Fast beampattern evaluation by polynomial rooting

P. Häcker, S. Uhlich, B. Yang
2011 Advances in Radio Science  
<p><strong>Abstract.</strong> Current automotive radar systems measure the distance, the relative velocity and the direction of objects in their environment. This information enables the car to support the driver. <br><br> The direction estimation capabilities of a sensor array depend on its beampattern. To find the array configuration leading to the best angle estimation by a global optimization algorithm, a huge amount of beampatterns have to be calculated to detect their maxima. In this
more » ... axima. In this paper, a novel algorithm is proposed to find all maxima of an array's beampattern fast and reliably, leading to accelerated array optimizations. The algorithm works for arrays having the sensors on a uniformly spaced grid. We use a general version of the gcd (greatest common divisor) function in order to write the problem as a polynomial. We differentiate and root the polynomial to get the extrema of the beampattern. In addition, we show a method to reduce the computational burden even more by decreasing the order of the polynomial.</p>
doi:10.5194/ars-9-145-2011 fatcat:g4pmzkke7bc3vg2moem7lkbwli