On the Mapping between Steering Direction and Frequency of a Uniform Linear Array with Fixed True Time Delays

Frequency dependent beam steering occurs when a wideband signal is transmitted or received by a uniform linear array and fixed true time delays tau of the order of the reciprocal bandwidth 1/fb are applied between adjacent antenna signals. The phenomenon is explained by the fact, that phase shifts depending on the product ftau between frequency and delay occur in the array propagation vector. In this work the mapping phi = g(f) between steering angle phiAOD and frequency that depends on carrier frequency fc via the antenna element spacing and relative bandwidth kappa = fb/fc is derived in closed form. The effect becomes implementable when the absolute bandwidth is of the order of 1 GHz or higher so that the required delays are multiples of the order of 1 ns, i. e. in mm wave and RADAR applications. It may be used for beam selection by estimating the receive power spectral density.