Articles | Volume 9
Adv. Radio Sci., 9, 145–152, 2011
https://doi.org/10.5194/ars-9-145-2011
Adv. Radio Sci., 9, 145–152, 2011
https://doi.org/10.5194/ars-9-145-2011

  29 Jul 2011

29 Jul 2011

Fast beampattern evaluation by polynomial rooting

P. Häcker, S. Uhlich, and B. Yang P. Häcker et al.
  • Chair of System Theory and Signal Processing, Universität Stuttgart, Pfaffenwaldring 47, 70550 Stuttgart, Germany

Abstract. 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.

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 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.