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Multi-hop route optimization in large-scale inhomogeneous networks is typically NP-hard, for most problem formulations, requiring the application of heuristics which, despite their relatively low processing complexity, find sub-optimal solutions. Where optimal solutions can be determined by Lagrangian based constrained optimization techniques for example, the processing complexity typically scales like $O(N^{3})$ , $N$ being the number of relays employed. Here, we propose an alternative approach to route optimization by considering the limit of infinite relay node density to develop a continuum model, which yields an optimized equivalent continuous relay path. The model is carefully constructed to maintain a constant connection density even though the node density scales without bound. This leads to a formulation for minimizing the end-to-end outage probability that can be solved using methods from the calculus of variations. With the continuum model, we show that the processing complexity scales linearly with the number of points that sample the continuous path, which can be lower than the number of relay nodes in a large scale network. We demonstrate the effectiveness of this new approach and its potential by considering a network subjected to point sources of interference. [ABSTRACT FROM AUTHOR]

This paper studies finding the secure path according to the secrecy connectivity probability (SCP) in the multihop ad hoc networks in the presence of inhomogeneous eavesdropper clusters. We consider both random and fixed eavesdropper clusters, where the former case assumes that there is no knowledge of the locations of the clusters and the latter case assumes that the locations of the clusters can be estimated accurately. First, we derive the end-to-end SCP to characterize the secrecy performance of a given path in a general multihop wireless network with half-duplex randomize-and-forward relaying. Then, we consider a full-duplex scheme at the legitimate receiver, which receives the useful information while broadcasting a jamming signal to the potential eavesdroppers to further enhance the secrecy connectivity. Then, a novel secure routing algorithm that can provide the maximum SCP for any legitimate transmitter/receiver pair in a distributed manner is proposed. The theoretical analysis is verified by Monte Carlo simulation results. The results show that our secure routing algorithm provides similar results compared to an exhaustive search. For the random eavesdropper cluster case, the optimal route is independent of the knowledge of the cluster, which is the same as the homogeneous eavesdropper case. However, for the case where eavesdropper clusters are fixed and their locations are knowna priori, the optimal path selection depends on the radii and locations of the eavesdropper clusters and the average number of eavesdroppers in each cluster. [ABSTRACT FROM AUTHOR]

In this paper, we study the connectivity between two fixed terminal nodes within a geometrically bounded network of relay nodes and fixed infrastructure nodes. We assume that a communication path, between the terminal nodes, can be established by direct connection (1-hop), via a relay node (2-hop) or via the infrastructure network; the choice is based on link viability in a Rayleigh fading environment. We adopt a probabilistic approach to our analysis considering a homogeneous spatial distribution of relay nodes and an inhomogeneous spatial distribution of infrastructure nodes. Our analysis of the relationship between relay and infrastructure densities for a prescribed outage probability shows that reliance on infrastructure connectivity can be appreciably reduced by employing direct and 2-hop connectivity. We further show that, as the relay density increases, optimum connectivity is achieved by employing a non uniform spatial thinning of the infrastructure, which is dependent upon the geometric extent of the network. Our analysis provides an insight into multi-mode connectivity in bounded network domains and has application in many fields including cellular and vehicle-to-infrastructure (V2X), which are often modelled as having finite extent and where reducing the reliance on fixed infrastructure can effectively reduce operating expenditure costs. [ABSTRACT FROM AUTHOR]

In this paper, we propose a full-duplex orthogonal frequency-division multiplexing (OFDM) device-to-device (D2D) system in two-hop networks, where multiple full-duplex decode-and-forward relays assist the transmission from D2D user equipment (DUE) transmitter to DUE receiver. By such a transmission mechanism, the signal transmitted by the DUE transmitter does not need to go through a base station. Meanwhile, due to the adoption of underlay D2D communication protocol, power control mechanisms are thereby necessary to be applied to mitigate the interference to conventional cellular communications. Based on these considerations, we analyze the outage performance of the proposed system, and derive the exact expressions of outage probabilities when bulk and per-subcarrier relay selection criteria are applied. Furthermore, closed-form expressions of outage probabilities are also obtained for special cases when the instantaneous channel state information between BS and cellular user equipments is not accessible, so that a static power control mechanism is applied. Subsequently, we also investigate the outage performance optimization problem by coordinating transmit power among DUE transmitter and relays, and provide a suboptimal solution, which is capable of improving the outage performance. All analyses are substantiated by numerical results provided by Monte Carlo simulations. The analytical and numerical results demonstrated in this paper can provide an insight into the full-duplex relay-assisted OFDM D2D systems, and serve as a guideline for its implementation in next generation networks. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel relay selection scheme for orthogonal frequency-division multiplexing systems by combining conventional bulk and per-subcarrier selection schemes and analyze its outage performance over equally spatially correlated channels. Specifically, the combined selection scheme selects only two relays at the first attempt and performs per-subcarrier selection over these two relays. We analyze the asymptotic outage performance of the combined selection scheme in the high signal-to-noise ratio (SNR) region and prove a generalized theorem. This theorem states that the combined selection can achieve an optimal outage probability equivalent to the per-subcarrier selection at a high SNR without using the full set of available relays for selection. This unique property is termed the equivalence principle, and it holds for all correlation conditions. To explore this principle, we consider three examples: decode-and-forward, fixed-gain amplify-and-forward (AF), and variable-gain AF relay systems. Furthermore, two extended applications, i.e., antenna selection and branch selection, are also considered to reveal the feasibility and the expandability of the equivalence principle. Our analysis is verified by Monte Carlo simulations. The proposed combined selection and the proved theorem provide a general and feasible solution to the tradeoff between system complexity and outage performance when relay selection is applied. [ABSTRACT FROM AUTHOR]

We develop an approximation for the outage probability of a parallel channel where the subchannel statistics satisfy mild conditions. The main result is in the form of a functional of the density function that describes the statistics of the subchannel powers. The error of the approximation is quantified to be O(\gamma^-n(q+1)-2), where $\gamma$ is the end-to-end SNR of a given subchannel, $n$ is the number of subchannels, and $q$ represents the inherent subchannel diversity. We illustrate the versatility and accuracy of the approximation by studying different statistical subchannel models, which reflect practical wireless communication systems, including line-of-sight links (Rician fading), transmissions affected by interference, and relay systems subject to amplifier distortion. [ABSTRACT FROM PUBLISHER]

A theorem that describes the high signal-to-noise ratio outage behavior of fixed-gain amplify-and-forward relay systems is given. Qualitatively, the theorem states that the outage probability decays according to a power law, where the power is dictated by the poles of the moments of the underlying per-hop fading distributions. The power-law decay is dampened by a logarithmic factor when the leading pole (furthest to the right in the plane) is of order two or more. The theorem is easy to apply, and several examples are presented to this effect. [ABSTRACT FROM PUBLISHER]