A fast-time coding waveform design method and a bound on cross-correlation

The transmit waveforms in multiple-input multiple-output (MIMO) radar are required to have low cross-correlation for the discrimination of the waveforms in the receiver. In this paper, we develop a new fast-time coding waveform design method for sets of waveforms greater than two. The method is based on using waveforms with different chirp rates and time shifts. In addition, with the constraint that the waveforms have a flat spectrum, we prove that the average cross-correlation between any two fast-time coding waveforms is constant and related to the time-bandwidth product. Moreover, we derive a lower bound for the maximum cross-correlation between any two fast-time coding waveforms, which is also related to the time-bandwidth product. Simulation results show that any two waveforms in the developed set have a flat cross-correlation level that is nearly equal to the lower bound. Moreover, simulation results are conducted to show the range-angle map of the developed waveforms.