Sub-Modularity and Antenna Selection in MIMO Systems

In this paper, we show that the optimal receive antenna subset selection problem for maximizing the mutual information in a point-to-point MIMO system is sub-modular. Consequently, a greedy step-wise optimization approach, where at each step, an antenna that maximizes the incremental gain is added to the existing antenna subset, is guaranteed to be within a (1-1/e)-fraction of the global optimal value independent of all parameters. For a single-antenna-equipped source and destination with multiple relays, we show that the relay antenna selection problem to maximize the mutual information is modular and a greedy step-wise optimization approach leads to an optimal solution.

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

[2]  Mérouane Debbah,et al.  Massive MIMO: How many antennas do we need? , 2011, 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[3]  Aria Nosratinia,et al.  Antenna selection in MIMO systems , 2004, IEEE Communications Magazine.

[4]  R. Nabar,et al.  Near-optimal selection of transmit antennas for a MIMO channel based on Shannon capacity , 2000, Conference Record of the Thirty-Fourth Asilomar Conference on Signals, Systems and Computers (Cat. No.00CH37154).

[5]  Arogyaswami Paulraj,et al.  Receive antenna selection for MIMO flat-fading channels: theory and algorithms , 2003, IEEE Trans. Inf. Theory.

[6]  Vijay V. Vazirani,et al.  Approximation Algorithms , 2001, Springer Berlin Heidelberg.

[7]  Raviraj S. Adve,et al.  Improving amplify-and-forward relay networks: optimal power allocation versus selection , 2006, IEEE Transactions on Wireless Communications.

[8]  A.F. Molisch,et al.  MIMO systems with antenna selection , 2004, IEEE Microwave Magazine.

[9]  Robert W. Heath,et al.  Antenna selection for spatial multiplexing systems with linear receivers , 2001, IEEE Communications Letters.

[10]  Huaiyu Dai,et al.  On the Diversity Order of Spatial Multiplexing Systems With Transmit Antenna Selection: A Geometrical Approach , 2006, IEEE Transactions on Information Theory.

[11]  Chiao-En Chen.  A computationally efficient near-optimal algorithm for capacity-maximization based joint transmit and receive antenna selection , 2010, IEEE Communications Letters.

[12]  R. Rado.  Note on Independence Functions , 1957 .

[13]  Mohammad Gharavi-Alkhansari,et al.  Fast antenna subset selection in MIMO systems , 2004, IEEE Transactions on Signal Processing.

[14]  Jack Edmonds,et al.  Matroids and the greedy algorithm , 1971, Math. Program..

[15]  Aria Nosratinia,et al.  Spectrally-efficient relay selection with limited feedback , 2008, IEEE Journal on Selected Areas in Communications.

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

[17]  Aggelos Bletsas,et al.  A simple Cooperative diversity method based on network path selection , 2005, IEEE Journal on Selected Areas in Communications.

[18]  Lizhong Zheng,et al.  Diversity and multiplexing: a fundamental tradeoff in multiple-antenna channels , 2003, IEEE Trans. Inf. Theory.

[19]  Thomas L. Marzetta,et al.  Noncooperative Cellular Wireless with Unlimited Numbers of Base Station Antennas , 2010, IEEE Transactions on Wireless Communications.

[20]  Robert W. Heath,et al.  Relay Subset Selection in Wireless Networks Using Partial Decode-and-Forward Transmission , 2007, VTC Spring 2008 - IEEE Vehicular Technology Conference.

[21]  Yindi Jing,et al.  Single and multiple relay selection schemes and their achievable diversity orders , 2009, IEEE Transactions on Wireless Communications.

[22]  K. J. Ray Liu,et al.  Cooperative communications with relay-selection: when to cooperate and whom to cooperate with? , 2008, IEEE Transactions on Wireless Communications.

[23]  Robert W. Heath,et al.  Maximizing reliability in multi-hop wireless networks , 2008, 2008 IEEE International Symposium on Information Theory.

[24]  Robert W. Heath,et al.  Nonregenerative MIMO Relaying With Optimal Transmit Antenna Selection , 2008, IEEE Signal Processing Letters.

[25]  D. Gale.  Optimal assignments in an ordered set: An application of matroid theory , 1968 .

[26]  M. L. Fisher,et al.  An analysis of approximations for maximizing submodular set functions—I , 1978, Math. Program..

[27]  Il-Min Kim,et al.  Joint Optimization of Relay-Precoders and Decoders with Partial Channel Side Information in Cooperative Networks , 2006, MILCOM 2006 - 2006 IEEE Military Communications conference.