In this study, a reconstructed continuous current distribution is employed to synthesise circular (one ring) antenna arrays with sparseness characteristics. The authors proposal achieves the reproduction of a continuous current distribution from an expansion in an orthogonal basis, taking the desired radiation beam pattern as target function. To obtain the sparseness characteristics, they employed a density tapering technique that provides the excitations and locations for each antenna element. They report three numerical experiments that show the performance of the proposal and compare it with other methods in this literature.