Novel sparse reconstruction algorithms are proposed for beamspace channel estimation in massive multiple-input multiple-output systems. The proposed algorithms minimize a least-squares objective having a nonconvex regularizer. This regularizer removes the penalties on a few large-magnitude elements from the conventional $\ell _{1}$ -norm regularizer, and thus it only forces penalties on the remaining elements that are expected to be zeros. Accurate and fast reconstructions can be achieved by performing gradient projection updates within the framework of difference of convex functions (DC) programming. A double-loop algorithm and a single-loop algorithm are proposed via different DC decompositions, and these two algorithms have distinct computational complexities and convergence rates. An extension algorithm is further proposed by designing new step sizes for the single-loop algorithm. The extension algorithm has a faster convergence rate and can achieve approximately the same level of accuracy as the proposed double-loop algorithm. Numerical results show significant advantages of the proposed algorithms over existing reconstruction algorithms in terms of reconstruction accuracies and runtimes. Compared with the benchmark channel estimation approaches, the proposed algorithms can achieve smaller channel reconstruction error and higher achievable spectral efficiency.

中文翻译：

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用于大规模 MIMO 信道估计的非凸正则梯度投影稀疏重建


提出了用于大规模多输入多输出系统中波束空间信道估计的新颖稀疏重建算法。所提出的算法最小化具有非凸正则化器的最小二乘目标。该正则化器从传统的 $\ell _{1}$ -norm 正则化器中删除了对一些大数值元素的惩罚，因此它仅对预计为零的剩余元素强制施加惩罚。通过在凸函数差分（DC）编程的框架内执行梯度投影更新，可以实现准确、快速的重建。通过不同的DC分解提出了双环算法和单环算法，这两种算法具有不同的计算复杂度和收敛速度。通过为单循环算法设计新的步长，进一步提出了一种扩展算法。该扩展算法具有更快的收敛速度，并且可以达到与所提出的双环算法大致相同的精度水平。数值结果表明，所提出的算法在重建精度和运行时间方面优于现有重建算法。与基准信道估计方法相比，所提出的算法可以实现更小的信道重建误差和更高的频谱效率。