Minimization of Energy Constraint Problem in Wireless Communication Network by Using Iterative Bisection Based Algorithm

Energy constraint problem is one of the major concerns in wireless communication networks. The problem of unconstrained energy consumption by the user terminals is both energy and cost inefficient for communication operators. Furthermore, energy conservation also leads to significant improvements in network coverage, which would benefit a major portion of users. This problem can be partially solved by setting an a priori upper threshold on the energy consumed per time unit. However, this solution fails to provide uniform power distribution in the case of spatially distributed user terminals. In order to address such issue, a minimization of energy constraint problem arises. Its goal is to establish an optimal energy compromise between the user terminal and the network. In practice, this is done by approaching the problem as an optimization problem with nonlinear equality and inequality constraints. The exact solution of such problem involves solving a nonlinear optimization problem. Under the assumption of long-term power budget constraints, the optimal solution of the problem can be obtained either by using the Lagrange multiplier approach or the interior-point method. Another efficient method for solving this problem is the Lagrangian relaxation, where the problem is transformed into a quadratic problem by relaxing the nonlinear constraints. This allows for the more accurate solution of the energy constraint problem, but with significantly higher computational complexity. Additionally, it is also possible to solve the energy constraint problem with game-theoretic approaches. This involves considering the user terminals as self-interested players with goals beneficial to all involved parties. Thus, it allows for the equitable and cost-effective sharing of the energy resource among the players. Overall, the minimization of energy constraint problem in wireless communication network is an important problem, as it ensures a proper balance between user terminal energy consumption and network efficiency. In order to obtain the optimal solution, several methods are currently available, such as nonlinear optimization, Lagrangian relaxation, and game-theoretic approaches. Each approach has its own limitations and advantages, and further research is needed to fully incorporate these methods into practical solutions.