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Considering the important role of the ambiguity function (AF) of a signal regarding the performance of a matched filter bank for the detection of targets and the estimation of their ranges and velocities, the thumbtack shape is assumed to be the desirable shape of the AF and the method of least squares for the synthesis of the AF is introduced. Then, an iterative method for the allocation of a proper phase to the desired AF is proposed to obtain better results. This method is then applied to select the proper codes for the synthesis of pulsed orthogonal frequency-division multiplexing signals. It is also shown how this method can reduce sidelobes, almost uniformly, throughout the entire ambiguity plane. Finally, an efficient algorithm is presented, which modifies the produced codes in order to reach a lower peak-to-average power ratio suitable for transmission.