Discrete and Continuous Optimization Methods for Self-Organization in Small Cell Networks - Models and Algorithms

Self-organization is discussed in terms of distributed computational methods and algorithms for resource allocation in cellular networks. In order to develop algorithms for different self-organization problems pertinent to small cell networks (SCN), a number of concepts from discrete and continuous optimization theory are employed. Self-organized resource allocation problems such as physical cell identifier (PCI) assignment and primary component carrier selection are formulated as discrete optimization problems. Distributed graph coloring and constraint satisfaction algorithms are used to solve these problems. The PCI assignment is also discussed for multi-operator heterogeneous networks. Furthermore, different variants of simulated annealing are proposed for solving a graph coloring formulation of the orthogonal resource allocation problem. In the continuous optimization domain, a network utility maximization approach is considered for solving different resource allocation problems. Network synchronization is addressed using greedy and gradient search algorithms. Primal and dual decomposition are discussed for transmit power and scheduling weight optimizations, under a network-wide power constraint. Joint optimization over transmit powers and multi-user scheduling weights is considered in a multi-carrier SCN, for both maximum rate and proportional-fair rate utilities. This formulation is extended for multiple-input multiple-output (MIMO) SCNs, where apart from transmit powers and multi-user scheduling weights, the transmit precoders are also optimized, for a generic alpha-fair utility function. Optimization of network resources over multiple degrees of freedom is particularly effective in reducing mutual interference, leading to significant gains in network utility. Finally, an alternate formulation of transmit power allocation is considered, in which the network transmit power is minimized subject to the data rate constraints of users. Thus, network resource allocation algorithms inspired by optimization theory constitute an effective approach for self-organization in contemporary as well as future cellular networks.