Owing to cognitive radar breaking the open-loop receiving–transmitting mode of traditional radar, adaptive waveform design for cognitive radar has become a central issue in radar system research. In this paper, the method of radar transmitted waveform design in the presence of clutter is studied. Since exact characterizations of the target and clutter spectra are uncommon in practice, a single-robust transmitted waveform design method is introduced to solve the problem of the imprecise target spectrum or the imprecise clutter spectrum. Furthermore, considering that radar cannot simultaneously obtain precise target and clutter spectra, a novel double-robust transmitted waveform design method is proposed. In this method, the signal-to-interference-plus-noise ratio and mutual information are used as the objective functions, and the optimization models for the double-robust waveform are established under the transmitted energy constraint. The Lagrange multiplier method was used to solve the optimal double-robust transmitted waveform. The simulation results show that the double-robust transmitted waveform can maximize SINR and MI in the worst case; the performance of SINR and MI will degrade if other transmitted waveforms are employed in the radar system.

Optimizing the energy spectrum density (ESD) of a transmitted waveform can improve radar performance. The design of a time–domain constant–modulus signal corresponding to the transmitted waveform ESD is practically important because constant–modulus signals can maximize transmission power and meet the hardware requirements of radar transmitters. Here, we present a time–domain signal design under dual constraints of energy and constant modulus. The mutual information (MI)–based waveform design method is used to design transmitted waveform ESD under the energy constraint. Then, the bacterial foraging optimization algorithm (BFOA) is proposed to design the time–domain constant–modulus signal. We use minimum mean square error (MMSE) in the frequency domain as the cost function. The BFOA monotonously decreases the MMSE with increasing iterations, which makes the ESD of the time–domain constant–modulus signal close to the MI–based optimal waveform ESD. The simulation results indicate that the proposed algorithm has advantages, including insensitivity to initial phases, rapid convergence, smaller MI loss, and MMSE compared with the iterative reconstruction algorithm.