Jarno Nousiainen

Maximum weight independent sets in an infinite plane with uni- and bidirectional interference models

We study the maximum weight independent sets of links between nodes distributed randomly in an infinite plane. Different definitions of the weight of a link are considered, leading to slight variations of what is essentially a spatial reuse problem in wireless multihop networks. A simple interference model is assumed with the interference radius equaling the transmission radius. In addition to unidirectional interference from a transmitter to the receivers of other links, also an RTS/CTS-type bidirectional handshake is considered. We study both the case where the transmission radius is fixed and tunable through power control. With a fixed transmission radius, we derive asymptotic results for the low- and high-density regimes. The main contribution is in the numerical results for the maximum weight, establishing some previously unknown parameters of stochastic geometry. The results are obtained by the Moving Window Algorithm that is able to find the maximum weight independent set in a strip of limited height but unlimited length. By studying the results as a function of the height of the strip, we are able to extrapolate to the infinite plane.

On the achievable forwarding capacity of an infinite wireless network

We consider the problem of finding the maximum directed packet flow that can be sustained in an infinite wireless multihop network. This ability of the network to relay traffic is called the forwarding capacity, and the problem appears when the spatial scales corresponding to the end-to-end paths (routing) and the neighboring nodes (forwarding) are strongly separated in a massively dense network. We assume a Boolean interference model. The infinite network is approximated with a finite but large network where the node locations form a spatial Poisson process. We study two constructive approaches to tighten the lower bound for the forwarding capacity by a significant amount. In path scheduling the packets traverse the network using predefined paths that do not interfere with each other, and coordination is thus required only between the nodes of a path. In greedy maximum weight scheduling, the transmissions are scheduled greedily according to queue-length based weights of the links. In addition to a fixed transmission radius, we consider greedy maximum weight scheduling with a transmission radius adjustable up to a given maximum. We are able to produce numerical results that characterize the achievable forwarding capacity under global coordination of the transmissions, providing, e.g., concrete points of reference for practical distributed implementations.

Optimal transmission modes by simulated annealing

We address the problem of finding efficient combinations of transmitting links between nodes distributed as a spatial Poisson process in an infinite plane using a stochastic optimization method called simulated annealing. A simple Boolean interference model with the interference radius equaling the transmission radius is used to verify the operation of the method. The same approach is then applied to SINR-determined data rates. The obtained numerical results shed light on the spatial reuse problem in wireless multihop networks. In particular, for the SINR-based interference model we obtain new results. We characterize the asymptotic behavior of the sum capacity of the optimal combination of transmitting links and the fraction of transmitting nodes in the low and high interference regimes. Additionally, the numerical results establish, in the interference-limited case of high node densities, the sum capacity (spectral efficiency) to be approximately equal to 1.2 bit/s/Hz per node.

Impact of Multidirectional Forwarding on the Capacity of Large Wireless Networks

We consider the capacity problem in large wireless multihop networks by separating the problem into macroscopic and microscopic level subproblems. At the macroscopic level, the task is to determine the routes that are geometric curves. At the microscopic level, we need to forward the traffic according to its directional distribution that results from the macroscopic level routes. Previous studies have treated the macroscopic level problem simply as that of load balancing, implying the use of time sharing to serve the traffic flowing in different directions. We study how a scheduling that truly interleaves the traffic flows in different directions affects the macroscopic level problem. We restrict the macroscopic routes to certain simple path sets. This together with earlier results on the microscopic level forwarding capacity allows us to obtain new results on the macroscopic level capacity that demonstrate the gains from multidirectional forwarding.

Instantaneous forwarding capacity under the SINR threshold interference model

Spatial reuse is a key aspect of wireless network design, and the choice of an appropriate interference model is important for capturing the intrinsic characteristics of such a network. We address the problem of finding optimal transmission modes, and their capacities, in a network consisting of nodes distributed as a spatial Poisson process in an infinite plane, i.e., such combinations of transmitting links that maximize the instantaneous forwarding capacity of the network. A stochastic optimization method called simulated annealing is used to obtain the results. The approach is applied to a SINR threshold interference model that treats the sum of all the other simultaneously transmitted signals as noise. We find out how the maximum capacity behaves for different network densities, signal attenuation coefficients, and thresholds for the required SINR. These numerical results shed light on the spatial reuse problem in wireless multihop networks. We further characterize the asymptotic behavior of the sum capacity of the optimal combination of transmitting links and the fraction of transmitting nodes in the low and high interference regimes.