Hazer Inaltekin

On unbounded path-loss models: effects of singularity on wireless network performance

This paper addresses the following question: how reliable is it to use the unbounded path-loss model G(d) = d-alpha, where alpha is the path-loss exponent, to model the decay of transmitted signal power in wireless networks? G(d) is a good approximation for the path-loss in wireless communications for large values of d but is not valid for small values of d due to the singularity at 0. This model is often used along with a random uniform node distribution, even though in a group of uniformly distributed nodes some may be arbitrarily close to one another. The unbounded path-loss model is compared to a more realistic bounded path-loss model, and it is shown that the effect of the singularity on the total network interference level is significant and cannot be disregarded when nodes are uniformly distributed. A phase transition phenomenon occurring in the interference behavior is analyzed in detail. Several performance metrics are also examined by using the computed interference distributions. In particular, the effects of the singularity at 0 on bit error rate, packet success probability and wireless channel capacity are analyzed.

Gaussian Approximation for the Wireless Multi-Access Interference Distribution

The problem of Gaussian approximation for the wireless multi-access interference distribution in large spatial wireless networks is addressed. First, a principled methodology is presented to establish rates of convergence of the multi-access interference distribution to a Gaussian distribution for general bounded and power-law decaying path-loss functions. The model is general enough to also include various random wireless channel dynamics such as fading and shadowing arising from multi-path propagation and obstacles existing in the communication environment. It is shown that the wireless multi-access interference distribution converges to the Gaussian distribution with the same mean and variance at a rate 1/√λ, where λ >; 0 is a parameter controlling the intensity of the planar (possibly non-stationary) Poisson point process generating node locations. An explicit expression for the scaling coefficient is obtained as a function of fading statistics and the path-loss function. Second, an extensive numerical and simulation study is performed to illustrate the accuracy of the derived Gaussian approximation bounds. A good statistical fit between the interference distribution and its Gaussian approximation is observed for moderate to high values of λ.

On Optimal Downlink Coverage in Poisson Cellular Networks with Power Density Constraints

This paper studies downlink coverage maximization for cellular networks in which base station (BS) locations are modeled using a spatial Poisson point process, considering three different coverage models, and under constraints on transmit power, BS density and transmit power density. Firstly, the coverage optimization problem is solved analytically for the first coverage model that focuses on noise-limited communication by ignoring interference and random fading effects. This model provides useful insights into the significance of bounded path loss models to obtain meaningful solutions for this problem. The other two coverage models are based on the users received signal-to-interference-plus-noise-ratio (sinr) from their associated BSs. For these models, it is shown that the coverage optimization problem can be reduced to a constrained single dimensional optimization problem without any loss of optimality. The related solutions can be obtained with limited computational complexity by resorting to a numerical search over a compact subset of candidate values. Bounds on the optimum BS density are also provided to further truncate the search space. All results are derived for general bounded path loss models. Specific applications are also illustrated to provide further design insights and to highlight the importance of using bounded path loss models for coverage analysis.

Delay of Social Search on Small-World Graphs

This article introduces an analytical framework for two small-world network models and studies the delay of targeted social search by considering messages traveling between source and target individuals in these networks. In particular, by considering graphs constructed on different network domains, such as rectangular, circular, and spherical network domains, analytical solutions for the average social search delay and the delay distribution are obtained as functions of source–target separation, distribution of the number of long-range connections and geometrical properties of network domains. Derived analytical formulas are first verified by agent-based simulations and then compared with empirical observations in small-world experiments. These formulas indicate that individuals tend to communicate with one another only through their short-range contacts and the average social search delay rises linearly, when the separation between the source and target is small. As this separation increases long-range connections are more commonly used, and the average social search delay rapidly saturates to a constant value and stays almost the same for all large values of the separation. These results do not require the dimensionality of the social space to be identical to the decay exponent of long-range social connections and are qualitatively consistent with experimental observations made by Travers and Milgram in 1969 as well as by others. Moreover, analytical distributions for the delay of social search predicted by the models introduced in this article are also compared with corresponding empirical distributions, and good statistical matches between them are observed. Other somewhat surprising conclusions of the article are that hubs have limited effect in reducing the delay of social search and variation in node degree distribution adversely affects this delay.

The feedback-capacity tradeoff for opportunistic beamforming under optimal user selection☆

Opportunistic beamforming is a reduced feedback communication strategy for vector broadcast channels which requires partial channel state information (CSI) at the base station for its operation. Although reducing feedback, this strategy in its plain implementations displays a linear growth in the feedback load with the total number of users in the system n, which is an onerous requirement for large systems. This paper focuses on a more stringent but realistic O(1) feedback constraint on the feedback load. Starting with a set of statistically identical users, we obtain the tradeoff curve tracing the Pareto optimal boundary between feasible and infeasible feedback-capacity pairs for opportunistic beamforming. Any point on this tradeoff curve can be obtained by means of homogeneous decentralized threshold feedback policies, which are rate-wise optimal, in which a user feeds back only if the received signal quality is good enough. The paper includes the derivation of these optimum policies, and further shows to what extent the O(1) feedback constraint must be relaxed to achieve the same sum-rate scaling as with perfect CSI. Extensions of these results to heterogeneous communication environments in which different users experience non-identical path-loss gains are also provided. We also show how threshold feedback policies can be used to provide fairness in a heterogeneous system, while simultaneously achieving optimal capacity scaling. Although most of our results are asymptotic in the sense that they are derived by letting n grow large, they provide promising performance figures with a close match to the asymptotically optimal results when used in finite size systems.

Gaussian approximation for the downlink interference in heterogeneous cellular networks

This paper derives Gaussian approximation bounds for the standardized aggregate wireless interference (AWI) in the downlink of dense K-tier heterogenous cellular networks when base stations in each tier are distributed over the plane according to a (possibly non-homogeneous) Poisson process. The proposed methodology is general enough to account for general bounded path-loss models and fading statistics. The deviations of the distribution of the standardized AWI from the standard normal distribution are measured in terms of the Kolmogorov-Smirnov distance. An explicit expression bounding the Kolmogorov-Smirnov distance between these two distributions is obtained as a function of a broad range of network parameters such as per-tier transmission power levels, base station locations, fading statistics and the path-loss model. A simulation study is performed to corroborate the analytical results. In particular, a good statistical match between the standardized AWI distribution and its normal approximation occurs even for moderately dense heterogenous cellular networks. These results are expected to have important ramifications for the characterization of performance upper and lower bounds for emerging 5G network architectures.

Optimal SNR-based coverage in Poisson cellular networks with power density constraints

This paper studies coverage maximization for cellular networks in which base station (BS) locations are modeled using a homogenous spatial Poisson point process, and user locations are arbitrary. A user is covered for communication if its received signal-to-interference-plus-noise-ratio (SINR) is above a given threshold value. Two coverage models are considered. In the first model, the coverage of a user is determined based on the received SINR only from the nearest BS. The nearest BS happens to be the BS maximizing the received SINR without fading. In the second model, on the other hand, the coverage of a user is determined based on the maximum SINR from all BSs in the network. The objective is to maximize the coverage probability under the constraints on transmit power density (per unit area). Using stochastic geometry, coverage probability expressions for both coverage models are obtained. Using these expressions, bounds on the coverage maximizing power per BS and BS density are obtained. These bounds truncate the search space of the optimization problem, and thereby simplify the numerical evaluation of optimum BS power and density values considerably. All results are derived for general bounded path loss models satisfying some mild conditions. Specific applications are also illustrated to provide further insights into the optimization problem of interest.

Selfish Random Access over Wireless Channels with Multipacket Reception

This paper analyzes layer 2 contention resolution strategies for wireless networks with multipacket reception by using noncooperative game theory. Necessary and sufficient conditions are obtained for a strategy profile to be a Nash equilibrium. Applications of the derived equilibrium conditions to predict selfish behavior and the resulting equilibrium performance are illustrated in specific communication scenarios along with various design insights. The collective equilibrium behavior of wireless networks with large user populations is also studied, and a Poisson-Bernoulli type approximation is obtained for the total number of packet arrivals. Finally, random access control with imperfect information structure is considered, the form of equilibrium strategies as well as uniqueness and existence results for general wireless channel models are obtained, and the best-response learning dynamics achieving an equilibrium are illustrated in specific instances.

Expected message delivery time for small-world networks in the continuum limit

Small-world networks are networks in which the graphical diameter of the network is as small as the diameter of random graphs but whose nodes are highly clustered when compared with the ones in a random graph. Examples of small-world networks abound in sociology, biology, neuroscience and physics as well as in human-made networks. This paper analyzes the average delivery time of messages in dense small-world networks constructed on a plane. Iterative equations for the average message delivery time in these networks are provided for the situation in which nodes employ a simple greedy geographic routing algorithm. It is shown that two network nodes communicate with each other only through their short-range contacts, and that the average message delivery time rises linearly if the separation between them is small. On the other hand, if their separation increases, the average message delivery time rapidly saturates to a constant value and stays almost the same for all large values of their separation.

Downlink outage performance of heterogeneous cellular networks

This paper derives tight performance upper and lower bounds on the downlink outage efficiency of K-tier heterogeneous cellular networks (HCNs) for general signal propagation models with Poisson distributed base stations in each tier. In particular, the proposed approach to analyze the outage metrics in a K-tier HCN allows for the use of general bounded path-loss functions and random fading processes of general distributions. Considering two specific base station (BS) association policies, it is shown that the derived performance bounds track the actual outage metrics reasonably well for a wide range of BS densities, with the gap among them becoming negligibly small for denser HCN deployments. A simulation study is also performed for 2-tier and 3-tier HCN scenarios to illustrate the closeness of the derived bounds to the actual outage performance with various selections of the HCN parameters.