Joint power and admission control via p norm minimization deflation

In an interference network, joint power and admission control aims to support a maximum number of links at their specified signal to interference plus noise ratio (SINR) targets while using a minimum total transmission power. In our previous work, we formulated the joint control problem as a sparse $\ell_0$-minimization problem and relaxed it to a $\ell_1$-minimization problem. In this work, we propose to approximate the $\ell_0$-optimization problem to a p norm minimization problem where $0<p<1$, since intuitively p norm will approximate 0 norm better than 1 norm. We first show that the $\ell_p$-minimization problem is strongly NP-hard and then derive a reformulation of it such that the well developed interior-point algorithms can be applied to solve it. The solution to the $\ell_p$-minimization problem can efficiently guide the link's removals (deflation). Numerical simulations show the proposed heuristic outperforms the existing algorithms.Comment: 2013 IEEE International Conference on Acoustics, Speech, and Signal Processin

Time and Location Aware Mobile Data Pricing

Mobile users' correlated mobility and data consumption patterns often lead to severe cellular network congestion in peak hours and hot spots. This paper presents an optimal design of time and location aware mobile data pricing, which incentivizes users to smooth traffic and reduce network congestion. We derive the optimal pricing scheme through analyzing a two-stage decision process, where the operator determines the time and location aware prices by minimizing his total cost in Stage I, and each mobile user schedules his mobile traffic by maximizing his payoff (i.e., utility minus payment) in Stage II. We formulate the two-stage decision problem as a bilevel optimization problem, and propose a derivative-free algorithm to solve the problem for any increasing concave user utility functions. We further develop low complexity algorithms for the commonly used logarithmic and linear utility functions. The optimal pricing scheme ensures a win-win situation for the operator and users. Simulations show that the operator can reduce the cost by up to 97.52% in the logarithmic utility case and 98.70% in the linear utility case, and users can increase their payoff by up to 79.69% and 106.10% for the two types of utilities, respectively, comparing with a time and location independent pricing benchmark. Our study suggests that the operator should provide price discounts at less crowded time slots and locations, and the discounts need to be significant when the operator's cost of provisioning excessive traffic is high or users' willingness to delay traffic is low.Comment: This manuscript serves as the online technical report of the article accepted by IEEE Transactions on Mobile Computin