Resource Allocation for Secure OFDMA Decode-and-Forward Relay Networks Derrick Wing Kwan Ng and Robert Schober Department of Electrical and Computer Engineering, University of British Columbia, Canada Email: wingn@ece.ubc.ca, rschober@ece.ubc.ca Abstract— In this paper, we formulate an optimization problem for resource allocation and scheduling in orthogonal frequency di- vision multiple access (OFDMA) half-duplex decode-and-forward (DF) relay assisted networks. Our problem formulation takes into account artificial noise generation to combat a multiple antenna eavesdropper. The secrecy data rate, power, and sub- carrier allocation policies are optimized to maximize the average secrecy outage capacity (bit/s/Hz securely delivered to the users via relays). The optimization problem is solved by dual decomposition which results in an efficient iterative algorithm. Simulation results illustrate that the proposed iterative algorithm converges in a small number of iterations and guarantees a non-zero secrecy date rate for a given target secrecy outage probability. I. I NTRODUCTION In recent years, there has been a growing interest in information-theoretic physical layer (PHY) security [1]-[7], as a complement to traditional cryptographic encryption adopted in the application/networks layer. The concept of creating a perfectly secure communication link was first established by Wyner [1]. Wyner demonstrated that a source and a destination can exchange perfectly secure messages, if the eavesdropper’s channel is a degraded version of the main channel. As a result, secure communication via different forms of artificial noise gen- eration has been proposed in the literature. In [2] and [3], power allocation problems for ergodic secrecy capacity maximization are studied for different system configurations. However, the assumption of ergodic channels in [2], [3] cannot be justified for delay constrained applications in practice, since the transmitted packets of these applications only experience slow fading. In [4] and [5], the resource allocation in OFDMA systems with PHY security considerations was studied. On the other hand, power allocation for systems employing cooperative jamming enabled by amplify-and-forward and decode-and-forward (DF) relays was investigated in [6] and [7], respectively. In these works, the global channel state information (CSI) of the eavesdroppers is assumed to be known at a centralized unit such that security can always be guaranteed. However, eavesdroppers are usually silent to hide their existence. Thus, the CSI of the eavesdroppers may not be available for the resource allocation in practice. As a result, a secrecy outage occurs whenever the scheduled data rate exceeds the secrecy capacity, which introduces a new quality of service (QoS) concern for secrecy. Motivated by the aforementioned prior works, in this paper, we derive an iterative resource allocation algorithm for OFDMA DF relaying systems, which ensures secure communication in slow fading by introducing artificial noise and converges fast to the optimal solution. II. OFDMA RELAY NETWORK MODEL We consider an OFDMA DF downlink system which consists of a base station (BS) with N T antennas, M relays with N T antennas each, an eavesdropper with N E antennas, and K mobile users equipped with a single antenna. We assume that N T >N E to ensure secure communication. Both the BS and the relays adopt multiple-input multiple-out beamforming (MIMO-BF) to enhance the system performance. The downlink transmission from the BSs to the users via the relays is accomplished in two time slots. In the first time slot, the BS transmits its signals to the relays. Then, in the second time slot, the relays decode the previously received signals and forward them to the corresponding users. Meanwhile, the eavesdropper attempts to eavesdrop the transmitted messages by receiving the signals in both time slots. A. Channel Model The impulse responses of all channels are assumed to be time-invariant (slow fading). We consider an OFDMA DF relay assisted system with n F subcarriers. The received symbols in the first time slot at relay m for user k and the eavesdropper on subcarrier i ∈{1,...,n F } are given by, respectively, y BRm [i] = H BRm [i]x k [i]+ n m [i] and (1) y B,E [i] = G B,E [i]x k [i]+ e 1 [i], (2) where x k [i] ∈ C NT ×1 denotes the transmitted symbol vector and C N×M is the space of all N ×M matrices with complex en- tries. H BRm [i] ∈ C NT ×NT denotes the channel matrix between the BS and relay m on subcarrier i and G B,E [i] ∈ C NE×NT is the channel matrix between the BS and the eavesdropper on subcarrier i. Both variables, H BRm [i] and G B,E [i], include the effects of path loss and multipath fading of the associated channels. n m [i] ∈ C NT ×1 and e 1 [i] ∈ C NE×1 are the additive white Gaussian noise (AWGN) in subcarrier i at relay m and the eavesdropper in the first time slot, respectively. Each entry in both vectors has distribution CN (0,N 0 ), where N 0 is the noise power spectral density. Here, CN (ν, σ 2 ) denotes a complex Gaussian random variable with mean ν and variance σ 2 . In the second time slot, relay m decodes the message x k [i] and re-encodes the message as q m,k [i] ∈ C NT ×1 . Then, relay m forwards the re-encoded message q m,k [i] to user k. Therefore, the signals received at user k and the eavesdropper on subcarrier i from relay m are given by, respectively, y Rm,k [i] = h Rm,k [i]q m,k [i]+ n k [i] and (3) y Rm,E [i] = G Rm,E [i]q m,k [i]+ e 2 [i]. (4) h Rm,k [i] ∈ C 1×NT and G Rm,E [i] ∈ C NE×NT denote the channel matrices from relay m to users k and from relay m to the eavesdropper on subcarrier i, respectively. n k [i] ∈ C 1×1 and e 2 [i] ∈ C NE×1 are the AWGN in subcarrier i at user k and the eavesdropper in the second time slot, respectively. For the sake of notational simplicity and without loss of generality, a normalized noise variance of N 0 =1 is assumed for all receivers in the following. We also assume that the CSI (path loss information and multipath fading) of the desired relays and users are perfectly known at the BS. On the other hand, since the CSI of the eavesdropper is unavailable at the BS and relays, in order to secure the desired wireless communication links, artificial noise signals are generated at both the BS and relays to degrade the channels between the BS/relays and the eavesdropper. Artificial Noise Generation: The BS and relay m choose x k [i] and q m,k [i] as the linear combination of the information bearing signal and an artificial noise signal, i.e., x k [i] = b m,k [i]u k [i]+ V B,Rm [i]v[i], (5) q m,k [i] = r m,k [i]u k [i]+ W Rm,k [i]w[i], (6) 978-1-4577-0742-1/11/$26.00 ©2011 IEEE 202