Choosing the optimization objective for the resource allocation problem
In the context of this thesis, the process of assigning multiple subcarriers to multiple users in a specified timing scheme is called a resource allocation method. Because of the variation in design objectives, network topologies, configuration limitations, and diversity in the application requirements, the problem of resource allocation has been attracted a great number of researchers. In the framework of optimization problems, an objective or utility function quantifies an abstract concept and develops a tangible performance metric. In this section, we review the optimization objectives defined for resource allocation problems in the literature. Throughput maximization, or maximizing the spectral efficiency has been one of the most popular optimization objectives in the relay-aided allocation problems (Al-Tous & Barhumi, 2016; Ho et al., 2015; Y. Liu & Chen, 2012; Ng & Schober, 2011; Phan, Le-Ngoc, Vorobyov, & Tellambura, 2009; Salem, Adinoyi, Yanikomeroglu, & Falconer, 2011; Son, Lee, Yi, & Chong, 2011). It is known that, selecting the best user for each OFDM subcarrier and adjusting the corresponding transmission power leads to maximum system spectral efficiency (Ng & Schober, 2011). A joint subcarrier and power allocation mechanism introduced in (Ng & Schober, 2011) that maximizes a concave utility function that is defined as the minimum of instantaneous rate between base station-relay link (BS-RS) and relay-user link (RS-UE). Authors of (Son et al., 2011) maximized the sum of weighted rates in a distributed manner for each base station.
Therein, to simplify the computation complexity, the subcarrier allocation is decoupled from power assignment. A joint subcarrier and transmission power allocation is proposed in (Al-Tous & Barhumi, 2016) with the objective to maximize the overall users weighted rates. Multiple approaches are then introduced considering both AF and DF relaying for high signal to noise ratio (SNR) channel condition, however these methods are not efficient for low SNR scenarios. The throughput-optimal allocation model introduced in (Y. Liu & Chen, 2012) improves the spectrum efficiency by enabling the base station to transmit during relaying sub-frame on subcarriers unused by the relay. In a high SNR assumption, authors of (Phan et al., 2009) formulate the throughput maximization objective of the relaying power allocation problem to a utility function that is the product of SNR values. A sum-rate optimization problem defined in (Ho et al., 2015), solved the power allocation problem for the two-hop cooperative uplink transmission. Despite the advantage of decreasing the messaging overhead for single carrier method in (Ho et al., 2015), it can cause extensive computation and signaling load in multicarrier scenarios.
Power minimization is another design objective that can be applied in the relay-aided resource allocation problem. For instance, authors of (M. Chen, Serbetli, & Yener, 2005) defined a power allocation scheme in a DF relaying system with the objective to minimize the total transmit power while satisfying a target level of SNR at the destination. Among several power allocation methods for relaying systems that are deployed in (Phan et al., 2009), one notable approach consists of minimizing the maximum transmit power at the base station following the rational that energy constraints is less sever on relays. Proportional fairness is a widely used resource allocation objective that compromises the network capacity and user fairness (Huang, Rong, Wang, Xue, & Schulz, 2007; Kelly, Maulloo, & Tan, 1998; Z. Tang & Wei, 2009; Viswanath, Tse, & Laroia, 2002). For instance, the method introduced in (Viswanath et al., 2002) allocates a resource unit to a user targeting to maximize the ratio of its achievable rate to the exponentially weighted average rate. The fact that a large number of papers have been dedicated to optimize the system throughput indicates the validity of this approach for optimal allocation of wireless resources.
We thus chose throughput maximization as our optimization objective targeting to fill the gap for an efficient method in low SNR regime. Aside from the main objective, it is important to efficiently define the optimization constraints to confine a feasible solution in regard to specific performance criteria. For instance, optimization constraints can be defined for limiting the power consumption (Ho et al., 2015), co-channel interference (Ho et al., 2015; Lin, Tao, Stüber, & Liu, 2013; Ng & Schober, 2011; Venturino, Prasad, & Wang, 2009) or outage probability (Ho et al., 2015; Zarakovitis, Ni, Skordoulis, & Hadjinicolaou, 2012). Cross-layer resource allocation In previous section we pointed out the methods that only employ PHY layer features in the allocation problem. However, it has been shown that the joint optimization of resources allocation across PHY layer and MAC layer features, so called cross-layer methods, leads to significant throughput gain and efficiency. One of the main features of the MAC layer is the buffering of data in Queue-based data structures. Queue length has been employed in cross layer methods as a means of fairness, delay control, or stability. For instance, the introduced utility function for throughput maximization defined in (Salem, Adinoyi, Rahman, et al., 2010; Salem et al., 2011) is formulated as the product of rate and differential backlog. The idea of differential backlog that implies the difference of buffer length between the transmitter and the receiver, has been first introduced in (Neely, Modiano, & Rohrs, 2005) for a power allocation problem in wireless networks. It is shown in (Salem et al., 2011), that coupling the rate and buffer length in resource allocation problem leads to a higher fairness in throughput compared to traditional proportional fair scheduling methods. A utility fair rate allocation in the downlink of cellular networks is considered in (Eryilmaz & Srikant, 2007). Therein, rates are allocated based on optimizing a queue-rate product utility function while the proposed admission control policy is in effect.
Numerical results and discussion
We defined a network consisting of a single cell and three relay stations fixed at a distance of 15 Km from the base station. The relay-aided users are randomly placed in a distance of 220 m from their corresponding relays, as depicted in Figure 2.1. There are 64 subcarriers available in the downlink subframe. Each subcarrier has 15 KHz bandwidth and the carrier center frequency is 2.5 GHz. The BS-RS and RS-UE links both follow the suggested 3GPP path loss model, i.e urban macrocell in LoS and urban microcell in NLoS, respectively (Universal Mobile Telecommunications System (UMTS); Spacial channel model for Multiple Input Multiple Output (MIMO) simulations, n.d.). Each RS-UE link, that is NLoS, suffers multipath Rayleigh fading that is modeled with i.i.d random variables of complex Gaussian distribution with zero mean and unit variance, i.e. CN (0,1) . The LoS BS-RS link experiences Rician fading with Rician factor κ = 6 dB that can be modeled by i.i.d random variable of complex Gaussian distribution whereCN ( κ 1+κ ,1 1+κ ). The shadowing coefficients are i.i.d random variable modeled by complex Gaussian distribution with zero mean and variance of 2 , 3 BS dB γ σ = and 2 , 8 RS dB γ σ = , respectively for BS-RS and RS-UE links.
The noise power density equals -174 dBm/Hz. The total transmission power of BS and RS equals 20W and 10W, respectively. The transmit power per subcarrier in BS and RS is fixed to the ratio of total power to the number of subcarriers. The length of a time slot is 5 ms. The entering data traffic at the base station can be modeled by a bursty On/Off traffic model (Lakani, Gagnon, 64 & Groleau, 2015). However, the length of On-time (normally 2 s) is far larger than the time slot length (5 ms), which resembles a constant bit rate (CBR) traffic during one time slot. For this reason, we consider CBR traffic arrival rate in the current work. To avoid complexity, all incoming traffic streams are assumed to have identical mean arrival rate and the users’ weight parameters are also amounted to unity i.e. ω(k) =1,k∈{1,2,…,K}. We apply MOSEK solver (MOSEK Apps., 2014) in CVX package (M. Grant & S. Boyd, 2014) for solving the Timeshared optimization problem. Because the channel samples are drawn from probabilistic distributions, we demonstrated the numerical results by averaging the performance values over 100 independent realization of the simulated system. During various simulation examinations, we verified that 100 realization is enough to prevent fluctuations in the performance trends.
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Table des matières
INTRODUCTION
CHAPTER 1 DESIGN METHODOLOGY AND LITERATURE REVIEW
1.1 Choosing a relaying technique
1.2 Choosing a channel access method
1.3 Choosing the optimization objective for the resource allocation problem
1.4 Cross-layer resource allocation
1.4.1 Delay optimal methods
1.4.2 System stabilizing methods
1.5 Choosing a solver
1.6 Challenges of multi-cell cooperation
1.6.1 Frequency planning
1.6.2 Inter-cell interference management
1.7 Conclusion
CHAPTER 2 CHANNEL- AND TRAFFIC-AWARE RESOURCE ALLOCATION CONSTRAINED TO SYSTEM STABILITY
2.1 System model
2.1.1 Channel capacity
2.1.2 Traffic-aware stability control
2.2 Defining an optimization model to solve the resource allocation problem
2.3 Time-shared subcarrier allocation
2.4 Exclusive subcarrier allocation
2.4.1 Anti-relaxation approach (ARA)
2.4.2 Two-Phase Heuristic Approach (TPHA)
2.4.3 Computation complexity of the binary allocation mechanisms
2.5 Numerical results and discussion
2.5.1 System stability
2.5.2 System throughput
2.6 Conclusion
CHAPTER 3 CHANNEL- AND QUEUE-AWARE RESOURCE ALLOCATION IN A MULTI-CELL RELAY-AIDED SYSTEM CONSTRAINED TO STABILITY AND INTERFERENCE CONTROL
3.1 System model
3.1.1 Adjustable time-slot partitioning
3.1.2 Channel capacity
3.1.3 Queue-aware stability control
3.2 Defining the optimization problem
3.3 The time-shared solution in multi-cell network
3.4 The Optimized Binary Resource Allocation (OBRA) approach
3.5 The Conservative Binary Resource Allocation (OBRA) approach
3.6 Comparison of computation complexity
3.7 Numerical results and discussion
3.7.1 System throughput
3.7.2 Energy efficiency
3.7.3 Impact of varying channel state on throughput
3.7.4 Impact of adaptive time-slot division on throughput
3.7.5 Impact of varying channel state and time-slot division on power consumption
3.7.6 System Stability
3.7.7 Offline tuning of a proper interference tolerance value
3.8 Conclusion
CHAPTER 4 LOW OVERHEAD AND DISTRIBUTED SUBCARRIER AND POWER ALLOCATION IN RELAY-AIDED MULTI-CELL NETWORK WITH STABILITY CONSTRAINTS
4.1 System model
4.1.1 Channel capacity
4.1.2 Queue-aware stability control
4.2 Distributed subcarrier and power allocation
4.2.1 Iterative power allocation mechanism
4.3 Further reducing the signaling overhead
4.4 Numerical results and performance evaluation
4.4.1 System throughput
4.4.2 Energy efficiency
4.4.3 System stability
4.5 Conclusion
CONCLUSION AND RECOMMENDATIONS
APPENDIX I CONVEX PROPERTTY OF THE PERSPECTIVE FUNCTION
APPENDIX II ADMISSION CONTROL POLICY
APPENDIX III REVIEW ON GEOMETRIC PROGRAMMING
APPENDIX IV CONVERSION OF OBJECTIVE FUNCTION OF CBRA
PROBLEM TO GP-COMPATIBLE FORMAT
APPENDIX V MONOMIAL APPROXIMATION EMPLOYED IN
CBRA PROBLEM
APPENDIX VI CONVERGENCE CONDITIONS OF THE ITERATIVE
GP PROBLEM IN CBRA METHOD
APPENDIX VII THE SELF-CONCORDANT PROPERTY
APPENDIX VIII LIST OF PUBLICATIONS
BIBLIOGRAPHY
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