Retrodirective Cross-Eye Jamming Recognition and Angle Estimation via Directional Modulation and Multiple-Signal Classification

This paper proposes a retrodirective cross-eye jamming (RCJ) recognition and angle estimation algorithm based on directional modulation and multiple signal classification (DM-MUSIC). Because RCJ intercepts the radar transmit waveform to produce a monopulse angle measurement result that deviates from the true target, the traditional phased-array (TPA) radar that radiates identical transmit waveforms across the spatial domain fails to recognize RCJ by calculating the normalized cross-correlation function (NCCF). In DM-MUSIC, the monopulse angle measurement result induced by RCJ is derived, and the transmit phase matrix synthesis criterion in digital array radar is then formulated to minimize the NCCFs between the transmit waveform for the detection direction and RCJ-induced monopulse angle deception directions by utilizing the flexibility of DM in the waveform domain. Sequential quadratic programming combined with the limited-memory Broyden–Fletcher–Goldfarb–Shanno algorithm is employed to calculate the transmit phase matrix. The RCJ system is then recognized by comparing the NCCFs of the received jamming signal associated with the DM transmit waveform in the detection direction and RCJ-induced monopulse angle deception directions. Finally, the synthesized DM transmit waveform and forward–backward spatial smoothing are used to decorrelate the jamming signals, and the RCJ angle is estimated by MUSIC. The simulation results demonstrate that DM-MUSIC achieves high recognition probability and accurate RCJ angle estimation. The recognition probability reaches 98.1% at a jamming-to-noise ratio (JNR) of 5dB, with an amplitude gain of 1 and a phase shift of 179°. At a JNR of 20dB, with an amplitude gain of 0.97 and a phase shift of 179°, the Root Mean Square Error of angle estimation result is reduced from 0.13° for FBSS-MUSIC to 0.063° for DM-MUSIC.