The ambiguity function (AF), which is used to evaluate the range and Doppler resolutions, plays an important role in radar systems. In this article, we consider the problems of jointly designing unimodular sequence and receiving filters, and also unimodular complementary sequences and corresponding receiving filters with desired AF shapes. The design problems are formulated as the minimization of the weighted integrated sidelobe level (WISL) and the minimization of the complementary integrated sidelobe level (CISL), respectively, under the constraint of the signal-to-noise ratio (SNR) loss. Algorithms based on the alternately iterative minimization method and the majorization-minimization method are developed to tackle the optimization problems. Numerical results are demonstrated to show the superior performance of the proposed algorithms in terms of the achieved objective and running time in comparison with the state-of-the-art algorithms. Meanwhile, the excellent capability of the designed sequences to detect multiple moving targets under the strong clutter is evaluated via simulations. Moreover, the designed sequences are also implemented on an indoor hardware system, and their performance is verified.