MIMO Channel Capacity p y of Static Channels

Zhe Chen Department of Electrical and Computer Engineering Tennessee Technological University Cookeville, TN38505 D December b 2008

Contents „ „ „ „

Introduction Parallel Decomposition of the MIMO Channel MIMO Channel Capacity – Static Channels Summary

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Introduction to MIMO „

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MIMO (Multiple Input Multiple Output) transmits two or more data streams in the same channel at the same time time, using multi-antennas at transmitter and receiver. Main features „ „

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Can achieve high throughput without consuming extra radio frequency Can achieve high link reliability of wireless communication

Main technical fields of MIMO „ „ „

Radio wave propagation Coding and information theory Signal g processing p g

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Narrowband MIMO Model „

y = Hx + n

„ „ „ „

x represents the Mt-dimensional transmitted symbol n is the Mr-dimensional noise vector H is the Mr * Mt matrix of channel gains y represents the Mr-dimensional received symbol

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Parallel Decomposition of the MIMO Channel (1 „

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Decompose a MIMO channel into a number of parallel independent channels Singular value decomposition (SVD) of H is „ „ „

is the rank of H, U: matrix, V: matrix is an diagonal matrix of singular values

of H.

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„

,

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Parallel Decomposition of the MIMO Channel (2 „

Transmit precoding & receiver shaping

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Parallel decomposition of the MIMO channel

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MIMO Channel Capacity – Static Channels (1) „

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Channel capacity is defined as:

If y and x are zero-mean circularly-symmetric y y complex p Gaussian random vectors, then

So the MIMO channel capacity is:

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The optimization relative to Rx will depend on whether or not H is known at the transmitter.

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MIMO Channel Capacity – Static Channels (2) If channel is known at transmitter (with CSIT and CSIR) „ By substituting the SVD of channel into the MIMO channel capacity formula, we get the MIMO capacity with CSIT and CSIR:

is the SNR associated with the i th channel at full power. power „

Solving the optimization leads to a water-filling power allocation for the MIMO channel: for some cutoff value

„

.

The resulting capacity is then: 8

MIMO Channel Capacity – Static Channels (3) If channel is unknown at transmitter „ If the distribution of H follows the zero zero-mean mean spatially white channel gain model, the best strategy is to allocate equal power to each transmit antenna. The mutual information of the channel h l can be b expressed d as:

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The appropriate capacity definition is capacity with outage: (the probability that the transmitted data will not be received correctly) tl )

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Summary „

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Parallel decomposition of the MIMO channel and MIMO channel capacity of static channels are introduced introduced. MIMO channels can provide very high data rates without requiring increased signal power or bandwidth. MIMO systems offer a promising solution for future generation wireless networks.

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References [1] A. Goldsmith, Wireless Communications, Cambridge, England: Cambridge University Press, 2005. [2] D. W. Bliss, K. W. Forsythe and A. M. Chan, “MIMO Wireless Communication,” Lincoln Laboratory Journal, vol.15, no.1, pp.97-125, 2005. [3] D. Tse and P. Viswanath, Fundamentals of Wireless Communication, Cambridge, England: l d Cambridge b d University Press, 2005. [4] T. M. Cover and J. A. Thomas, Elements of Information Theory, New York: Wiley, 1991. [5] S. S Salous, S l “M lti l input “Multiple i t multiple lti l output t t systems t : capacity it and d channel h l measurements,” SCI2003, Florida, July 2003. [6] S. Vergerio, J. Rossi and P. Sabouroux, “MIMO Capacity Estimation at 2 GHz with a Ray Model in Urban Cellular Environment, Environment ” Radio Engineering, vol.17, vol 17 no.2, pp.37-41, June 2008. [7] S. Min, An Introduction to MIMO Technology, Ohtsuki Lab, 2007. http://www.sasase.ics.keio.ac.jp/jugyo/2007/MIMO.pdf p // jp/j gy / / p [8] S. Kethulle, An Overview of MIMO Systems in Wireless Communications, NTUT, 2004. http://www.iet.ntnu.no/projects/beats/documents/mimo.pdf 11

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