线谱估计是指从时域或者空域估计信号的频域信息，其在雷达和通信领域得到了广泛的应用。然而，随着雷达和通信系统带宽的提升，高精度和高采样率的量化器大大提高了系统的经济成本和硬件能耗。一个有效的解决方案即是在接收机采用低精度量化技术。由于低精度量化数据含有丰富的谐波，传统的离散傅里叶变换方法会过高地估计模型阶数，因此低精度量化这种非线性影响必须加以考虑。利用期望传播，本项目拟将此问题的求解分解为无量化异方差模块和最小均方误差估计模块。一方面，最小均方误差估计模块迭代地修正无量化异方差模型的观测值和噪声方差，使其越来越接近真实的无量化模型；另一方面，无量化异方差模块迭代地修正线谱，得到更为准确的外信息送入最小均方误差估计模块。这两个模块迭代地进行消息传递，并逐渐改善线谱估计的性能。在上述研究成果的基础上，项目将其拓展并应用于到达角和信道估计问题。项目的研究成果，必将具有重要的理论意义和应用价值。

Line spectral estimation (LSE) aims to extract the parameters of a superposition of complex exponential functions from noisy measurements. As a fundamental problem in signal processing fields, it has many applications such as direction of arrival estimation and channel estimation. Because of the larger bandwidths that accompany both high resolution radar and high data rate mmWave communication system, the cost and power consumption are huge due to high precision (e.g., 10~12 bits) analog-to-digital converters (ADCs). Consequently, low precision (e.g., 1~3 bits) ADCs are employed to relieve this ADC bottleneck. Theoretical analysis reveals that there exists plentiful harmonics of the heavily quantized samples. As a result, conventional methods such as fast Fourier transform (FFT) often overestimate the model order. This research resorts to expectation propagation (EP) and grid-less variational Bayesian method. According to EP, the challenging quantized model of line spectral estimation is iteratively approximated via the minimum mean square error (MMSE) module as a sequence of simple pseudo unquantized heteroscedastic models (different components having different variance), a variant of the variational LSE (VALSE) is re-derived. For the MMSE module, it refines the pseudo observations and variances of the unquantized model. While for the pseudo unquantized model, VALSE iteratively refines the frequency estimates. The two modules iteratively exchange the information and improve the estimation gradually. In addition, this project also extends the above algorithm to solve the direction of arrival estimation and channel estimation problems. To sum up, this project is not only important for solving the fundamental LSE from heavily quantized samples, but also helpful for application in array signal processing and communication fields.