Poisson Wireless Networks Research Articles

Meta Distributions—Part 2: Properties and Interpretations

In the companion letter (Part 1), we have defined and exemplified meta distributions (MDs) as a natural extension of the concepts of the mean and distribution of a random variable. Here we provide an in-depth discussion of the properties and interpretations of MDs. It includes original results on the calculation of MDs in the monotone case and two applications to simple Poisson wireless networks models.

Optimal interference range for minimum Bayes risk in binomial and Poisson wireless networks

Interference is the main performance-limiting factor in most wireless networks. Protocol interference model is extensively used in the design of wireless networks. However, the setting of interference range, a crucial part of the protocol interference model, is rather heuristic and remains an open problem. In this paper, we use the stochastic geometry and the direct approach to obtain the associated feasibility distributions. After that, we use the binary hypothesis testing to achieve the Bayes risk under binomial point process (BPP) and Poisson point process (PPP), respectively. According to the first derivative of the Bayes risk, we provide the equation to achieve the optimal interference range for minimum Bayes risk. We extend the method proposed by Wildman et al. to a more general situation. Furthermore, we show that for infinite PPP, those two methods converge to the same results. Several numerical results for wireless networks under BPP, finite PPP, and infinite PPP are given. Simulation results show that in the finite wireless network, the BPP method performs better than the PPP method.

On Protocol and Physical Interference Models in Poisson Wireless Networks

This paper analyzes the connection between the protocol and physical interference models in the setting of Poisson wireless networks. A transmission is successful under the protocol model if there are no interferers within a parameterized guard zone around the receiver, while a transmission is successful under the physical model if the signal to interference plus noise ratio at the receiver is above a threshold. The parameterized protocol model forms a family of decision rules for predicting the success or failure of the same transmission attempt under the physical model. For Poisson wireless networks, we employ stochastic geometry to determine the prior, evidence, and posterior distributions associated with this estimation problem. With this in hand, we proceed to develop six sets of results: 1) the maximum correlation of protocol and physical model success indicators; 2) the minimum Bayes risk in estimating physical success from a protocol observation; 3) the receiver operating characteristic (ROC) of false rejection (Type I) and false acceptance (Type II) probabilities; 4) the impact of Rayleigh fading versus no fading on the correlation and ROC; 5) the impact of multiple prior protocol model observations in the setting of a wireless network with a fixed set of nodes in which the nodes employ the slotted Aloha protocol in each time slot; and 6) a numerical investigation of the effect of different pathloss models.

지향성 안테나기반 포아송 무선 네트워크에서의 간섭 분석

본 논문은 지향성 안테나를 활용한 무선 송수신기가 포아송 분포로 무작위적으로 분포하는 무선통신 네트워크에서 간섭의 통계적인 특성을 분석한다. 본 논문에서 제시한 이상적인 섹터 안테나 이득을 이용하여 일반적인 지향성 안테나 이득을 상한 근사화할 수 있음을 제시한다. 또한, 시뮬레이션을 통하여 빔폭에 따른 포아송 무선 네트워크의 간섭의 통계적 특성을 보인다.BR

Exact SNR and SIR analysis in Poisson wireless networks

The probability density function and cumulative distribution function of the received signal-to-noise ratio (SNR) and the received signal-to-interference ratio (SIR), for interference-limited systems is derived, at the nth nearest neighbour node in a Poisson point process wireless random network. The analytical expressions are given in terms of the Meijer G-function and reveal the impact of node spatial density, transmit power, interference power, and path-loss exponent on the connectivity probability of a broadcast wireless transmission. The analytical results are validated with computer simulation.

Modeling and Analysis of Opportunistic Beamforming for Poisson Wireless Networks

This paper introduces a model to study both single tier and multitier wireless communication systems consisting of a multitude of wireless access points (AP), and operating according to the classical opportunistic beamforming framework. The AP locations in the proposed network model are determined by using planar Poisson point processes. The extreme value distribution of signal-to-interference-plus-noise-ratio ( ${\rm{ SINR}}$ ) on a beam is of fundamental importance for obtaining performance bounds for such an opportunistic communication system. Two tight distribution approximation results are provided for the distribution of maximum ${\rm{ SINR}}$ on a beam, which is hard to obtain due to correlation structure of the underlying inter-AP interference field, using key tools from stochastic geometry. These approximations hold for general path loss models that satisfy some mild conditions. Simulations and numerical evaluations are presented to validate the results, to provide further insights into the derived approximate maximum beam ${\rm{ SINR}}$ distributions, and to illustrate the utility of these approximations in obtaining performance bounds for opportunistic communication systems having multiple interfering APs. In particular, key performance measures such as beam outage probability and ergodic aggregate data rate of an AP are derived by utilizing the approximated distributions.

Throughput analysis of cognitive wireless networks with Poisson distributed nodes based on location information

This paper provides a statistical characterization of the individual achievable rates in bits/s/Hz and the spatial throughput of bipolar Poisson wireless networks in bits/s/Hz/m2. We assume that all cognitive transmitters know the distance to their receiver’s closest interferers and use this side-information to autonomously tune their coding rates to avoid outage events for each spatial realization. Considering that the closest interferer approximates the aggregate interference of all transmitters treated as noise, we derive closed-form expressions for the probability density function of the achievable rates under two decoding rules: treating interference as noise, and jointly detecting the strongest interfering signals treating the others as noise. Based on these rules and the bipolar model, we approximate the expected maximum spatial throughput, showing the best performance of the latter decoding rule. These results are also compared to the reference scenario where the transmitters do not have cognitive ability, coding their messages at predetermined rates that are chosen to optimize the expected spatial throughput – regardless of particular realizations – which yields outages. We prove that, when the same decoding rule and network density are considered, the cognitive spatial throughput always outperforms the other option.

Outage Probability of Opportunistic Relaying in Poisson Wireless Networks

In this paper, the performance of opportunistic decode-and-forward relaying network over Rayleigh fading channels is analyzed. We assume that the intermediate relay nodes are distributed according to a homogeneous Poisson point process with fixed density. We also consider a sectorized relay selection region to reduce the signaling overhead (e.g., link quality feedback) for establishing reliable connections between the source and destination. The "best relay" is selected among those potential relay nodes that lie in this region such that can achieve the highest signal-to-noise ratio at the destination node. In particular, the density of the potential relay nodes and the closed-form expression for outage probability of the system with maximal ratio combining (MRC) receiver at the destination, is derived based on the theory of point processes. Our results demonstrate that cooperative communication with MRC receiver deliver significant performance gains compared to direct transmission in spatially random networks. Simulation results show the validity of the analysis and point out the effect of key system parameters on the outage probability of the system.