Theoretical Insights and Practical Algorithms for Transceiver Design of PMCW Radar

Phase-modulated continuous-wave (PMCW) radar can fundamentally solve the growing mutual interference problems suffered by the widely used linear frequency-modulated continuous-wave automotive radar. To achieve this objective, long binary periodic probing sequences, characterized by low auto-correlation sidelobes, arbitrary period lengths, and substantial diversity, should be transmitted by the PMCW radar. To further decrease the sidelobe levels, at the slight cost of the signal-to-noise ratio (SNR), mismatched receive filters are viable options for PMCW radar. We focus on designing periodic binary probing sequences and mismatched receiver filter to achieve almost zero cross-correlation sidelobes levels at small SNR loss. We also introduce an algorithm to optimize mismatched receive filters subject to the constraint of a pre-determined maximum allowable SNR loss. We prove that if the cross-correlation sidelobes of a binary sequence can be completely eliminated by a mismatched filter at a small SNR loss, then it will also have low auto-correlation sidelobes. However, the reverse is not necessarily true. We investigate the properties of the widely used m-sequences under the mismatched receive filter framework as a specific example. Numerical examples are provided to validate our theoretical analysis and showcase the effectiveness of the proposed transceiver design algorithms for PMCW radar.