The random propagation of molecules in a fluid medium is characterized by the spontaneous diffusion law as well as the interaction between the environment and molecules. In this paper, we embody the anomalous diffusion theory for modeling and analysis in molecular communication. We employ H-diffusion to model a non-Fickian behavior of molecules in diffusive channels. H-diffusion enables us to model anomalous diffusion as the subordinate relationship between self-similar parent and directing processes and their corresponding probability density functions with two H-variates in a unified fashion. In addition, we introduce standard H-diffusion to make a bridge of normal diffusion across well-known anomalous diffusions such as space-time fractional diffusion, Erdélyi-Kober fractional diffusion, grey Brownian motion, fractional Brownian motion, and Brownian motion. We then characterize the statistical properties of uncertainty of the random propagation time of a molecule governed by H-diffusion laws by introducing a general class of molecular noise-called H-noise. Since H-noise can be an algebraic-tailed distribution, we provide a concept of H-noise power using finite logarithm moments based on zero-order statistics. Finally, we develop a unifying framework for error probability analysis in a timing-based molecular communication system with a concept of signal-to-noise power ratio.

Molecular communication in nature can incorporate a large number of nano-things in nanonetworks as well as demonstrate how nano-things communicate. This paper presents molecular communication where transmit nanomachines deliver information molecules to a receive nanomachine over an anomalous diffusion channel. By considering a random molecule concentration in a space-time fractional diffusion channel, an analytical expression is derived for the first passage time (FPT) of the molecules. Then, the bit error rate of the $\ell $ th nearest molecular communication with timing binary modulation is derived in terms of Fox's $H$ -function. In the presence of interfering molecules, the mean and variance of the number of the arrived interfering molecules in a given time interval are presented. Using these statistics, a simple mitigation scheme for timing modulation is provided. The results in this paper provide the network performance on the error probability by averaging over a set of random distances between the communicating links as well as a set of random FPTs caused by the anomalous diffusion of molecules. This result will help in designing and developing molecular communication systems for various design purposes.

We consider molecular communication in a nanonet-work in the presence of stochastic interfering molecules where transmit nanomachines deliver information messages to a receive nanomachine over an anomalous diffusion channel. Specifically, a set of interfering molecules is assumed to be scattered in a region according to a Cox process. We first characterize statistics (mean and variance) of the number of interfering molecules arrived in a given time interval using Campbell's theorem. Since the interfering molecules significantly degrade the bit error rate performance in timing modulation scheme, we provide a simple mitigation scheme using the statistics of the number of interfering molecules.

Cochannel interference is one of the inevitable deleterious components in designing and analyzing of a wireless network. The use of multiple antennas at both transmitting and receiving nodes is a promising technique to suppress and/or alleviate the effect of cochannel interference on capacity. In this paper, we assess the effects of both antenna correlation and cochannel interference on the ergodic capacity of multiple-input multiple-output channels with covariance feedback. In particular, we consider a general family of spatial fading correlation model-called unitary-independent-unitary-which encompasses most of zero-mean channels with arbitrary fading profiles including the popular separable correlation channel models. We derive the average minimum mean-square error and signal-to-interference-plus-noise ratio of the parallel spatial streams using Berezin's supermathematics. We then put forth the structure of optimal input covariance matrix maximizing the mutual information connected with the necessary and sufficient conditions as a generalization of the noise-limited case, which is tested by a simple iterative algorithm. Together with the powerful supermathematical framework, the result in the paper enables us to quantify the multiuser MIMO interference effects on the capacity in terms of spatial correlation and interference power heterogeneity.

Wireless localization has a great importance in a variety of areas including commercial, service, and military positioning and tracking systems. In harsh indoor environments, it is hard to localize an agent with high accuracy due to non-line-of-sight (NLOS) radio blockage or insufficient information from anchors. Therefore, NLOS identification and mitigation are highlighted as an effective way to improve the localization accuracy. In this paper, we develop a robust and efficient algorithm to enhance the accuracy for (ultrawide bandwidth) time-of-arrival localization through identifying and mitigating NLOS signals with relevance vector machine (RVM) techniques. We also propose a new localization algorithm, called the two-step iterative (TSI) algorithm, which converges fast with a finite number of iterations. To enhance the localization accuracy as well as expand the coverage of a localizable area, we continue to exploit the benefits of RVM in both classification and regression for cooperative localization by extending the TSI algorithm to a centralized cooperation case. For self-localization setting, we then develop a distributed cooperative algorithm based on variational Bayesian inference to simplify message representations on factor graphs and reduce communication overheads between agents. In particular, we build a refined version of Gaussian variational message passing to reduce the computational complexity while maintaining the localization accuracy. Finally, we introduce the notion of a stochastic localization network to verify proposed cooperative localization algorithms.

The H-transforms are integral transforms that involve Fox's H-functions as kernels. A large variety of integral transforms can be put into particular forms of the H-transform since H-functions subsume most of the known special functions including Meijer's G-functions. In this paper, we embody the H-transform theory into a unifying framework for modeling and analysis in wireless communication. First, we systematize the use of elementary identities and properties of the H-transform by introducing operations on parameter sequences of H-functions. We then put forth H-fading and degree-2 irregular H-fading to model radio propagation under composite, specular, and/or inhomogeneous conditions. The H-fading describes composite effects of multipath fading and shadowing as a single H-variate, including most of typical models such as Rayleigh, Nakagami-m, Weibull, α-μ, N*Nakagami-m, (generalized) K-fading, and Weibull/gamma fading as its special cases. As a new class of H-variates (called the degree-ζ irregular H-variate), the degree-2 irregular H-fading characterizes specular and/or inhomogeneous radio propagation in which the multipath component consists of a strong specularly reflected or line-of-sight (LOS) wave as well as unequal-power or correlated in-phase and quadrature scattered waves. This fading includes a variety of typical models such as Rician, Nakagami-q, κ-μ, η-μ, Rician/LOS gamma, and κ-μ/LOS gamma fading as its special cases. Finally, we develop a unifying H-transform analysis for the amount of fading, error probability, channel capacity, and error exponent in wireless communication using the new systematic language of transcendental H-functions. By virtue of two essential operations-called Mellin and convolution operations-involved in the Mellin transform and Mellin convolution of two H-functions, the H-transforms for these performance measures culminate in H-functions. Using the algebraic asymptotic expansions of the H-transform, we further analyze the error probability and capacity at high and low signal-to-noise ratios in a unified fashion.

Wireless localization systems have a great importance in a variety of fields such as positioning and tracking systems. Specifically, in hash conditions, e.g., indoor environments, it is difficult to localize an agent with high accuracy due to radio blockage or insufficient information of anchors. Therefore, identification and mitigation of non-line-of-sight (NLOS) radio propagation are highlighted as a solution for improving localization accuracy by overcoming these limitations. In this paper, we develop a robust and efficient localization algorithm using relevance vector machine (RVM). We first design a RVM classifier to identify NLOS signals using features extracted from the received waveform. We then design a RVM regressor to predict a probability density function of range estimates (pair-nodes distance) by exploiting its prediction ability. Numerical results show that the RVM localization algorithm provides high localization accuracy with low complexity.

Physical-layer multicast transmission, which seeks to deliver information messages to all users simultaneously, is becoming more important in wireless systems with demand for various multimedia mobile applications such as Multimedia Broadcast Multicast Services. The spatial randomness of communicating nodes in a wireless network is one of inevitable uncertainties in the design and analysis of network information flow and connectivity. The use of multiple antennas at both transmitting and receiving nodes is the most promising strategy to increase spectral efficiency and communication reliability as well as to enhance physical-layer confidentiality of wireless systems. In this paper, we characterize multicasting in such a stochastic multiple-input multiple-output (MIMO) network where a probe transmitter broadcasts confidential data with sectorized transmission to legitimate receivers sitting in a region R. We first put forth a measure of the total amount of information flow, called the space-time capacity, into R in a spatial random field of legitimate receivers without accounting for intrinsic confidentiality at the physical layer. We then derive the space-time capacity into the sectoral region R and the nth nearest ergodic capacity in a Poisson field to characterize the spatial average and ordering of MIMO ergodic capacity achieved by legitimate receivers in R. Using the Mar\u{c}enko-Pastur law, we further assess the asymptotic space-time capacity and the nth nearest ergodic capacity per receive antenna as the antenna numbers tend to infinity. In the presence of eavesdropping, we determine a total amount of confidential information flow per receive antenna, called the space-time secrecy rate, into R in Poisson fields of receiving equivalents-with asymptotic arguments. Using an asymptotic secrecy graph on R, we also characterize local confidential connectivity such as the secrecy range, out-degree, and out-isolation probability of the probe transmitter. The framework developed in this work enables us to quantify the local information flow in random MIMO wireless networks by averaging first small-scale fading processes over time and then large-scale path losses over space.

The use of multiple antennas at both transmitting and receiving nodes is the most promising strategy to increase spectral efficiency and communication reliability as well as to leverage physical-layer confidentiality of wireless systems. In this paper, we characterize secure connectivity in a stochastic multiple-input multiple-output (MIMO) multicast network where a probe transmitter broadcasts common confidential data with sectorized transmission to legitimate receivers sitting in a region R in the presence of passive eavesdroppers. We first determine a total amount of common confidential information flow per receive antenna, called the space-time secrecy rate, into R in Poisson fields of receiving equivalents — with asymptotic arguments. Using an asymptotic secrecy graph on R, we then characterize local secure connectivity such as the secrecy range, out-degree, and out-isolation probability of the probe transmitter.

In this paper, we integrate key wireless propagation effects such as the path loss, shadowing, and multipath fading into a single Fox's H-variate using the H-preserving property under products, powers, quotients, and their combinations. We then establish a unifying framework to analyze the error probability and channel capacity for V2V communication in a Cox field of vehicles, using again the language of Fox's H-functions. This framework enables us to characterize intervehicle communication in the doubly stochastic vehicular ad-hoc network (VANET) by averaging both small- and large-scale fading processes in time and (random) distance-dependent path losses in space.

Safety message dissemination in a vehicular ad-hoc network (VANET) requires vehicle-to-vehicle (V2V) communication with low latency and high reliability. The dynamics of vehicle passing and queueing as well as high mobility create distinctive propagation characteristics of wireless medium and inevitable uncertainty in space-time patterns of the vehicle density on a road. It is therefore of great importance to account for random vehicle locations in V2V communication. In this paper, we characterize intervehicle communication in a random field of vehicles, where a beacon or head vehicle (transmitter) broadcasts safety or warning messages to neighboring client vehicles (receivers) randomly located in a cluster on the road. To account for a doubly stochastic property of the VANET, we first model vehicle's random locations as a stationary Cox process with Fox's H-distributed random intensity (vehicle concentration) and derive the distributional functions of the lth nearest client's distance from the beacon in such a Fox Cox field of vehicles. We then consolidate this spatial randomness of receiving vehicles into a path loss model and develop a triply-composite Fox channel model that combines key wireless propagation effects such as the distance-dependent path loss, large-scale fading (shadowing), and small-scale fading (multipath fading). In Fox channel modeling, each constituent propagation effect is described as Fox's H-variate, culminating again in Fox's H-variate for the received power or equivalently the instantaneous signal-to-noise ratio at the lth nearest client vehicle. Due to versatility of Fox's H-functions, this stochastic channel model can encompass a variety of well-established or generalized statistical propagation models used in wireless communication; be well-fitted to measurement data in diverse propagation environments by varying parameters; and facilitate a unifying analysis for fundamental physical-layer performances, such as error probability and channel capacity, using again the language of Fox's H-functions. This work serves to develop a unifying framework to characterize V2V communication in a doubly stochastic VANET by averaging both the small- and large-scale fading effects as well as the (random) distance-dependent path losses.

The need for bandwidth and the incitation to reduce power consumption lead to the reduction of cell size in wireless networks. This allows reducing the distance between a user and the base station, thus increasing the capacity. A relatively inexpensive way of deploying small-cell networks is to use femtocells. However, the reduction in cell size causes problems for coordination and network deployment, especially due to the intra- and cross-tier interference. In this paper, we consider a two-tier multiple-input multiple-output (MIMO) network in the downlink, where a single macrocell base station with multiple transmit antennas coexists with multiple closed-access MIMO femtocells. With multiple receive antennas at both the macrocell and femtocell users, we propose an opportunistic interference alignment scheme to design the transmit and receive beamformers in order to mitigate intra- (or inter-) and cross-tier interference. Moreover, to reduce the number of macrocell and femtocell users coexisting in the same spectrum, we apply a random spectrum allocation on top of the opportunistic interference alignment. Using stochastic geometry, we analyze the proposed scheme in terms of the distribution of a received signal-to-interference-plus-noise ratio, spatial average capacity, network throughput, and energy efficiency. In the presence of imperfect channel state information, we further quantify the performance loss in spatial average capacity. Numerical results show the effectiveness of our proposed scheme in improving the performance of random MIMO femtocell networks.

Safety message dissemination in a vehicular ad-hoc network (VANET) is in desperate need of vehicle-to-vehicle (V2V) communication with low latency and high reliability. The dynamics of vehicle passing and queueing as well as high mobility create distinctive propagation characteristics of wireless medium and inevitable uncertainty in space-time patterns of the vehicle density on a road. It is therefore of great importance to integrate stochastic geometry of vehicle locations into V2V channel modeling. In this paper, we characterize intervehicle communication in a random field of vehicles, where a beacon or head vehicle (transmitter) geobroadcasts safety or warning messages to neighboring client vehicles (receivers) randomly located in a cluster on the road. To account for a doubly stochastic spatial property of the VANET, we first model vehicle's random locations as a stationary Cox process with Fox's H-distributed random intensity (vehicle concentration) and derive the distributional functions of the `th nearest client's distance from the beacon in such a Fox Cox field of vehicles. We then consolidate this spatial randomness of receiving vehicles into a path loss model and develop a triply-composite Fox channel model that combines key wireless propagation effects such as the distance-dependent path loss, large-scale fading (shadowing), and small-scale fading (multipath fading).

The physical-layer multicast transmission that seeks to deliver the common information messages to the all users simultaneously is becoming more important in wireless systems with demand for various multimedia mobile applications such as Multimedia Broadcast Multicast Services. The spatial randomness of communicating nodes in a wireless network is one of inevitable uncertainty in design and analysis of network information flow and connectivity. In this paper, we characterize local information flow in a stochastic multiple-input multiple-output (MIMO) multicast network where a probe transmitter geobroadcasts common data with sectorized transmission to receivers sitting in a region R. We first put forth a measure of the total amount of common information flow, called the space-time capacity, into R in a spatial random field of receivers. We then derive the space-time capacity into a sectoral region R and the nth nearest ergodic capacity in a Poisson field to characterize the spatial average and ordering of MIMO ergodic capacity achieved by receivers in R. Using the Marčenko-Pastur law, we further assess the asymptotic space-time capacity and the nth nearest ergodic capacity per receive antenna as the antenna numbers tend to infinity. The framework developed in this work enables us to quantify the local information flow in random MIMO wireless networks by averaging both small-scale fading processes on time and large-scale path losses on space.

A femtocell technology-towards the deployment of small-cell networks-is a key enabler for improving indoor coverage and throughput per network area at a low cost in future wireless networks. However, these small-cell networking inevitably increases cochannel interference due to aggressive (even uncontrolled) reuse of spectral resources. One of the attractive approaches to alleviating the cochannel interference is a multiple-antenna technique for which accurately characterizing the effects of interference is crucial but challenging. To elucidate this important problem, we analyze the performance of interference rejection diversity combining, often called the optimum combining, in an uplink two-tier femtocell network. Specifically, we consider that a single-antenna femtocell user (transmitter) communicates with a closed femtocell access point (receiver) with multiple antennas in the presence of single-antenna cochannel interferers from co-tier (femtocells) and cross-tier (macrocell) networks. We introduce a new mathematical methodology to analyze the average symbol error probability of optimum combining diversity systems in Rayleigh fading, accounting for multiple unequal-power interferers, each is spatially correlated across receiving antennas. The analysis resorts to the so-called Berezin's supermathematics that treats both commuting and Grassmann anticommuting variables on an equal footing. This powerful supermathematical framework enables us to quantify the cross- and co-tier interference effects in terms of interference power heterogeneity and spatial correlation.

A femtocell technology-towards the deployment of small-cell networks-is a key enabling feature for future wireless networks to improve indoor coverage and throughput per network area at a low cost. However, these small-cell networking inevitably increases cochannel interference due to aggressive (even uncontrolled) reuse of spectral resources. One of the attractive approaches to alleviating the cochannel interference is a multiple-antenna technique, where accurately characterizing the effects of cross- and co-tier interference on the performance of multiple-antenna communications is crucial but challenging. We apply superanalysis framework to provide further numerical results on the optimum combining diversity systems in an uplink two-tier femtocell network. Specifically, we consider that a single-antenna femtocell user (transmitter) communicates with a closed femtocell access point (receiver) with multiple antennas in the presence of single-antenna cochannel interferers from co-tier (femtocells) and cross-tier (macrocell) networks. We then quantify the cross- and co-tier interference effects in terms of degrees of interference power heterogeneity and spatial correlation.

We analyze the performance of optimum combining in a general cochannel interference environment with thermal noise. Specifically, we consider multiple unequal-power interferers, each is spatially correlated across receiving antennas. We develop a new mathematical methodology to analyze the average symbol error probability (SEP) of optimum combining diversity systems in Rayleigh fading. The analysis resorts to the so-called Berezin's supermathematics that treats both commuting and Grassmann anticommuting variables on an equal footing. This superanalysis framework enables us to derive the exact SEP expression for an arbitrary number of interferers with spatial correlation and possibly different power levels. Our results therefore encompass all the previous analytical results, based on the theory of multivariate statistics relating to complex Wishart matrices, for equal-power and/or spatially-uncorrelated interferers. Connecting the powerful supermathematical framework to the analysis of wireless diversity systems with optimum combining, we quantify the interference effects in terms of the degree of power unbalance and the amount of spatial correlation.

Cognitive radio (CR) is an advanced enabling technology for improving the spectrum utilization in wireless systems. Specially, spectrum underlay systems assign licensed bandwidth to a secondary network while guaranteeing the quality of service (QoS) for a primary network. In this paper, we consider downlink CR underlay multiple-input single-output (MISO) networks comprising primary and secondary transmitters serving multiple user. In particular, we formulate the following beamforming optimization problems: 1) total transmit power minimization problem; 2) mean-square error balancing problem; and 3) network interference power minimization problem. In the presence of perfect channel state information (CSI), we formulate the optimization algorithms in a centralized manner and determine the optimal beamformers using standard convex optimization techniques. To account imperfect CSI, we also propose robust algorithms through the worst-case design to mitigate the effect of channel uncertainty. Finally, numerical results are provided to illustrate the validity of our proposed algorithms.