Reconstruction of Complex Discrete-Valued Vector via Convex Optimization With Sparse Regularizers
Reconstruction of Complex Discrete-Valued Vector via Convex Optimization With Sparse Regularizers
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DOI：
10.1109/access.2018.2878886
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发表时间：
2018-10
期刊：
影响因子：
3.9
通讯作者：
Ryo Hayakawa;K. Hayashi
中科院分区：
文献类型：
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作者：
Ryo Hayakawa;K. Hayashi
在本文中，我们提出了一种方法，用于重建一个复杂的离散值向量的线性测量。特别是，我们主要集中在欠定的情况下，其中的测量数小于未知的复离散变量，并提出了一种重建的方法来解决一个优化问题称为复杂稀疏正则化（SCSR）优化的总和。目标函数中的稀疏正则化子之和可以直接利用未知向量在复域中的离散性质。我们还提出了一个算法的基础上交替方向法的乘子的SCSR优化问题。对于所提出的凸正则化子，我们解析地证明了所提出的算法得到的序列收敛到问题的最优解。为了获得更好的重建性能，我们进一步提出了一种迭代的方法命名为迭代加权SCSR（IW-SCSR），其中我们更新的目标函数中的参数在每次迭代中使用的试探性估计在前一次迭代。仿真结果表明，IW-SCSR能够从欠定线性测量重构出复离散向量，在过载多输入多输出信号检测和信道均衡等应用中具有良好的性能。
In this paper, we propose a method for the reconstruction of a complex discrete-valued vector from its linear measurements. In particular, we mainly focus on the underdetermined cases, where the number of measurements is less than that of the unknown complex discrete variables, and propose a reconstruction approach of solving an optimization problem called sum of complex sparse regularizers (SCSR) optimization. The sum of sparse regularizers in the objective function can directly utilize the discrete nature of the unknown vector in the complex domain. We also propose an algorithm for the SCSR optimization problem on the basis of alternating direction method of multipliers. For the proposed convex regularizers, we analytically prove that the sequence obtained by the proposed algorithm converges to the optimal solution of the problem. To obtain better reconstruction performance, we further propose an iterative approach named iterative weighted SCSR (IW-SCSR), where we update the parameters in the objective function in each iteration by using the tentative estimate in the previous iteration. Simulation results show that IW-SCSR can reconstruct the complex discrete-valued vector from its underdetermined linear measurements and achieve good performance in the applications of overloaded multiple-input multiple-output signal detection and channel equalization.