and the MS uses to receve antennas. Assumng that the user s under servce from sector m, the receved sgnal of the user can be represented as y = H x + H x + n m m m m m = H x + H x + m m m m Ω, m here x denotes the data of sector th unt average poer, denotes the receved sgnal strength (RSS from sector, H s the ( M channel matrx from sector, denotes an ( M beam eght from sector, n s the ( addtve hte Gaussan nose (AWGN vector, and Ω denotes an actve set comprsng sectors defned by ( ˆ Ω= δ, S N. ( m Here δ denotes a threshold value for the actve set, and denotes the ( nterference plus nose vector except the nterference from sectors belongng to Ω, hch can be assumed to be ero-mean complex Gaussan th covarance { } denotes a ( = N [5], here dentty matrx. The beam eght s determned by the egenvector correspondng to the maxmum egenvalue of the channel covarance matrx. t s assumed that, here denotes the Frobenus norm [6].. PROPOS MULT-SCTOR BAMFORMNG Consder the use of mult-sector beamformng th cooperaton beteen sectors n the same cell to enhance the performance near the sector boundary. The mult-sector M to beamformng confguraton can be extended from ( ( M antenna confguraton by concatenatng to adjacent sectors. Assume that the BS transmts the user sgnal through sector m and. Then, the receved sgnal can be represented as y = H x + H x + (3 m m n Ω, m, T T T here = m and H are respectvely the ( M beamformng vector and ( M channel matrx from sector m and to the user, gven by [ ] H = H H Λ. (4 m m Here Λ denotes the normaled RSS matrx represented n an ( M M dagonal matrx hose frst and last M dagonal elements are all one and / m, respectvely, and the superscrpt T denotes transpose. Note that the transmt poer of s lmted by ( M ( m m max tr Λ = max + / = (5 here tr[ ] denotes the trace of a matrx. t can be seen that = hen the cooperatng sectors have the same RSS (.e., m = m. The channel covarance matrx can be represented as R { HH} / ( {[ ] [ ]}/ = Λ H H H H Λ m m m m here { } denotes the expectaton, the superscrpt denotes transpose conjugate. t can be seen that the RSS of to cooperatng sectors changes the channel covarance. Snce R s Hermtan and postve defnte, t can be decomposed as [8] (6 R = QΣ Q (7 here Q = [ q q ] s an ( M M M untary matrx hose columns { q } are the egenvectors of R, and ( M M Σ s a dagonal matrx hose dagonal terms are descendng-ordered egenvalues (.e., λ λm of R. The channel matrx can be represented as [8] here / H = HR (8 / R denotes the square root of R and H s the ( M spatally hte complex Gaussan channel matrx [6]. The beam eght can be gven by = + / q. (9 m Thus, the effectve channel of the desred sgnal can be represented by

3 H = + / H R q h s the ( / m = + / m λ h. ( here spatally hte complex Gaussan channel vector [6]. The output SNR of an recever can be represented by [9] ( ( γ m = H K H ( here K denotes the covarance matrx of the nterference plus nose, defned as Ω, m, ( ( K = H H + N. ( Assumng that the major nterference s from only sector, the mult-sector beamformng can avod ths major nterference (.e., K = N. n ths case, the average output SNR can be gven by s an M -dmensonal unt-norm vector, the effectve channel from sector Ω, m, can be represented as h s a ( here, defned by [6] H = ε h (7, spatally hte Gaussan channel vector, { h h,, } =, =, (8 {( ( } / { / } ε = H H = H H. (9 Snce ε corresponds to the Raylegh quotent of the covarance matrx of H, t belongs to a range beteen the mnmum and the maxmum egenvalue [7]. Thus, K can be rertten as N { } m { γ } = ( H ( H = λ ( m + N (3 K = C P C +N. ( n the presence of L nterferences from sectors { j Ω; m,, =,, L}, C s a ( L random matrx comprsng L nterference vectors as columns,.e., Hoever, hen the nterference comes from other cells, t s requred to consder the covarance K of the nterference plus nose. n ths case, the probablty densty functon (pdf of the output SNR γ can be represented as [9] here ( γ = exp( { σ} γ p B (4 = B = { σ } ( { σ } { σ } (5 = =, and σ denotes the egenvalue of KG. Here, G denotes the covarance of the sgnal, gven by {( ( } G = H H m ( m { hh } ( m = λ + = λ +. (6 t can be seen from (4 that the pdf of the output SNR can be determned by the mean egenvalue of KG. Snce n ( P s an ( C = h, j h, j h, j L ( and L L dagonal matrx hose -th dagonal elements are j ε j. Lettng { β } be the mean egenvalue of CC, t can be shon that [] { β } ( + 3 L L L = L L L L = + ( { β } { β } = L. (3 Lettng { μ } be the egenvalue of CPC n ( hen the nterferers have arbtrary poer, t can be shon that Snce [7] { μ} = μ = { tr CPC }. = = L L = j ε j { c j } = j ε j = = (4

4 = μ = det CPC t can be approxmated as [ C ] [ P] β [ P] = det det = det = (5 { μ} { β} det[ P ] (6 = = here det[ ] denotes the determnant of a matrx. Smlarly, t can be shon that Snce [7] = { σ } = { tr KG } = tr { { } + N } CPC G L = j ε tr. j N + = (7 Ω ( { } { }, m, N Γ + / + Γ + Ω, m, Ω, m, β β ε here ( ε / N and γ (3 Γ = denotes the average SNR of sector γ ( tr ( / N det = G G s the average SNR of the sgnal. The frst term n the denomnator of (3 represents the degradaton due to the nterference. Assumng that users near the cell/sector boundary experence nterference at most from to sources, the multsector beamformng can avod nterference from the adjacent sector, mang users experence a sngle domnant nterference (.e., Γ j. The average output SNR of the recever ncreases n proporton to the average SNR,.e., { γ} ( { β} { β} N γ here { β } = and { } Γ j + γ / Γ + Γ + j j β =. t can be shon that (3 = σ det KG = t can be approxmated as = det CPC + N det = ( μ + N det = (8 γ ( m tr G λ + N det N = =. (33 Thus, the use of mult-sector beamformng can acheve large transmt array gan and poer gan as ell as nterference cancellaton compared to the use of a sngle sector beamformng. { σ} ( { μ} N det G. (9 = = + Thus, the average output SNR can be approxmated as { } ( γ = γ p γ dγ ( { μ} + N = = { σ } { σ } ε + N = det tr Ω, m, =. t can further be approxmated usng (4 and (6 as (3 V. PRFORMANC VALUATON The analytc desgn and performance of the proposed beamformng scheme are verfed by computer smulaton. The proposed scheme s appled to a ( MMO confguraton n correlated MMO fadng channel th covarance matrx Δ ρ gven by ( p q Δ ( ρ = ρ exp j( p q π pq, (34 here ρ denotes the magntude of the correlaton coeffcent beteen to adjacent transmtter antennas, and [ ] p, q denotes the element of the p -th ro and the q -th column. That s, {[ m ] [ m ]} /= ( ρ H H H H Δ. ε can be set to one assumng that s ndependent of H. t s also assumed that sector allocates the resource to the user at each frame.

5 The performance s evaluated n terms of the geometry defned by G = = = + + N + N Ω, Ω Ω, Ω, Γ. Γ+ (35 n the follong fgures, the legend BF_, BF_, MSBF_, SHO_, M_, and FSS_ denote the statstcal egen-beamformng th recever, the statstcal egen-beamformng th maxmum rato combnng (, the mult-sector beamformng th recever, the softer handover th recever, the macro dversty handover th recever, and the FSS th mutng and recever, respectvely. Also BF_ denotes the egenbeamformng th recever, hch transmts the sgnal th the strongest egenmode of the nstantaneous CS [], causng a consderable amount of feedbac sgnalng burden. Fgure depcts the analytc and smulaton results accordng to Γ, assumng a sngle nterference from adjacent sector th the same RSS as the servng sector (.e., Ω= {,} and Γ =Γ. n ths case, the mult-sector beamformng can avod the nterference from the adjacent sector hle ncreasng the transmt array gan and doublng the transmt poer gan. t can be seen that the recever ncreases the average output SNR n proporton to Γ, hle the can not manly due to domnant nterference. t can also be seen that the analytc results agree ell th the smulaton results. The larger ρ, the hgher the performance of the proposed scheme due to the ncrease of the transmt array gan. t can be seen that the statstcal egen-beamformng provdes performance smlar to the egen-beamformng th nstantaneous CS. Thus, the proposed scheme th the longterm CS s effectve n spatally correlated channel th a margnal ncrease of feedbac sgnalng burden. Fgure depcts the analytc and smulaton results accordng to Γ n the presence of to nterferences; one from adjacent sector and the other from sector (.e., Ω= {,, }, and Γ =Γ and Γ =Γ + db. t can be seen that the recever th the sngle-sector beamformng schemes ( BF_ and BF_ suffer from untreated nterference, hle the recever th the mult-sector beamformng ors ell by properly removng the domnant nterference. t can be seen that the average output SNR of the mult-sector beamformng ncreases n proporton to Γ and that the gap beteen the sngle-sector and the mult-sector beamformng ncreases as the SNR ncreases. Fgure 3 and 4 depct the performance n 9- cell envronments (th S = 3, here the cell radus s m, the path loss follos log( d, d s the dstance (n meters beteen the sector and the user, and the sector antenna pattern follos 7 (-3dB beamdth th a front-to-bac rato of db [7]. t s assumed that sectors havng an RSS Average output SNR (db Average output SNR (db TABL. TH SNR OF SRVNG AN NGHBORNG SCTORS NAR TH SCTOR BOUNARY. G (db Ω SNR (db -.5 {, } Γ =Γ=9. - {, } Γ =Γ=5.7 - {, } Γ =Γ=. -4 {,,} Γ =Γ=.3, Γ =.3-5 {,,} Γ =Γ=., Γ =. -7 {,,} TABL. Γ =Γ=-.8, Γ =. TH SNR OF TH SRVNG AN NGHBORNG SCTORS AT A GOMTRY OF -5 db. recton ( Ω SNR (db 6 {,, } Γ = Γ =., Γ =. 58 {,, } Γ =-., Γ =-.4, Γ =.5 56 {,, } Γ =-., Γ =-.8, Γ =. 54 {, } Γ =-.6, Γ =-4.3, Γ = ρ =.6 ρ =.9 MS SNR, Γ (db 5 5 Fgure. Performance n the presence of nterference from a sngle adjacent sector. ρ =.6 ρ =.9 MS SNR, Γ (db Fgure. Performance n the presence of nterference from to adjacent sectors.

6 Average output SNR (db Average output SNR (db ρ =.6 ρ =.9 MS FSS - SHO - M Geometry (db Fgure 3. Performance of users near the sector boundary. MS FSS - M - ρ =.6 ρ = recton of MS th respect to the broadsde of the sector array Fgure 4. Performance accordng to the drecton of user at a geometry of -5dB. larger than one half that of the servng sector belong to the actve set (.e., δ =-3dB, and that the user s located near the boundary beteen sector and and experences nterference form sector at the same tme. Table summares the actve set and the correspondng SNR. t can be seen from Fgure 3 that the mult-sector beamformng outperforms the FSS th mutng and the macro dversty handover manly due to the transmt array gan through beamformng. Fgure 4 depcts the performance hen users are located near the cell boundary at a drecton of beteen 54 and 6 th respect to the broadsde of the sector array, and experence geometry of -5dB at all drectons. t can be seen from Table that the RSS of the adjacent sector (.e., sector decreases as the user moves aay from the sector boundary. n ths case, the mult-sector beamformng can not suffcently obtan the transmt array gan and transmt poer gan. Snce the analytc results agree ell th the smulaton results, the operatng pont of the mult-sector beamformng can analytcally be determned. V. CONCLUSONS We have consdered the use of mult-sector beamformng for the servce of users near the sector boundary n the donln of cellular systems n spatally correlated channel envronments. The performance of the proposed mult-sector 54 beamformng scheme combned th recever has been analyed n terms of the average output SNR. The smulaton results sho that the mult-sector beamformng s very effectve for users near the sector boundary, outperformng conventonal schemes such as the egen-beamformng, softer handover, macro dversty handover and FSS th mutng. RFRNCS [] Y. Xang, J. Luo and C. Hartmann, nter-cell nterference mtgaton through flexble resource reuse n OFMA based communcaton netors, n Proc. uropean Wreless Conf., Apr. 7. [] WMAX Forum, A comparatve analyss of Moble WMAX deployment alternatves n the access netor, May 7. [3] J. Kermoal, L. Schumacher, K. Pedersen, P. Mogensen and F Fredersen, A stochastc MMO rado channel model th expermental valdaton, J. Select. Areas. Commun., vol., no. 6, pp. -6, Aug.. [4] H. Sampath, V. rceg and A. Paulraj, Performance analyss of lnear precodng based on feld trals results of MMO-OFM system, Trans. Wrel. Commun., vol. 4, no. 5, pp , Mar. 5. [5] J. Cho, S. Km and. Cho, Statstcs egen- beamformng th selecton dversty for spatally correlated OFM donln, Trans. Veh. Technol., vol. 56, pp , Sept. 7. [6] WMAX Forum, Moble WMAX-Part : A. Techncal overve and performance evaluaton, Feb. 6. [7] 3GPP TR 5.996, 3GPP techncal specfcaton group rado access netor; Spatal channel model for MMO smulatons, V6.., Sept. 3. [8] 3GPP TR 5.84, 3GPP techncal specfcaton group rado access netor; Physcal layer aspects for evolved UTRA, V7.., Sept. 6. [9] J. Wnters, Optmum combnng n dgtal moble rado th cochannel nterference, J. Select. Areas Commun., vol. 33, pp , Aug []. Tse and P. Vsanath, Fundamentals of Wreless Communcaton, Cambrdge Unversty Press, 5. [] S. Shama and B. Zadel, nhancng the cellular donln capacty va co-processng at the transmttng end, n Proc. Veh. Technol. Conf., vol. 3, pp , May. [] S. Jafar, G. Foschn and A. Goldsmth, PhantomNet: explorng optmal multcellular multple antenna systems, n Proc. Veh. Technol. Conf., vol., pp. 6-65, Sept.. [3] L. Shao and S. Roy, onln multcell MMO-OFM: an archtecture for next generaton reless netors, n Proc. WCNC., vol., pp. -5, Mar. 5. [4] A. Mormoto, K. Hguch and M. Saahash, Performance comparson beteen fast sector selecton and smultaneous transmsson th softcombnng for ntra-node B macro dversty n donln OFM rado access, n Proc. Veh. Technol. Conf., vol., pp. 57-6, 6. [5] S. Plass, A. ammann and S. Kaser, Analyss of coded OFMA n a donln mult-cell scenaro, n Proc. OFM orshop (nowo 4, Sept. 4. [6] A. Paulraj, R. Nabar and. Gore, ntroducton to Space-Tme Wreless Communcatons, Cambrdge Unverse Press, 3. [7] G. Strang, Lnear Algebra and ts Applcatons, Harcourt Brace Jovanovch College Publshers, 988. [8] P. Amers, et al., Survey of channel and rado propagaton models for reless MMO systems, URASP Jour. On Wreless Commun., 97, 7. [9] T. Pham and K. Balman, Multpath performance of adaptve antennas th multple nterferers and correlated fadngs, Trans. Veh. Technol., vol. 48, pp , Mar [] M. Chan, M. Z. Wn, A. Zanella, R. Mall and J. Wnters, Bounds and approxmatons for optmum combnng of sgnals n the presence of multple cochannel nterferers and thermal nose, Trans. Commun., vol. 5, no., pp 96-37, Feb. 3.