Jeffrey Wildman

On the Joint Impact of Beamwidth and Orientation Error on Throughput in Directional Wireless Poisson Networks

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.

Delay minimizing user association in cellular networks via hierarchically well-separated trees

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 problems 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.

Minimizing the Bayes risk of the protocol interference model in wireless Poisson networks

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.

A primal-dual approach to delay minimizing user association in cellular networks

We study network utility maximization (NUM) within the context of cellular single user association (SUA) policies that map each mobile user (MU) to a single base station (BS) and make use of the generalized α-proportional fairness utility measure across downlink rates. Finding an exact solution to many such centralized user association problem is known to be NP-hard, so we are motivated to consider the integer relaxation of the SUA NUM problem. On this front, we provide separate characterizations of i) the fairness measures under which the SUA NUM problem integrality gap is exactly 1, and ii) the fairness measures yielding non-convex SUA NUM problem formulations. Next, we analyze the fairness measure corresponding to delay minimization and find a more natural linearization of the non-convex minimum delay SUA problem compared to our related previous work. We propose and construct a primal-dual algorithm to approximate the linearized minimum delay SUA problem. Our primal-dual algorithm is shown to achieve smaller performance gaps and runtimes over i) an intuitive baseline rounding algorithm applied to the linearized min delay SUA problem, as well as ii) two greedy heuristics that emphasize associations with minimal MU-BS distances and maximal downlink SINR ratios, respectively.

Simulation of waveform interactions for interference analysis of military networks

Efficient use of spectrum requires an accurate determination of interference effects. In this paper, we introduce a Radio to Radio (R2R) factor that quantifies the interference effects of one radio waveform on another based on multiple waveform properties instead of solely on intermediate frequency (IF) signal power. The R2R factor is formulated as a dimensionless correction term in the victims communication link budget. The factor provides an effective interference margin in the link budget, taking into account modulation schemes, frequency offset, and power offsets of the intended source of communication (“victim”) and the interferer. For a specified set of modulation parameters we simulate a scenario where the victim signal is interfered by the interferer signal. The interfered victim signal is then demodulated by the intended receiver in the presence of additive white Gaussian noise (AWGN). The sent and received data streams are compared to determine a bit error rate (BER) induced by the interference. This BER is then mapped to an effective signal to noise and interference ratio that produces the same BER in an AWGN channel. The R2R factor is then the difference between this effective signal to noise and interference ratio and the actual signal to noise and interference ratio of the communication link. In this paper we demonstrate how the R2R factor may be computed, and show examples for several cases of victim and interferer modulations.

Using an emulation testbed to measure OSPF routing overhead due to mobility in wireless ad hoc networks

In mobile wireless IP networking domains (i.e., MANETs), the network topology may be frequently changing due to node mobility. Under such network dynamics, simulation has shown that the OSPF routing protocol performs poorly (e.g., increased overhead and data loss), but can be modified with dasiaMANET extensionspsila to better its performance. To provide complementary validation of these observations, this paper separately measures the routing protocol overhead generated by OSPF and its MANET extensions due to node mobility using an emulation testbed. The networking experiments were constructed using several off-the-shelf Linux workstations interconnected by Ethernet. Several modeling efforts were necessary to represent the network under testpsilas partial mesh connectivity, wireless interfaces, and node mobility on the immobile, non-wireless testbed. To validate these modeling efforts, the experimental results from the emulation testbed were cross-validated against OPNET simulation. For networks under test of increasing size, our emulation (and simulation) testing showed that the MANET extensions to OSPF consistently exhibited lower amounts of routing protocol overhead, and lower growth trends, when compared to OSPF. Our emulated results reaffirm previous simulation efforts.

Performance and Scaling of Wireless Ad Hoc IPv6 Stateless Address Autoconfiguration under Mobile Gateways

Autoconfiguration mechanisms in general, and stateless address autoconfiguration in particular, are highly desirable capabilities of military mobile ad hoc networks (MANETs). However, IPv6 stateless autoconfiguration schemes for MANETs still have to be refined, and a convincing demonstration is needed to show that these schemes can cope with the dynamic, infrastructure-free environment wherein MANETs operate. In this paper we provide a literature survey of autoconfiguration schemes designed for MANETs. In addition, we look at a specific stateless autoconfiguration scheme (by Jelger and Noel, SECON 2005). This scheme provides globally routable IPv6 prefixes to a MANET, attached to the Internet via gateways. We examine this approach through OPNET simulation, applying new mobility models to encourage squad-like clusters around gateways, introducing mobility to the gateways, and scaling the number of ad hoc nodes and the number of gateways independently. We then comment on the performance of the Jelger-Noel addressing scheme in terms of protocol overhead, autoconfiguration time, prefix hold times, and prefix stability.

On the incompatibility of connectivity and local pooling in Erdős-Rényi Graphs

For a wireless communications network, Local Pooling (LoP) is a desirable property due to its sufficiency for the optimality of low-complexity greedy scheduling techniques. However, LoP in network graphs with a primary interference model enforces an edge sparsity that may be prohibitive to other desirable properties in wireless networks, such as connectivity. In this paper, we investigate the impact of the edge density on both LoP and the size of the largest component under the primary interference model, as the number of nodes in the network grows large. For Erdös-Rényi graphs, we employ threshold functions to establish critical values for the edge probability necessary for these properties to hold. These thresholds demonstrate that LoP and connectivity (or even the presence of a giant component) cannot both hold asymptotically for a large class of edge probability functions. A similar incompatibility for random geometric graphs is suggested by our simulation results.

RTS/CTS Data Link Abstractions for Mobile Ad Hoc Networks

The running time for high fidelity simulation of large-scale mobile ad hoc networks can be prohibitively high. The execution time of physical effects calculations for a single transmission alone can grow unmanageable to account for all potential receivers. Discrete event simulators can also suffer from excessive generation and processing of events, both due to network size and model complexity. In this paper, we present three levels of abstracting the IEEE 802.11 RTS/CTS channel access mechanism. In the process of assessing their ability to mitigate runtime-cost while retaining comparable results to that of a commercially available simulator, OPNET, we found that the abstractions were better suited to collecting one metric over another

On Characterizing the Local Pooling Factor of Greedy Maximal Scheduling in Random Graphs

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 graphs 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.