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.

We study the application of the protocol interference model, in place of the more complex physical interference model, in order to evaluate transmission success/outage in wireless networks. Under the protocol model a transmission is successful if and only if there are no interferers within a specified guard zone around the receiver. We first recognize that the protocol model, parameterized by a guard zone radius, forms a family of decision rules for estimating the physical model feasibility of a typical transmission. We proceed to cast the problem using a binary hypothesis testing framework. For wireless Poisson networks, we employ stochastic geometry to determine the prior and posterior distributions associated with the estimation problem. We then develop expressions for false rejection (Type I) and false acceptance (Type II) rates associated with the protocol model, and investigate the optimal guard zone minimizing the total probability of error associated with the protocol model.

The study of the optimality of low-complexity greedy scheduling techniques in wireless communications networks is a very complex problem. The Local Pooling (LoP) factor provides a single-parameter means of expressing the achievable capacity region (and optimality) of one such scheme, greedy maximal scheduling (GMS). The exact LoP factor for an arbitrary network graph is generally difficult to obtain, but may be evaluated or bounded based on the network graph's particular structure. In this paper, we provide rigorous characterizations of the LoP factor in large networks modeled as Erdös-Rényi (ER) and random geometric (RG) graphs under the primary interference model. We employ threshold functions to establish critical values for either the edge probability or communication radius to yield useful bounds on the range and expectation of the LoP factor as the network grows large. For sufficiently dense random graphs, we find that the LoP factor is between 1/2 and 2/3, while sufficiently sparse random graphs permit GMS optimality (the LoP factor is 1) with high probability. We then place LoP within a larger context of commonly studied random graph properties centered around connectedness. We observe that edge densities permitting connectivity generally admit cycle subgraphs that form the basis for the LoP factor upper bound of 2/3. We conclude with simulations to explore the regime of small networks, which suggest the probability that an ER or RG graph satisfies LoP and is connected decays quickly in network size.

We study downlink delay minimization within the context of cellular user association policies that map mobile users to base stations. We note the delay minimum user association problem fits within a broader class of network utility maximization and can be posed as a non-convex quadratic program. This non-convexity motivates a split quadratic objective function that captures the original problem's inherent tradeoff: association with a station that provides the highest signal-to-interference-plus-noise ratio (SINR) vs. a station that is least congested. We find the split-term formulation is amenable to linearization by embedding the base stations in a hierarchically well-separated tree (HST), which offers a linear approximation with constant distortion. We provide a numerical comparison of several problem formulations and find that with appropriate optimization parameter selection, the quadratic reformulation produces association policies with sum delays that are close to that of the original network utility maximization. We also comment on the more difficult problem when idle base stations (those without associated users) are deactivated.

We introduce a model for capturing the effects of beam misdirection on coverage and throughput in a directional wireless network using stochastic geometry. In networks employing ideal sector antennas without sidelobes, we find that concavity of the orientation error distribution is sufficient to prove monotonicity and quasi-concavity (both with respect to antenna beamwidth) of spatial throughput and transmission capacity, respectively. Additionally, we identify network conditions that produce opposite extremal choices in beamwidth (absolutely directed versus omni-directional) that maximize the two related throughput metrics. We conclude our paper with a numerical exploration of the relationship between mean orientation error, throughput-maximizing beamwidths, and maximum throughput, across radiation patterns of varied complexity.