Introducing Space into MIMO Capacity Calculations

The large spectral efficiencies promised for multiple-input multiple-output (MIMO) wireless fading channels are derived under certain conditions which do not fully take into account the spatial aspects of the channel. Spatial correlation, due to limited angular spread or insufficient antenna spacing, significantly reduces the performance of MIMO systems. In this paper we explore the effects of spatially selective channels on the capacity of MIMO systems via a new capacity expression which is more general and realistic than previous expressions. By including spatial information we derive a closed-form expression for ergodic capacity which uses the physics of signal propagation combined with the statistics of the scattering environment. This expression gives the capacity of a MIMO system in terms of antenna placement and scattering environment and leads to valuable insights into the factors determining capacity for a wide range of scattering models.

[1]  J. Sadowsky,et al.  On the correlation and scattering functions of the WSSUS channel for mobile communications , 1998 .

[2]  W.C.-Y. Lee Effects on Correlation Between Two Mobile Radio Base-Station Antennas , 1973, IEEE Trans. Commun..

[3]  D. Goeckel On the Capacity of Fixed Length Linear Antenna Arrays Under Bandlimited Correlated Fading , 2002 .

[4]  Chen-Nee Chuah,et al.  Capacity of multi-antenna array systems in indoor wireless environment , 1998, IEEE GLOBECOM 1998 (Cat. NO. 98CH36250).

[5]  Peter F. Driessen,et al.  On the capacity formula for multiple input-multiple output wireless channels: a geometric interpretation , 1999, 1999 IEEE International Conference on Communications (Cat. No. 99CH36311).

[6]  M. Omizo,et al.  Modeling , 1983, Encyclopedic Dictionary of Archaeology.

[7]  A. J. Levy,et al.  Theory and measurement of the angle of arrival and time delay of UHF radiowaves using a ring array , 1997 .

[8]  J. Davenport Editor , 1960 .

[9]  Ammar B. Kouki,et al.  New compound upper bound on MIMO channel capacity , 2002, IEEE Communications Letters.

[10]  Preben E. Mogensen,et al.  A stochastic MIMO radio channel model with experimental validation , 2002, IEEE J. Sel. Areas Commun..

[11]  R. G. Vaughan Pattern translation and rotation in uncorrelated source distributions for multiple beam antenna design , 1998 .

[12]  M. Kalkan,et al.  Prediction of the space-frequency correlation function for base station diversity reception , 1997 .

[13]  W. R. Braun,et al.  A physical mobile radio channel model , 1991 .

[14]  T. Lo,et al.  Angles of arrival of indoor multipath , 1992 .

[15]  R.A. Kennedy,et al.  Spatial correlation for general distributions of scatterers , 2002, IEEE Signal Processing Letters.

[16]  Rodney A. Kennedy,et al.  Antenna saturation effects on dense array MIMO capacity , 2003, 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)..

[17]  J. H. Winters,et al.  Effect of fading correlation on adaptive arrays in digital mobile radio , 1994 .

[18]  Ali Abdi,et al.  A space-time correlation model for multielement antenna systems in mobile fading channels , 2002, IEEE J. Sel. Areas Commun..

[19]  J. Powell Mathematical Methods in Physics , 1965 .

[20]  Ananda Sanagavarapu Mohan,et al.  Angles-of-arrival of multipath signals in indoor environments , 1996, Proceedings of Vehicular Technology Conference - VTC.

[21]  Ali Abdi,et al.  A parametric model for the distribution of the angle of arrival and the associated correlation function and power spectrum at the mobile station , 2002, IEEE Trans. Veh. Technol..

[22]  Matthias Patzold,et al.  Modeling, analysis, and simulation of nonfrequency-selective mobile radio channels with asymmetrical Doppler power spectral density shapes , 1997 .

[23]  M. J. Gans,et al.  On Limits of Wireless Communications in a Fading Environment when Using Multiple Antennas , 1998, Wirel. Pers. Commun..

[24]  Chen-Nee Chuah,et al.  Capacity scaling in MIMO Wireless systems under correlated fading , 2002, IEEE Trans. Inf. Theory.

[25]  Helmut Bölcskei,et al.  MIMO wireless channels: capacity and performance prediction , 2000, Globecom '00 - IEEE. Global Telecommunications Conference. Conference Record (Cat. No.00CH37137).

[26]  R. Valenzuela,et al.  Capacities of multi-element transmit and receive antennas: Correlations and keyholes , 2000 .

[27]  Michael A. Jensen,et al.  A statistical model for angle of arrival in indoor multipath propagation , 1997, 1997 IEEE 47th Vehicular Technology Conference. Technology in Motion.

[28]  R. K. Cook,et al.  Measurement of Correlation Coefficients in Reverberant Sound Fields , 1955 .

[29]  E. Bonek,et al.  High-resolution 3-D direction-of-arrival determination for urban mobile radio , 1997 .

[30]  Anirvan M. Sengupta,et al.  Capacity of multivariate channels with multiplicative noise: I.Random matrix techniques and large-N expansions for full transfer matrices , 2000, physics/0010081.

[31]  W. Lee,et al.  Finding the approximate angular probability density function of wave arrival by using a directional antenna , 1973 .

[32]  Angel E. Lozano,et al.  Effect of antenna separation on the capacity of BLAST in correlated channels , 2000, IEEE Communications Letters.

[33]  Rodney A. Kennedy,et al.  Spatial decomposition of MIMO wireless channels , 2003, Seventh International Symposium on Signal Processing and Its Applications, 2003. Proceedings..

[34]  Rodney A. Kennedy,et al.  On dimensionality of multipath fields: Spatial extent and richness , 2002, 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[35]  David Gesbert,et al.  From theory to practice: an overview of MIMO space-time coded wireless systems , 2003, IEEE J. Sel. Areas Commun..

[36]  Klaus I. Pedersen,et al.  Power azimuth spectrum in outdoor environments , 1997 .

[37]  Emre Telatar,et al.  Capacity of Multi-antenna Gaussian Channels , 1999, Eur. Trans. Telecommun..

[38]  H. Wyld,et al.  Mathematical Methods for Physics , 1976 .

[39]  Helmut Bölcskei,et al.  Outdoor MIMO wireless channels: models and performance prediction , 2002, IEEE Trans. Commun..

[40]  Matthias Patzold,et al.  A study of a land mobile satellite channel model with asymmetrical Doppler power spectrum and lognormally distributed line-of-sight component , 1998 .

[41]  Joseph M. Kahn,et al.  Fading correlation and its effect on the capacity of multielement antenna systems , 2000, IEEE Trans. Commun..

[42]  R. Kress,et al.  Inverse Acoustic and Electromagnetic Scattering Theory , 1992 .

[43]  Kanti V. Mardia,et al.  Statistics of Directional Data , 1972 .

[44]  David Gesbert,et al.  Capacity limits of dense palm-sized MIMO arrays , 2002, Global Telecommunications Conference, 2002. GLOBECOM '02. IEEE.

[45]  Alexei Gorokhov Transmit diversity versus SDMA: analytic and numerical comparisons , 2000, 2000 IEEE International Conference on Communications. ICC 2000. Global Convergence Through Communications. Conference Record.

[46]  K. Pedersen,et al.  A stochastic multiple-input-multiple-output radio channel model for evaluation of space-time coding algorithms , 2000, Vehicular Technology Conference Fall 2000. IEEE VTS Fall VTC2000. 52nd Vehicular Technology Conference (Cat. No.00CH37152).

[47]  W. C. Jakes,et al.  Microwave Mobile Communications , 1974 .

[48]  R. Michael Buehrer,et al.  Spatial fading correlation function of circular antenna arrays with Laplacian energy distribution , 2002, IEEE Communications Letters.