Sensitivity of co-prime arrays to shape perturbation

Co-prime arrays offer savings in both implementation and computation by reducing the number of array elements. For passive beamforming, a pair of specially-spaced sparse arrays organized as a co-prime array provides unambiguous source bearings through the cancellation of the grating lobes inherent in the pattern response of each array if processed by itself. In the ocean environment, however, towed line arrays are difficult to keep aligned and take on a time-varying shape. Hodgkiss (IEEE JOE, 1983) showed that array shape perturbation can lead to beam broadening, an effect which may interfere with the grating lobe cancellation of co-prime arrays. In the present paper, performance degradation of co-prime sparse arrays are examined under the condition of perturbed array shape. Simulations are used to compare a co-prime array of known element spacing and position to an array with small uncertainties in both element location and interelement spacing along the array. Possible correction methods are examined.