Joint Optimization of Transmission-Order Selection and Channel Allocation for Bidirectional Wireless Links—Part II: Algorithms

Uykan, Zekeriya; Jäntti, Riku

doi:10.1109/twc.2014.2314639

Cited by 10 publications

(6 citation statements)

References 42 publications

(87 reference statements)

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“…Furthermore, without loss of generality, in both Example 1 and 2 below, we model the channel gains as in e.g. [36,37] where the attenuation factor is 3, the log-normally distributed slow fading is generated according to the model in [36], and the lognormal variance is 6 dB. The transmit powers vary from 1 mW to 1 W. A unit variance Gaussian noise is added to the received signal at each node.…”

Section: Simulation Resultsmentioning

confidence: 99%

A modified GADIA-based upper-bound to the capacity of Gaussian general N-relay networks

Uykan

Jäntti

2021

Wireless Netw

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In this paper, we present a general Gaussian N-relay network by allowing relays to communicate to each other and allowing a direct channel between source and destination as compared to the standard diamond network in Nazaroğlu et al. (IEEE Trans Inf Theory 60:6329–6341, 2014) at the cost of extra channel uses. Our main focus is to examine the min-cut bound capacities of the relay network. Very recently, the results in Uykan (IEEE Trans Neural Netw Learn Syst 31:3294–3304, 2020) imply that the GADIA in Babadi and Tarokh (IEEE Trans Inf Theory 56:6228–6252, 2010), a pioneering algorithm in the interference avoidance literature, actually performs max-cut of a given power-domain (nonnegative) link gain matrix in the 2-channel case. Using the results of the diamond network in Nazaroğlu et al. (2014) and the results in Uykan (2020), in this paper, we (i) turn the mutual information maximization problem in the Gaussian N-relay network into an upper bound minimization problem, (ii) propose a modified GADIA-based algorithm to find the min-cut capacity bound and (iii) present an upper and a lower bound to its min-cut capacity bound using the modified GADIA as applied to the defined “squared channel gain matrix/graph”. Some advantages of the proposed modified GADIA-based simple algorithm are as follows: (1) The Gaussian N-relay network can determine the relay clusters in a distributed fashion and (2) the presented upper bound gives an insight into whether allowing the relays to communicate to each other pays off the extra channel uses or not as far as the min-cut capacity bound is concerned. The simulation results confirm the findings. Furthermore, the min-cut upper bound found by the proposed modified-GADIA is verified by the cut-set bounds found by the spectral clustering based solutions as well.

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Section: Simulation Resultsmentioning

confidence: 99%

A modified GADIA-based upper-bound to the capacity of Gaussian general N-relay networks

Uykan

Jäntti

2021

Wireless Netw

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“…Similarly, for the same vertex n in cluster s(n) at time t, we obtain the sum of shadow-cuts J SC (t) in (3) using (27) and (39) as follows:…”

Section: A Indirect Greedy and Nongreedy Algorithms For L ≥mentioning

confidence: 99%

“…Most of the graph partitioning and graph clustering problems assume that graph edges are nonnegative (see [26]). For example, a wireless system can be represented by a graph with nonnegative edges (see [38], [39]). However, when graphs are allowed to have both negative and positive edges, the problem becomes much more complicated (see [27], [28]).…”

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confidence: 99%

Shadow-Cuts Minimization/Maximization and Complex Hopfield Neural Networks

Uykan

2021

IEEE Trans. Neural Netw. Learning Syst.

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In this article, we continue our very recent work by extending it to the complex case. Having been inspired by the real Hopfield neural network (HNN) results, our investigations here yield various novel results, some of which are as follows. First, extending the "biased pseudo-cut" concept to the complex HNN (CHNN) case, we introduce a "shadowcut" that is defined as the sum of intercluster phased edges. Second, while the discrete-time real HNN strictly minimizes the "biased pseudo-cut" in each neuron state change, the CHNN "tends" to minimize the shadow-cut (as the CHNN energy function is minimized). Third, these definitions pose a novel L-phased graph clustering (partitioning) problem in which the sum of the shadow-cuts is minimized (or maximized) for the Hermitian complex and the directed graphs whose edges are (possibly arbitrary positive/negative) complex numbers. Finally, combining the CHNN and the pioneering algorithm GADIA of Babadi and Tarokh and their modified versions, we propose simple indirect algorithms to solve the defined shadow-cuts minimization/maximization problem. The proposed algorithms naturally include the CHNN as well as the GADIA as its special cases. The computer simulations confirm the findings. Index Terms-Associative memory, clustering, complex Hopfield neural networks (CHNNs), GADIA, graphs with (positive and negative) complex edges, L-phased partitioning problem. I. INTRODUCTION AND MOTIVATION C OMPLEX-VALUED neural networks are becoming an emergent and rapidly developing field because they recently widened the scope of their applications to machine learning, imaging, remote sensing, optoelectronics, quantum neural systems, physiological neural systems, and artificial neural information processing [33], [34]. Complex-valued neural networks are as follows. 1) They are highly suitable not only for representing graphs with complex edges but also for processing the amplitude and phase. This is one of the core concepts in physical systems dealing with electromagnetic, light, and ultrasonic waves, as well as quantum waves [33]. 2) They utilize complex arithmetic, showing specific dynamic characteristics in their learning, self-organizing, and processing [33], [34]. These facts bring critical advantages to representing and modeling complicated relations among the nodes in complex graphs for solving various machine learning problems. In addition, they bring critical advantages in analyzing and processing Manuscript

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“…In contrast to unidirectional links assumed in the TX-RX pair model, Uykan and Jäntti [175], [176] discussed a channel assignment problem for bidirectional links and proposed a joint transmission order and channel assignment algorithm.…”

Section: Channel Assignment To Manage Received and Generated Interfermentioning

confidence: 99%

A Comprehensive Survey of Potential Game Approaches to Wireless Networks

Yamamoto

2015

IEICE Trans. Commun.

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SUMMARY Potential games form a class of non-cooperative games where the convergent of unilateral improvement dynamics is guaranteed in many practical cases. The potential game approach has been applied to a wide range of wireless network problems, particularly to a variety of channel assignment problems. In this paper, the properties of potential games are introduced, and games in wireless networks that have been proven to be potential games are comprehensively discussed. key words: potential game, game theory, radio resource management, channel assignment, transmission power control IntroductionThe broadcast nature of wireless transmissions causes cochannel interference and channel contention, which can be viewed as interactions among transceivers. Interactions among multiple decision makers can be formulated and analyzed using a branch of applied mathematics called game theory [61], [131]. Game-theoretic approaches have been applied to a wide range of wireless communication technologies, including transmission power control for code division multiple access (CDMA) cellular systems [153] and cognitive radios [132]. For a summary of game-theoretic approaches to wireless networks, we refer the interested reader to [68] [189].In this paper, we focus on potential games [126], which form a class of strategic form games with the following desirable properties:• The existence of a Nash equilibrium in potential games is guaranteed in many practical situations [126] (Theorems 1 and 2 in this paper), but is not guaranteed for general strategic form games. Example 2 in Sect. 2. We provide an overview of problems in wireless networks that can be formulated in terms of potential games. We also clarify the relations among games, and provide simpler proofs of some known results. Problem-specific learning algorithms [92], [168] are beyond the scope of this paper.The remainder of this paper is organized as follows: In Sect. 2, 3, and 4, we introduce strategic form games, potential games, and learning algorithms, respectively. We then discuss various potential games in Sects. 5 to 18, as shown in Table 1. Finally, we provide a few concluding remarks in Sect. 19.The notation used here is shown in Table 2. Unless the context indicates otherwise, sets of strategies are denoted by calligraphic uppercase letters, e.g., A i , strategies are denoted by lowercase letters, e.g., a i ∈ A i , and tuples of strategies are denoted by boldface lowercase letters, e.g., a. Note that a i is a scalar variable when A i is a set of scalars or indices, a i is a vector variable when A i is a set of vectors, and a i is a set variable when A i is a collection of sets.We use R to denote the set of real numbers, R + to denote the set of nonnegative real numbers, R ++ to denote the set of positive real numbers, and C to denote the set of complex numbers. The cardinality of set A is denoted by |A|. The power set of A is denoted by 2 A . Finally, ½condition is the indicator function, which is one when condition is true and is zero otherwise.We treat many sy...

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Joint Optimization of Transmission-Order Selection and Channel Allocation for Bidirectional Wireless Links—Part II: Algorithms

Cited by 10 publications

References 42 publications

A modified GADIA-based upper-bound to the capacity of Gaussian general N-relay networks

A modified GADIA-based upper-bound to the capacity of Gaussian general N-relay networks

Shadow-Cuts Minimization/Maximization and Complex Hopfield Neural Networks

A Comprehensive Survey of Potential Game Approaches to Wireless Networks

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