Performance of line arrays of vector and higher order sensors

Arrays of vector and higher order directional sensors are of current interest in a number of applications. The performance of these arrays as a function of frequency and steering direction is examined. Results are presented for arrays of zero-th order (omni-directional), first order vector (omni + first spatial derivative) and second order combined (omni + first spatial directions derivatives + second spatial derivatives) sensors. The beampattern product theorem provides insight into to contribution of the individual components of the directional sensors. For endfire array steering, previous results are extended to higher order sensors. Only the axial components are important at endfire. Sensors with axial components up to order n can cancel up to n grating lobes providing extra gain up to (n+1) times the design frequency at which the sensors are spaced at one-half wavelength. Away from endfire only the cross-axial components are important. Simple techniques are presented for overcoming left/right ambiguity of horizontal line arrays using only the omni-directional and horizontal cross axial components. The results of simple deterministic processing approaches are found to be near optimum when compared with those achieved by optimum processing based on covariance matrix inversion.