Mobile Information Systems

Volume 2016, Article ID 9720256, 13 pages

http://dx.doi.org/10.1155/2016/9720256

## Cross-Layer Cooperative Power Control in Heterogeneous Multihop Networks

Key Lab of Broadband Wireless Communication and Sensor Network Technology, Nanjing University of Posts and Telecommunications, Ministry of Education, Nanjing 210003, China

Received 11 December 2015; Revised 29 February 2016; Accepted 31 March 2016

Academic Editor: Lin Gao

Copyright © 2016 Feng Tian et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper investigates how to perform optimal cooperative power control for the coexistence of heterogeneous multihop networks. Although power control on the node level in multihop networks is a difficult problem due to its large design space and the coupling relationship of power control with scheduling and routing, we formulate a multiobjective optimization problem for the total power consumption of the two heterogeneous multihop networks with discretized power level. We reformulate the nonlinear constraint (relationship between power and capacity) into the linear one by piecewise linearization procedure and offer an in-depth study of cooperative power control in terms of its optimal power—the minimum power consumption with discretized power level for both heterogeneous multihop networks. Through a novel approach based on adaptive weighted-sum method, we transform the multiobjective optimization problem into a single-objective optimization problem and find the set of Pareto-optimal points iteratively. Using the Pareto-optimal points, we construct the minimum power curve. Using numerical results, we demonstrate that it can save more energy with cooperative power control than the case without cooperative power control.

#### 1. Introduction

The ever-increasing number of wireless systems leads to the scarcity of available spectrum. It is necessary to enable highly efficient spectrum sharing among diverse wireless networks [1]. Most of them are heterogeneous in hardware and software capabilities, physical layer technologies, or network protocol standards and are expected to be deployed in the same region and overlapped with each other in time, frequency, and space. Some examples of existing and future radio devices/networks that need cooperative power control include IEEE 802.11 (Wi-Fi), 802.15.4 (ZigBee), 802.16 (WiMAX), and Bluetooth in the ISM bands and IEEE 802.22 (WRAN) and IEEE 802.11af (WLAN) in the TV white space [2–5]. Often, there is no central administration or planning for the coexistence of such networks. In order to avoid interference and achieve optimal network performance under the paradigm of spectrum sharing, it inevitably leads to cooperative power control between multiple heterogeneous multihop networks, which is based on the node level.

As a fundamental problem for wireless networks, power control is challenging because it directly affects upper layers scheduling and routing. Meanwhile, when each node in multiple heterogeneous multihop networks is allowed to perform power control, the problem becomes even more difficult due to its large optimization space. In [6], the authors developed a formal mathematical model for a joint per-node based power control, scheduling, and flow routing problem. And they explored a unified solution procedure based on branch-and-bound framework and convex hull relaxation that guarantees optimal solution, where is a small prespecified error tolerance parameter. In [7], the authors investigated the network capacity problem for multihop CRNs in the SINR model. They considered how to maximize the rates of sessions with a mathematical model combining power control, frequency band scheduling, and flow routing. And they formulated a mixed-integer nonlinear program (MINLP) problem to be solved by an algorithm also based on the branch-and-bound and optimal solution. Although these works are solid for power control on the node level, they only involve a single objective in one single network and their approximate optimal algorithm is rather complex.

Beyond power control on the node level in one single homogeneous wireless network [6, 7], the authors mainly focused on power control in heterogeneous cellular networks rather than heterogeneous multihop networks [8–12]. Although the joint optimization of power, bandwidth allocation, and interference alignment was explored in [13–18], they only consider the single-objective function without the cooperative interaction between multiple heterogeneous networks. In this paper, we consider the total power consumption minimization of two heterogeneous multihop networks with discretized power level through cooperative power control, respectively, to formulate a multiple optimization problem to be a* multiobjective mixed-integer nonlinear programming* (MO-MINLP) one. By the aid of piecewise linearization procedure, we reformulate the nonlinear constraint (relationship between power and capacity) into the linear one and obtain a multiobjective mixed-integer linear programming (MO-MILP) problem and offer an in-depth study of cooperative power control in terms of its optimal power curve—the minimum power consumption for both heterogeneous multihop networks. Through a novel approach based on adaptive weighted-sum method, we transform the multiobjective optimization problem into a single-objective optimization problem, that is, mixed-integer linear programming (MILP) solved by commercial software (e.g., CPLEX), and find the set of Pareto-optimal points iteratively. With these Pareto-optimal points, we finally construct the minimum power curve with discretized power level. And by applying the solution procedure on two heterogeneous multihop networks generated randomly, we validate this solution procedure and offer additional insights into the behavior of cooperative power control in heterogeneous multihop networks. The main motivation of the two heterogeneous networks is to enable the cooperation between two independent and colocated networks on the power plane, such as the example of coexistence of ZigBee and Z-Wave in Smart Home Networking but not limited to this application in practice. For the case of more heterogeneous networks coexistence, we can extend our proposed approach to achieve the similarly optimal results.

The remainder of this paper is organized as follows. In Section 2, we develop a mathematical model of cooperative power control on the node level, scheduling, and flow routing for two heterogeneous multihop networks. In Section 3, we formulate a multiobjective cross-layer optimization problem and reformulate it into a MO-MILP problem. Section 4 describes a solution procedure based on adaptive weighted-sum method to this cross-layer optimization problem. In Section 5, we use numerical results to validate the efficacy of the solution procedure. Section 6 concludes this paper.

#### 2. Mathematical Modeling

In this section, we develop a mathematical model for simultaneously optimizing the total power consumption for both heterogeneous networks (i.e., Network 1 and Network 2). Denote as the combined set of nodes consisting of both the set of Network 1’s nodes and the set of Network 2’s nodes ; that is, . In the combined network, denote as the set of nodes (including nodes from two heterogeneous networks) located within node ’s transmission range on time slot with under full power , where can be a node from either Network 1 or Network 2 (i.e., ). Denote as the set of nodes (including nodes from two heterogeneous networks) located within node ’s interference range on time slot with under full power , where can be a node from either Network 1 or Network 2 (i.e., ). Denote and as the set of active Network 1’s and Network 2’s sessions, respectively.

##### 2.1. Power Control, Scheduling, and Their Relationship

In this paper, we consider scheduling in the time domain in the form of time slots since scheduling for transmission at each node in the primary and secondary networks can be done in either time domain or frequency domain and these two scheduling schemes are equivalent in terms of achievable rate region.

Now, we formalize a mathematical model for the joint relationship between each node of two heterogeneous networks based on power control and scheduling as shown in Figure 1. For example, there are two links “” and “” in Network 1 and two links “” and “” in Network 2, which are all active due to cooperative power control on the node level between two heterogeneous networks. For the first case without cooperative power control between two heterogeneous networks, node 7 unilaterally increases its transmission power as node 5 to be the maximum power, and then links “” and “” are all inactive. For the second case without cooperative power control between two heterogeneous networks, nodes 1 and 3 simultaneously increase their transmission power and keep links “” and “” in Network 1 active, but links “” and “” in Network 2 are all inactive. Obviously, we find that the four links in the two heterogeneous networks can simultaneously become active with cooperative power control between two heterogeneous networks, which achieves the best performance for the two networks.