Downlink Beamforming with Transmit-Side Channel Correlation: A Large System Analysis

In this paper, we consider a large system analysis of regularized channel inversion (RCI) beamforming for MISO broadcast channels (BC) with transmit-side channel correlation. In the analysis, we assume that both the number of users and transmit antennas grow unbounded with a constant ratio. We also assume that the channel correlation model is separable. Under this channel condition, we are particularly interested to find the optimal regularization parameter of RCI that maximizes the signal to interference plus noise ratio (SINR). First, we derive the large system limit of the SINR of each user by applying some results on large random matrices. Then, we determine the cor- responding optimal regularization parameter and show that this optimal regularization parameter is not affected by the transmit correlation. We verify this result through simulations where the channel has the exponential transmit-correlation model.

[1]  J. W. Silverstein,et al.  On the empirical distribution of eigenvalues of a class of large dimensional random matrices , 1995 .

[2]  Shlomo Shamai,et al.  The Capacity Region of the Gaussian Multiple-Input Multiple-Output Broadcast Channel , 2006, IEEE Transactions on Information Theory.

[3]  Martin Haardt,et al.  An introduction to the multi-user MIMO downlink , 2004, IEEE Communications Magazine.

[4]  R. Couillet,et al.  Large System Analysis of Linear Precoding in MISO Broadcast Channels with Limited Feedback , 2009 .

[5]  Robert W. Heath,et al.  Shifting the MIMO Paradigm , 2007, IEEE Signal Processing Magazine.

[6]  Arnold Neumaier,et al.  Solving Ill-Conditioned and Singular Linear Systems: A Tutorial on Regularization , 1998, SIAM Rev..

[7]  Andrea J. Goldsmith,et al.  Capacity limits of MIMO channels , 2003, IEEE J. Sel. Areas Commun..

[8]  Antonia Maria Tulino,et al.  Random Matrix Theory and Wireless Communications , 2004, Found. Trends Commun. Inf. Theory.

[9]  Björn E. Ottersten,et al.  Asymptotic eigenvalue distributions and capacity for MIMO channels under correlated fading , 2004, IEEE Transactions on Wireless Communications.

[10]  Gene H. Golub,et al.  Tikhonov Regularization and Total Least Squares , 1999, SIAM J. Matrix Anal. Appl..

[11]  Stephan ten Brink,et al.  A close-to-capacity dirty paper coding scheme , 2004, ISIT.

[12]  Martin Haardt,et al.  Zero-forcing methods for downlink spatial multiplexing in multiuser MIMO channels , 2004, IEEE Transactions on Signal Processing.

[13]  Jamie S. Evans,et al.  Large system performance of linear multiuser receivers in multipath fading channels , 2000, IEEE Trans. Inf. Theory.

[14]  Tareq Y. Al-Naffouri,et al.  How much does transmit correlation affect the sum-rate scaling of MIMO gaussian broadcast channels? , 2009, IEEE Transactions on Communications.

[15]  Mérouane Debbah,et al.  Asymptotic Analysis of Correlated Multi-Antenna Broadcast Channels , 2009, 2009 IEEE Wireless Communications and Networking Conference.

[16]  Mérouane Debbah,et al.  Large System Analysis of Linear Precoding in Correlated MISO Broadcast Channels Under Limited Feedback , 2009, IEEE Transactions on Information Theory.

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

[18]  Robert M. Gray,et al.  Toeplitz and Circulant Matrices: A Review , 2005, Found. Trends Commun. Inf. Theory.

[19]  Robert M. Gray,et al.  Toeplitz And Circulant Matrices: A Review (Foundations and Trends(R) in Communications and Information Theory) , 2006 .

[20]  Jamie S. Evans,et al.  Multiuser Transmit Beamforming via Regularized Channel Inversion: A Large System Analysis , 2008, IEEE GLOBECOM 2008 - 2008 IEEE Global Telecommunications Conference.

[21]  David Tse,et al.  Linear Multiuser Receivers: Effective Interference, Effective Bandwidth and User Capacity , 1999, IEEE Trans. Inf. Theory.

[22]  Robert Tibshirani,et al.  The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd Edition , 2001, Springer Series in Statistics.

[23]  Antonia Maria Tulino,et al.  Impact of antenna correlation on the capacity of multiantenna channels , 2005, IEEE Transactions on Information Theory.

[24]  Ying-Chang Liang,et al.  Asymptotic Performance of MMSE Receivers for Large Systems Using Random Matrix Theory , 2007, IEEE Transactions on Information Theory.

[25]  J. W. Silverstein,et al.  No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices , 1998 .

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

[27]  A. Lee Swindlehurst,et al.  A vector-perturbation technique for near-capacity multiantenna multiuser communication-part I: channel inversion and regularization , 2005, IEEE Transactions on Communications.