Reply to “Comments on Waveform Optimization for Transmit Beamforming With MIMO Radar Antenna Array”

First of all, we want to thank the authors of [1] for their interest in our work [2]. In [2], the waveform design was carried out in the space domain only (coding the phases for different elements at the same moment) to form a desired transmit beam pattern at a given moment. However, if the MIMO radar waveforms are designed to satisfy the requirements in transmit beamforming (i.e., generating radiation nulls in specific directions) as well as the orthogonality between the waveforms transmitted from different elements, they must be coded simultaneously in space-time domains [3]. It turns out that the space-time coded waveforms cannot be exactly orthogonal in time domain. More specifically, to form a beam pattern with radiation null on a preselected direction, the waveforms can be optimized to be near-orthogonal with their cross correlation levels of about 1/ $N$ with $N $ being the coding length. In [1], the authors questioned if the radiation energy in the preselected target direction could really be reduced or minimized based on (2). Since the cross correlations of the designed waveforms are nontrivial for a reasonable coding length, (2) does not hold true for the designed waveforms, and thus, cannot refute the conclusions obtained in [2]. In addition, the evaluation of (2), which is similar to the result of matched filtering, requires the full knowledge of the transmitted waveforms and cannot be done by a noncooperative target. Therefore, the designed MIMO radar waveforms in [2] and [3] would generate near-zero or very weak radiation (defocused beam) in the intended direction and are theoretically undetectable by noncooperative targets in the same direction.¹ However, for MIMO radar itself with full knowledge of transmit waveforms, target detection can be performed with the maximum gain through refocusing transmit-receive beam via space-time matched filtering processing at the radar receiver.