We consider the design of sets of discrete-phase, including binary/quaternary, sequences for phase-modulated continuous-wave multiple-input multiple-output radar in the presence of nonnegligible Doppler shift. We consider the peak sidelobes of auto- and cross-correlations in a desired interval of the Doppler shift as the performance metric of the design. Then, the design problem is formulated via imposing the discrete-phase constraint for each element of the sequences, with emphasis on binary as well as quaternary cases. This problem is nonconvex and hence hard to solve. We introduce a method based on the block coordinate descent framework to solve the optimization problem. We also modify the proposed method to efficiently update the subproblem associated with each iteration. Also, we extend it to account for only a low-correlation zone in the presence of Doppler shift. Numerical examples are provided to illustrate the effectiveness and performance of the proposed algorithm in comparison with the existing methods.

中文翻译：

---

MIMO雷达的多普勒敏感离散相位序列集设计

我们考虑在存在不可忽略的多普勒频移的情况下为相位调制连续波多输入多输出雷达设计离散相位集，包括二进制/四进制序列。我们将多普勒频移的所需间隔中自相关和互相关的峰值旁瓣视为设计的性能指标。然后，通过对序列的每个元素施加离散相位约束来制定设计问题，重点是二元和四元情况。这个问题是非凸的，因此很难解决。我们引入了一种基于块坐标下降框架的方法来解决优化问题。我们还修改了所提出的方法，以有效地更新与每次迭代相关的子问题。还，我们将其扩展为仅在存在多普勒频移的情况下考虑低相关区域。提供了数值例子来说明与现有方法相比所提出算法的有效性和性能。