Energy and spectral efficiency trade-off in OCDMA-PON assisted by non-linear programming methods
Introduction
The large number of communication technologies, as well as new broadband and internet services, have transformed telecommunications networks into a structure that allows people from different locations to use different categories of systems and equipment to communicate quickly and safely. Due to the high demand for internet traffic motivated by the new multimedia services in broadband, access networks have been demanding the ability to handle higher data rates in order to offer better QoS to their users [1].
Passive optical networks (PONs) provide bandwidth, QoS and low operating cost, in addition to allowing high transmission rates and longer transmission distances, enabling the sharing of fiber between different users [2].
In the topology of PON networks there are no active components between the equipment center and the end user’s facilities. One of the main advantages of the PON architecture is in the reduction of the implementation and maintenance costs, since the network elements are passive. PON networks interconnects the optical line terminal (OLT) and the optical network units (ONUs) [3]. Optical fiber stretches are used in common by the UNs, thus requiring the use of techniques for the control of multiple access in order to avoid the clash between user data resulting in loss of information and degradation of performance.
Because of the inevitable green networking trend, energy efficiency (EE) quickly became one of the key performance metrics to evaluate communication systems, together with spectral efficiency (SE). Earlier studies have demonstrated that the performance with QoS requirements in the wire or wireless transmission can be measured through effective capacity, capturing the channel characteristics and the QoS requirements, such as delay and data rate. Under this context, SE is defined as effective capacity per unit frequency bandwidth, and EE is defined as the energy consumed per useful capacity bit. Both circuit power and transmission laser power (in the context of optical networks) must be considered in the energy model, based on which one can derive the generalized EE formulation.
Several multiple access techniques are investigated for the use of PON networks. Among these techniques, optical code division multiple access (OCDMA) in which all users transmit simultaneously sharing all the available bandwidth in the optical channel, and each user has his own code orthogonal to the codes of other users [4], [5]. The EE of such optical systems has became paramount and an attractive focus of research in the current context of increasing energy demand of 5G communication systems [6]. In this context, recent works such as [4] analyze the maximum energy efficiency in OCDMA-PON networks considering a multi-rate scenario with different QoS. In turn, the spectral efficiency (SE) indicates the efficiency with which a limited spectrum resource is used, but fails to provide any information on how energy is consumed efficiently, which is of high practical interest in providing high efficient communication systems. Studies such as [7] have proposed spectral efficient hybrid precoding aiming to maximize the projection of hybrid precoding matrix onto the optimal precoding matrix. As a motivation to carry out further analyzes on the EE–SE trade-off, one can point out the exponential increasing on the traffic demand, forcing the telecom carriers to upgrade their networks to be able to rely on higher data rates and an increased spectral efficiency systems. Thus, EE and SE are two important metrics for improving the overall performance of optical communications systems.
One of the most important issues in multiple access communication environment, such as OCDMA communication systems, is the EE–SE trade-off characterization and, as a consequence, its optimization. Although the motivation for using OCDMA is not its efficiency in using bandwidth, spectral efficiency can nevertheless be one of several important measures considered in the design and performance of the communication system. Thus, the analysis of the EE metric may not adequately consider the use of bandwidth. Hence, in an OCDMA network, SE affects the communication rate per user, the number of active users allowed in the network and, as a consequence, the cost per user of the system. Hence, to exploit EE and SE’s trade-off with QoS (data-rate) considerations, we propose to solve the EE–SE analytical formulation using the weighted sum method combined with the majoration–minimization (MaMi) nonlinear programming (WS-MaMi). The impacts of QoS and circuit power consumption on EE–SE trade-off are analyzed. Data-rate requirement and circuit power consumption affect the EE–SE trade-off differently. In the low-SNR regime, circuit power shows more impact on the EE–SE trade-off, whereas data-rate QoS remarkably impacts the EE–SE trade-off in the high-SNR regime.
Several works in the literature are dedicated to solving multi-objective optimization (MOO) problems related to resource allocation in optical networks. In [8], a novel technique, namely superior population generation algorithm (SPGA), is conceived as a regular evolutionary genetic algorithm (GA) modification aiming to incorporate the capabilities of conventional techniques in solving the crucial SE–EE trade-off problem for the fifth generation (5G) heterogeneous networks using the key future technologies, such as carrier aggregation (CA). The SPGA technique outperforms the conventional GA; however, this GA-based method requires initial population selection highly dependable on the problem nature and dimensionality. Besides, SPGA should be developed and tuned as a common evolutionary heuristic. Hence, for more significant dimensionality problems, one can expect a substantial increase in the computational cost. On the other hand, the analytical-iterative WS-MaMi method proposed herein presents low computational complexity and simplicity of implementation, even for higher dimensionality. Moreover, [9] investigates the trade-off between EE and SE in downlink orthogonal frequency division multiplexing access (OFDMA) systems while considering the channel estimation cost and the corresponding effect of imperfect channel state information on the SE and EE.
In different communication system context, the EE-SE trade-off has been analyzed. For instance, [10] investigates the EE–SE trade-off in a downlink non-orthogonal multiple access (NOMA)-based heterogeneous networks (HetNets). In this work, the EE–SE problem is formulated as a MOO problem. Moreover, [11] analyzes the jointly EE and SE maximization in millimeter-wave backhaul small-cell networks with the user’s QoS guarantee. Furthermore, to explore the fundamental trade-off between the SE and EE in massive multiple-input multiple-output (M-MIMO) systems with linear precoding and transmit antenna selection, [12] investigates two evolutionary heuristic particle swarm optimization (PSO) based approaches: the WS-PSO and the normal-boundary-intersection particle swarm optimization (NBI-PSO) algorithm. Simulation results demonstrated that the PSO-based algorithms could achieve the Pareto optimal EE–SE trade-off, with NBI-PSO providing more evenly distributed solutions than WS-PSO. Besides, the optimal precoding and transmit antenna selection solutions based on both evolutionary heuristic techniques suffer the same drawback of significantly computational complexity increases when the problem dimensionally arising, besides the necessity of input parameter tuning for each system and channel configurations. Finally, the EE of multiuser MIMO in downlink multi-cell networks has been analyzed and optimized in [13]. Analytical expressions of system EE and SE are deployed to analyze the impact of the number of base station antennas (BS) and the number of users served on the overall system performance.
In realistic scenarios, the optimum EE and SE cannot always be attained simultaneously; such metrics are often conflicting in almost all operating-system configurations. Resource efficiency (RE) metric has been analyzed in [14], [15] aiming to balance EE and SE regarding the total power consumed by the system and occupied bandwidth. Hence, in [14], the EE-SE trade-off optimization problem was defined as a MOO problem where classical methods of nonlinear programming (NLP), including the Augmented Lagrangian and SQP methods combined with the MOO techniques, such as the weight sum (WS) method, have been deployed to determine possible solutions in the Pareto front.The numerical results indicate that the analytical-iterative NLP-based techniques are promising and often result in low-computational cost. However, in [14] no comparison was made with heuristic methods, while the solutions based on analytical NLP provides in those works require more complex computational implementations when compared with our proposed WS-MaMi technique for EE-SE optimization in OCDMA-PON.
Insightful observations on the EE-SE trade-off analysis have been offered in [16], considering (non-) cooperative architectures for femtocell 5G wireless networks. Authors in [17] investigate the EE-SE trade-off in downlink OFDMA systems. In [7], transmit antenna selection was investigated aiming at maximizing EE and SE in downlink OFDMA. Moreover, in [4] the authors apply the MaMi optimization method to the EE problem using the strategy of rewriting the constraints of the original problem as linear.
Contribution. The contribution of this work is threefold: (a) proposition and analysis of an efficient and promising hybrid optimization method, namely WS-MaMi, based on analytical iterative nonlinear programming approach; (b) an extensive EE-SE trade-off analysis using the proposed WS-MaMi optimization method in OCDMA networks have been provided; the proposed WS-MaMi method is compared to the association WS-SQP from [4]; (c) the EE–SE trade-off numerology for a wide range of realistic OCDMA systems applications have been established.
The remainder of this paper is divided as follows. Section 2 presents a system model for the OCDMA systems equipped with 2D spreading codes. Section 3 formulates the EE–SE trade-off problem for OCDMA networks, describing the main features of each approach adopted. Section 4 describes details for the optimization procedures based on NLP. Extensive numerical analyses are developed in Section 5 to find efficient Pareto solutions deploying realistic OCDMA networks context, by comparing both BOO approaches proposed with a reference method, namely WS-ES available in the literature. Finally, Section 6 concludes the paper.
Section snippets
System model
Traffic on the PON networks in the downstream sense leaves from the OLT to the ONUs, making a broadcast to all optical network units, through the optical power slitters. The upstream sense is directed from the ONUs to the OLTs. In this case, stretches of optical fibers are used in common by the UNs demanding techniques to control multiple access in order to avoid possible collisions between user data.
The OCDMA technique for PON networks stands out as an important alternative for deployment in
Multi-objective EE-SE trade-off problem
In this section, the optimal Pareto concepts are defined for analyzing the solution of the EE–SE commitment problem addressed in this work. Theoretical results are analyzed that support the numerical results achieved.
Optimization procedures
In this section, we present the methods used in this work to analyze the problem of bio-subjective optimization of the commitment EE–SE in OCDMA networks, which can be applied to solve (11).
The WS method re-scales the objective functions of the original bi-objective problem as a mono objective problem, and for this, we use (10). The metric-related BOO problem (10) can be described by the weighted sum method: being
Numerical results
In this section the main results of the simulations performed will be presented, considering optical networks that operate to each user ( denotes the number of users of the class ) of service class , corresponding to different classes of multimedia defined QoS and bit rate. Each class defined by must satisfy different minimum QoS requirements corresponding to specific SINR. Hence, the total number of active users in the OCDMA network is defined by .
For the
Conclusions
This work has dealt with the EE–SE trade-off in OCDMA-PON systems. We have demonstrated that it can be suitably addressed through the WS strategy combined with NLP methods. As the EE–SE OCDMA-PON optimization problem is multi-objective, one should find regular solutions for the Pareto front’s EE–SE problem. Our numerical results demonstrate that the proposed analytical-iterative WS-MaMi method significantly reduces the computational burden regarding the WS-SQP method while surpassing the
CRediT authorship contribution statement
Cristiane A. Pendeza Martinez: Conceptualization, Methodology, Formal analysis, Writing - original draft, Writing - review & editing, Software. Taufik Abrão: Supervision, Conceptualization, Validation, Methodology, Writing - review & editing. André Luís Machado Martinez: Software, Formal analysis, Writing - review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This work was supported in part by the National Council for Scientific and Technological Development (CNPq) of Brazil under Grant 10681/2019-7; in part by Londrina State University, Paraná State Government (UEL), Brazil; and in part by Federal Technological University of Paraná, Cornélio Procópio Campus (UTFPR), Paraná, Brazil .
Cristiane A. Pendeza Martinez received the M.S. Degree in Applied and Computational Mathematics from the Paulista State University (UNESP), São Paulo, Brazil, in 2006. She is a D.R. Degree in electrical engineering at UEL/UTFPR and Professor in Department of Mathematics at Technologic Federal University of Parná (UTFPR) at Cornélio Procópio, Brazil. Her research interest has been non linear program, heuristic and optimization aspects of networks.
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Cristiane A. Pendeza Martinez received the M.S. Degree in Applied and Computational Mathematics from the Paulista State University (UNESP), São Paulo, Brazil, in 2006. She is a D.R. Degree in electrical engineering at UEL/UTFPR and Professor in Department of Mathematics at Technologic Federal University of Parná (UTFPR) at Cornélio Procópio, Brazil. Her research interest has been non linear program, heuristic and optimization aspects of networks.
Taufik Abrão received the B.S., M.Sc., and Ph.D. degrees in electrical engineering from the Polytechnic School of the University of São Paulo, São Paulo, Brazil, in 1992, 1996, and 2001, respectively. Since March 1997, he has been with the Communications Group, Department of Electrical Engineering, Londrina State University, Paraná, Brazil, where he is currently an Associate Professor in Telecommunications and the Head of the Telecomm. Signal Processing Lab. He is a Productivity Researcher from the CNPq Brazilian Agency (Pq-1D) . From July-October 2018 he was with the Connectivity section, Aalborg University as a Guest Researcher. In 2012, he was an Academic Visitor with the Southampton Wireless Research Group, University of Southampton, Southampton, U.K. From 2007 to 2008, he was a Post-doctoral Researcher with the Department of Signal Theory and Communications, Polytechnic University of Catalonia (TSC/UPC), Barcelona, Spain. He has participated in several projects funded by government agencies and industrial companies. He is involved in editorial board activities of several journals in the telecommunications area and has served as TPC member in several symposiums and conferences. He has also served as an Associate Editor for the IEEE ACCESS since 2016, the IET Journal of Engineering since 2014, the IET Signal Processing since Dec-2018, and JCIS-SBrT journal since 2018. Previously, he served as AE of the IEEE Communication Surveys Tutorials (2013–2017). Moreover, Prof. Abrao has been served as Executive Editor of the ETT-Wiley journal since 2016. He is a member of SBrT and a senior member of IEEE. His current research interests include communications and signal processing, especially massive MIMO, ultra-reliable low latency communications, detection and estimation, multicarrier systems, cooperative communication and relaying, resource allocation, as well as heuristic and convex optimization aspects of 5G wireless systems. He has supervised 27 M.Sc. and 4 Ph.D. students, as well as 3 postdocs, co-authored twelve book chapters on mobile radio communications and +280 research papers published in international journals and conferences.
André Luís Machado Martinez received the M.S. Degree in Mathematics from the State University of Maringá (2006) and doctorate in Applied Mathematics from the State University of Campinas (2009). He is currently an associate professor at the Federal Technological University of Paraná. Has experience in Mathematics, with emphasis on Optimization, acting on the following subjects: numerical optimization, mathematical analysis, non-linear programming.