## 1 Introduction  
To keep pace with the development of mobile communication and wireless internet, advanced wireless transmission technology is needed to achieve high speed communication. However, high-rate data communication is limited by frequency selective fading from multi-path of the wireless channel [1,2]. Orthogonal frequency division multiplexing (OFDM) is a reliable technique for high speed data access systems [3] such as IEEE 802.11 a/g and IEEE 802.16 wireless LAN. Wireless sensor network is a self-organizing network which consists of a large number of low-cost, low-power tiny sensor nodes, and it has become a hotspot in the sensor applications. Therefore, research on sensor applications in wireless sensor networks is of great significance. Compared with traditional wireless sensor networks, high speed wireless sensor networks, which provide the acquisition and processing of the sensors with large amount of data and information, have a great application prospect. Benefited from the advantage of high spectral efficiency and strong anti-multipath fading ability, orthogonal frequency division multiplexing (OFDM) becomes the key physical layer technique for high speed wireless sensor networks. In an OFDM system, the broadband carrier is divided into a number of frequency orthogonal subcarriers. Each subcarrier performs a quadrature amplitude modulation (QAM). The subcarriers are combined through the way of an inverse fast Fourier transform (IFFT) at the transmitter [4]. Before being transmitted into the channel, a cyclic prefix (CP) is added to the symbol. If the length of CP is longer than the channel delay length, the inter-symbol interference (ISI) can be eliminated. The receiver performs such corresponding operations as CP removal, FFT and QAM demodulation [5]. With the development of wireless sensor networks, the types and amount of data increase rapidly in the sensor networks. It is in turn necessary to improve the resource utilization of bandwidth and power. If there is no effective resource allocation strategy, it is impossible for advanced transmission technology to give full play to its advantages, due to the limitation of resources. Therefore, research on the resource allocation strategy, which aims at achieving a high system sum rate in large-scale and power-limit wireless sensor networks, has important scientific and academic values. In orthogonal frequency division multiple access (OFDMA), a combination of OFDM and FDMA, different subcarriers are assigned to different users and multiple access is thus achieved [6]. As an advanced wireless transmission technology, OFDMA is widely used in the sensor networks [7, 8, 9, 10, 11, 12] and each sensor is regarded as one of the users in an OFDMA system. In an OFDMA system, due to the frequency selective fading of each subcarrier, the subchannel gains are not the same for different users [12]. Therefore, how to assign subcarriers and power to different users reasonably is of great significance. The issue of resource allocation, which focuses on assigning subcarriers and system power to users, has been an important concern in OFDMA systems [13, 14, 15, 16, 17]. Two classes of resource allocation schemes have been proposed according to different optimization objectives, called margin adaptive (MA) [18] and rate adaptive (RA), respectively [19, 20]. The goal of MA optimization is to minimize the systempower cost by the constraints on the system sum rate. The objective of RA is to achieve the maximum system sum rate with a fixed total system transmit power. It has been proved in [19] that when each subcarrier is allocated to the user with optimal subchannel gain and then power allocation is performed by water-filling algorithm, the system can achieve the maximum sum rate. In addition, in [19], equal power distribution method is adopted instead of water-filling algorithm to reduce the computational complexity. However, the proportional fairness is not considered in [19]. The proportional fairness has been studied in [21] in multiuser OFDM systems.