In this paper, we investigate resource allocation algo rithms for Orthogonal Frequency Division Multiplexing (OFDM) based dual hop systems including a source, multiple relays, and multiple destinations and utilizing Decode-and-Forwarded (DF) relaying. The main objective is to maximize the spectral efficiency under the total power constraint. We first propose an algorithm which simultaneously allocates transmission power and transmission time used by each hop in every time frame. Then we propose a more tractable algorithm which decomposes the original problem in two subproblems. The first subproblem is to solve the optimization problem for a given value of transmission time used by each hop, and the second subproblem is to compute the value of transmission time. The discussed algorithms are also compared with each other and with other resource allocation schemes. Simulation results are also provided which verify the performance improvement by adopting of the proposed algorithms.
I. I NTRODUCTIONThere are many advantages for multi hop wireless networks over the conventional wireless networks such as coverage extension, enhancing spectrum efficiency and diversity gain [1]. Therefore, they are considered recently in design and development of the broadband wireless networks. Orthogonal Frequency Division Multiplexing (OFDM) is also considered as physical layer technology in such networks [2]. It divides the available bandwidth into the orthogonal subcarriers which deals the frequency selectivity of the wireless channel. By adding a Cyclic Prefix (CP) with a length longer than the maximum delay spread of the wireless channel to each OFDM symbol, the Inter Symbol Interference (lSI) caused by multi path can be significantly reduced. This advantages have drew attention to OFDM relay systems in recent years and many methods have been introduced for resource allocation in such systems, see, e.g., [3].Decode and Forward (DF) and Amplify and Forward (AF) relaying techniques are two main forwarding schemes which have been extensively used in multihop OFDM relay systems [4]. Considering such systems, it is shown that when data is transmitted through two or three hop paths, significant gain on throughput is obtained [5].Radio resource allocation is a very important topic in multihop OFDM systems which has been considered in the related literature, see,e.g., [6], [7], [8]. the difficulty of the resource allocation is the non convexity of the problem caused by the interrelationship of all resources. In such research studies, optimal radio resource allocation is considered and classic methods such as Lagrange multiplier and dual de composition is then adopted to find/approximate the optimal solution. In [6], power and subcarrier allocation is conducted with the objective of total rate maximization. In [6], separate power constraints are considered for Base Station (BS) and intermediate relays. In cases when the corresponding Relay Station (RS) channel suffers bad condition, allocation more transmit power to this relay in [6], doesn...