Minimum Redundancy MIMO Array Synthesis by means of Cyclic Difference Sets

Antenna array synthesis is an important issue in MIMO radars. By judiciously designing antenna positions, one can create a very long virtual array steering vector with a small number of antennas and therefore achieve very high spatial resolution at a small cost. This paper presents a combinatorial methodology based on cyclic difference sets (CDSs) for minimum redundancy (MR) MIMO array synthesis which seeks to maximize the virtual array aperture for a given number of antennas. First, the key features of CDSs and the CDS-based MR-MIMO layouts are described. Then, the analytical expression of the maximum contiguous virtual array aperture is derived. Further, based on this expression, an enumerative shifting procedure is developed for identifying the optimal CDS-based MR-MIMO layout. Selected examples are analyzed to point out the computational effectiveness of the CDS-based MR-MIMO array synthesis.

[1]  Wen-Qin Wang,et al.  MIMO Antenna Array Design with Polynomial Factorization , 2013 .

[2]  L. E. Kopilovich,et al.  Square Array Antennas Based on Hadamard Difference Sets , 2008, IEEE Transactions on Antennas and Propagation.

[3]  A. F. Jacob,et al.  Particle swarm optimization of minimum-redundancy MIMO arrays , 2011, 2011 German Microwave Conference.

[4]  Butrus T. Khuri-Yakub,et al.  Minimally Redundant 2-D Array Designs for 3-D Medical Ultrasound Imaging , 2009, IEEE Transactions on Medical Imaging.

[5]  Andrea Massa,et al.  Rectangular Thinned Arrays Based on McFarland Difference Sets , 2011, IEEE Transactions on Antennas and Propagation.

[6]  Rick S. Blum,et al.  Performance of MIMO radar systems: advantages of angular diversity , 2004, Conference Record of the Thirty-Eighth Asilomar Conference on Signals, Systems and Computers, 2004..

[7]  L. D. Baumert.  Cyclic Difference Sets , 1971 .

[8]  Andrea Massa,et al.  Genetic algorithm (GA)-enhanced almost difference set (ADS)-based approach for array thinning , 2011 .

[9]  P. P. Vaidyanathan,et al.  Minimum redundancy MIMO radars , 2008, 2008 IEEE International Symposium on Circuits and Systems.

[10]  A. Massa,et al.  Linear Array Thinning Exploiting Almost Difference Sets , 2009, IEEE Transactions on Antennas and Propagation.

[11]  P. P. Vaidyanathan,et al.  Nested Arrays: A Novel Approach to Array Processing With Enhanced Degrees of Freedom , 2010, IEEE Transactions on Signal Processing.

[12]  A. Moffet.  Minimum-redundancy linear arrays , 1968 .

[13]  I. S. Gál.  On the Representation of 1, 2, . . . , N by Differences , 2004 .

[14]  A Massa,et al.  Hybrid ADS-Based Techniques for Radio Astronomy Array Design , 2011, IEEE Transactions on Antennas and Propagation.

[15]  A. Massa,et al.  On the Robustness to Element Failures of Linear ADS-Thinned Arrays , 2011, IEEE Transactions on Antennas and Propagation.

[16]  Wei Guo,et al.  A Combinatorial Method for Antenna Array Design in Minimum Redundancy MIMO Radars , 2009, IEEE Antennas and Wireless Propagation Letters.

[17]  Qingxia Li,et al.  A Method for Seeking Low-Redundancy Large Linear Arrays in Aperture Synthesis Microwave Radiometers , 2010, IEEE Transactions on Antennas and Propagation.

[18]  A. Massa,et al.  ADS-Based Guidelines for Thinned Planar Arrays , 2010, IEEE Transactions on Antennas and Propagation.

[19]  Guisheng Liao,et al.  Performance Analysis of Beamforming for MIMO Radar , 2008 .

[20]  D. Leeper,et al.  Isophoric arrays-massively thinned phased arrays with well-controlled sidelobes , 1999 .

[21]  A. Massa,et al.  Synthesis of Nonuniform MIMO Arrays Through Combinatorial Sets , 2012, IEEE Antennas and Wireless Propagation Letters.

[22]  A. Massa,et al.  Peak sidelobe level reduction with a hybrid approach based on GAs and difference sets , 2004, IEEE Transactions on Antennas and Propagation.

[23]  Y. Bar-Ness,et al.  A new approach to array geometry for improved spatial spectrum estimation , 1985, Proceedings of the IEEE.

[24]  P. P. Vaidyanathan,et al.  MIMO Radar Space–Time Adaptive Processing Using Prolate Spheroidal Wave Functions , 2008, IEEE Transactions on Signal Processing.

[25]  Wen-Qin Wang,et al.  Virtual Antenna Array Analysis for MIMO Synthetic Aperture Radars , 2012 .

[26]  D.W. Bliss,et al.  Multiple-input multiple-output (MIMO) radar: performance issues , 2004, Conference Record of the Thirty-Eighth Asilomar Conference on Signals, Systems and Computers, 2004..

[27]  Ioannis G. Tollis,et al.  Difference bases and sparse sensor arrays , 1993, IEEE Trans. Inf. Theory.

[28]  Andrea Massa,et al.  Fully interleaved linear arrays with predictable sidelobes based on almost difference sets , 2010 .

[29]  Alexander M. Haimovich,et al.  Spatial Diversity in Radars—Models and Detection Performance , 2006, IEEE Transactions on Signal Processing.

[30]  Daniel W. Bliss,et al.  Multiple-input multiple-output (MIMO) radar and imaging: degrees of freedom and resolution , 2003, The Thrity-Seventh Asilomar Conference on Signals, Systems & Computers, 2003.