Robust radar waveform design for extended targets with multiple spectral compatibility constraints

•Distinguishing from the radar waveform design for the point-like target, this paper formulates the robust waveform design for extended targets under the multiple spectral compatibility constraints as well as similarity constraint.•Two SUM based algorithms, namely, SUMR and SUMD, are devised to solve the resultant max-min waveform optimization problem. Furthermore, comparisons for the two algorithms are given to illustrate its advantages and disadvantages.•The convergence properties of the SUMR and SUMD algorithms are formally analyzed, which facilities the practical applications of the proposed algorithms.