We investigate low-cost GNSS anti-jamming using beamforming with inexpensive 2-bit phase shifters, constraining each complex array weight to one of four QPSK phase states (real/imaginary = -1 or +1). This severe quantization sharply limits the beampattern solution space, making conventional real-valued beamforming and naive weight quantization highly suboptimal. We formulate a discrete optimization that trades interference suppression against satellite-direction gain, and benchmark known combinatorial optimization methods across array sizes and interference conditions. Simulations show that performance improves with array size, with oracle and greedy search achieving up to 34 dB nulling, but oracle incurs exponential latency and greedy sampling is stochastic. To obtain deterministic low-latency performance, we propose an ML-aided method based on gradient-boosted decision trees followed by local search, which performs similar to the oracle for larger arrays at fixed latency. We further validate the approach experimentally using a fully digital emulation of the QPSK oracle beamformer and compare against a GNSS receiver without beamforming capability. Under mild jamming (J/S approximately 44 dB) both receivers maintain adequate tracking, with QPSK yielding a 4.2 dB higher average C/N0 (37.3 vs. 33.1 dB-Hz). Under moderate and strong jamming (J/S approximately 62-70 dB) the benefit is substantial. At J/S = 70 dB the unprotected receiver degrades to near tracking limits (avg C/N0 = 9.3 dB-Hz) while the QPSK oracle sustains an average C/N0 of 20.8 dB-Hz. These results confirm that 2-bit phase-shift beamforming provides considerable anti-jamming benefit over a standard GNSS receiver, motivating further research on oracle-level practical methods.

翻译：本文研究利用低成本2比特移相器进行波束形成以实现GNSS抗干扰，将每个复数组权值约束为四个QPSK相位状态之一（实部/虚部 = -1或+1）。这种严重的量化严格限制了波束方向图解空间，使得传统实值波束形成和朴素权值量化高度次优。我们构建了一个离散优化问题，在干扰抑制与卫星方向增益之间进行权衡，并针对不同阵列规模和干扰条件，对已知的组合优化方法进行了基准测试。仿真结果表明，性能随阵列规模增大而提升，其中理想搜索和贪心搜索可实现高达34 dB的零陷深度，但理想搜索面临指数级延迟，而贪心采样具有随机性。为获得确定性的低延迟性能，我们提出了一种基于梯度提升决策树结合局部搜索的机器学习辅助方法，在固定延迟下，该方法对大阵列的性能与理想搜索相当。我们进一步通过全数字仿真QPSK理想波束形成器进行实验验证，并与无波束形成能力的GNSS接收机对比。在轻度干扰（J/S≈44 dB）下，两种接收机均能保持良好跟踪，QPSK波束形成方案的平均C/N0高出4.2 dB（37.3 vs. 33.1 dB-Hz）。在中度和强干扰（J/S≈62-70 dB）下，优势更为显著。当J/S = 70 dB时，无保护接收机退化至接近跟踪极限（平均C/N0 = 9.3 dB-Hz），而QPSK理想波束形成器仍维持平均C/N0为20.8 dB-Hz。这些结果证实，2比特相移波束形成相比标准GNSS接收机具有显著抗干扰优势，为后续研究实用化的理想级抗干扰方法提供了动力。