JOINT TRANSMIT ARRAY INTERPOLATION AND TRANSMIT BEAMFORMING FOR SOURCE LOCALIZATION IN MIMO RADAR WITH ARBITRARY ARRAYS Aboulnasr Hassanien * , Sergiy A. Vorobyov *† * Dept. of ECE, University of Alberta Edmonton, AB, T6G 2V4, Canada † Dept. of Signal Processing and Acoustics Aalto University, Finland {hassanie,svorobyo}@ualberta.ca Joon-Young Park Samsung Thales Co., Ltd. Core Technology Group Chang-Li 304, Namsa-Myun, Cheoin-Gu Yongin-City, Gyeonggi-D, Korea 449-885 jy97.park@samsung.com ABSTRACT We consider a MIMO radar with arbitrary multi-dimensional array, and propose a method for transmit array interpolation that maps an arbitrary transmit array into an array with a cer- tain desired structure. A properly designed interpolation ma- trix is used to jointly achieve transmit array interpolation and design transmit beamforming. The transmit array interpola- tion problem is cast as a convex optimization problem based on minmax criterion. Our designs enable to control the side- lobe levels of the transmit beampattern and enforce different transmit beams to have rotational invariance with respect to each other, a property that enables the use of computation- ally efficient direction finding techniques. It is shown that the rotational invariance can be achieved independently in both the elevation and the azimuth spatial domains, allowing for independent elevation and azimuth direction finding. Index Terms— Arbitrary arrays, array interpolation, di- rection finding, MIMO radar, rotational invariance property. 1. INTRODUCTION Multiple-input multiple-output (MIMO) radar has been re- cently the focus of intensive research [1]–[6]. It has been shown that MIMO radar with collocated transmit antennas suffers from the loss of coherent transmit processing gain as a result of omnidirectional transmission of orthogonal wave- forms [6]. The concepts of phased-MIMO radar and transmit energy focussing have been developed to address the latter problem [6], [7]. Other transmit beamforming approaches have been also developed [8]–[13], but all of them address the case of one dimensional (1D) transmit array. Despite the great practical interest in two dimensional (2D) transmit ar- rays [14], the fact that the performance of MIMO radar with less number of waveforms than the number of transmit anten- nas and with transmit processing gain is better than the perfor- mance of MIMO radar with full waveform diversity and with no transmit beamforming gain [7] becomes more evident in the case when the transmit array contains a large number of antennas, e.g., 2D transmit arrays. In this paper, we consider a MIMO radar with arbitrary multi-dimensional arrays and develop a method for transmit array interpolation that maps an arbitrary transmit array into an array with a certain desired structure, e.g., a uniform rect- angular array or an array with two perpendicular uniform lin- ear arrays. A properly designed interpolation matrix is used to jointly achieve transmit array interpolation and design trans- mit beamforming. The transmit array interpolation problem is cast as a convex optimization problem based on the min- max criterion. Such formulation is flexible and enables apply- ing constraints on the transmit power distribution across the array elements, controlling the sidelobe levels of the trans- mit beampattern, and enforcing different transmit beams to have rotational invariance with respect to each other, a prop- erty that enables efficient computationally cheap 2D direction finding at the receiver. The rotational invariance is achieved independently in both the elevation and the azimuth spatial domains, allowing for independent elevation and azimuth di- rection finding at the receiver using simple 1D techniques. 2. SIGNAL MODEL Consider a mono-static MIMO radar with transmit and re- ceive arrays of M and N elements, respectively. Both the transmit and receive arrays are assumed to be planar arrays with arbitrary geometries. In a Cartesian two-dimensional space, the transmit antennas are assumed to be located at p m  [x m y m ] T ,m =1,...,M where (·) T stands for the transpose operator. The antenna locations are measured in wavelength. The M × 1 steering vector of the transmit array is defined as a(θ,φ)= [ e −j2πμ T (θ,φ)p1 ,...,e −j2πμ T (θ,φ)pM ] T (1) where θ and φ denote the elevation and azimuth spatial angles, respectively, and μ(θ,φ) = [sin θ cos φ sin θ sin φ] T denotes the propagation vector. 4139 978-1-4799-0356-6/13/$31.00 ©2013 IEEE ICASSP 2013