Transmit Diversity

MIMO Systems and Transmit Diversity 1 Introduction

So far we have investigated the use of antenna arrays in interference cancellation and for receive diversity. This final chapter takes a broad view of the use of antenna arrays in wireless communications. In particular, we will investigate the capacity of systems using multiple transmit and/or multiple receive antennas. This provides a fundamental limit on the data throughput in multipleinput multiple-output (MIMO) systems. We will also develop the use of transmit diversity, i.e., the use of multiple transmit antennas to achieve reliability (just as earlier we used multiple receive antennas to achieve reliability via receive diversity). The basis for receive diversity is that each element in the receive array receives an independent copy of the same signal. The probability that all signals are in deep fade simultaneously is then significantly reduced. In modelling a wireless communication system one can imagine that this capability would be very useful on transmit as well. This is especially true because, at least in the near term, the growth in wireless communications will be asymmetric internet traffic. A lot more data would be flowing from the base station to the mobile device that is, say, asking for a webpage, but is receiving all the multimedia in that webpage. Due to space considerations, it is more likely that the base station antenna comprises multiple elements while the mobile device has only one or two. In addition to providing diversity, intuitively having multiple transmit/receive antennas should allow us to transmit data faster, i.e., increase data throughput. The information theoretic analysis in this chapter will formalize this notion. We will also introduce a multiplexing scheme, transmitting multiple data streams to a single user with multiple transmit and receive antennas. This chapter is organized as follows. Section 2 then presents a theoretical analysis of the capacity of MIMO systems. The

References: [1] T. M. Cover and J. A. Thomas, Elements of Information Theory. John Wiley, 1991. [2] C. Schlegel, “Statistical communication theory.” Lecture Notes for ELEN 7950-4, University of Utah, Spring 2002. 36 [3] P. Viswanath, D. N. C. Tse, and R. Laroia, “Opportunistic beamforming using dumb antennas,” IEEE Transactions on Information Theory, vol. 48, pp. 1277–1294, June 2002. [4] D. Tse and P. Viswanath, “Fundamentals of wireless communication.” Lecture Notes for EE 290S, U.C. Berkeley, Fall 2002. [5] E. Telatar, “Capacity of multi-antenna gaussian channels,” European Transactions on Telecommunications, vol. 10, pp. 585–595, November 1999. [6] S. Haykin, Adaptive Filter Theory. Prentice Hall, 4th ed., 2002. [7] A. T. James, “Distributions of matrix variates and latent roots derived from normal samples,” Annals of Mathematical Statistics,, vol. 35, pp. 475–501, 1964. [8] G. J. Foschini and M. J. Gans, “On limits of wireless communications in a fading environment when using multiple antennas,” Wireless Personal Communications, vol. 6, pp. 311–335, 1998. [9] S. M. Alamouti, “A simple transmit diversity technique for wireless communications,” IEEE Journal on Select Areas in Communications, vol. 16, pp. 1451–1458, August 1998. [10] V. Tarokh, N. Seshadri, and A. R. Calderbank, “Spacetime codes for high data rate wireless communication: Performance criterion and code construction,” IEEE Transactions on Information Theory, vol. 44, pp. 744–765, March 1998. [11] V. Tarokh, H. Jafarkhani, and A. R. Calderbank, “Spacetime block codes from orthogonal designs,” IEEE Transactions on Information Theory, vol. 45, pp. 1456–1467, July 1999. [12] G. Ganesan and P. Stoica, “Spacetime block codes: A maximum snr approach,” IEEE Transactions on Information Theory, vol. 47, pp. 1650–1656, May 2001. [13] V. Tarokh, H. Jafarkhani, and A. R. Calderbank, “Spacetime block coding for wireless communications: performance results,” IEEE Journal on Select Areas in Communications, vol. 17, pp. 451–460, March 1999. [14] V. Tarokh, A. Naguib, N. Seshadri, and A. R. Calderbank, “Combined array processing and spacetime coding,” IEEE Transactions on Information Theory, vol. 45, pp. 1121–1128, May 1999. [15] G. D. Golden, G. J. Foschini, R. A. Valenzuela, and P. W. Wolniansky, “Simplified processing for high spectral efficiency wireless communication employing multi-element arrays,” Journal on Selected Areas in Communications, vol. 17, p. 18411852, November 1999. [16] B. Hassibi and B. M. Hochwald, “High-rate codes that are linear in space and time,” IEEE Transactions on Information Theory, vol. 48, pp. 1804–1824, July 2002. [17] L. Zheng and D. Tse, “Diversity and multiplexing: a fundamental tradeoff in multiple-antenna channels,” IEEE Transactions on Information Theory, vol. 49, pp. 1073–1096, May 2003. [18] H. Bolcskei, D. Gesbert, C. Papadias, and A. van der Veen, Space-Time Wireless Systems. Cambridge University Press, 2006. 37