基于解耦原子范数最小化的二维谱线谱估计
Efficient Two-Dimensional Line Spectrum Estimation Based on Decoupled Atomic Norm Minimization
摘要：
本文提出了一种有效的无网格{2-D}谱谱估计优化方法--解耦原子范数最小化（D-ANM）。原子范数最小化（ANM）的框架被认为是，它已成功地应用于1-D问题，允许相关源的超分辨率频率估计，即使当快照的数量是非常有限的。最先进的2-D ANM方法将2-D测量向量化为它们的1-D等价物，这导致巨大的计算成本，并且对于实际应用来说可能变得过于昂贵。我们通过半定规划（SDP）开发了一种新的解耦2-D ANM方法，该方法引入了一种新的矩阵形式的原子集，可以在不损失最优性的情况下自然地解耦两个维度的联合观测。相应地，原来的大规模的2-D问题是等价地通过两个解耦的一级Toeplitz矩阵，这可以解决简单的1-D频率估计配对。与传统的矢量化方法相比，建议的D-ANM技术的计算复杂度降低了几个数量级的问题大小。它还保留了ANM在精确的信号恢复，少量所需的测量和源相关性的鲁棒性方面的优点。复杂性优势对于大规模多输入多输出、雷达信号处理和射电天文学等大规模天线系统特别有吸引力。
英文摘要：
This paper presents an efficient optimization technique for gridless {2-D} line spectrum estimation, named decoupled atomic norm minimization (D-ANM). The framework of atomic norm minimization (ANM) is considered, which has been successfully applied in 1-D problems to allow super-resolution frequency estimation for correlated sources even when the number of snapshots is highly limited. The state-of-the-art 2-D ANM approach vectorizes the 2-D measurements to their 1-D equivalence, which incurs huge computational cost and may become too costly for practical applications. We develop a novel decoupled approach of 2-D ANM via semi-definite programming (SDP), which introduces a new matrix-form atom set to naturally decouple the joint observations in both dimensions without loss of optimality. Accordingly, the original large-scale 2-D problem is equivalently reformulated via two decoupled one-level Toeplitz matrices, which can be solved by simple 1-D frequency estimation with pairing. Compared with the conventional vectorized approach, the proposed D-ANM technique reduces the computational complexity by several orders of magnitude with respect to the problem size. It also retains the benefits of ANM in terms of precise signal recovery, small number of required measurements, and robustness to source correlation. The complexity benefits are particularly attractive for large-scale antenna systems such as massive MIMO, radar signal processing and radio astronomy.
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