• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.10
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• pp.4835-4855
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• 2018

In this paper, we study the sparse signal recovery that uses information of both support and amplitude of the sparse signal. A convergent iterative algorithm for sparse signal recovery is developed using Majorization-Minimization-based Non-convex Optimization (MM-NcO). Furthermore, it is shown that, typically, the sparse signals that are recovered using the proposed iterative algorithm are not globally optimal and the performance of the iterative algorithm depends on the initial point. Therefore, a modified MM-NcO-based iterative algorithm is developed that uses prior information of both support and amplitude of the sparse signal to enhance recovery performance. Finally, the modified MM-NcO-based iterative algorithm is used to estimate the time-varying sparse wireless channels with temporal correlation. The numerical results show that the new algorithm performs better than related algorithms.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.3
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• pp.107-116
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• 2021

We introduce optimization algorithms using Bregman Divergence for solving non-negative matrix factorization (NMF) problems. Bregman divergence is known a generalization of some divergences such as Frobenius norm and KL divergence and etc. Some algorithms can be applicable to not only NMF with Frobenius norm but also NMF with more general Bregman divergence. Matrix Factorization is a popular non-convex optimization problem, for which alternating minimization schemes are mostly used. We develop the Bregman proximal gradient method applicable for all NMF formulated in any Bregman divergences. In the derivation of NMF algorithm for Bregman divergence, we need to use majorization/minimization(MM) for a proper auxiliary function. We present algorithmic aspects of NMF for Bregman divergence by using MM of auxiliary function.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.18 no.1
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• pp.59-69
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• 2018

In this paper, we present a robust beamforming design to tackle the weighted sum-rate maximization (WSRM) problem in a multicell multiple-input multiple-output (MIMO) - non-orthogonal multipleaccess (NOMA) downlink system for 5G wireless communications. This work consider the imperfectchannel state information (CSI) at the base station (BS) by adding uncertainties to channel estimation matrices as the worst-case model i.e., singular value uncertainty model (SVUM). With this observation, the WSRM problem is formulated subject to the transmit power constraints at the BS. The objective problem is known as on-deterministic polynomial (NP) problem which is difficult to solve. We propose an robust beam forming design which establishes on majorization minimization (MM) technique to find the optimal transmit beam forming matrix, as well as efficiently solve the objective problem. In addition, we also propose a joint user clustering and power allocation (JUCPA) algorithm in which the best user pair is selected as a cluster to attain a higher sum-rate. Extensive numerical results are provided to show that the proposed robust beamforming design together with the proposed JUCPA algorithm significantly increases the performance in term of sum-rate as compared with the existing NOMA schemes and the conventional orthogonal multiple access (OMA) scheme.