Algorithm for the design of broadband, constant-beamwidth, point-element linear arrays with constant sidelobe level

Abstract

An algorithm has been designed that allows one to calculate the individual element weights, as a function of frequency, required to achieve specified values of sidelobe level and half-power beamwidth. The arrays considered had linear geometry and an odd number of evenly spaced, point elements. The input parameters are the sidelobe level, half-power beamwidth, and the number of elements. For different values of the input parameters, the bandwidth that produced realizable solutions was determined numerically. Upon choosing values for the input parameters that yield realizable solutions, the weighting functions for each element are determined by an explicit calculation. An array may be combined with a scaled version of itself to increase the bandwidth. The element weights for an octave bandwidth broadside array were calculated using this algorithm and this array was combined with a scaled version of itself to extend the bandwidth to two octaves. Microphone and loudspeaker arrays based on these calculated weights were implemented with a digital signal processor. Measurements of the directivity patterns in an anechoic room were compared to the desired directivity patterns to assess the design procedure. [Work supported by NSF Graduate Research Fellowship and Uniden Endowed Thrust 2000 Fellowship.]