Space Time Equalization-space time codes System Model for STCM
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1 Space Tme Eualzaton-space tme codes System Model for STCM The system under consderaton conssts of ST encoder, fadng channel model wth AWGN, two transmt antennas, one receve antenna, Vterb eualzer wth deal CSI, denterleaver, and decoder. { u ST Encoder { { symbol Interleaver symbol Interleaver { s { s Fadng Channel Fadng Channel AWGN { û ST Decoder { d Denterleaver { e Eualzer { r Fgure The system model for space-tme coded modulaton scheme The nformaton bts { u s passed to the ST encoder, whch outputs the symbol seuences { and {. The symbol seuence { s transmtted over the frst transmt antenna and the symbol seuence { s transmtted over second transmt antenna. Both of symbol seuences are nterleaved ndvdually before sendng through each channel. Interleavng s the typcal way to mtgate the effect of burst errors n a fadng channel. There are two fadng channels due to two transmt antennas. The fadng channel s modeled as a dscrete-tme channel as wll be descrbed later. Two symbol seuences are combned wth AWGN before enterng receve antenna. Then, the receved symbol seuences { r enter the Vterb eualzer that provdes hard-output { e or enter to Suboptmum Soft-Output eualzer that provdes soft-output for decodng process. The hard-output or soft-output
2 nformaton s denterleaved to eep the orgnal order of the seuence { d. The ST decoder, mamum lelhood decoder, combnes and employs receved hard-output or soft-output nformaton for decodng to the receved nformaton bts seuence { û. ST Encoder The ST encoder employs delay scheme. The sgnal constellaton s 4-PSK, where the sgnal ponts are labeled by,, and. Ths encoder has a very smple descrpton n term of seuence ( b, a ) of bnary nputs at tme. From Append A, a dversty gan = places an upper bound on the transmsson rate of R b = bt/s/hz. The ST encoder and trells dagram are shown n Fgure and Fgure, respectvely. { u Demultpleer { b { a { b { a 4-PSK Sgnal Mapper { { Fgure ST encoder system for 4-PSK Fgure Four-state trells dagram for STCM [Taroh et al., 997]
3 The nformaton bts are frst separated nto two bt streams. In ths smulaton, total 4 nformaton bts nput to demulpleer, each bt streams s nformaton bts. At tme nstant, two bts { b, { a from the memory and another two bts { b, { a from demulpleer enter the QPSK sgnal mapper fromng two transmtted symbols { and {. Then each transmtted symbols entered the followng symbol nterleaver, t means that total transmtted bts are 8 bts, so the code rate s (see Eample ). Eample The nformaton bts are. After passng through demultpleer, the nformaton bts are dvded nto two nformaton seuences, { b = { and { a = {. Assumng that ntal values of { b and { a are { and {, so at tme, 4 bts enter mapper at the same are shown below, tme, { and { ( ) b (,) + a (,) + b (,) + a (,), = [Taroh et al., 997] { b { a { b { a { { From ths result, ths s a delay scheme, t means that { delays { symbol. one
4 Symbol Interleaver and Denterleaver The symbol nterleaver s assumed to be a bloc nterleaver wth rows and columns. The symbols from the encoder are wrtten n by row and read out by column. The proposed nterleaver s shown n Fgure 4. So, the nterleavng delay per one bloc s -symbol duraton. The denterleaver whch reverses the functon of the nterleaver are located before the decoder. However, n ths research the nterleaver s bloc symbol nterleaver, but the denterleaver s bloc b-symbol denterleaver. Input symbols Output symbols Fgure 4 Interleaver of STCM system Eualzer After two symbol seuences pass through freuency-selectve Raylegh fadng channel ndvdually, both of symbol seuences are combned together wth AWGN. So, there are 6 possble b-symbols n the sgnal constellaton, where the sgnal ponts are labeled by,,,,4,5,6,7,8,9,,,,,4 and 5 (see Table ). 4
5 5 Then, the b-symbol seuences enter one eualzer due to one receved antenna. The eualzer needs 6-state trells dagram to get hard-output nformaton for VE and get soft-output nformaton for SSE, t s shown n Fgure 4.5. The transton branches are labeled by A, B, C, D, E, F, G, H, I, J, K, L, M, N, O and P, there are 6 branches n each state, and 6 states have same labeled branches. We used the decson delay 5 = δ for SSE Table The label of sgnal constellaton Fgure 5 6-state trells dagram for STCM eualzer The branch metrc for Vterb eualzer (VE) Assumng that r s the receved sgnal at the receved antenna at the tme, and the sgnals from the transmtted antenna transmt through p-memory channel. The branch metrc for a transton labeled n L L n L L L s gven by A B C D E F G H I J K L M N O P
6 m L n r = p= = g, p, p The Vterb algorthm s the used to compute the path wth the lowest accumulated metrc n the Vterb eualzer. Note that p are labeled by M-PSK. The branch metrc for Suboptmum Soft-output eualzer (SSE) Let D s the decson delay, and two transmtted antennas, one receved antenna. The branch metrc of SSE s same as the one of VE. The Suboptmum Softoutput algorthm (SSA) wll select the path wth the mnmum APM. Therefore, n ths research the soft-output corresponds to two symbols, one from each antenna. The soft-output from SSE s also called nformaton pacet: Decoder mn ( Γ + ( π )), mn ( Γ + ( π )),..., mn ( Γ + ( π π Q ( D,,) π Q ( D,,) π Q ( D, M, M ) Mamum lelhood decoder s employed wth the receved soft-output nformaton from the eualzer. To use the Vterb algorthm (VA), trells dagram of the codng scheme must be nown. A path through the trells from the ntal node to the fnal node corresponds to a codeword. Mamum lelhood decdng chooses the path wth the mnmum path metrc to be the decoded codeword. The decoder uses VA for the cases of STCM-VE and STCM-SSE. But, the branch metrc for both of them s dfferent. For VE, at tme, the branch metrc s gven by )) n = 6
7 where s hard-output that corresponds to two symbols n ths research, one from each antenna =. And, the branch metrc of Vterb decoder for SSE s soft-output from the eualzer correspondng to the symbols on a branch n the decoder trells, that s shown n E. 4-. Note that are labeled by M-PSK. b ( r ) ( ) The trells complety of the space-tme code s at least = = 4, so n ths smulaton, the trells complety of the space tme code s 4 states. Eample In non-error stuaton, hard-output b-symbol codeword from eualzer s {84, and ths codeword enters decoder. Then, output symbol seuences of decoder are {. As ST encoder s a delay scheme, the orgnal nformaton bts can be obtaned by QPSK sgnal constellaton and deletng one of the repetton symbol. It s shown below, Smulaton Model for RS-STCM The system components conssts of RS-outer code encoder, bt nterleaver, ST-nner code encoder, symbol nterleaver, channel model wth AWGN due to transmt antennas, Vterb eualzer, symbol denterleaver, ST-nner code decoder, denterleaver and RS-nner code decoder. Note that demodulator s omtted here because the lowpass euvalent dscrete-tme channel model wll be used. Fgure 6 shows the smulaton system. 7
8 { u RS-Outer Encoder { v Bt nterleaver { w ST-Inner Encoder { { Symbol nterleaver Symbol nterleaver { s { s Fadng Channel Fadng Channel { û RS-Inner Encoder { vˆ Bt Denterleaver { ŵ ST-Inner Decoder { d Symbol Denterleaver { e Vterb Eualzer { r Fgure 6 The smulaton system for RS-ST concatenated codng scheme The hard-output nformaton s denterleaved frst and then used n the STnner decoder that s Vterb decoder. It outputs hard-decson bts seuence { ŵ. To eep the orgnal order of the seuence, { ŵ s denterleaved to { vˆ. The RS-outer code decoder then decodes the comng bt stream to the correspondng nformaton bts { û. Reed-Solomon (RS) Outer Code Encoder and Decoder The RS scheme s decded to be RS(6,57). Frst, the nformaton seuence s dvded nto 57 = 7symbols of 6-bt each. These 7 symbols are appled to the nput of RS encoder that wll generate 89 output symbols. The output symbols seuence then enter the followng bt-nterleaver. For the selected RS scheme, the mnmum dstance wll be n-+=6-57+=7. Hence, t can correct up to (n-)/=(6-57)/= 6-bt symbols error. The RS outer decoder employs an algebrac method, Berleamp-Massey algorthm, whch gets the hard-decson output bytes from the STCM nner decoder after bt denterleaver. 8
9 Bt Interleaver and Denterleaver To mprove the error correctng performance of RS, the bt-nterleaver s ntroduced. It s an array of rows by 6 columns. Each array component contans one 6-bt byte. The 6 bytes of RS codeword enter the nterleaver by columns and read out by rows. It shows n Fgure 7. The denterleaver s appled before the outer decoder. The number of bts reured to fll the nterleaver s 6 6 = 4 bts. Input Symbols 6-bt byte Output bts Symbol Interleaver and Denterleaver Fgure 7 Bt-nterleaver of RS-ST scheme The symbol nterleaver s assumed to be a bloc nterleaver wth rows and 7 columns. The symbols from the encoder are wrtten n by row and read out by column. The proposed nterleaver s shown n Fgure 8. The nterleavng delay per one bloc s 567-symbol duraton. The denterleaver whch reverses 6 Input symbols Output symbols 9
10 the functon of the nterleaver are located before the decoder. Channel Model Fgure 8 Symbol nterleaver of RS-ST scheme The freuency-selectve Raylegh fadng channel can be nterpreted as N- path flat fadng channel wth ISI. So, t s modeled by tapped delay lne wth comple coeffcents. The coeffcents are comple Gaussan random varables. The ampltude of the coeffcent s Raylegh dstrbuted and the phase s unform dstrbuted. The receved sgnal r for the th symbol can be shown as L = = ( ) n r s g + = Where the tap coeffcents g ( ) are uncorrelated zero-mean comple Gaussan random processes and g ( ) are Raylegh dstrbuted at any tme nstant. The tap coeffcents of the overall tme-varyng channel are assumed to be perfectly estmated by recever and the phase of receved sgnal s fully compensated. In E., n s the comple zero-mean Addtve Whte Guassan nose wth dentcal varance σ N. The varance of the smulated Gaussan source for a specfed E b N (n db) s σ N = Eb N 4 Note that, wth QPSK, E = E. s b In ths research, two-tap delay lne model s used and shown n Fgure 9. The delay s eual to one symbol duraton. Two sgnal paths are assumed to have eual average power. Doppler effect wll not be consdered. Each channel s normalzed to unt varance.
11 Whte Gaussan Nose Source Whte Gaussan Nose Source Whte Gaussan Nose Source Whte Gaussan Nose Source Transmtted Sgnal from Frst Antenna D Lowpass Gaussan Nose Receved Sgnal Whte Gaussan Nose Source Whte Gaussan Nose Source Whte Gaussan Nose Source Whte Gaussan Nose Source Transmtted Sgnal from Second Antenna D Fgure 9 The freuency-selectve Raylegh fadng channel model wth - tap delay and wthout Doppler effect From E. t s reasonable to assume that varance of the tap coeffcents g ( ) s.5 for STCM, RS-STCM schemes and uncoded-qpsk scheme.
12 Smulaton Results and Dscusson Three STCM schemes mentoned n earler sectons wll be studed n a freuency-selectve Raylegh fadng channel. Doppler effect s not ncluded n ths secton. Monte-Carlo smulaton wll be carred out untl one hundred or more error bts are found. Fgures to present the smulaton results for the STCM schemes wth two types of eualzer and wth RS outer code. The.E+.E- QPSK_VE STCM_VE.E-.E-.E-4.E Eb/No (db) uncoded QPSK are plotted as the reference system. The bt error rate (BER) s plotted versus sgnal-to-nose rato (E b /N ) n decbel. Fgure BER performance of STCM codes wth VE over freuencyselectveraylegh fadng channel, whch compared wth uncoded-qpsk
13 .E+.E-.E- QPSK_VE STCM_VE RS-STCM_VE.E-.E-4.E-5.E-6.E Eb/No (db) Fgure BER performance of STCM codes over freuency-selectve Rayleghfadng channel, whch compared wth RS-STCM.E+.E-.E- QPSK_VE STCM_VE QPSK_SSE STCM_SSE.E-.E-4.E Eb/No (db) Fgure BER performance of STCM codes wth SSE over freuencyselectve Raylegh fadng channel, whch compared wth uncoded-qpsk
14 From the smulaton results llustrated n Fgure - we observe the followng. The performance of STCM wth Vterb eualzer s worse than the performance of uncoded-qpsk. In Fgure the eualzer for QPSK system s VE. As epected, the performance of RS-STCM s better than the performance of uncoded-qpsk. At BER level - t gves db gan over STCM. Note that n Fgure 4. the eualzer for RS-STCM system s VE. From Fgure and Fgure, at the low SNR the uncoded system outperforms RS-STCM system. At hgh SNR (greater than db) the error performance s reversed. The system performance enhancement due to usng a better and softoutput eualzer can be observed from Fgure. When SSE s employed, the performance of STCM gves about 5-6dB codng gan over QPSK. And, more than 9dB mprovement over STCM-VE at any BER level. To summarze, the performance of STCM over freuency selectve Raylegh fadng channel has been presented. Our smulaton results show that uncoded QPSK performance n the proposed system outperforms STCM scheme wth VE. The system model that combnes nterleaver, hard-decson STCM Vterb decoder and hard-output eualzer s not sutable for STCM system. It s seen that soft-decson STCM Vterb decoder and soft-output eualzer (SSE) show a 5-6dB codng gan n SNR. In the paper [Bauch and Nagub, 999], t overcomes the problem of eualzaton space-tme codes wth transmt dversty to employ MAP eualzaton. The performance of SEE s close to that of MAP [Tarasa and Raatheva ]. It can be eplaned that why we can employ SSE for STCM scheme. As epected, at hgh SNR the performance of RS-STCM outperforms uncoded QPSK. 4
15 References:. Bauch G. and Nagub A. F., (999). MAP Eualzaton of Space-Tme Coded Sgnals over Freuency Selectve Channels, IEEE Wreless Communcatons and Networng Conference, Vol., pp Tarasa P. and Raatheva R.M.A.P., Comparson of TCM and BCM schemes on Freuency-Selectve Raylegh Fadng Channels wth Soft-output Algorthms, ICC, New Orleans, June.. Taroh, V., Seshadr, N., and Calderban, A. R., (997a). Space-Tme Codes for Wreless Communcaton: Code Constructon, IEEE VTC. 4. Taroh, V., Seshadr, N., and Calderban, A. R., (997b). Space-Tme Codes for Hgh Data Rate Wreless Communcaton: Performance Crteron and Code Constructon, IEEE Transacton on Informaton Theory, Vol. 44, No., pp , March. 5. Jung C. C., Performance Of Space-Tme Coded Modulaton Over Freuency-Selectve Raylegh Fadng Channels, Research Report, Asan Insttute of Technology,
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