Channel Assignment Problem Research Articles

On Radio k – Chromatic Number for Mycielski of Some Graphs

Objectives: In radio networks, the main difficulty is managing the radio spectrum, assigning radio frequencies to transmitters optimally without any interferences. This study aims to find the smallest span of Mycielski of some graphs, the maximum color assigned to any node is called span. Methods : This study focused on the problem of reducing interference by modeling it with a radio k - coloring problem on graphs. Where transmitters are modeled as nodes in a graph, with edges connecting nodes that represent transmitters in close proximity to one another. For a graph , with node set , edge set and an integer , a radio k - coloring of is a function satisfying the condition for any two nodes and , where is the distance between and in . The radio k - coloring of , is the maximum color assigned to any node of and it is denoted by . The radio k -chromatic number of is the minimum value of taken over all radio k - coloring of and it is denoted by . Findings: This study obtained the radio k-chromatic number for Mycielski of some graphs for and 3 Novelty: To solve the channel assignment problem in radio transmitters, the interference graph is developed, and the channel assignment has been converted into a graph coloring. Reducing the interference by a radio k - coloring problem will motivate many researchers to find the radio k - coloring in various graphs. Keywords: Radio k – Coloring, Mycielski graph, Double Star graph, Triple Star graph, Sunlet graph, Helm graph and Closed Helm graph

Multi‐objective spectrum assignment in heterogeneous cognitive radio networks for internet of things

SummaryInternet of Things (IoT) applications have massively increased in the last few years. Future‐generation IoTs are going to be massive in number, heterogeneous in nature, and extremely demanding in terms of computation and communication requirements. Therefore, effective techniques are needed to optimize the use of scarce communication resources. This work proposes a novel multi‐objective framework to investigate the channel assignment problem in cognitive radio network (CRN)‐based IoT applications. The multi‐objective optimization framework comprises three objective functions. The first objective aims to maximize the overall system throughput fairness, the second objective aims to maximize the overall system residual energy, and the third objective aims to increase the user satisfaction level by maximizing the overall priority index. The problem of channel assignment is modeled and solved using Mixed Integer Linear Programming (MILP) and ‐constraint technique. This technique generates a set of Pareto efficient solutions, and an optimal solution among these solutions is selected using a fuzzy logic decision mechanism. Moreover, power level selection is incorporated by solving the problem multiple times for different power levels and obtaining a preferred solution for each power level. The simulations are conducted to unveil an interesting trade‐off between the conflicting system design objectives, that is, the overall throughput and the overall residual energy while incorporating the significance of primary user (PU) activity when preforming channel assignment in CRN.

Radio number of $ 2- $ super subdivision for path related graphs

<abstract><p>We studied radio labelings of graphs in response to the Channel Assignment Problem (CAP). In a graph $ G, $ the radio labeling is a mapping $ \varpi:V(G) \rightarrow \{0, 1, 2, ..., \}, $ such as $ |\varpi(\mu')-\varpi(\mu'')|\geq diam(G)+1-d(\mu', \mu''). $ The label of $ \mu $ for under $ \varpi $ is defined by the integer $ \varpi(\mu), $ and the span under is defined by $ span(\varpi) = max \{|\varpi(\mu')-\varpi(\mu'')|: \mu', \mu'' \in V(G)\}. $ $ rn(G) = min_{\varpi} span(\varpi) $ is defined as the radio number of $ G $ when the minimum over all radio labeling $ \varpi $ of $ G $ is taken. $ G $ is said to be optimal if its radio labeling is $ span(\varpi) = rn(G). $ A graph H is said to be an $ m $ super subdivision if $ G $ is replaced by the complete bipartite graph $ K_{m, m} $ with $ m = 2 $ in such a way that the end vertices of the edge are merged with any two vertices of the same partite set $ X $ or $ Y $ of $ K_{m, m} $ after removal of the edge of $ G $. Up to this point, many lower and upper bounds of $ rn(G) $ have been found for several kinds of graph families. This work presents a comprehensive analysis of the radio number $ rn(G) $ for a graph $ G $, with particular emphasis on the $ m $ super subdivision of a path $ P_{n} $ with $ n (n \geq 3) $ vertices, along with a complete bipartite graph $ K_{m, m} $ consisting of $ m $ v/ertices, where $ m = 2 $.</p></abstract>

Energy-efficient non-anchor channel allocation in NB-IoT cellular networks

In Narrowband Internet of Things (NB-IoT), a base station can provide multiple non-anchor channels to release the burden of anchor channels. NB-IoT devices can use non-anchor channels to execute data transmission to save energy. However, we creatively observe a new important property in the NB-IoT; allocating more non-anchor channels to a base station may even cause an increase in the energy consumption of devices during the data transmission procedure. Unlike traditional channel assignment problems, this new property in the NB-IoT leads to the non-anchor channel allocation being a non-convex problem. This article studies the energy-efficient non-anchor channel allocation in the NB-IoT to minimize the energy consumption of devices to finish their data requests. Because of the non-convex property, this article proposes a dynamic programming algorithm without considering frequency reuse to determine how many non-anchor channels each base station should use. We prove that the dynamic programming algorithm can get an optimal solution. Then, we propose an energy-efficient non-anchor channel reuse algorithm to minimize the energy consumption of devices. Compared with two baselines, the simulation results show that the proposed algorithms reduce the energy consumption by 66%, and blind decoding consumes the most energy of a device.

Neighbor Distinguishing Colorings of Graphs with the Restriction for Maximum Average Degree

Neighbor distinguishing colorings of graphs represent powerful tools for solving the channel assignment problem in wireless communication networks. They consist of two forms of coloring: neighbor distinguishing edge coloring, and neighbor distinguishing total coloring. The neighbor distinguishing edge (total) coloring of a graph G is an edge (total) coloring with the requirement that each pair of adjacent vertices contains different color sets. The neighbor distinguishing edge (total) chromatic number of G is the smallest integer k in cases where a neighbor distinguishing edge (total) coloring exists through the use of k colors in G. The maximum average degree of G is the maximum of the average degree of its non-empty subgraphs. In this paper, we characterize the neighbor distinguishing edge (total) chromatic numbers of graphs with a maximum average degree less than four by means of the discharging method.

The F/DR-D-10 Algorithm: A Novel Heuristic Strategy to Solve the Minimum Span Frequency Assignment Problem Embedded in Mobile Applications

Wireless communication supports various real-world applications, such as aeronautical navigation, satellite and TV broadcasting, wireless LANs, and mobile communications. The inherent characteristics of the electromagnetic spectrum impose constraints on telecommunication channels and their frequency bandwidths within mobile networks. A persistent challenge in these applications is providing high-demand services to mobile users, where frequency assignment problems, also known as channel assignment problems, assume significance. Researchers have developed several modeling approaches to address different facets of this problem, including the management of interfering radio signals, the assessment of available frequencies, and optimization criteria. In this paper, we present improved algorithms for solving the Minimum Span Frequency Assignment Problem in mobile communication systems using the greedy optimization approach known as F/DR. We solved and evaluated twenty well-known benchmark cases to assess the efficacy of our algorithms. Our findings consistently demonstrate that the modified algorithms outperform the F/DR approach with comparable computational complexity. The proposed algorithm notably achieves the following benchmarks: The modified algorithms consistently produce at least one local optimum better than the traditional algorithm in all benchmark tests. In 95% of the benchmarks evaluated, the probability of discovering a local optimum value (calculated by the modified algorithm) that is better than or equal to the one found by the conventional algorithm exceeds 50%.

On the Span of ℓ Distance Coloring of Infinite Hexagonal Grid

For a graph [Formula: see text] and [Formula: see text], an [Formula: see text] distance coloring is a coloring [Formula: see text] of [Formula: see text] with [Formula: see text] colors such that [Formula: see text] when [Formula: see text]. Here [Formula: see text] is the distance between [Formula: see text] and [Formula: see text] and is equal to the minimum number of edges that connect [Formula: see text] and [Formula: see text] in [Formula: see text]. The span of [Formula: see text] distance coloring of [Formula: see text], [Formula: see text], is the minimum [Formula: see text] among all [Formula: see text] distance coloring of [Formula: see text]. A class of channel assignment problem in cellular network can be formulated as a distance graph coloring problem in regular grid graphs. The cellular network is often modelled as an infinite hexagonal grid [Formula: see text], and hence determining [Formula: see text] has relevance from practical point of view. Jacko and Jendrol [Discussiones Mathematicae Graph Theory, 2005] determined the exact value of [Formula: see text] for any odd [Formula: see text] and for even [Formula: see text], it is conjectured that [Formula: see text] where [Formula: see text] is an integer, [Formula: see text] and [Formula: see text]. For [Formula: see text], the conjecture has been proved by Ghosh and Koley [[Formula: see text]nd Italian Conference on Theoretical Computer Science, 2021]. In this paper, we prove the conjecture for any even [Formula: see text].

Routing and Resource Scheduling for Air-Ground Integrated Mesh Networks

Due to the advantage of achieving scalable connectivity and low-latency communications, air-ground integrated mesh networks (AGIMNs) will play an important role in the next generation wireless communication systems. However, due to the heterogeneous character of AGIMNs, it is challenging to manage the network and optimize the communication resources for improving the end-to-end (E2E) performance. Therefore, in this paper, we study a joint routing and time-frequency resource scheduling problem aiming at minimizing the total weighted E2E delay for heterogeneous AGIMNs. To capture the features of this complex system, we mathematically model the network constraints and formulate an optimization problem. To solve the original nonconvex problem, a suboptimal solution is proposed. First, we propose an optimal minimum-weight routing method, in which the hop count, conflict delay, and contention delay are taken into consideration. Then, we transform the time-frequency resource scheduling subproblem into a series of tractable problems for maximizing the number of active links through channel assignment in successive time slots. Finally, the successive convex approximation (SCA) technique is utilized to solve the channel assignment problem per time slot. Extensive simulation results show the performance superiority of the proposed solution compared to the benchmarks in terms of the total E2E delay.

A Novel Radio Geometric Mean Algorithm for a Graph

Radio antennas switch signals in the form of radio waves using different frequency bands of the electromagnetic spectrum. To avoid interruption, each radio station is assigned a unique number. The channel assignment problem refers to this application. A radio geometric mean labeling of a connected graph G is an injective function h from the vertex set, V(G) to the set of natural numbers N such that for any two distinct vertices x and y of G, h(x)·h(y)≥diam+1−d(x,y). The radio geometric mean number of h, rgmn(h), is the maximum number assigned to any vertex of G. The radio geometric mean number of G, rgmn(G) is the minimum value of rgmn(h), taken over all radio geometric mean labeling h of G. In this paper, we present two theorems for calculating the exact radio geometric mean number of paths and cycles. We also present a novel algorithm for determining the upper bound for the radio geometric mean number of a given graph. We verify that the upper bounds obtained from this algorithm coincide with the exact value of the radio geometric mean number for paths, cycles, stars, and bi-stars.

Efficient dynamic channel assignment through laser chaos: a multiuser parallel processing learning algorithm

As laser chaos has been proven to be a robust tool to solve the multi-armed bandit (MAB) problem, this study investigates the problem of multiuser dynamic channel assignment using laser chaos in cognitive radio networks with K-orthogonal channels and M secondary users. A novel dynamic channel assignment algorithm with laser chaos series for multiple users, named parallel processing learning with laser chaos (PPL-LC) algorithm, is proposed to efficiently address two main objectives: stable channel assignment and fuzzy stable channel assignment. The latter objective accounts for the realistic scenario where users have fuzzy preferences and do not necessarily pursue the best preference. The PPL-LC algorithm uses the randomness properties of laser chaos to learn the assignment of channels to multiple users without any limitations on the number of channels, which has not been considered in existing laser chaos algorithms. Moreover, the PPL-LC is equipped with parallel processing channel selections, resulting in higher throughput and stronger adaptability with environmental changes over time than comparison algorithms, such as distributed stable strategy learning and coordinated stable marriage MAB algorithms. Finally, numerical examples are presented to demonstrate the performance of the PPL-LC algorithm.

Qubit Reduction and Quantum Speedup for Wireless Channel Assignment Problem

Qubit Reduction and Quantum Speedup for Wireless Channel Assignment Problem

Distributed coloring and the local structure of unit-disk graphs

Coloring unit-disk graphs efficiently is an important problem in the global and distributed setting, with applications in radio channel assignment problems when the communication relies on omni-directional antennas of the same power. In this context it is important to bound not only the complexity of the coloring algorithms, but also the number of colors used. In this paper, we consider two natural distributed settings. In the location-aware setting (when nodes know their coordinates in the plane), we give a constant time distributed algorithm coloring any unit-disk graph G with at most 4ω(G) colors, where ω(G) is the clique number of G. This improves upon a classical 3-approximation algorithm for this problem, for all unit-disk graphs whose chromatic number significantly exceeds their clique number. When nodes do not know their coordinates in the plane, we give a distributed algorithm in the LOCAL model that colors every unit-disk graph G with at most 5.68ω(G)+1 colors in O(log⁎⁡n) rounds. This algorithm is based on a study of the local structure of unit-disk graphs, which is of independent interest. We conjecture that every unit-disk graph G has average degree at most 4ω(G), which would imply the existence of a O(log⁡n) round algorithm coloring any unit-disk graph G with (approximately) 4ω(G) colors in the LOCAL model. We provide partial results towards this conjecture using Fourier-analytical tools.

A note on the L(2,1)-labelling problem of G(k,m)

The L ( 2 , 1 ) -labelling problem is a special case of the channel assignment problem. For a given graph G , a k - L ( 2 , 1 ) -labelling is defined as a function f : V ( G ) → { 0 , 1 , 2 , … , k } such that | f ( u ) − f ( v ) | ≥ 2 when d G ( u , v ) = 1 and | f ( u ) − f ( v ) | ≥ 1 when d G ( u , v ) = 2 . The L ( 2 , 1 ) -labelling number of G , denoted by λ ( G ) , is the smallest number k such that G has a k - L ( 2 , 1 ) -labelling. A graph G ∈ G ( k , m ) if G is ( m + 1 ) -partite graph with V ( G ) = V 0 ∪ V 1 ∪ ⋯ ∪ V m , where | V 0 | = | V 1 | = ⋯ = | V m | = k and the induced subgraph G [ V i ∪ V j ] is a perfect matching for any 0 ≤ i < j ≤ m . Lu and Zhai asked whether λ ( G ) = 2 m if G ∈ G ( k , m ) in [An extremal problem on non-full colorable graphs, Discrete Appl. Math. 155 (2007) 2165–2173]. We give a negative answer and prove that for every k ≥ 3 and m ≥ 4 , there exists a graph G ∈ G ( k , m ) with λ ( G ) = 2 m − 1 .

Radio antipodal number of honeycomb derived networks

The communication in a wireless network mainly depends on the frequencies or channels assigned to them. The channels must be assigned to all the transmitters in the network without interference for effective communication. This problem is said to be a channel (frequency) assignment problem (CAP). With the limited availability of channels, CAP has become a challenging problem. This problem is modeled as a graph, where each transmitter is represented by a vertex, and two vertices are adjacent when their corresponding transmitters are close. The labelling technique in graph theory has played an important role in solving CAP, thereby the time and cost will be saved. In radio antipodal labeling, the channels were reused again for the antipodal vertices. It will reduce the usage of the number of channels, with minimum interference. Hence it is a better labeling compared to other labelings. It is a mapping tau from the vertex set of a graph T to the set of natural numbers such that the condition d(alpha ,eta )+mid tau (alpha )-tau (eta )mid ge diam(T), is satisfied. The span of the antipodal labeling tau is the maximum label allotted in a graph and is given by sp(tau )=max{mid tau (alpha )-tau (eta )mid :alpha ,eta in V(T)}. The lowest value of all the spans of the antipodal labeling of graph T is said to be radio antipodal number. It is denoted by an(T). The value of the minimum span gives the bandwidth or spectrum of the channels. The honeycomb network plays an important role in communication engineering because of its structure. In this paper, the bounds of the antipodal number of honeycomb derived networks—triangular and rhombic honeycomb were obtained and represented graphically. These bounds give the optimum number of channels (bandwidth) needed for these honeycomb derived networks for effective communication without interference.

QoS aware routing protocol using robust spatial gabriel graph based clustering scheme for ad hoc network

SummaryMANET (mobile ad hoc network) comprises of a set of wireless mobile node connected in a self‐healing and self‐configured network devoid of any fixed infrastructure. The cognitive radio (CR) in the MANET system has been developed for addressing the spectrum congestion issue. However, the existing techniques failed to solves the complex convex problem of channel assignment. To address this issue, the proposed protocol is designed. In the proposed scheme, both primary user (PU) and secondary user (SU) are clustered initially based on the graph theory process. After that, in each cluster, formation of robust spatial Gabriel graph (RS‐GG) takes place at which the neighboring nodes are predicted by estimating the weighted end‐to‐end delay. Once the multi path decision‐making condition is satisfied, the route path is established, and the communication takes place based on QoS constraint. This can lead to the enhancement of PDR, network connectivity maintenance and network lifetime. The performance analysis of the proposed methods is carried out for PDR, control overheads, energy consumption, and End‐to‐End delay and the analysis is compared with existing protocols to prove the effectiveness of proposed design. The simulation outcomes illustrate that the suggested strategy performs well and improves the data transmission.

LoRa-RL: Deep Reinforcement Learning for Resource Management in Hybrid Energy LoRa Wireless Networks

LoRa wireless networks are considered as a key enabling technology for next generation internet of things (IoT) systems. New IoT deployments (e.g., smart city scenarios) can have thousands of devices per square kilometer leading to huge amount of power consumption to provide connectivity. In this paper, we investigate green LoRa wireless networks powered by a hybrid of the grid and renewable energy sources, which can benefit from harvested energy while dealing with the intermittent supply. This paper proposes resource management schemes of the limited number of channels and spreading factors (SFs) with the objective of improving the LoRa gateway energy efficiency. First, the problem of grid power consumption minimization while satisfying the system's quality of service demands is formulated. Specifically, both scenarios the uncorrelated and time-correlated channels are investigated. The optimal resource management problem is solved by decoupling the formulated problem into two sub-problems: channel and SF assignment problem and energy management problem. Since the optimal solution is obtained with high complexity, online resource management heuristic algorithms that minimize the grid energy consumption are proposed. Finally, taking into account the channel and energy correlation, adaptable resource management schemes based on Reinforcement Learning (RL), are developed. Simulations results show that the proposed resource management schemes offer efficient use of renewable energy in LoRa wireless networks.

Joint optimization for RIS-assisted multicast D2D communications

Multicast device-to-device (D2D) communication is an important technique to overcome the problem of spectrum shortage. Due to the channel gain difference between users in different locations, receivers in the same multicast D2D group still suffer from the problem of different quality of service (QoS) levels. This paper proposes a novel reconfigurable intelligent surface (RIS)-assisted multicast D2D communication system to enhance the QoS of users, in which RIS solves the problem of different QoS between users through intelligent resource optimization. To maximize the achievable sum rate of all multicast D2D users, we formulate a joint optimization problem. This problem combines channel assignment, power allocation, and reflection matrix design by considering the QoS fairness among different D2D users. To solve this problem, we propose a novel joint optimization algorithm, which has three steps. First, we propose a matching algorithm based on swap operations to solve the channel assignment problem. Then, we propose a successive convex approximation (SCA) method to solve the power allocation problem. Finally, we present the optimization of the RIS reflection coefficients with mathematical analysis. The numerical results demonstrate that the proposed algorithm can effectively enhance the QoS of users in the multicast D2D group. With the aid of RIS, the proposed algorithm decreases the service disparities between users in different locations. Furthermore, it reveals that it is helpful to deploy the RIS closer to the receivers or the transmitters.

Highly Reliable Transmission and Channel Assignment for CR-IoT Networks

In this article, we propose a highly reliable transmission strategy based on exploiting channel diversity for Internet of Things (IoT) networks equipped with cognitive radio (CR) capabilities (referred to as CR-IoT networks). Specifically, we investigate the channel-assignment problem with the objective of minimizing the number of assigned channels for each CR transmission subject to link reliability, data rate, and success probability constraints. We use the theory of continuous-time Markov chains to derive mathematical expressions for channel availability and reliability. These expressions are employed in a binary linear program model to formulate the channel assignment optimization problem, which is suboptimally solved using a polynomial-time sequential fixing procedure. Theoretical performance analysis of the proposed channel assignment scheme is derived in terms of a lower bound on the achievable probability of successful packet transmission. Through simulation experiments, we demonstrate significant performance enhancement compared to existing reliability-unaware CR channel assignment algorithms.

Channel Assignment Based on CSMA-Aware Interference Model With Overlapped Channels in Multiradio Multichannel Wireless Mesh Networks

Multi-radio Multi-channel Wireless Mesh Networks (MRMC WMNs) implemented on IEEE 802.11 standards are widely used owing to their adaptability in practical network scenarios. The channel assignment problem in MRMC WMNs has been extensively studied. However, in most of the existing works, only orthogonal wireless channels are considered owing to the complexity of the channel assignment problem, which results in a low level of spatial utilization. This paper introduces partially overlapping channels into the CSMA-aware interference and shared link capacity models to fully exploit the spectrum resource and improve network capacity, utilizing both orthogonal channels and partially overlapping channels in IEEE 802.11 2.4 GHz bands. We formulate this problem as a mixed-integer linear program (MILP). We propose a traffic-demand-aware collision-free partially overlapping channel assignment (TAC-POCA), which uses all the available channels and achieves collision-free end-to-end flow transmissions to attain load balance. Simulation results show that TAC-POCA leads to better utilization of the spectrum resource and throughput improvement in both grid and random topology networks than in the case of using only orthogonal channels.

Comparison of Metaheuristic Algorithms for Interface-Constrained Channel Assignment in a Hybrid Dynamic Spectrum Access – Wi-Fi Infrastructure WMN

In this work, we evaluate the application of four different metaheuristic optimisation algorithms for solving the channel assignment problem in a multi-radio multi-channel Wireless Mesh Network (WMN) using Dynamic Spectrum Access (DSA). The work advances a near optimal channel assignment (CA) in a WMN that uses DSA by applying soft computing methods. While CA in a WMN is well-studied, and CA for secondary user cognitive radio networks has also been studied in the literature, CA for our specific scenario of an infrastructure DSA-WMN is novel. This scenario poses new challenges because nodes are spread out geographically and so may have different allowed channels and experience different levels of external interference in different channels. A solution must meet two conflicting requirements simultaneously: 1) to avoid interference within the network and with external interference sources, and 2) maintain connectivity within the network; all while staying within the radio interface constraint, i.e., only assigning as many channels to a node as it has radios. We present a novel algorithm, used alongside the metaheuristic optimisation algorithms, which ensures the feasibility of solutions in the search space. Average Signal to Interference and Noise Ratio (<inline-formula> <tex-math notation="LaTeX">$SINR$ </tex-math></inline-formula>) over the network is used as the performance measure, with the goal of optimisation being to find the highest average <inline-formula> <tex-math notation="LaTeX">$SINR$ </tex-math></inline-formula>. This is a more realistic performance measure than the binary on/off conflict-based measures most common in the literature. Our energy-based method also has the unique advantage that it is protocol-agnostic, being able to avoid interference from external sources that use different protocols and standards. The algorithms that are compared in this work are Simulated Annealing (SA), the Genetic Algorithm (GA), Particle Swarm Optimisation (PSO), and Differential Evolution (DE). These algorithms were evaluated through the use of simulation in Network Simulator 3. Various parameters were experimented with for each of the employed algorithms. The resultant best set of parameters was used for the comparison of the four metaheuristic algorithms. It was found that the population-based algorithms (PSO, GA, and DE) all perform satisfactorily for this problem, although DE is superior to the others. SA can give acceptable solutions, but performs poorly in comparison to the population-based algorithms. The paper also considers the computational complexity of the methods. It is found that SA and DE perform well in this regard.