Effective SNR Based MIMO Switching in Mobile WiMAX Systems

Transcription

1 Effectve SNR Based MIMO Swtcng n Moble WMAX Systems Myoung-Seob Km and Yong-wan Lee Scool of Electrcal Engneerng and INMC, Seoul Natonal Unversty Kwanak P. O. Box, Seoul -600 Korea Emal: mseob@ttl.snu.ac.kr and ylee@snu.ac.kr Abstract e moble WMAX system consders te use of ( ) multple-nput multple-output (MIMO) scemes for performance mprovement. It s requred for moble statons to approprately swtc te MIMO mode; space tme block code (SBC) or vertcal spatal multplexng (). In ts paper we consder a novel swtcng sceme for te MIMO mode based on effectve sgnal-tonose rato. Assumng te use of a mnmum mean square error (MMSE) recever for te and a maxmum rato combnng recever for te SBC, te tresold for te mode swtcng s analytcally derved n a closed form. Smulaton results sow tat te proposed swtcng sceme outperforms conventonal swtcng scemes n terms of te capacty and outage probablty.. Introducton e moble WMAX system (m-wmax) based on te IEEE 80.6e-00 specfcatons consders te use of ( ) multple-nput multple-output (MIMO) antenna tecnologes to mprove te system performance []. e system profle for te m-wmax [] ncludes two MIMO modes for te downlnk. One s ( ) vertcal spatal multplexng () [] and te oter s space tme block code (SBC) for transmt dversty []. e mode can mprove te system capacty by generatng multple spatal layers wen te number of receve antennas s larger tan or equal to tat of te transmt antennas, enablng to remove nterference sgnals from oter layers []. o obtan a spatal multplexng gan, owever, te MIMO cannel sould be spatally ndependent. As te rank of te MIMO cannel decreases, te performance of te can abruptly deterorate. Moreover, wen te sgnal to nose (SNR) s low, te capacty of te system can sgnfcantly decrease due to splt transmt power over multple spatal layers. On te oter and, te SBC mode explots spatal dversty by employng multple antennas at te transmtter and possbly at te recever. Snce t utlzes te wole transmt power for te transmsson of a sngle data stream, t can effectvely be appled to low SNR envronments. e spatal dversty gan enables te recever to relably decode te sgnal n fadng cannels, almost ndependent of te property of te cannel rank. owever, t cannot aceve substantal capacty gan due to te absence of spatal multplexng gan []. It s desrable to maxmze te system capacty of te m- WMAX by transmttng data wt te use of a proper MIMO mode accordng to te tme-varyng cannel condton. Prevous studes consder te predcton and selecton of a MIMO mode by usng sort-term cannel state nformaton (CSI) [], [6] or long-term CSI of te cannel [7] [9]. e MIMO mode can be selected to maxmze te mnmum dstance of te receved sgnal constellaton, ncreasng te spectral effcency [], [6]. owever, ts swtcng sceme was desgned for uncoded transmsson scemes and tus t may not work well n coded ones. e MIMO mode swtcng based on approxmated performance may cause swtcng errors, resultng n performance degradaton. Long-term CSI based swtcng scemes [7] [9].consder te mode selecton to maxmze te cannel capacty n an average sense, sgnfcantly reducng te system complexty and feedback sgnalng overead due to slow tme-varyng nature of te longterm cannel caracterstcs. owever, te use of only long-term CSI may degrade te swtcng performance due to te fact tat t may not properly track nstantaneous cannel condton wc vares muc faster tan te longterm cannel caracterstcs. In ts paper, we consder te use of nstantaneous CSI for te MIMO mode swtcng assocated wt tmevaryng cannels. We select te MIMO mode based on te effectve SNR of te receved sgnal wc s drectly related to te nstantaneous capacty of te MIMO cannel. By dervng te effectve SNR of te and SBC scemes n a smple closed form, te MIMO mode can easly be swtced usng a smple tresold. It s sown tat te proposed sceme outperforms te prevous scemes n bot te capacty and te outage probablty. e rest of ts paper s organzed as follows. e system model n consderaton s descrbed n Secton II. e effectve SNR of te and SBC s derved n a closed form and ten t s appled to te swtcng of te MIMO mode n Secton III. e performance of te

2 g.. M-WMAX wave- system wt adaptve MIMO swtcng. proposed swtcng sceme s verfed by computer smulaton n Secton IV. nally, conclusons are summarzed n Secton V.. System model Consder ( ) MIMO (.e., two transmt and two receve antennas) scemes suggested n te IEEE 80.6e-00 specfcatons [] and te m-wmax wave- profle, as llustrated n g. []. e receved sgnal can be represented as r x+ n () were x [ x x] and r [ r r] denote te transmt and receved sgnal vector, respectvely, s te ( ) MIMO cannel gven by and [ n ], () n [ ] n denotes zero-mean addtve wte Gaussan nose (AWGN) wt covarance N 0 I. ere, te superscrpt denotes te matrx transpose, I denotes a ( ) dentty matrx, j denotes te cannel response from transmt antenna to receve antenna j, and denotes te cannel vector orgnated from transmt antenna. Lettng P E[ x x ] be te transmsson power, te average SNR can be defned as P. () N0 e transmt sgnal vector n te mode can be represented as x [ s s], were s and s are data symbols transmtted by transmt antenna and, respectvely. e mode can aceve a spatal multplexng gan by transmttng ndependent data streams troug two transmt antennas. In te SBC mode, data symbol s and s are transmtted durng twosymbol duraton: te transmt sgnal vector s x [ s s] and x s s durng te frst and second symbol tme, respectvely. e receved sgnal n te SBC can be represented as [] r x + n () were, s te symbol tme ndex. In te m-wmax system, te moble staton (MS) determnes te MIMO mode and reports te ndex of te selected mode to te base staton (BS) va a low-rate feedback cannel n te uplnk []. Lettng and SBC be a performance metrc of te and te SBC, respectvely, te MIMO mode can be determned wt te correspondng ndex π as 0, <SBC π. (), >SBC. Proposed Adaptve MIMO Swtcng It s desrable to defne a proper performance metrc for eac MIMO mode to optmze te MIMO performance. In ts paper, we consder an effectve SNR as te performance metrc for te MIMO mode selecton... Performance metrc of te mode In te mode, te transmt sgnal s, wose transmt power s P /, can be decoded usng an approprate recever wegt vector w. Assumng te use of a mnmum mean-square error (MMSE) recever, w can be determned by [] P N0 + k k k w I. (6) en, te receved sgnal after te MMSE flterng can be represented as w r w s + w ksk + n k (7) w s + w z were te frst term s te desred sgnal and te second term s te nterference sgnal from oter layer plus AWGN. e post detecton SNR of te receved sgnal s []

3 P w. (8) e correspondng system capacty of te mode can be represented as C log ( + ) + log ( + ) log( + ( + ) + ) (9) log + ( ) were represents te effectve SNR of te mode gven by ( + ) +. (0) o ts end, frst calculate te post detecton SNR assocated wt wegt P N0 + w I. () Usng a matrx nverson formula [0] P N0I+ * + (), P * {( + ) + } + t can be sown tat det ( ) + P w, () ( + ) were denotes te robenus norm. Smlarly, t can be sown tat te post detecton SNR for te second layer s det ( ) + ( + ). () nally, te effectve SNR of te mode can be represented as det ( ) + +. () ( + )( + ) e term det ( ) gly depends on te egenvalues of and t can be represented by te product of two egenvalues of. Wen te MIMO cannel s gly correlated, one of te egenvalues of s lkely very small, resultng n a small det ( ). s mples tat te mode may not be applcable n spatally correlated cannel envronments... Performance metrc of te SBC mode Assumng tat te cannel caracterstcs are not notceably varyng durng two-symbol tme duraton, te receved sgnal vectors n te SBC mode at symbol tme and can respectvely be represented as r s n r +, (6),, r, n s, r s n r. (7) *,, * r, n + s, r, r, r, r,,,,, rom (6) and (7), lettng y and n n n n n, te receved sgnal vectors can be rewrtten as P s y + s n (8) P s eff +. s n e combned sgnal after te MRC can be represented as P ' eff y Is+ n, (9) ' were n eff n denotes an equvalent nose vector. en te effectve SNR of te SBC sceme s gven by SBC. (0). Crteron for te MIMO mode swtcng e MIMO mode can be selected based on te effectve SNR as π > () < SBC were π denotes te selected MIMO mode ndex. Snce () can be rewrtten as

4 det ( ) + + > < ( + )( + ) π e swtcng crteron can furter be smplfed to ( ) π det > + det( ) < +.(). (). Performance evaluaton e performance of te proposed swtcng sceme s verfed by computer smulaton, were te system parameters are summarzed n able. or comparson, te performance of a prevous swtcng sceme n [] s consdered, were te mode s selected based on te mnmum Eucldean dstance as π λmn d > mn, vsm d mn, stbc N <. () N ere, λ mn s te mnmum egenvalue of, and d mn,vsm and d mn,stbc are te mnmum dstance of te receved sgnal constellaton n te and te SBC mode, respectvely. or reference, te performance of non-adaptve MIMO scemes tat use a fxed MIMO mode (.e., or SBC) s also consdered. e performance of te proposed sceme s evaluated n terms of te capacty n te presence of transmt antennas correlaton, were te spatal correlaton s defned by { } E ρ. () e performance s evaluated n Rayleg flat fadng cannel as n te prevous sceme []. g. depcts te capacty performance wen te transmt cannel s weakly (e.g., ρ 0. ) and gly (e.g., ρ 0.9 ) correlated. It can be seen tat te proposed sceme outperforms te oter scemes by properly swtcng te MIMO mode accordng to te cannel condton. Especally, t can also be seen tat te prevous swtcng sceme as severe performance degradaton n ρ 0. and g SNR regon were te mode s preferred to te SBC mode. s s manly due to te fact tat te prevous sceme s desgned to favor te SBC mode, wc leads to capacty loss at te cost of relable transmsson. e proposed sceme provdes a capacty gan of about 0.8 bps/z over te prevous sceme wen ρ 0. and 0. bps/z wen ρ 0.9 at SNR 0 db. g. depcts te capacty performance accordng to Parameters Cannel model Cannel estmaton # of X antenna # of RX antenna Recever algortm Capacty (bps/z) Capacty (bps/z) able. Smulaton parameters. Rayleg fadng Perfect non-adaptve (SBC) non-adaptve () adaptve (prevous) adaptve (proposed) Values MMSE () / Lnear MRC (SBC) non-adaptve (SBC) non-adaptve () adaptve (prevous) adaptve (proposed) (a) Wen ρ (b) Wen ρ 0.9 g.. Capacty performance of te proposed sceme. te spatal correlaton at SNR 0dB. Wen te cannel s eavly correlated, t s desrable to employ te SBC mode. On te oter and, wen te cannel s uncorrelated, te mode s preferred to te SBC mode n an average sense. owever, tere are cases wen te SBC mode works better tan te mode even n

5 Capacty (bps/z) Outage probablty... non-adaptve (SBC) non-adaptve () adaptve (prevous) adaptve (proposed) Spatal correlaton ( ρ ) g.. Capacty performance accordng to ρ at SNR 0dB non-adaptve (SBC) non-adaptve () adaptve (prevous) adaptve (proposed) g.. Outage performance of te proposed swtcng sceme wen ρ 0.9. low spatal correlaton cannel, and vce versa. As a consequence, t can be seen tat te proposed swtcng sceme provdes te best performance rrespectve of spatal correlaton condton. Snce te prevous swtcng almost selects te SBC sceme at SNR 0dB, t provdes capacty performance very smlar to te SBC sceme rrespectve of te spatal correlaton. g. depcts te outage probablty at an outage capacty of bps/z wen te cannel s gly correlated. It can be seen tat te SBC mode s superor to te mode and te dfference ncreases as te SNR ncreases, wc s manly due to larger dversty gan of te SBC sceme. It can be seen tat, altoug te proposed sceme sows less advantages n ts condton, t stll as a notceable performance gan over te oter scemes. In fact, te proposed sceme as a gan over te prevous swtcng sceme about 0. db wen ρ 0.9 n terms of te outage probablty.. Conclusons We ave proposed a new swtcng sceme for te selecton of te MIMO mode n te m-wmax system. Assumng te use of a MMSE recever n te mode and a MRC recever n te SBC mode, te MIMO mode s smply swtced based on a tresold wc s analytcally determned n terms of te effectve SNR. e proposed sceme can outperform prevous MIMO swtcng scemes n terms of te capacty and outage probablty by explotng te dversty and multplexng gan. e smulaton results sow tat te proposed swtcng sceme works well rrespectve of te spatal correlaton and SNR condton. References [] IEEE Std 80.6e, Part 6: Ar Interface for xed and Moble Broadband Wreless Access Systems, Dec. 00. [] WMAX orum, WMAX orum Moble System Profle v.0.0, May 006. [] P. W. Wolnansky, G. J. oscn, G. D. Golden and R. A. Valenzuela,, V-BLAS: An arctecture for realzng very g data rates over te rcscatterng wreless cannel, n Proc. ISSSE-98, Psa, Italy, Sept [] S. Alamout, A smple transmt dversty tecnque for wreless communcatons, IEEE J. Sel. Areas Commun., vol. 6, pp. -8, Oct [] R. eat Jr. and A. Paulraj, Swtcng between dversty and multplexng n MIMO systems, IEEE rans. Commun., vol., no. 6, pp , June 00. [6] C. Cae; M. Katz, C. Su, and. Jeong, "Adaptve spatal modulaton for MIMO-ODM," n Proc. WCNC 00, vol., pp. 87-9, Mar. 00. [7] A. orenza, M. R. McKay, I. B. Collngs and R. W. eat Jr., Swtcng between OSBC and spatal multplexng wt lnear recevers n spatally correlated MIMO cannels, n Proc. IEEE VC 006, vol., pp. 87-9, May 006. [8] A. orenza, M. McKay, A. Pandarpande, R. eat Jr. and I. Collngs, Capacty enancement va mult-mode adaptaton n spatally correlated MIMO cannels, n Proc. IEEE PIMRC 00, vol., pp. 7-78, Sept. 00. [9] R. Bagavatula, A. orenza and R. eat Jr., Impact of antenna geometry on adaptve swtcng n MIMO cannels, n Proc. WPMC 006, Sept [0] G. Strang, Lnear algebra and ts applcatons, Brooks-Cole, 988. [] D. se and P. Vsvanat, undamentals of wreless communcaton, Cambrdge Unversty Press, 00.