Performance Analysis of an Evolutionary Allocation Scheme for a 2-hop Virtual Cellular Network Gerard J. PARAISON, Student Member, Eisuke KUDOH, Member IEEE Dept. of Communication Engineering Graduate School of Engineering Tohoku Institute of Technology Sendai, Japan 982-8577 Email: gerardjimmyp@ieee.org, kudoh@tohtech.ac.jp Abstract—Multi-hop networks are expected to increase the data transmission rate in the next generation mobile networks. An evolutionary allocation scheme (EAS) was proposed for a 2- hop virtual cellular network (VCN). The performance of EAS was evaluated based on the normalized transmission power. The number of wireless ports (WPs), their location in the VCN, along with the number of mobile terminals (MTs) can affect the performance of a scheme. Hence, this paper studies the performance of EAS based on the number of WPs and allocated MTs, and the distance ratio for the location of the WPs in the VCN. The results are compared with those of an iterative allocation scheme (IAS). The simulation results suggest that adding more WPs contributes to enhance the ergodic channel capacity of the VCN when EAS is applied in a single cell environment. With IAS applied, increasing the number of WPs is only beneficial in the noise dominant transmission power region. An optimal distance ratio for the location of the WPs lies in the interval 0.2∼0.4 when EAS is applied. This optimal interval is independent of the transmission power. As for IAS, for the noise dominant transmission power region, the interval is the same as for EAS. In case of high transmission power, the results suggest to increase the distance ratio to maximize the channel capacity. For both schemes, the ergodic channel capacity of the VCN augments as the number of MTs increases; with EAS achieving higher capacity than IAS in the presence of intra-cell interference. Index Terms—VCN, Resource allocation, SINR, Multi-hop net- work, Multi-user resource allocation, OFDMA, Channel capacity, Virtual cellular network, Iterative scheme, Evolutionary scheme. I. I NTRODUCTION To satisfy the increase demand of high data transmission rate in mobile wireless networks, without increasing the trans- mission power, multi-hop networks have been proposed [1]– [4]. The proposed multi-hop virtual cellular network (VCN) in [3], [4] considers the relay stations to be fixed nodes. In the VCN, the signal transmitted from a central port (CP) is relayed to the mobile terminals (MTs) using many distributed wireless ports (WPs). The CP acts as a gateway to the core network. This paper focuses on a 2-hop VCN. In recent studies, researchers involved in resource allocation schemes have shown great interest in OFDMA (Orthogonal Frequency Division Multiple Access) as the access scheme be- cause of its multi-user diversity and its resilience to frequency selectivity in mobile wireless environment [5], [6]. In order to provide high data transmission rate in the downlink, recent technologies, such as 3GPP LTE (third Generation Partnership Project Long Term Evolution) [7] and WiMAX [8], have also made used of OFDMA as their access scheme. Taking into account the benefit of using OFDMA, this paper considers OFDMA as the access scheme. Multiple resource allocation schemes have been proposed for 2-hop networks [5], [9]–[14]. The authors of [13] have proposed an iterative allocation scheme (IAS) where the MTs are selected in a successive order for resource allocation. In [14], using an evolutionary allocation scheme (EAS), the simultaneous allocation of resources to MTs has been inves- tigated. The results in [14] show that EAS can significantly improve the ergodic channel capacity of the VCN compared to IAS in the interference dominant transmission power region. The performance analysis presented in [14] was only based on the normalized transmission power. Considering that the number of WPs, their location in the VCN, along with the number of MTs can highly influence the performance of a scheme, this paper aims at shedding light on the performance of EAS and IAS based on the number of WPs and MTs, and the distance ratio between the CP and the WPs. This paper is organized as follows: Section II describes the system model used; Section III briefly presents EAS and IAS; Section IV discusses the simulation results; and Section V concludes the paper. II. SYSTEM MODEL A. System description This paper considers a single virtual cell (VC) with a set Q of Q MTs, a set W of W WPs, and a CP. The allocated bandwidth is divided into a set K of K subcarriers. In the downlink transmission assumed in this paper, a subcarrier can be reused concurrently in multiple links. Parallel relaying transmission is used to transmit data to an MT. In the parallel relaying transmission method, the transmitting data of an MT is divided into data streams. The CP transmits those data streams to the MT using multiple parallel logical routes (LRs). An LR is defined as set of a physical route and subcarriers allocated in each link along the physical route (see Fig. 1). Figure 1 illustrates the case of three physical routes (two 2-hop link routes and one direct link route) represented by dash dotted lines and an LR constructed