Capacity Bounds for MIMO Nakagami- $m$ Fading Channels

This paper studies the ergodic capacity limits of multiple-input multiple-output (MIMO) antenna systems with arbitrary finite number of antennas operating on general fading environments. Through the use of majorization theory, we first investigate in detail the ergodic capacity of Nakagami-m fading channels, for which we derive several ergodic capacity upper and lower bounds. We then show that a simple expression for the capacity upper bound is possible for high signal-to-noise ratio (SNR), which permits to analyze the impact of the channel fading parameter m on the ergodic capacity. The asymptotic behavior of the capacity in the large-system limit in which the number of antennas at one or both side(s) goes to infinity, is also addressed. Results demonstrate that the capacity scaling laws for Nakagami-m and Rayleigh-fading MIMO channels are identical. Finally, we employ the same technique to distributed MIMO (D-MIMO) systems undergoing composite log-normal and Nakagami fading, where we derive similar ergodic capacity upper and lower bounds. Monte Carlo simulation results are provided to verify the tightness of the proposed bounds.

[1]  Mohamed-Slim Alouini,et al.  Capacity of MIMO Rician channels , 2006, IEEE Transactions on Wireless Communications.

[2]  Matthew R. McKay,et al.  General capacity bounds for spatially correlated Rician MIMO channels , 2005, IEEE Transactions on Information Theory.

[3]  Joachim Hagenauer,et al.  Iterative decoding of binary block and convolutional codes , 1996, IEEE Trans. Inf. Theory.

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

[5]  Xiaohu You,et al.  On the Ergodic Capacity of Rank-$1$ Ricean-Fading MIMO Channels , 2007, IEEE Transactions on Information Theory.

[6]  Arogyaswami Paulraj,et al.  Outage performance of the distributed antenna systems in a composite fading channel , 2002, Proceedings IEEE 56th Vehicular Technology Conference.

[7]  Adel A. M. Saleh,et al.  Distributed Antennas for Indoor Radio Communications , 1987, IEEE Trans. Commun..

[8]  M. Nakagami.  The m-Distribution—A General Formula of Intensity Distribution of Rapid Fading , 1960 .

[9]  John M. Cioffi,et al.  On the MIMO Channel Capacity for the Nakagami-$m$ Channel , 2007, IEEE Transactions on Information Theory.

[10]  J.E. Mazo,et al.  Digital communications , 1985, Proceedings of the IEEE.

[11]  Pravin Varaiya,et al.  Capacity of fading channels with channel side information , 1997, IEEE Trans. Inf. Theory.

[12]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[13]  Zhenming Feng,et al.  Generic procedure for tightly bounding the capacity of MIMO correlated Rician fading channels , 2005, IEEE Transactions on Communications.

[14]  Some majorization inequalities for functions of exchangeable random variables , 1990 .

[15]  Helmut Bölcskei,et al.  Characterizing the statistical properties of mutual information in MIMO channels: insights into diversity-multiplexing tradeoff , 2002, Conference Record of the Thirty-Sixth Asilomar Conference on Signals, Systems and Computers, 2002..

[16]  Mohamed-Slim Alouini,et al.  Capacity of correlated MIMO Rayleigh channels , 2006, IEEE Transactions on Wireless Communications.

[17]  D. Owen.  Handbook of Mathematical Functions with Formulas , 1965 .

[18]  Hyundong Shin,et al.  On the capacity of doubly correlated MIMO channels , 2005, IEEE Transactions on Wireless Communications.

[19]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[20]  H. Vincent Poor,et al.  On the capacity of multiple-antenna systems in Rician fading , 2005, IEEE Transactions on Wireless Communications.

[21]  Alex J. Grant,et al.  Rayleigh Fading Multi-Antenna Channels , 2002, EURASIP J. Adv. Signal Process..

[22]  Hyundong Shin,et al.  Capacity of multiple-antenna fading channels: spatial fading correlation, double scattering, and keyhole , 2003, IEEE Trans. Inf. Theory.

[23]  M. J. Gans,et al.  Fiber optic microcellular radio , 1991, [1991 Proceedings] 41st IEEE Vehicular Technology Conference.

[24]  Brian L. Hughes,et al.  The asymptotic capacity of multiple-antenna Rayleigh-fading channels , 2005, IEEE Transactions on Information Theory.

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

[26]  Jack H. Winters,et al.  On the Capacity of Radio Communication Systems with Diversity in a Rayleigh Fading Environment , 1987, IEEE J. Sel. Areas Commun..

[27]  仲上 稔,et al.  The m-Distribution As the General Formula of Intensity Distribution of Rapid Fading , 1957 .

[28]  Hyundong Shin,et al.  Asymptotic statistics of mutual information for doubly correlated MIMO channels , 2008, IEEE Transactions on Wireless Communications.

[29]  Joseph Lipka,et al.  A Table of Integrals , 2010 .

[30]  Xavier Mestre,et al.  Capacity of MIMO channels: asymptotic evaluation under correlated fading , 2003, IEEE J. Sel. Areas Commun..

[31]  John M. Cioffi,et al.  On the MIMO Channel Capacity for the Nakagami-m Channel , 2008, IEEE Trans. Inf. Theory.

[32]  Feng Zheng,et al.  On the Channel Capacity of Multiantenna Systems with Nakagami Fading , 2006, EURASIP J. Adv. Signal Process..

[33]  Moe Z. Win,et al.  On the capacity of spatially correlated MIMO Rayleigh-fading channels , 2003, IEEE Trans. Inf. Theory.

[34]  R C Robertson,et al.  Digital Communications Over Fading Channels , 2004 .

[35]  Matthias Pätzold,et al.  On the Statistical Properties of the Capacity of Spatially Correlated Nakagami-M MIMO Channels , 2008, VTC Spring 2008 - IEEE Vehicular Technology Conference.

[36]  M. Abramowitz,et al.  Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55) , 1965 .

[37]  Yi Jiang,et al.  MIMO Transceiver Design via Majorization Theory , 2007, Found. Trends Commun. Inf. Theory.

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

[39]  A. Glavieux,et al.  Near Shannon limit error-correcting coding and decoding: Turbo-codes. 1 , 1993, Proceedings of ICC '93 - IEEE International Conference on Communications.

[40]  M. Evans.  Statistical Distributions , 2000 .

[41]  Keith Q. T. Zhang,et al.  Very tight capacity bounds for MIMO-correlated Rayleigh-fading channels , 2005, IEEE Transactions on Wireless Communications.

[42]  I. Olkin,et al.  Inequalities: Theory of Majorization and Its Applications , 1980 .

[43]  N. K. Shankaranarayanan,et al.  Performance of simulcast wireless techniques for personal communication systems , 1996, IEEE J. Sel. Areas Commun..

[44]  Hirofumi Suzwi,et al.  A Statistical Model for Urban Radio Propagation , 1977 .

[45]  H. Suzuki,et al.  A Statistical Model for Urban Radio Propogation , 1977, IEEE Trans. Commun..

[46]  Andrea Giorgetti,et al.  Level crossing rates and MIMO capacity fades: impacts of spatial/temporal channel correlation , 2003, IEEE International Conference on Communications, 2003. ICC '03..

[47]  Sergios Theodoridis,et al.  A Novel Efficient Cluster-Based MLSE Equalizer for Satellite Communication Channels with-QAM Signaling , 2006, EURASIP J. Adv. Signal Process..

[48]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[49]  Holger Boche,et al.  Majorization and Matrix-Monotone Functions in Wireless Communications , 2007, Found. Trends Commun. Inf. Theory.

[50]  Andrea Giorgetti,et al.  MIMO capacity, level crossing rates and fades: The impact of spatial/temporal channel correlation , 2003, Journal of Communications and Networks.

[51]  Huaiyu Dai,et al.  Some Analysis in Distributed MIMO Systems , 2007, J. Commun..

[52]  Robert W. Heath,et al.  Ergodic Capacity of Spatial Multiplexing MIMO Systems with ZF Receivers for Log-Normal Shadowing and Rayleigh Fading Channels , 2007, 2007 IEEE 18th International Symposium on Personal, Indoor and Mobile Radio Communications.