# Fractal Antenna Configurations for MIMO Radar Applications

Christoph Dahl, Michael Vogt, Ilona Rolfes

Kleinheubacher Tagung 2016, U.R.S.I. Landesausschuss in der Bundesrepublik Deutschland e.V., Miltenberg, Germany, Sep 26-28, 2016

## Abstract

Imaging radar systems offer great opportunities for industrial applications, such as volume measurement of bulk solids. Multiple-input multiple-output (MIMO) radar systems can be used to reduce the systems cost by minimizing the number of transmitting and receiving channels. A common MIMO antenna configuration is based on two linear arrays, one for transmitting and one for receiving, which are positioned perpendicularly to each other. The antenna array topology of a MIMO radar can be analyzed by introducing a virtual array, that is formed by a convolution of the transmitting and the receiving array topologies. In the case of two linear arrays, a virtual array with a rectangular shape is formed. As the radiation pattern of the virtual array corresponds with the two-way radiation pattern of the MIMO array, a pencil-shaped beam is formed. In order to optimize the angular resolution and the side lobe suppression for a fixed number of antenna elements, a circularly shaped virtual array is desired for a MIMO radar system. Regarding these aspects, array topologies based on the so-called Fudgeflake fractal and the Gosper island fractal have been investigated. For the first iteration of the Fudgeflake fractal, the topology of the transmitting array consists of three antennas forming an equilateral triangle. The receiving antenna array is a scaled and rotated version of the transmitting array. The resulting topology of the virtual array is the second iteration of the Fudgeflake fractal, consisting of nine virtual antennas. The transmitting array for the first iteration of the Gosper island fractal consists of seven antennas positioned in a hexagonal shape. Also in this case, the receiving array is a scaled and rotated version of the transmitting array and the virtual array is the second iteration of the Gosper is land fractal. By combining higher iterations of both fractals, larger MIMO arrays can be formed. The fractal concepts have been combined for a MIMO configuration with 21 transmitting and 21 receiving antennas. The virtual array consists of 441 antenna elements and offers a 60° rotational symmetry. For a half-wavelength antenna spacing, the corresponding two-way radiation pattern has a beam width of 4.6° and a side lobe suppression of 16.3 dB. A comparable perpendicular antenna configuration leads to a rectangular shaped virtual array with 441 elements positioned on a rectangular grid. In comparison with the perpendicular antenna concept, the fractal configuration has a 0.3° better angular resolution and a 3.1 dB better side lobe suppression. The antenna concepts have been compared in a reference scenario using a frequency modulated continuous wave (FMCW) radar system. The virtual arrays of the different proposed concepts have been sampled using a horn antenna. The resulting radar images confirm the advantages regarding the angular resolution and side lobe suppression obtained by using the fractal antenna concept.