Elsevier

Computer Communications

Volume 31, Issue 17, 20 November 2008, Pages 4089-4097
Computer Communications

Distributed power control and random access for spectrum sharing with QoS constraint

https://doi.org/10.1016/j.comcom.2008.08.016Get rights and content

Abstract

Distributed spectrum sharing with minimum quality of service (QoS) requirement and interference temperature (IT) constraint is studied in this paper. This problem can be formulated as a non-convex optimization problem with conflicting constraints. To make solutions to this problem feasible, random access and power control are jointly considered. The challenges in solving this problem arise from the coupling in utility functions, the conflicting constraint sets, and coupled control variables. Moreover, there is no centralized controller or base station in networks to coordinate unlicensed users’ transmission and protect active users’ QoS under IT constraint. By introducing variable substitution and transformation, we derive a distributed random access and power control algorithm that can achieve global optimal solution to the original problem. Convergence of the algorithm is proven theoretically. Simulation results demonstrate that both QoS guarantee and interference avoidance can be achieved even with channel gain variations.

Introduction

The frequency spectrum for radio signal transmission is currently allocated in a static manner, where bands are licensed to users by government agencies and thus licensed users have the exclusive rights to access the allocated band. At the same time, studies show that the spectrum has been used inefficiently in licensed bands [1]. In contrast, the spectrum left by licensed users cannot meet the increasing demands for radio resources. To solve this demand and utilization dilemma, dynamic spectrum sharing approaches appear to be a good alternative. One of the approaches, called the underlay sharing approach exploits the spread spectrum techniques in cellular networks. Once a spectrum allocation map has been acquired, unlicensed devices can coexist with licensed users on the same frequency, provided that unlicensed users can limit the interference to licensed users. To quantify the interference, the Federal Communication Commission (FCC) proposed a new metric named the interference temperature (IT) [2]. The IT is defined to be the radio frequency power measured at a receiving antenna per unit bandwidth.

In this paper, we focus on the underlay spectrum sharing in ad hoc networks where all unlicensed users spread their transmission powers across the entire available band under the IT constraint. In this context, power control is used to limit interference among unlicensed users and to licensed receivers and, hence, maximize spectrum usage. The signal-to-interference-and-noise ratio (SINR) at the unlicensed receiver determines the successful transmission at physical layer. However, to satisfy the minimum SINR requirement that characterizes the quality of service (QoS) constraint on the bit-error rate at individual receivers, the transmitting power of an unlicensed user may exceed its maximum value or even violates the IT constraint. To balance the minimum SINR requirement and IT constraint, and further to efficiently and fairly utilize spectrum, transmission power and channel access must be determined by coordination among unlicensed users [3]. In ad hoc networks without infrastructure, this coordination should be implemented distributively.

Taking these factors into consideration, we formulate a joint random access and power control problem under IT and QoS constraints. To protect the primary transmission, some nodes called measurement points are deployed to monitor the real-time IT of the concerned band at their locations. Due to the interference relationship among wireless links and coupling between transmission power and channel access, the formulated problem is non-convex and non-separable in control variables. After variable transformation and introduction of an auxiliary variable, the optimization problem can be turned into a convex one. Then a distributed random access and power control algorithm is proposed within the framework of layering as optimization decomposition [4]. The transmission power of a link is updated not only to maintain its own QoS but also to limit interference to peer unlicensed users as well as licensed users. The random access of a transmission is aimed at satisfying its own channel access requirement and supporting other active links’ QoS requirement. The only involvement of a measurement point in the implementation of this algorithm is that when the aggregate IT violates the given upper bound the measurement point will broadcast the current IT to all the unlicensed transmitters. Furthermore, we prove that the proposed algorithm can converge to the global optimum. Simulation demonstrates that convergence of this algorithm can be ensured even with channel gain variations.

The rest of this paper is organized as follows. In Section 2, we review some related work on spectrum sharing and non-convex optimization. The system model is presented in Section 3. The spectrum sharing problem is formulated in Section 4. In Section 5, we propose our joint random access and power control algorithm for spectrum sharing. Convergence results of the algorithm are also given in Section 5. Section 6 includes performance evaluation of the proposed algorithms. We conclude the paper and give future research direction in Section 7.

Section snippets

Related work

Spectrum sharing between licensed users and unlicensed users can be classified as overlay and underlay schemes. In the overlay spectrum sharing unlicensed users access the network dynamically by using a portion of spectrum that has not been used by licensed users. For more discussions on the overlay spectrum sharing, see [5], [2]. We focus on the underlay spectrum sharing, especially the scheme based on IT model. In [6], Huang et al. proposed the uplink spectrum sharing algorithm based on

System model

The wireless network considered here is formulated as a set L of radio links with each link corresponding to an unlicensed transmitter and a receiver. Each transmitter is assumed to have a fixed channel gain to its intended receiver as well as fixed gains to all other receivers in the network. The quality of each link is determined by the SINR at the intended receiver. In a network with L interfering links we denote the SINR for the ith user asγi=Giipiη2+(ji,jLGijpj)/S,where Gij>0 is the

Problem formulation

The demand for QoS from unlicensed transmission is denoted by a utility of SINR, ul(γl), l, where ul(·) is a twice differentiable, increasing function of γl. The minimum QoS requirement of link l is γl0. The social utility maximization problem with QoS and IT constraints can be formulated as follows:(P1)maxpPlLul(γl)subject toγlγl0l,i=1LpiG0iT,where P={pl,lL0plplmax}. To introduce the criterion of finding a feasible solution p¯P that solves (P1), a normalized link gain matrix G¯

Equivalent convex formulation

First, we give the following notations. Let yl=γ¯l and logarithmic change of variables: qˆl=logql, pˆl=logpl l. Correspondingly, the domains of these variables by excluding the boundary region can be denoted as Pˆ={pˆl,lL-Mpˆllogplmax}, Qˆ={.qˆl,lL-Mqˆl0}, Yˆ={yˆl,lL-Myˆllogylmax}, where M is a sufficiently large positive constant. Note that ylmaxplmaxGll/η2. Let uˆl(yˆl)=ul(eyˆl), vˆl(qˆl)=vl(eqˆl), Iˆl(pˆ-l,qˆ-l)=η2+jle(logGlj/S+pˆj+qˆj) and rewrite the constraint sets in (P2)

Simple network scenario

We first present a simple network topology to illustrate the effects of network parameters and control parameters on algorithm performance. Consider an ad hoc network consisting of four transmission pairs. The parameters are set as follows except otherwise specified. The target SINR is γ0=12 and the background noise is η2=5×10-13. The low rate data users are considered with a spreading gain of S=128. The IT bound is 4×10-8. The maximum power for each transmission pair is 0.5 W. The channel gain

Conclusions and future work

The distributed spectrum sharing among unlicensed users with interference temperature and QoS constraints is studied in this paper. To find feasible transmission powers for supporting active links’ QoS, unlicensed users are allowed to access networks opportunistically. Then joint random access and power control is formulated as a non-convex optimization problem. After variable substitution and log transformation, the problem is then transformed to a convex optimization problem, and

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    This work was supported in part by the Research Grants Council of Hong Kong SAR, P.R. China, under Grant Cityu 112907, the China National Outstanding Youth Foundation under Grant 60525303, NSFC under Grant 60604012, 60804030. This material was also based upon work supported by the National Science Foundation under Grant OISE-0430145. Part of this work was accomplished when the first author was visiting the Polytechnic Institute of New York University under a WICAT Fellowship.

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