in Fig. 2. More specifically, the E-step of the MAP-EM algorithm Moreover, without CSI, after 4-5 Turbo iterations, the turbo re- is exactly the same as the E-step of the Em algorithm; but the ceiver performs close to the approximated ml lower bound in all M-step of the MAP-EM algorithm includes an extra term P(X), three types of channels with a Doppler frequency as high as 200Hz which represents the a priori probability of x that is fed back by As a final remark, the EM-based iterative receiver techniques the outer- channel-code decoder from the previous Turbo iteration proposed in this paper are also applicable to other space-time cod (For the details of the MAP-EM algorithm, see [7)) ing(STC)systems, such as the STTC-OFDM system [5], but at an increased receiver complexity compared with that of the STBC V. SIMULATION RESULTS receivers developed here vide computer simulation results to illustrate REFERENCES the performance of our proposed iterative receivers for STBC OFDM systems, with or without outer channel coding. The char- [1 V. Tarokh, H Jafarkhani, and A R. Calderbank, "Space-time block codes from acteristics of the fading channels are described in Section Il; specif- rthogonal designs, " IEEE Trans. Inform. Theary, voL 45, Pp. 1456-1467, July ically, the receiver performance is simulated in three typical chan- [2] D. Agrawal, V Tarokh, A Naguib, and N Seshadri, "Space-time coded OFDM nel models with different delay profiles, namely the two ray and the typical urban(TU) model with 50Hz and 200Hz Doppler fre- quencies [12]. In the following simulations the available band- 3】]J The Turbo principle: Tutorial introduction and state of the art, width is 800 KHz and is divided into 128 subcarriers. These cor- rance, Sept 19g>al Symposium on Turbo Codes and Related Topics, Brest, respond to a subcarrier symbol rate of 5 KHz and OFDM word (41 [4] G Bauch,"Concatenation of space-time block codes and"Turbo-TCM, "in duration of 160us. In each OFDM word, a guard interval of 40p Proc. 1999 Internatiomal Conference on Communications. ICC99, Vancouver is inserted, hence the duration of one OFDM word T=200, For all simulations two transmitter antennas and two receiver an- [5]Y. Li, N. Seshadri, and S. Ariyavisitakul, "Channel estimation for OFDM sys- tennas are used; and the g1 StBC is adopted [13]. The modulator bile wireless channels, IEEEJ. sele Areas Commun, vol 17, pp 461-471, Mar. 1999 uses QPSK constellation V-A. Performance of eM-ML Receiver [71 G.J. McLachlan and T. Krishnan, The EM Algorithm and Extensions, John Wiley Sons, Inc, New York, NY, 1997 In an STBC-OFDM system without outer channel cod, 512 infor- [8] C N. Georghiades and J C Han, Sequence estimation in the presence of crs via the EM algorithm, IEEE Trans. CoNm mation bits are transmitted from 128 subcarriers during two(P 300-308,Mar.1997. 2)OFDM slots, therefore the information rate is 1.6 bits/sec/Hz. [9] C Cozzo and B. L. Hughes, "Joint detection and estimation in space-time cod- In Fig. 3-4, Mnen idea channel state information( CSI) is assumed ailable at the receiver side, the ml performance is shown in Computers, Sydney, Oct. 1999, Pp 613-617 Conference on Signals.Systems dashed lines, denoted by Ideal CSI. Without the CSl. the EM- [10]Y Li, C.N. Georghiades, and G. Huang,"EM-based sequence estimation for based ML receiver as derived in Section Ill is adopted; further- Theory, Sorrento, Italy, June 2000. psm::mPmt上:1m单hmam and the initialization of the EM algorithm [cf. Eq 8). From the figures, it is seen that the receiver performance is significantly [12] Y. Li and N.R. Sollenberger, Adaptive antenna arrays for OFDM systems ih cochannel interference, IEEE Trans. Commun., vol. 47, pp. 217- roved through the EM iterations. Furthermore, although the re ever is designed under the assumption that the channel remains 13]s.M. Alamouti“As static over one StBC code word ( whereas the actual channel varies cations,IEEE J. Select. Areas Commnz, vol. 16, pp. 1451-1458, O during one STBC code word), it can perform close to the ML per- [14] H V. Poor, An Introduction to Signal Detection and Estimation, formance with ideal CSi after two or three em iterations for al three types of channels with a Doppler frequency as high as 200Hz. V-B. Performance of MAP-EM-Turbo Receiver nE MPSK B⊥ tsModu1at ]回了 A 4-state, rate-1/2 convolutional code with generator(5,7)in octal notation is adopted as the outer channel code, as depicted in Fig. 2 The overall information rate for this system is 0. 8 bit/sec/Hz. Fig 5-6 show the performance of the Turbo receiver employing the EM STBCDecis⊥ons MAP-EM algorithm as derived in Section IV, for this concatenated Decc STBC-OFDM system. During each Turbo iteration, three EM iter- ations are carried out in the map-em stbc decoder. ldeal CSI denotes the approximated ML lower bound, which is obtained by performing the MAP STBC decoder with ideal CSI and iterating In⊥t⊥a1 sufficient number of Turbo iterations(six iterations in our simu- lations)between the MAP Stbc decoder and the map convolu- nal decoder. From the simulation results, it is seen that by em- Figure 1: Transmitter and receiver structure for an STBC-OFDM ploying an outer channel code, the receiver performance is signif- antly improved(at the expense of lowering spectral efficiency)in Fig. 2. More specifically, the E-step of the MAP-EM algorithm is exactly the same as the E-step of the EM algorithm; but the M-step of the MAP-EM algorithm includes an extra term ✝✶✆✜ ✠ , which represents the a priori probability of ✜ that is fed back by the outer-channel-code decoder from the previous Turbo iteration. (For the details of the MAP-EM algorithm, see [7].) V. SIMULATION RESULTS In this section, we provide computer simulation results to illustrate the performance of our proposed iterative receivers for STBC￾OFDM systems, with or without outer channel coding. The char￾acteristics of the fading channels are described in Section II; specif￾ically, the receiver performance is simulated in three typical chan￾nel models with different delay profiles, namely the two-ray and the typical urban (TU) model with 50Hz and 200Hz Doppler fre￾quencies [12]. In the following simulations the available band￾width is 800 KHz and is divided into ✱✓➆✫Ø subcarriers. These cor￾respond to a subcarrier symbol rate of 5 KHz and OFDM word duration of ✱✓Ù❆❈❝Ús. In each OFDM word, a guard interval of Û ❈✓Ús is inserted, hence the duration of one OFDM word ❼Ü✔Ý➆❆❈✓❈✓Ús. For all simulations, two transmitter antennas and two receiver an￾tennas are used; and the Þ✚ STBC is adopted [13]. The modulator uses QPSK constellation. V-A. Performance of EM-ML Receiver In an STBC-OFDM system without outer channel cod, ß ✱✓➆ infor￾mation bits are transmitted from ✱✓➆✓Ø subcarriers during two (✝ ✔ ➆ ) OFDM slots, therefore the information rate is 1.6 bits/sec/Hz. In Fig. 3–4, when ideal channel state information (CSI) is assumed available at the receiver side, the ML performance is shown in dashed lines, denoted by Ideal CSI. Without the CSI, the EM￾based ML receiver as derived in Section III is adopted; further￾more, as in [12], the 7-tap significant-tap-catching scheme is ap￾plied to simplify the implementation of the E-step [cf. Eq.(6)] and the initialization of the EM algorithm [cf. Eq.(8)]. From the figures, it is seen that the receiver performance is significantly im￾proved through the EM iterations. Furthermore, although the re￾ceiver is designed under the assumption that the channel remains static over one STBC code word (whereas the actual channel varies during one STBC code word), it can perform close to the ML per￾formance with ideal CSI after two or three EM iterations for all three types of channels with a Doppler frequency as high as 200Hz. V-B. Performance of MAP-EM-Turbo Receiver A 4-state, rate-1/2 convolutional code with generator (5,7) in octal notation is adopted as the outer channel code, as depicted in Fig. 2. The overall information rate for this system is 0.8 bit/sec/Hz. Fig. 5–6 show the performance of the Turbo receiver employing the MAP-EM algorithm as derived in Section IV, for this concatenated STBC-OFDM system. During each Turbo iteration, three EM iter￾ations are carried out in the MAP-EM STBC decoder. Ideal CSI denotes the approximated ML lower bound, which is obtained by performing the MAP STBC decoder with ideal CSI and iterating sufficient number of Turbo iterations (six iterations in our simu￾lations) between the MAP STBC decoder and the MAP convolu￾tional decoder. From the simulation results, it is seen that by em￾ploying an outer channel code, the receiver performance is signif￾icantly improved (at the expense of lowering spectral efficiency). Moreover, without CSI, after 4-5 Turbo iterations, the Turbo re￾ceiver performs close to the approximated ML lower bound in all three types of channels with a Doppler frequency as high as 200Hz. As a final remark, the EM-based iterative receiver techniques proposed in this paper are also applicable to other space-time cod￾ing (STC) systems, such as the STTC-OFDM system [5], but at an increased receiver complexity compared with that of the STBC receivers developed here. REFERENCES [1] V. Tarokh, H. Jafarkhani, and A. R. Calderbank, “Space-time block codes from orthogonal designs,” IEEE Trans. Inform. Theory, vol. 45, pp. 1456–1467, July 1999. [2] D. Agrawal, V. Tarokh, A. Naguib, and N. Seshadri, “Space-time coded OFDM for high data-rate wireless communication over wideband channels,” in IEEE Vehicular Technology Conference, 1998. VTC’98., May 1998. [3] J. Hagenauer, “The Turbo principle: Tutorial introduction and state of the art,” in Proc. International Symposium on Turbo Codes and Related Topics, Brest, France, Sept. 1997. [4] G. Bauch, “Concatenation of space-time block codes and ‘Turbo’-TCM,” in Proc. 1999 International Conference on Communications. ICC’99, Vancouver, June 1999. [5] Y. Li, N. Seshadri, and S. Ariyavisitakul, “Channel estimation for OFDM sys￾tems with transmitter diversity in mobile wireless channels,” IEEE J. Select. Areas Commun., vol. 17, pp. 461–471, Mar. 1999. [6] Y. Li, “Simplified channel estimation for OFDM systems with multiple transmit antennas,” submitted to IEEE J. Select. Areas Commun., Nov. 1999. [7] G. J. McLachlan and T. Krishnan, The EM Algorithm and Extensions, John Wiley & Sons, Inc, New York, NY, 1997. [8] C. N. Georghiades and J. C. Han, “Sequence estimation in the presence of random parameters via the EM algorithm,” IEEE Trans. Commun., vol. 45, pp. 300–308, Mar. 1997. [9] C. Cozzo and B. L. Hughes, “Joint detection and estimation in space-time cod- à ing and modulation,” in Thirty-Third Asilomar Conference on Signals, Systems Computers, Sydney, Oct. 1999, pp. 613–617. [10] Y. Li, C. N. Georghiades, and G. Huang, “EM-based sequence estimation for space-time coded systems,” in IEEE International Symposium on Information Theory, Sorrento, Italy, June 2000. [11] Y. Li, L. J. Cimini, and N. R. Sollenberger, “Robust channel estimation for OFDM systems with rapid dispersive fading channels,” IEEE Trans. Commun., vol. 46, pp. 902–915, July 1998. [12] Y. Li and N. R. Sollenberger, “Adaptive antenna arrays for OFDM systems with cochannel interference,” IEEE Trans. Commun., vol. 47, pp. 217–229, Feb. 1999. [13] S. M. Alamouti, “A simple transmit diversity technique for wireless communi￾cations,” IEEE J. Select. Areas Commun., vol. 16, pp. 1451–1458, Oct. 1998. [14] H. V. Poor, An Introduction to Signal Detection and Estimation, Springer￾Verlag, 2nd edition, 1994. IFFT . IFFT . . . . . . . . . . . Modulator MPSK STBC Bits Encoder Info. FFT FFT Decoder EM STBC EM Alg. Initial. X (0) Decisions Pilot (p=0) (p=0) o o Figure 1: Transmitter and receiver structure for an STBC-OFDM system