In this paper, we present a comprehensive investigation on the secrecy performance of opportunistic relay selection systems employing the decode-and-forward protocol over Rayleigh fading channels. Considering a practical setting where direct link between the source node (Alice) and the destination node (Bob) is available, we study the secrecy performance of three different diversity combining schemes, namely, maximum ratio combining (MRC), distributed selection combining (DSC), and distributed switch-and-stay combining (DSSC). Throughout the analysis, we consider two different scenarios based on the availability of the eavesdropper's channel state information (CSI) i.e., Scenario A: the eavesdropper's CSI is not available at Alice and the relay, and Scenario B: Alice and the relay have knowledge about the eavesdropper's CSI. For Scenario A, we derive exact closed-form expressions for secrecy outage probability and simple asymptotic approximations for the secrecy outage probability which enable the characterization of the achievable secrecy diversity order and coding gains. For Scenario B, we derive closed-form expressions for the achievable secrecy rates. For both scenarios, we investigate the impact of feedback delay (outdated CSI) on the secrecy performance wherein exact and asymptotic of secrecy outage probability, and closed-form expressions of the secrecy achievable rates are obtained. Our analytical findings suggest that both the MRC and DSC schemes achieve the maximum diversity order of K + 1 where K is the number of relays. In addition, the feedback delay has a significant impact on the achievable secrecy performance by reducing the achievable diversity order to two.

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In this paper, we propose general-order transmit antenna selection to enhance the secrecy performance of multipleinput multiple-output multi-eavesdropper channels with the outdated channel state information (CSI) at the transmitter. To evaluate the effect of outdated CSI on the secure transmission of the system, we investigate the secrecy performance for two practical scenarios, i.e., Scenario I: the eavesdropper's CSI is not available at the transmitter, and Scenario II: the eavesdropper's CSI is available at the transmitter. For Scenario I, we derive exact and asymptotic closed-form expressions for the secrecy outage probability in Nakagami-m fading channels. In addition, we also derive the probability of non-zero secrecy capacity and the ε-outage secrecy capacity, respectively. Simple asymptotic expressions for the secrecy outage probability reveal that the secrecy diversity order is reduced when CSI is outdated at the transmitter, and is independent of the number of antennas at each eavesdropper NE, fading parameter of the eavesdropper's channel mE, and the number of eavesdroppers M . For Scenario II, we make a comprehensive analysis of the average secrecy capacity obtained by the system. Specifically, new closed-form expressions for the exact and asymptotic average secrecy capacity are derived, which are valid for general systems with arbitrary number of antennas, number of eavesdroppers and fading severity parameters. Resorting to these results, we also determine the high signal-to-noise ratio power offset to explicitly quantify the impacts of the main channel and the eavesdropper's channel on the average secrecy capacity.Index Terms-MIMO wiretap channel, physical layer security, transmit antenna selection, Nakagami-m fading.

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In this paper, we propose a distributed cluster formation (CF) and resource allocation (RA) framework for non-ideal non-orthogonal multiple access (NOMA) schemes in heterogeneous networks. The imperfection of the underlying NOMA scheme is due to the receiver sensitivity and interference residue from non-ideal successive interference cancellation (SIC), which is generally characterized by a fractional error factor (FEF). Our analytical findings first show that several factors have a significant impact on the achievable NOMA gain. Then, we investigate fundamental limits on NOMA cluster size as a function of FEF levels, cluster bandwidth, and quality of service (QoS) demands of user equipments (UEs). Thereafter, a clustering algorithm is developed by taking feasible cluster size and channel gain disparity of UEs into account. Finally, we develop a distributed α-fair RA framework where α governs the trade-off between maximum throughput and proportional fairness objectives. Based on the derived closed-form optimal power levels, the proposed distributed solution iteratively updates bandwidths, clusters, and UEs' transmission powers. Numerical results demonstrate that proposed solutions deliver a higher spectral and energy efficiency than traditionally adopted basic NOMA cluster size of two. We also show that an imperfect NOMA cannot always provide better performance than orthogonal multiple access under certain conditions. Finally, our numerical investigations reveal that NOMA gain is maximized under downlink/uplink decoupled (DUDe) UE association.

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In this paper, we consider an non-ideal successive interference cancellation (SIC) receiver based imperfect nonorthogonal multiple access (NOMA) schemes whose performance is limited by three factors: 1) Power disparity & sensitivity constraints (PDSCs), 2) Intra-cluster interference (ICRI), and 3) Intercell-interference (ICI). By quantifying the residual interference with a fractional error factor (FEF), we show that NOMA cannot always perform better than orthogonal multiple access (OMA) especially under certain receiver sensitivity and FEF levels. Assuming the existence of an offline/online ICI management scheme, the proposed solution accounts for the ICI which is shown to deteriorate the NOMA performance particularly when it becomes significant compared to the ICRI. Then, a distributed cluster formation (CF) and power-bandwidth allocation (PBA) approach are proposed for downlink (DL) heterogeneous networks (HetNets) operating on the imperfect NOMA. We develop a hierarchically distributed solution methodology where BSs independently form clusters and distributively determine the power-bandwidth allowance of each cluster. A generic CF scheme is obtained by creating a multi-partite graph (MPG) via partitioning user equipments (UEs) with respect to their channel gains since NOMA performance is primarily determined by the channel gain disparity of cluster members. A sequential weighted bi-partite matching method is proposed for solving the resulted weighted multi-partite matching problem. Thereafter, we present a hierarchically distributed PBA approach which consists of the primary master, secondary masters, and slave problems. For a given cluster power and bandwidth pair, optimal power allocations and Lagrange multipliers of slave problems are derived in closed-form. While power allowance of clusters is updated by the secondary masters based on dual variables of slave problems, bandwidth proportions of clusters are iteratively allocated by the primary master as per the utility achieved by the secondary masters at the previous iteration. Finally, the proposed CF and PBA approaches under the operation of imperfect NOMA are investigated and compared to the OMA scheme by extensive simulations results in DL-HetNets.Index Terms-Imperfect SIC, residual interference, intra-cell interference, inter-cell interference, hierarchical decomposition, distributed resource allocation. multi-partite matching.

Abstract-Being capable of serving multiple users with the same radio resource, non-orthogonal multiple access (NOMA) can provide desirable performance enhancements in a fair and spectral efficient manner. In this paper, we investigate the resource allocation (RA) and cluster formation (CF) aspects of NOMA for downlink (DL) uplink (UL) decoupled (DUDe) heterogeneous networks (HetNets). A non-ideal NOMA scheme is considered with power disparity and sensitivity constraints (PDSCs), delay tolerance, and residual interference after cancellation. Taking the PDSCs into account, we analytically show that using the DL decoding order limits UL-NOMA performance by that of OMA, while employing an inverse order result in a performance gain that is mainly determined by the channel gain disparity of users. Thereafter, a generic CF method is proposed for any type of user graph, which iteratively forms clusters using Blossom algorithm. Finally, highly non-convex RA problem is converted into a convex form by employing geometric programming (GP) where power and bandwidth are optimized to maximize network sumrate and max-min fairness objectives.