In integrated sensing and communication systems, the beampattern of a sensor array affects angular resolution in sensing applications and interference suppression in communication systems. Under constrained hardware costs, sparse arrays become an attractive option for achieving a large aperture with few sensors. However, many existing sparse arrays exhibit undesirable grating lobes in their beampatterns. The grid-based sensor locations in sparse arrays can also yield a high-complexity combinatorial array design. This paper presents a framework for the design of gridless sparse arrays. The array geometry is optimized using an objective function based on a kernelwindowed power pattern. The Fourier relation enables a modified objective function that is differentiable with respect to the gridless sensor locations. This property admits the gradientbased optimized array with spacing constraints (GBOA-SC) with a polynomial-time solution. Furthermore, a grid-based sparse array, denoted as R-GBOA-SC, is obtained by rounding the GBOA-SC to an integer grid. Numerical examples demonstrate the power patterns of GBOA-SC and R-GBOA-SC. In particular, GBOA-SC and R-GBOA-SC mitigate the grating lobes, compared with several array geometries.
