On the Optimal Power Control of Parallel OFDM Relaying Networks Yingnan ZHANG and Qiao WANG School of Information Science and Engineering Southeast University Nanjing, 210096, China Email: {zhangyingnan, qiaowang}@seu.edu.cn Abstract—We investigate the power allocation problem for dual-hop parallel OFDM relaying networks where an aggregate power constraint is imposed on all of the amplify-and-forward relays. Based on Y. Zhao et al’s recent work, we first formulate the problem to how to optimally allocate the total power among all subcarriers such that the system instantaneous information rate is maximized, then we decompose it into a group of subproblems which can be solved with Lagrange multiplier method. Considering the prohibitive complexity to calculate the optimal solution, we further propose a low-complexity iterative algorithm to construct a suboptimal solution which converges very quickly. The simulation results show the performance gap between suboptimal and the optimal solutions is negligible. I. I NTRODUCTION The use of wireless relays is essential to provide broad coverage for wireless system, hence relaying network has been regarded as one of the most promising architectures for future wireless networks. Power efficiency is a critical design consideration for wire- less relaying system. Efficient power allocation (PA) among nodes can improve system performance in terms of instan- taneous information rate (or end-to-end instantaneous SNR). In the frequency-flat fading scenario, [1]–[4] focused on the model of all relays simultaneously transmitting signals to the destination under different types of power constraint on all relays. Among them, [1],[2] considered the individual constraint case, [3] researched the aggregate constraint case, and [4] considered the hybrid constraint case. For the parallel model where all relays send signals to the destination in pre-assigned non-overlapping time slots, [5]–[7] investigated the joint PA problem among source and all relays. In the frequency-selective fading scenario, most of the literatures such as [8]–[10] only considered the single-relay case. For instance, [8] solved the PA problem at source/relay through a unified approach, [9] [10] investigated the joint PA problem where an aggregate power constraint is imposed on both the source and the relay. For multi-relay case, [11] researched the model of all relays operating simultaneously where an aggregate power constraint is imposed on all relays and the power distribution at the source is given. This work is supported by 863 Project of China under Grant No. 2007AA01Z262, the Excellent Research Fellow Program under Grant No. 07-E-016 of Jiangsu Province, and Innovation Fund of Southeast University. Comparing with [11], in this paper we investigate the PA problem among relays for amplify-and-forward OFDM relaying networks under the parallel model. Based on the recent result in the frequency-flat fading scenario [6], we first simplify the problem to how to optimally allocate the total power among all subcarriers such that the system instantaneous information rate is maximized. Then we solve it by solving K N subproblems using Lagrange multiplier method, where K and N denote the number of relays and subcarriers respec- tively. Moreover, we propose a quickly convergent iterative algorithm to construct a suboptimal solution whose perfor- mance is shown to be very close to that of the optimal one, in which the number of iterations to calculate the suboptimal solution is very small (about 3) and is insensitive to K and N . The rest of this paper is organized as follows. Section II describes the system model and formulates the problem. Section III introduces the result in the frequency-flat fading scenario. Based on that, in section IV the problem is solved and a suboptimal solution is also proposed. Section V provides several numerical results and Section VI concludes the paper. II. SYSTEM MODEL AND PROBLEM FORMULATION Consider a relaying network that consists of one source/destination pair and K non-coherent amplify-and- forward relays [4]. All relays are assumed to be placed randomly within the region between source and destination. The destination is supposed to be unable to receive the signals from the source directly which may result from high shadowing between them [8]. OFDM is used for broadband communication and the available bandwidth is divided into N subcarriers, in which all channels are assumed to be frequency- flat fading. In the j -th subcarrier, the channels from source to the i-th relay and from the i-th relay to destination are denoted by h ij and g ij respectively. All relays are supposed to operate in pre-assigned non-overlapping time slots [6] (parallel model), hence the data transmission from source to destination is over K +1 time slots using two hops. During the first time slot, on the j -th subcarrier the source sends signal s j with power P s j to all relays, and the received signal of the i-th relay on that subcarrier is r ij = h ij s j + w ij This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2009 proceedings. 978-1-4244-4148-8/09/$25.00 ©2009