Rate allocation based on spectrum pricing function in collaborative transmission over heterogeneous wireless access networks

This article studied rate allocation in collaborative transmission over heterogeneous wireless access networks. With the introduced pricing function, which uses the occupied spectrum to describe the cost in data transmission, rate allocation is formulated as a concave optimization problem and the explicit solution has been obtained. Instead of transmitting through all available networks in pursuit of fairness, the proposed rate allocation scheme distributes traffic to available networks in an unbalanced way according to both spectral efficiency and network status. Simulation results have shown that compared with other methods, the new scheme can maximize the total utility gained in collaborative transmission and avoid congestion effectively. Introduction Nowadays a mobile terminal (MT) with multiple radio transceivers can connect to different wireless access networks. Meanwhile, applications such as voice, video as well as bulk datamay need to be run on theMT simultaneously and some of them are bandwidth-hungry. However, any single type of existing wireless and mobile networks cannot meet these requirements. Therefore, heterogeneous wireless access networks have become more and more attractive and they have been built up as a shortdistance wireless access network to satisfy different kinds of applications, such as wireless meeting rooms, wireless E-education, smart houses, and so on. Since the traffic flow can be distributed among different available access networks to fulfil one transmission task, the rate allocation problem can be regarded as how to divide the traffic among networks that might be loaded differently. Rate allocation over heterogeneous networks (HetNets) can make full use of available resources in different networks and has been studied in [1-5]. In [1,2], cooperative game theory has been applied to rate control and rate allocation at the network level, where the quality of service (QoS) can be guaranteed as long as the required *Correspondence: [email protected] School of Electronic and Information Engineering, South China University of Technology, 381 Wushan Road, Guangzhou 510640, Guangdong Province, China transmission rate is satisfied. The non-cooperative game framework of bandwidth allocation in 4G heterogeneous wireless access networks has been discussed in [3]. In [4], an H∞-optimal control formulation for allocating rates to devices over multiple access networks with heterogeneous time-varying characteristics has been proposed for the worst-case scenario. To support multiple video streams, a pricing-based mechanism has been introduced to the bitrate allocation [5], where the price is adjusted based on the difference between supply and demand for the current slot. In all the above works, the throughput gain has been chosen as the optimization objective without considering the heterogeneity of spectral efficiency and network status and all the available networks must participate in collaborative transmission. Then the heavy-load network will be easily saturated and packets will be dropped. Furthermore, it makes no sense for a low traffic flow to be distributed to different networks in pursuit of fairness, where the cost of packet disassembling and resembling cannot be ignored. Therefore, network status should be considered in rate allocation over HetNets. It can be described using the resource utilization since a network is more saturated with more resources occupied. Then similar as [6], a pricing function can be used to allocate the transmission rate according to network status and distribute more traffic to light-load networks to prevent network congestion. In © 2012 Liu et al.; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Liu et al. EURASIP Journal onWireless Communications and Networking 2012, 2012:236 Page 2 of 8 http://jwcn.eurasipjournals.com/content/2012/1/236 this article we have focused on networks such as WiMax, UWB, Cellular networks, etc., where frequency sub-bands are the resources to be allocated [7]. With the utilized resource described by the occupied spectrum, the pricing function is modelled as the resource cost in data transmission and the utility of an MT can be formulated as the throughput gain minus the resource cost. Then rate allocation becomes a global optimization problem, where the traffic is transmitted at a minimum resource cost, and an explicit solution can be obtained based on the convex optimization theory. It is straightforward to extend our scheme to other cases, such as time-slotted systems, where the pricing function is introduced based on occupied time-slots and the rate allocation problem can be formulated using a similar framework to prevent network congestion. Model and problem formulation Wireless transmission In wireless communications, transmission rate can be adjusted dynamically based on the channel quality using the adaptive modulation. Assume n networks are built up with overlapped coverage. Then the bit error rate (BER) over a single-input single-output Gaussian noise channel in network i for the uncoded quadrature amplitudemodulation (QAM) with square constellation can be calculated as follows [6,8] BERi = 0.2 exp ( −1.5γi (2εi − 1) ) , (1) where γi is the signal to noise ratio (SNR) at the receiver and εi denotes the spectral efficiency of the selected modulation scheme in network i. To guarantee the quality of transmission, BER should not exceed a certain level, denoted by BERtar i . Then the spectral efficiency of transmission for an MT in network i can be obtained from εi = log2 ( 1+ 1.5 ln ( 0.2/BERtar i )γi ) . (2) Assume that the value of BER is available at the transmitter by using channel estimation. Then the transmission rate ri (in bits per second) can be calculated according to the occupied spectrum fi, i.e.,