A multifrequency radar signal is considered. It uses M subcarriers simultaneously. The subcarriers are phase modulated by M different sequences that constitute a complementary set. Such a set can be constructed, for example, from the M cyclic shifts of a perfect phase-coded sequence of length M (e.g. P4). The subcarriers are separated by the inverse of the duration of a phase element tb, yielding orthogonal frequency division multiplexing (OFDM), well known in communications. A single pulse of such a signal exhibits a thumbtack ambiguity function with delay resolution of tb/M. The power spectrum is relatively flat, with width of M/tb. The signal can be constructed by power combining M fixed-amplitude signals. The resulting signal, however, is of variable amplitude. The peak-to-mean envelope power ratio can be maintained below 2. A train of complementary pulses and a weight function along the frequency axis are useful for further sidelobe reduction.