Global Optimization for the Sum of Concave-Convex Ratios Problem

Zhou, Xiaoqing; Yang, Ji-Hui

doi:10.1155/2014/879739

Cited by 3 publications

(4 citation statements)

References 16 publications

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“…P m,k and P o m,k are the optimal power solution, and the two solutions are the same with each other. Therefore, we prove (35) is the unique optimal solution of problem (34). □…”

Section: Optimization Problem Of Maximizing Minimum User-ratementioning

confidence: 83%

“…the first user suffers no inter-cluster interference, and the second user experiences the interference caused by the first user. Following this principle, we can obtain the power allocation with the expression in (35) if and only if R m,k = Ȓ is satisfied.…”

Section: Optimization Problem Of Maximizing Minimum User-ratementioning

confidence: 99%

“…Lemma Given a non‐negative function

F_{n} false(boldx false) = \frac{A_{n} false(boldx false)}{B_{n} false(boldx false)}, x \in X

, where all other things are equal to that in Lemma 1. The multiple‐ratio problem [35],

\max_{boldx} \sum_{n = 1}^{N} F_{n} false(boldx false), s.t. x \in X,

is equivalent to

\max_{x, z} \sum_{n = 1}^{N} f_{boldz} false(boldx, boldZ false), s.t. x \in X,

where

f_{boldz} false(boldx, boldZ false) = (2 Z_{n} \sqrt{A_{n} (x)} - Z_{n}^{2} B_{n} (x)),

and

Z_{n}

is an auxiliary variable to reformulate the form of sum‐of‐ratios. Proof See Appendix 9.2.

□

…”

Section: Long‐term Fairness Power Allocationmentioning

confidence: 99%

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Fairness‐aware power allocation in downlink MIMO‐NOMA systems

et al. 2021

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Non-orthogonal multiple access (NOMA) has attracted great attention due to its potential of providing high spectral efficiency and massive connectivity. Combining it with multipleinput multiple-output (MIMO) technology can further improve the spectrum efficiency. In this paper, the power allocation problem in downlink multi-cluster MIMO-NOMA systems is investigated for maximizing the fairness utility function. First, a long-term fairness function is considered and the optimization problem is formulated as a weighted sum-rate maximization problem. The problem is transformed into a convex form by introducing two sets of auxiliary variables, and propose an iterative algorithm to update the weight factors and the auxiliary variables. Then, an instantaneous fairness is considered and the optimization problem is formulated as a minimum data-rate maximization problem. It is transfiormed into a one-dimensional optimization problem based on an iterative algorithm and a closed-form power allocation expression is deduced. Simulation results illustrate that the proposed two fairness power allocation schemes have better performance of edge-user rate than the comparable schemes.

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“…P m,k and P o m,k are the optimal power solution, and the two solutions are the same with each other. Therefore, we prove (35) is the unique optimal solution of problem (34). □…”

Section: Optimization Problem Of Maximizing Minimum User-ratementioning

confidence: 83%

Section: Optimization Problem Of Maximizing Minimum User-ratementioning

confidence: 99%

“…Lemma Given a non‐negative function

F_{n} false(boldx false) = \frac{A_{n} false(boldx false)}{B_{n} false(boldx false)}, x \in X

, where all other things are equal to that in Lemma 1. The multiple‐ratio problem [35],

\max_{boldx} \sum_{n = 1}^{N} F_{n} false(boldx false), s.t. x \in X,

is equivalent to

\max_{x, z} \sum_{n = 1}^{N} f_{boldz} false(boldx, boldZ false), s.t. x \in X,

where

f_{boldz} false(boldx, boldZ false) = (2 Z_{n} \sqrt{A_{n} (x)} - Z_{n}^{2} B_{n} (x)),

and

Z_{n}

is an auxiliary variable to reformulate the form of sum‐of‐ratios. Proof See Appendix 9.2.

□

…”

Section: Long‐term Fairness Power Allocationmentioning

confidence: 99%

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Fairness‐aware power allocation in downlink MIMO‐NOMA systems

et al. 2021

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“…denotes the auxiliary variable, and the optimal θ * j = A j (x)/B j (x) [45], [46]. According to Lemma 1, we rewrite the optimization problem (13) by the following quadratic transform with introduced variables {θ n,k }, as…”

Section: Lemma 1: Define a Sum-of-ratio Optimization Problemmentioning

confidence: 99%

Low-Complexity Power Allocation in NOMA Systems With Imperfect SIC for Maximizing Weighted Sum-Rate

Wang

Chen

et al. 2019

IEEE Access

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In this paper, we investigate the power allocation for maximizing weighted sum rate (WSR) in downlink multiple carriers non-orthogonal multiple access (MC-NOMA) systems with imperfect successive interference cancellation (SIC). We formulate the power allocation problem as a non-convex optimization problem with the total power constraint of all sub-channels while considering often-neglected issues of SIC error and power order constraints at users. First, we discuss that the optimization problem assuming receivers can perform perfect SIC, and we provide a concavity condition of the WSR maximization problem for the MC-NOMA system. When the concavity condition is not satisfied, a fractional quadratic transformation is used to overcome the difficulty of problem non-convexity. Based on the transformation, we propose an iterative power allocation algorithm. Then, we consider the SIC error and the power order constraints in the optimization problem and present a power allocation method with imperfect SIC. Moreover, for both the perfect and imperfect SIC, we derive some propositions of the optimal power allocation solution to the WSR maximization problem and propose a low-complexity power allocation algorithm based on these propositions. Finally, we provide a joint user scheduling and power allocation algorithm for maximizing the WSR. The simulation results illustrate that the proposed resource allocation methods have a better performance than the existing schemes.

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A branch-and-cut algorithm for a class of sum-of-ratios problems

Ashtiani

Ferreira

2015

Applied Mathematics and Computation

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Global Optimization for the Sum of Concave-Convex Ratios Problem

Cited by 3 publications

References 16 publications

Fairness‐aware power allocation in downlink MIMO‐NOMA systems

Fairness‐aware power allocation in downlink MIMO‐NOMA systems

Low-Complexity Power Allocation in NOMA Systems With Imperfect SIC for Maximizing Weighted Sum-Rate

A branch-and-cut algorithm for a class of sum-of-ratios problems

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