In this letter, a ray tracing (RT) acceleration method based on rank minimization is proposed. RT is a general tool used to simulate wireless communication environments. However, the simulation is time consuming because of the large number of ray calculations. This letter focuses on radio map interpolation as an acceleration approach. In the conventional methods cannot appropriately estimate short-span variation caused by multipath fading. To overcome the shortage of the conventional methods, we adopt rank minimization based interpolation. A computational simulation using commercial RT software revealed that the interpolation accuracy of the proposed method was higher than those of other radio map interpolation methods and that RT simulation can be accelerated approximate five times faster with the missing rate of 0.8.

This paper proposes an image inpainting algorithm based on multiple linear models and matrix rank minimization. Several inpainting algorithms have been previously proposed based on the assumption that an image can be modeled using autoregressive (AR) models. However, these algorithms perform poorly when applied to natural photographs because they assume that an image is modeled by a position-invariant linear model with a fixed model order. In order to improve inpainting quality, this work introduces a multiple AR model and proposes an image inpainting algorithm based on multiple matrix rank minimization with sparse regularization. In doing so, a practical algorithm is provided based on the iterative partial matrix shrinkage algorithm, with numerical examples showing the effectiveness of the proposed algorithm.

Heterogeneous networks (HetNets) technology is expected to be applied in next generation cellular networks to boost system capacity. However, applying HetNets introduces a significant amount of interference among different tiers within the same cell. In this paper, we propose a weighted rank constrained rank minimization (WRCRM) based interference alignment (IA) approach for three-tier HetNets. The concept of RCRM is applied in a different way to deal with the basic characteristic of different tiers: their different interference tolerance. In the proposed WRCRM approach, interference components at different tiers are weighted with different weighting factors (WFs) to reflect their vulnerability to interference. First, we derive an inner and a loose outer bound on the achievable degrees of freedom (DoF) for the three-tier system that is modeled as a three-user mutually interfering broadcast channel (MIBC). Then, the derived bounds along with the well-known IA feasibility conditions are used to show the effectiveness of the proposed WRCRM approach. Results show that there exist WF values that maximize the achievable interference-free dimensions. Moreover, adjusting the required number of DoF according to the derived bounds improves the performance of the WRCRM approach.

This letter deals with the signal declipping algorithm based on the matrix rank minimization approach, which can be applied to the signal restoration in linear systems. We focus on the null space of a low-rank matrix and provide a block adaptive algorithm of the matrix rank minimization approach to signal declipping based on the null space alternating optimization (NSAO) algorithm. Numerical examples show that the proposed algorithm is faster and has better performance than other algorithms.

This letter deals with a system identification problem with unknown model order, which can be formulated as the matrix rank minimization problem by applying the subspace identification method. A sequential rank minimization algorithm is provided by modifying the null space based alternating optimization (NSAO) algorithm, and a model order identification algorithm is proposed. Numerical examples show that the proposed sequential algorithm can adaptively identify the model order of switched systems whose model order changes.