The Distribution of Minimum of Ratios of Two Random Variables and Its Application in Analysis of Multi-hop Systems

The distributions of random variables are of interest in many areas of science. In this paper, ascertaining on the importance of multi-hop transmission in contemporary wireless communications systems operating over fading channels in the presence of cochannel interference, the probability density functions (PDFs) of minimum of arbitrary number of ratios of Rayleigh, Rician, Nakagami-m, Weibull and α-µ random variables are derived. These expressions can be used to study the outage probability as an important multi-hop system performance measure. Various numerical results complement the proposed mathematical analysis

On Amplify-and-Forward Relaying Over Hyper-Rayleigh Fading Channels

Relayed transmission holds promise for the next generation of wireless communication systems due to the performance gains it can provide over non-cooperative systems. Recently hyper-Rayleigh fading, which represents fading conditions more severe than Rayleigh fading, has received attention in the context of many practical communication scenarios. Though power allocation for Amplify-and-Forward (AF) relaying networks has been studied in the literature, a theoretical analysis of the power allocation problem for hyper-Rayleigh fading channels is a novel contribution of this work. We develop an optimal power allocation (OPA) strategy for a dual-hop AF relaying network in which the relay-destination link experiences hyper-Rayleigh fading. A new closed-form expression for the average signal-to-noise ratio (SNR) at destination is derived and it is shown to provide a new upper-bound on the average SNR at destination, which outperforms a previously proposed upper-bound based on the well-known harmonic-geometric mean inequality. An OPA across the source and relay nodes, subject to a sum-power constraint, is proposed and it is shown to provide measurable performance gains in average SNR and SNR outage at the destination relative to the case of equal power allocation

Level Crossing Rate and Average Fade Duration of the Multihop Rayleigh Fading Channel

We present a novel analytical framework for the evaluation of important second order statistical parameters, as the level crossing rate (LCR) and the average fade duration (AFD) of the amplify-and-forward multihop Rayleigh fading channel. More specifically, motivated by the fact that this channel is a cascaded one, which can be modelled as the product of N fading amplitudes, we derive novel analytical expressions for the average LCR and AFD of the product of N Rayleigh fading envelopes, or of the recently so-called N*Rayleigh channel. Furthermore, we derive simple and efficient closed-form approximations to the aforementioned parameters, using the multivariate Laplace approximation theorem. It is shown that our general results reduce to the specific dual-hop case, previously published. Numerical and computer simulation examples verify the accuracy of the presented mathematical analysis and show the tightness of the proposed approximations

On the Second Order Statistics of the Multihop Rayleigh Fading Channel

Second order statistics provides a dynamic representation of a fading channel and plays an important role in the evaluation and design of the wireless communication systems. In this paper, we present a novel analytical framework for the evaluation of important second order statistical parameters, as the level crossing rate (LCR) and the average fade duration (AFD) of the amplify-and-forward multihop Rayleigh fading channel. More specifically, motivated by the fact that this channel is a cascaded one and can be modeled as the product of N fading amplitudes, we derive novel analytical expressions for the average LCR and the AFD of the product of N Rayleigh fading envelopes (or of the recently so-called N*Rayleigh channel). Furthermore, we derive simple and efficient closed-form approximations to the aforementioned parameters, using the multivariate Laplace approximation theorem. It is shown that our general results reduce to the corresponding ones of the specific dual-hop case, previously published. Numerical and computer simulation examples verify the accuracy of the presented mathematical analysis and show the tightness of the proposed approximations

Error Analysis of Fixed-Gain AF Relaying with MRC Over Nakagami-m Fading Channels

This article investigates the error performance of wireless communication systems that employ binary modulations and Amplify-and-Forward (AF) relaying over flat Nakagami-m faded links with maximum ratio combining (MRC) at destination. Specifically, we derive a simple yet accurate closed-form approximation for the average bit error probability (ABEP) and closed-form expressions for its tight upper and lower bounds. The effect of power imbalance between the relayed links is also studied. Numerical investigations show good agreement between proposed theoretical results and simulations whereas our performance bounds are shown to be tighter than previously proposed bounds for the case of unbalanced relayed links

Throughput Scaling of Wireless Networks With Random Connections

This work studies the throughput scaling laws of ad hoc wireless networks in the limit of a large number of nodes. A random connections model is assumed in which the channel connections between the nodes are drawn independently from a common distribution. Transmitting nodes are subject to an on-off strategy, and receiving nodes employ conventional single-user decoding. The following results are proven: 1) For a class of connection models with finite mean and variance, the throughput scaling is upper-bounded by $O(n^{1/3})$ for single-hop schemes, and $O(n^{1/2})$ for two-hop (and multihop) schemes. 2) The $\Theta (n^{1/2})$ throughput scaling is achievable for a specific connection model by a two-hop opportunistic relaying scheme, which employs full, but only local channel state information (CSI) at the receivers, and partial CSI at the transmitters. 3) By relaxing the constraints of finite mean and variance of the connection model, linear throughput scaling $\Theta (n)$ is achievable with Pareto-type fading models.Comment: 13 pages, 4 figures, To appear in IEEE Transactions on Information Theor

Statistics of α - μ random variables and their applications in wireless multihop relaying and multiple scattering channels

Exact results for the probability density function (PDF) and cumulative distribution function (CDF) of the sum of ratios of products (SRP) and the sum of products (SP) of independent α-μ random variables (RVs) are derived. They are in the form of 1-D integral based on the existing works on the products and ratios of α-μ RVs. In the derivation, generalized Gamma (GG) ratio approximation (GGRA) is proposed to approximate SRP. Gamma ratio approximation (GRA) is proposed to approximate SRP and the ratio of sums of products (RSP). GG approximation (GGA) and Gamma approximation (GA) are used to approximate SP. The proposed results of the SRP can be used to calculate the outage probability (OP) for wireless multihop relaying systems or multiple scattering channels with interference. The proposed results of the SP can be used to calculate the OP for these systems without interference. In addition, the proposed approximate result of the RSP can be used to calculate the OP of the signal-to-interference ratio (SIR) in a multiple scattering system with interference