Sudarshan Guruacharya

Hierarchical Competition for Downlink Power Allocation in OFDMA Femtocell Networks

This paper considers the problem of downlink power allocation in an orthogonal frequency-division multiple access (OFDMA) cellular network with macrocells underlaid with femtocells. The femto-access points (FAPs) and the macro-base stations (MBSs) in the network are assumed to compete with each other to maximize their capacity under power constraints. This competition is captured in the framework of a Stackelberg game with the MBSs as the leaders and the FAPs as the followers. The leaders are assumed to have foresight enough to consider the responses of the followers while formulating their own strategies. The Stackelberg equilibrium is introduced as the solution of the Stackelberg game, and it is shown to exist under some mild assumptions. The game is expressed as a mathematical program with equilibrium constraints (MPEC), and the best response for a one leader-multiple follower game is derived. The best response is also obtained when a quality-of-service constraint is placed on the leader. Orthogonal power allocation between leader and followers is obtained as a special case of this solution under high interference. These results are used to build algorithms to iteratively calculate the Stackelberg equilibrium, and a sufficient condition is given for its convergence. The performance of the system at a Stackelberg equilibrium is found to be much better than that at a Nash equilibrium.

Hierarchical Competition in Femtocell-Based Cellular Networks

This paper considers the downlink power allocation problem in a cellular network where a bi-level hierarchy exists. The network is comprised of the macrocells underlaid with femtocells. The objective of each station in the network is to maximize its capacity under power constraints. The problem is formulated as a Stackelberg game with the macrocell base stations as the leaders and the femtocell access points as the followers. The leaders are assumed to have enough information and foresight to consider the response of the followers while formulating their strategies. To characterize such interaction between leaders and followers, Stackelberg equilibrium is introduced; and it is shown to exist under the assumption of continuity of best response function of the leader sub-game. %For the case of Nash games, the relationship between the upper and lower sub-game equilibrium is explored.

Dynamic Coalition Formation for Network MIMO in Small Cell Networks

In this paper, we apply the concepts of network multiple-input-multiple-output (MIMO) to small cell networks. To do so, the issue of imperfect channel state information (CSI) at the transmitter is considered when frequency-division duplexing is used, for which the feedback channel is limited. We first introduce a regret based learning approach to optimize the transmit beamforming parameters for the cases when the feedback channel is temporarily unavailable during deep fades. We then propose a coalition formation game model to cluster the small cell base stations so that they can perform cluster-wise joint beamforming. We take the \tit{recursive core} as the solution concept of the coalition formation game. To obtain the recursive core, we first consider a typical merge-split algorithm. However, we show that this algorithm can be unstable. Alternatively, we adopt the merge-only algorithm which guarantees the formation stability and show that its outcome belongs to the recursive core. Finally, we analyze the average number and the average size of coalitions that can form during such a coalition formation process. Numerical simulations are given to illustrate the behavior of the coalition formation among small cell base stations.

Access control via coalitional power game

This paper considers the problem of access control in the uplink transmission of an OFDMA femtocell network. An underlying noncooperative power game has been devised, based on which a coalition game is formulated by taking a suitable value function. Only two complementary coalitions are allowed to exist in order to reflect the set of transmitters connected to either the macro base station or the femto access point. The transmitters in the same coalition cooperate by operating on non-interfering subchannels, while those in the complementary coalition are assumed to operate so as to cause maximum jamming. The value of a coalition is obtained as the max-min of utility sum of each individual in the given coalition. In the process, we also examine the optimal jamming strategy of the complementary coalition. Finally, we argue that the obtained value function cannot be super-additive. Since the super-additivity property is required for some of the solutions of cooperative game theory, we resort to the Shapley value solution, for which the super-additivity need not hold, to allocate the payoff to each user in a given coalition. Assuming that the transmitters want to be in the coalition that maximizes their payoff, we form a Markov model to obtain the stable coalition structure. We take these stable coalition structures as the required solution of our access control problem.

Integral Approximations for Coverage Probability

This letter gives approximations to an integral appearing in the formula for downlink coverage probability of a typical user in Poisson point process (PPP)-based stochastic geometry frameworks of the form f0∞ exp{-(Ax + Bxα/2)} dx. Four different approximations are studied. For systems that are interference-limited or noise-limited, conditions are identified when the approximations are valid. For intermediate cases, we recommend the use of Laplace approximation. Numerical results validate the accuracy of the approximations.

Saddle Point Approximation for Outage Probability Using Cumulant Generating Functions

This letter proposes the use of saddle point approximation (SPA) to evaluate the outage probability of wireless cellular networks. Unlike traditional numerical integration-based approaches, the SPA approach relies on cumulant generating functions (CGFs) and eliminates the need for explicit numerical integration. The approach is generic and can be applied to a wide variety of distributions, given that their CGFs exist. We illustrate the usefulness of SPA on channel fading distributions such as Nakagami-m, Nakagami-q (Hoyt), and Rician distributions. Numerical results validate the accuracy of the proposed SPA approach.

Multi-operator spectrum sharing using matching game in small cells network

In this paper, we study a problem where multiple operators (OPs) need to share a common pool of spectrum with each other. Our objective is to maximize the social welfare, defined as the overall weighted sum rate of the OPs. The problem is decomposed into two parts: the first part is to allocate RBs to OPs, which we do so by extending the framework of many-to-one matching game with externalities. The second part is to allocate power of small cell base stations (SBSs) belonging to each OP, which is accomplished using reinforcement learning. Assuming that the SBSs associated with each OPs are spatially distributed according to Poisson point process (PPP), we show that pairwise stable matchings achieve local maximas of the social welfare function. We propose two algorithms to search for the stable matchings. Simulation results show that these algorithms are well behaved in terms of convergence and efficiency of the solutions.

Resource allocation for co-primary spectrum sharing in MIMO networks

We study co-primary spectrum sharing concept in two small cell multiuser network. Downlink transmission is explored with Rayleigh fading in interfering broadcast channel. Both base stations and all the users are equipped with multiple antennas. Resource allocation with joint precoder and decoder design is proposed for weighted sum rate (WSR) maximization problem. The problem becomes mixed-integer and non-convex. We factor the main objective problem into two subproblems. First subproblem is subcarrier allocation where we assume that each subcarrier can be allocated to multiple users. Gale-Shapley algorithm based on stable marriage problem and transportation method are implemented for subcarrier allocation part. For the second subproblem, a joint precoder and decoder design is proposed to obtain the optimal solution for WSR maximization. Monte Carlo simulation is employed to obtain the numerical results to compare the two methods.

Multi-Operator Spectrum Sharing for Small Cell Networks: A Matching Game Perspective

One of the many problems faced by current cellular network technology is the underutilization of the dedicated licensed spectrum of network operators. An emerging paradigm to solve this issue is to allow multiple operators to share some parts of each other’s spectrum. Previous works on spectrum sharing have failed to integrate the theoretical insights provided by recent developments in stochastic geometrical approaches to cellular network analysis with the objectives of network resource allocation problems. In this paper, we study the non-orthogonal spectrum assignment with the goal of maximizing the social welfare of the network, defined as the expected weighted sum rate of the operators. We adopt the many-to-one stable matching game framework to tackle this problem. Moreover, using the stochastic geometrical approach, we show that its solution can be both stable as well as socially optimal. To obtain the maxima of social welfare, the computation of the game theoretical solution using the generic Markov Chain Monte Carlo method is proposed. We also investigate the role of power allocation schemes using Q-learning, and we numerically show that the effect of resource allocation scheme is much more significant than the effect of power allocation for the social welfare of the system.

Robust bandwidth allocation in wireless mesh network

Bandwidth allocation is important for a mesh network to meet quality of service (QoS) requirements of the users. This bandwidth allocation has to ensure that the maximum throughput is achieved. However, this problem becomes more challenging when the information about a network (e.g., channel quality and hence link capacity) is not accurately known, especially, in a real system whose parameters are uncertain. Therefore, in this paper, we apply the robust optimization technique to develop a model that can tolerate the uncertainty of the system parameters. First, we formulate the bandwidth allocation problem as a constrained optimization problem and its robust counterpart is obtained. Then, we suggest an approach to choose the suitable system parameters so that with a certain high probability, the feasibility of the solution from optimization formulation is ensured for all meaningful realizations of the system parameters. Moreover, we introduce the reduced conservativeness approach for the bandwidth allocation. In this approach, the tradeoff between throughput and robustness to the uncertainty of a system parameter is explored. Specifically, the decrease in throughput will be minimized given the target robustness.