Distributed power control and random access for spectrum sharing with QoS constraint☆
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 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 interfering links we denote the SINR for the th user aswhere is the
Problem formulation
The demand for QoS from unlicensed transmission is denoted by a utility of SINR, where is a twice differentiable, increasing function of The minimum QoS requirement of link l is The social utility maximization problem with QoS and IT constraints can be formulated as follows:where To introduce the criterion of finding a feasible solution that solves (P1), a normalized link gain matrix
Equivalent convex formulation
First, we give the following notations. Let and logarithmic change of variables: . Correspondingly, the domains of these variables by excluding the boundary region can be denoted as where M is a sufficiently large positive constant. Note that Let 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 and the background noise is . The low rate data users are considered with a spreading gain of The IT bound is . 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.