As the target radar signature (TRS) is target-radar orientation sensitive and time-varying in wideband cognitive radar (WCR), the TRS information of WCR should be recursively updated by the receiver on the fly. Therefore, in WCR waveform design for target detection, TRS estimation ability should also be considered to provide the prior knowledge for the optimization of the next waveform. To address this problem, a WCR waveform design method is proposed for target detection by maximizing the average SCNR of the received echo on the premise of ensuring the TRS estimation precision. By constraining the estimation performance, a convex cost function is established and the optimal solution can be obtained by the existing convex programming algorithm. Furthermore, for the convenience of waveform optimization in real time, a fast hierarchical scheme is also proposed with comparative performance. Numerical results show that, the proposed methods are able to improve the target detection performance under given estimation performance constraint.