Iterative Detection and Decoding (IDD) MIMO-OFDM HARQ Algorithm with Antenna Scheduling

Transcription

1 Iteratve Detecton and Decodng (IDD) MIMO-OFDM HARQ Algorthm wth Antenna Schedulng KyooHyun Km, SeungWon Kang, Manar Mohasen, and KyungH Chang he Graduate School of I & elecommuncatons, InHa Unversty Incheon, Korea E-mal: makewsh79@paran.com, swkang79@hanmal.net, lemanar@hotmal.com, khchang@nha.ac.kr Abstract In ths paper, a multple-nput-multple-output (MIMO) hybrd-automatc repeat request (HARQ) algorthm based on antenna schedulng s proposed. It retransmts the packet usng the scheduled antennas accordng to the state of the communcaton lnk, nstead of retransmttng the packet through the same antennas. he proposed MIMO-OFDM HARQ system based on antenna schedulng s shown to be superor to conventonal MIMO HARQ systems due to ts spatal dversty gan. Key words: MIMO-OFDM, I-BLAS, Sphere Decodng, Chase Combnng, Incremental Redundancy, Antenna Schedulng.. Introducton MIMO systems that employ several transmt and receve antennas at both ends are capable of provdng a large ncrease n capacty compared to tradtonal sngle antenna systems. However, MIMO systems suffer from co-antenna nterference (CAI) and frequency-selectve fadng. CAI, one of the major drawbacks n MIMO systems, can be mtgated by employng an teratve detecton and decodng (IDD) type of recever. he basc dea of IDD s the exchange of nformaton between the detector and the decoder n an teratve fashon, untl the performance no longer can be mproved []. he robustness on frequencyselectve fadng can be mproved by combnng OFDM wth MIMO technques []-[3]. Many modern data communcaton systems make use of HARQ schemes, whch combne forward error correcton (FEC) and ARQ protocols. here are many varants of HARQ schemes. Among them, chase combnng (CC) and ncremental redundancy (IR) are the most usual applcatons. When the orgnal transmsson fals, CC resends the same copy agan to be combned wth what sent n the orgnal transmsson, whle IR re-sends the packets by applyng lower code rate and combnes those wth orgnal transmtted packets [4]-[5]. For a conventonal MIMO HARQ system, f the channel status of the communcaton lnk for the antenna contnues to operate under bad condtons, the retransmtted packets can also be erroneous, whch would ncrease the number of retransmssons, causng the system to functon poorly. herefore, n ths paper, a modfed MIMO HARQ algorthm ncorporated wth antenna schedulng s proposed to solve the problem mentoned above. Furthermore, to ncrease the data rate and to mprove the performance further, the IDD-based Bell laboratory layered space-tme (I-BLAS) system s utlzed wth the proposed MIMO HARQ algorthm. hs paper s organzed as follows: In Sect., the I- BLAS system and sphere decodng (SD) algorthm are brefly descrbed. In Sect. 3, the detals of the I-BLAS system wth the proposed HARQ algorthm wth antenna schedulng s descrbed. In Sect. 4, the performance of the I-BLAS system and the proposed HARQ algorthm s evaluated by computer smulaton, and fnally n Sect. 5, the conclusons are gven.. I- BLAS System he major factor degradng the performance of the BLAS system s the aforementoned CAI, whch s caused by transmttng the sgnal usng n antennas. hs ssue, however, can be cancelled applyng an IDD recever, creatng what has been termed the I-BLAS system.. ransmtter of I-BLAS System Fgure shows the transmtter archtecture of the I- BLAS system wth n transmttng antennas, ncludng the conventonal V-BLAS (Vertcal BLAS) system wth a dagonal space (DS) nterleaver. he nput bt sequence b s de-multplexed and encoded by an errorcorrectng code to generate the coded bt sequence c, whch s further nterleaved by a dagonal space bt nterleaver to obtan the nterleaved coded bt sequence c. Fg. ransmtter archtecture of the I-BLAS system.

2 = log s S 0 s S exp( r Hs ) Pr[ s] σ exp( r Hs ) Pr[ s] σ Fg. Dagonal space nterleaver. ( Π) E E Fgure shows the dagonal space nterleaver based on the dagonal layerng of each ndependently coded substream. It s nterestng to note that unlke D-BLAS (Dagonal BLAS), no boundary wastage occurs [5]. he nterleaved sequence c has q coded bts n each transmttng antenna branch to be mapped by M-QAM, so the total q n coded bts are n a, where q= log M. he n dmensonal sgnal vector a= [ a, a,, a n ] s forwarded to the OFDM modulator, whch performs an nverse fast Fourer transform (IFF) followed by a vrtual carrer / guard nterval (GI) nserton. It s then transmtted through n antennas.. Recever of I-BLAS System Fgure 3 shows the archtecture of the teratve recever used n I-BLAS. he man components of the recever are the nner soft-nput soft-output (SISO) decoder, the DS (de-) nterleaver and the parallel outer SISO decoder. Assumng an n OFDM symbol vector s s transmtted over an x n MIMO channel H, the x receved sgnal vector r can be expressed by Eq. (). ( k ) ( k ) ( k ) r = Hs + n () In Eq. (), k s the symbol ndex and n s the n R addtve whte Gaussan nose wth a zero mean and varanceσ I. he LLR (Log Lkelhood Rato) of the nterleaved bt sequence c = [ c, c,, c qn ] s defned then by Eq. () [], [6]. Pr[ c = r] L( c ) = log, =,,, q n Pr[ c = 0 r] usng Bay's rule, Pr[ r c = ]Pr[ c = ] = log Pr[ r c = 0]Pr[ c = 0] () Ĥ L M L MnR L A L E L AnR L EnR A ( Π ) A M M Fg. 3 Recever archtecture of the I-BLAS system. In Eq. (), Pr[ c = b], where b has a value of 0 or, s the c ntrnsc nformaton of the coded bt c, and S s wrtten as Eq. (3). c S = { μ( c ) c = [ c, c,, c ], c = c} (3) q n Here, μ() denotes a modulaton functon. Durng the frst teraton, the ntal ntrnsc probabltes of all symbol bts are assumed to be / (.e., equally lkely). Usng the approxmate expresson of P max{ P}, Eq. () s rewrtten as Eq. (4) [6]. Lc ( ) [mn{ r Hs logpr[ s]}] σ σ s S [mn{ r Hs 0 log Pr[ s ]}] s S b b A-pror LLR value LE ( c ) obtaned by Eq. (4) s denterleaved and used for the outer SISO decoder. c n Eq. (4) becomes c after the DS de-nterleaver ( Π ), and becomes c agan after the DS nterleaver ( Π) n the feedback path. he relatonshp of the LLRs () c and Lc ( ) s gven by Eq. (5). c =Π Lc ( ) =Π{ ( c)} () {()} L c (4) (5)

3 Based on the a-pror nformaton A( c), the outer SISO decoder yelds a-posteror nformaton M ( c ) as expressed by Eq. (6). ( c ) = ( c ) + ( c ) (6) M A E In above equaton, E ( c ) s termed extrnsc nformaton and s obtaned through a decodng process. hs value s nterleaved and calculated for Eq. (7). In Eq. (9), Re{ } and Im{ } represent the real and magnary part of a complex sgnal, respectvely. Each symbol s n the vector s s referred to as a layer; each s constraned to a fnte set μ n Eq. (0). QPSK : μ {, + } 6QAM: μ { 3,, +, + 3} 64QAM: μ { 7, 5, 3,, +, + 3, + 5, + 7} (0) Pr[ s] = qn = c [exp{ LE( c )}] + exp[ L ( c )] E (7) Eq. (7) s used as a-pror probablty A( c) n Eq. (6) at the next teraton. As the number of teratons ncreases, the performance of the I-BLAS system s mproved due to the more accurate a pror probablty n Eq. (7) [6]..3 Detecton for I-BLAS System Maxmum lkelhood (ML) decodng over a mult-path channel requres an exhaustve search over all possble codewords. hus, the computatonal complexty of the optmal decodng exponentally ncreases accordng to the length of the codeword. An effcent ML detecton technque has been proposed to lower the computatonal complexty wthout sacrfcng the performance compared to the case of the optmal ML, whch s known as the sphere decodng (SD) algorthm [7]. he prncple of the sphere decodng algorthm s to fnd the closest lattce pont to the receved sgnal wthn a sphere radus where each codeword s represented by a lattce pont n a constellaton coordnator. o employ the sphere decodng algorthm, the notaton of Eq. () s changed to Eq. (8). r = Ms + n (8) Here, r, M, s and n are real values of the receved sgnal, channel matrx, transmtted sgnal, and nose vector, respectvely. r = [Re{ r} Im{ r}] Re{ H} -Im{ H} M = Im{ } Re{ } H H s = [Re{ s} Im{ s}] n = [Re{ n} Im{ n}] (9) Fg. 4 Geometrcal representaton of the sphere decodng algorthm. Descrpton of the SD algorthm s llustrated n Fg. 4. Intally, Eq. () s defned to lead to the SD algorthm. s = arg mn( z s ) M M( z s ) () SD s μ Here, z = ( M M) M r s a zero-forcng pont. At each recurson, the SD stores n radus C, whch s the best vector value prevously found, where radus C s gven as Eq. (). C = d( zs, ), where d : Eucldean Dstance () It s nterestng to note that there s no need to contnue and check vectors that can only be worse than ths pont; therefore, the search can be constraned to a sphere as Eq. (3) [8]. ( z s ) M M( z s ) C (3) Usng a factorzaton such as Cholesky or QR [9], the matrx MMcan be transformed nto R R, where R s a n n upper trangular matrx. R, R, n R = (4) 0 R n, n Usng Eq. (4), Eq. (3) can be rewrtten as

4 nr n Rj ( z s ) C. (5) = j= 3. MIMO HARQ Algorthm wth Antenna Schedulng Conventonal MIMO HARQ algorthms retransmt packets usng the same antennas when the transcever receves the negatve acknowledgement (NAK) on ts feedback lnk. If the channel status of the communcaton lnk for the antenna remans n a poor condton, the retransmtted packet may contnue to be erroneous, and the number of retransmssons would then ncrease contnuously, leadng to addtonal poor system performance. In ths secton, a MIMO HARQ algorthm based on antenna schedulng s proposed. he proposed algorthm retransmts the packet usng scheduled antennas accordng to the state of the communcaton lnk, as opposed to retransmttng the packet through the same antennas. A stop-and-wat (SAW) ARQ scheme s assumed, whch transmts the next packet after recevng the ACK or NAK. Fg. 5 ransmtter archtecture of I-BLAS wth the proposed HARQ algorthm wth antenna schedulng. (a) 3. System Model Fgure 5 shows the I-BLAS transmtter archtecture wth the proposed MIMO HARQ algorthm wth antenna schedulng. he man components of the transmtter are a cyclc redundancy check (CRC) encoder, conventonal transmt blocks of I-BLAS, a transmt antenna selecton block and a resource scheduler. he CRC encoder generates a CRC code to check whether an error occurs n the CRC decoder. he x antenna selecton block selects the L transmttng antenna branches, whch has hgh channel-sum values n Eq. (7), among total n antennas. Utlzng feedback nformaton, the resource scheduler controls the code rate of the turbo encoder and determnes the antennas that wll transmt the sgnal. In Fg. 5, { I, ACK}, j =,,, n n are the channel sum and ACK value, respectvely. Fgure 6 (b) shows the recever archtecture of I- BLAS wth the proposed MIMO HARQ algorthm wth antenna schedulng. he man components of the recever are the conventonal receve blocks of I-BLAS, the receve antenna selecton block and the CRC decoder. Estmated channel values are used to calculate the channel sum and to select the LR L antennas. (b) Fg. 6 (a) Jont x/rx antenna selecton block. (b) Recever archtecture of I-BLAS wth the proposed HARQ algorthm wth antenna schedulng. A jont transmt / receve antenna selecton algorthm s used to select the LR L antennas among nr n antennas. he CRC decoder extracts the CRC sequence from the turbo-decoded bt sequence and determnes whether an error has occurred. 3. Proposed MIMO HARQ Algorthm wth Antenna Schedulng Fgure 7 shows a flow chart of the proposed MIMO HARQ algorthm n the downlnk. ransmtter receves the feedback nformaton of channel sum values and ACK values, as expressed by Eq. (6). It then determnes the strategy of retransmsson, as follows.

5 { I, ACK }, j =,,, n (6) n j Intally, among n antennas accordng to the order of the channel sum values L x antennas are selected I n n Eq. (7). Also chosen are the antennas for retransmsson accordng to the order of the channel sum values. he scheduler at the transmtter sde then checks the ACK value of each antenna. If all x antennas receve the value of (NAK), then an ncremental redundancy scheme s employed to acheve robust packet retransmsson over the communcaton lnk. In ths case, all L antennas are utlzed for the retransmsson. If the number of ACKs s greater than or equal to the number of NAKs, the scheduler retransmts by applyng chase combnng usng as many ACK antennas as the number of NAKs. If the number of NAKs s greater than the number of ACKs, the scheduler retransmts by applyng chase combnng usng the ACK antennas, and by applyng ncremental redundancy usng as many NAK antennas as n: (number of NAK antennas number of ACK antennas). In Eq. (8), Px ( ), Gx ( ), Qx ( ), and Rx ( ) are the nformaton polynomal, CRC polynomal, quota, and remander, respectvely. If the remander Rx ( ) s zero, there are no transmsson errors. 4. Smulatoesults In ths secton, the performance of I-BLAS s evaluated through computer smulaton and an optmal teraton number for the IDD s determned. he performance of MIMO detecton algorthms are compared wth each other, and the performance of a conventonal MIMO-HARQ algorthm s also compared wth the proposed antenna schedulng-based MIMO-HARQ algorthm to show the gan due to the spatal dversty. On the recever sde, channel sum values are obtaned by Eq. (7). nr Sum,,,, n Hmn n n m= I = = n Sum R,,,, m Hmn m nr n= I = = (7) After calculatng the channel sum values, the Rx antenna selector selects L R Rx antennas among nr antennas, whch are selected accordng to the order of the channel sum values I R m n Eq. (7). he recever then checks whether the receved packet s a retransmtted packet. For retransmtted packet recepton, the recever combnes the retransmtted packet wth the orgnal receved packet n the buffer, and CRC decodng s then performed. he determnaton of an error s examned usng Eqs. (8) and (9). [0] Px ( ) Error Check : = Q( x) + R( x) Gx ( ) (8) (a) (b) Fg. 7 (a) he proposed MIMO HARQ algorthm at the downlnk transmtter sde. (b) he proposed MIMO HARQ algorthm at the downlnk recever sde. he MIMO channel model used for smulaton s spatal channel model extenson (SCM-E) of 3 rd generaton partnershp project ad-hoc group (3GPP AHG) [].he smulaton parameters are summarzed n able. Fgure 8 shows the structure of sub-frame constructon and plot assgnment per antenna, whch s beng employed n 3GPP LE (Long erm Evoluton) standardzaton []. 0 : No Error f Rx ( ) = 0 ACK = : Error f Rx ( ) 0 (9)

6 able Smulaton parameters. Parameters Carrer Frequency Bandwdth of Operaton Value GHz 0 MHz Number of FF Ponts 048 Cyclc Prefx 46 Modulaton Sub-frame Duraton QPSK, 6QAM 0.5 ms OFDM Symbol per Sub-frame 7 Moble Speed MIMO Fadng Channel Model Channel Estmaton MIMO Detecton x / Rx Antenna Confguraton (Selected Antenna Confguraton) 0 km/h SCM-E Sub-urban Macro Practcal ZF, MMSE SIC, SD 6 x 6 (4 x 4) x / Rx Antenna Dstance 0λ / 0.5λ Channel Codng urbo Codng Mother Code Rate /3 HARQ Algorthm CC, IR, Proposed Retransmsson Code Rate of IR 3/5, 8/5, /, /5 Max Retransmsson Number 4 Fg. 9 4 x 4 QPSK uncoded BER performance of the I-BLAS system accordng to the teraton number. 4. Performance of I-BLAS System Fgs. 9 and 0 show the 4 x 4 QPSK uncoded BER and the 4 x 4 6QAM coded BER performance of the I- BLAS system accordng to the teraton number. In the case of the uncoded QPSK n Fg. 9, at a target BER of 0-4, SNR mprovements by three and fve teratons are about 4.8 db and 5. db, respectvely, compared to the case wth no teraton. In the case of the coded 6QAM shown n Fg. 0, at a target BER of 0-5, the SNR mprovements after three and fve teratons are approxmately 3 db and.7 db, respectvely, compared to the case wth no teraton. From the above results, t can be observed that the detecton error, channel estmaton error and nterference components are nearly elmnated after three teratons. hus, the deal number of teratons s determned to be three. Fg. 8 he structure of the plot assgnment per antenna. Fg. 0 4 x 4 6QAM coded BER performance of the I-BLAS system accordng to the teraton number.

7 Fg. 4 x 4 6QAM coded BER performance of I-BLAS accordng to MIMO detecton methods. 4. Performance of MIMO Detectors he 4 x 4 6QAM coded BER performance of the I-BLAS system s tred wth the MIMO detectons of the zero forcng (ZF), mnmum mean-square error (MMSE), ZF successve nterference cancellaton (ZF-SIC), MMSE-SIC, and the SD n Fg.. It s observed that the SD shows the best performance; the ZF s the smplest but shows the worst performance, as expected. At a target BER of 0-5, the SD gans more than 0 db of SNR compared to ZF detecton. he ZF-SIC and MMSE-SIC schemes are superor to the ZF and MMSE schemes due to the nterference cancellaton characterstc of SIC among the antennas. Fg. 3 4 x 4 6QAM coded BER performance of I-BLAS applyng HARQ algorthm based on the proposed antenna schedulng. 4.3 Performance of the Proposed MIMO HARQ Algorthm wth Antenna Schedulng In ths subsecton, the performance of the transmt / receve antenna selecton process and the proposed HARQ scheme wth antenna schedulng s dscussed. Antenna selecton n ths subsecton s based on the channel sum n Eq. (7) and the channel norm n Eq. (0). nr Norm,,, n H mn n n m= n Norm R,,, m H mn m nr n= I = = I = = (0) Fg. 4 x 4 6QAM coded BER performance of I-BLAS accordng to antenna selecton method. Fg. 4 4 x 4 6QAM PER performance of I-BLAS applyng HARQ algorthm based on the proposed antenna schedulng.

8 Fgure shows the 4 x 4 6QAM coded BER performance of the I-BLAS system accordng to the antenna selecton method. he sum-based and norm-based selecton methods show nearly dentcal performances, hence the antenna selecton was chosen based on the channel sum due to ts smplcty. Fgs. 3 and 4 show the performance of the I- BLAS system wth the proposed HARQ algorthm wth antenna schedulng. In ths smulaton, the stop-and-wat (SAW) ARQ scheme s used. he SAW ARQ scheme transmts the packet after recevng ACK or NAK from the recever, and the new packet s not transmtted durng retransmsson. In Fg. 3, at the target BER of 0-5, the proposed algorthm s superor to the cases of antenna schedulng wth conventonal chase combnng and wth ncremental redundancy by the SNR values of 3 db and 0.5 db, respectvely. In Fg. 4, at the target PER of 0-3, the gan wth the two aforementoned schemes by the proposed algorthm becomes db and 0.7 db, respectvely. hs gan by the proposed HARQ algorthm comes from the spatal dversty due to the proposed antenna schedulng. [5] J. M. Shea, Relablty-based hybrd ARQ, IEEE Electroncs Letters, vol. 38, pp , June 00. [6] JnHo Cho, Adaptve and Iteratve Sgnal Process n Communcatons. Cambrdge, 006. [7] E. Vterbo and J. Boutros, A unversal lattce code decoder for fadng channels, IEEE rans. on Informaton heory, vol. 45, pp , July 999. [8] A. Wesel, X. Mestre, A. Pages, and J. R. Fonollosa, Effcent mplementaton of sphere demodulaton, n Proc. IEEE Sgnal Processng Advances n Wreless Comms., June 003, pp [9] D. Wubben, R. Bohnke, J. Rnas, V.Kuhn, and K. D. Kammeyer, Effcent algorthm for decodng layered space-tme codes, IEEE Electroncs Letters, vol. 37, pp , Oct. 00. [0] 3 rd Generaton Partnershp Project (3GPP) echncal Specfcaton 5. Rev , Multplexng and channel codng (FDD), June 004. [] 3GPP & 3GPP Spatal Channel Model AHG, Spatal channel model text descrpton-rev 7.0, Aug [] Motorola, R-0659, E-URA downlnk reference-sgnal structure, ext Proposal, Jan Conclusons In ths paper, the MIMO HARQ algorthm based on the antenna schedulng s proposed. It retransmts a packet usng scheduled antennas accordng to the state of the communcaton lnk, as opposed to retransmttng the packet usng the same antennas. For the MIMO HARQ system wth I-BLAS, the optmal number of teratons s determned, and the performances of detecton schemes ncludng sphere decodng are compared. For the proposed antenna schedulng, a channel sum type of antenna selecton s adopted consderng the tradeoff between performance and complexty. Fnally, the proposed MIMO HARQ system based on antenna schedulng s shown to be superor to conventonal MIMO HARQ systems due to ts spatal dversty gan. References [] M. Sellathura and S. Haykn, URBO-BLAS for wreless communcatons: heory and experments, IEEE rans. on Sgnal Processng, vol. 50, No. 0, pp , Oct. 00. [] Marc Engels, Wreless OFDM Systems. Kluwer, 00. [3] G. L. Stuber, J. Barry, S. McLaughln, Y. L, M. A. Ingram, and. Pratt, Broadband MIMO-OFDM wreless communcatons, n Proc. of IEEE, vol. 9, Feb. 004, pp [4] J. L and H. Ima, Performance of hybrd-arq protocols wth rate compatble turbo codes, n Proc. Int. Symp. on urbo Codes, Sept. 997, pp