This paper addresses the problem of transmit signal design for target localization in a frequency diverse array (FDA) radar. For this purpose, we derive the Cramér-Rao bound (CRB) for target localization in FDA radar. The derived CRB is optimized with respect to the transmit signal parameters. It is commonly assumed that in radar systems the direction-of-arrival (DOA) estimation accuracy and resolution are determined by the transmit-receive array aperture. In FDA radar, a coupling between range and DOA estimation is generated. Using the derived CRB, we show that in FDA radar one is able to improve the DOA estimation accuracy and resolution by increasing the transmit signal bandwidth. The target localization performance is analyzed theoretically and via simulations, and it is shown that using the proposed approach for transmit signal optimization, results in superior target localization performance compared to conventional methods.