This paper investigates the topology formation mechanisms provided by IEEE 802.15.4 to create tree-based topologies, in the context of a multi-sink wireless sensor network. the topology formation protocol is simulated starting from a random deployment of a given number of nodes, to obtain statistics of the position of those nodes belonging to given tree levels. It is shown that under some circumstances the nodes belonging to any level can be assumed to be uniformly distributed over the plane. Under such assumption, a mathematical formulation is used to optimize the average number of children per parent and the number of levels in the tree (that is, the tree height), through maximization of the network association probability

We investigate a hierarchical wireless hybrid network, implementing two different network paradigms: ad hoc and infrastructure-based systems, where mobile gateways, equipped with both cellular and infrastructure-less air interfaces, allow integration of the two separate paradigms. The paper reports results achieved through a mathematical analysis of the topology of wireless links, providing the distribution of the number of lowest-level nodes attached to the highest level. Nodes have a maximum capacity, and seek service at the upper level through a retry mechanism where the nodes are addressed according to a ranked list based on the level of received power. The mathematical analysis provides a means to allow access control, depending on the maximum number of radio resource units available at each node and the maximum number of retries at each level. Wireless nodes at different levels are uniformly distributed over the bi-dimensional plane with different densities; path loss and shadowing are included with different propagation parameters, different air interfaces are used, and different hard capacities characterise the nodes at the different levels. With respect to other papers recently presented by the authors to other conferences, this work focuses on the role of the node capacity limitations and the maximum number of retries

This paper investigates the effects of directed retry (DR) in cellular networks characterized by a nonuniform environment, that is, with unequal distribution of users and/or radio resources. We propose an analytical model able to take both propagation and network aspects into account. The nonuniform environment is modeled assuming the superposition on a uniform scenario of a circular area characterized by different offered load or radio capacity. The case of a hot spot of users is included. Path loss and lognormal shadowing have been considered. This is done through a statistical approach which is very general, and provides an expression for the probability of receiving a suitable power level from a given number of base stations within a fixed distance from the mobile. A comparison to simulation results is performed to validate the model. We show that the impact of DR on the blocking probability depends largely on the propagation parameters considered.

This paper considers points which can communicate with one another and which are uniformly and randomly distributed on the plane, assuming an inverse power law for attenuation and log-normal shadowing. First, a probability distribution is obtained for the distance between a pair of such points. Communication is assumed to be possible if the attenuation of a signal transmitted from one point, say a mobile phone, does not exceed some specified value by the time it reaches the other, say a base station. The probability distribution of the number of base stations which can hear such a signal from a given mobile is found. An example shows how the probability that a mobile is in a handover region between two or more base stations can be evaluated. The analysis is extended to the case where the power law changes at a specified distance from the mobile, and also to consider the effect of an area within the plane containing a greater density of mobiles and/or base stations (a hot spot). A final result gives the conditional distribution for the number of base stations within some specified area of the plane, given the number within some larger area containing that specified area. The results also apply to the number of mobiles within range of a base station and, in an ad hoc network, to the number of nodes within range of a given node.

This paper considers two sets of points which can communicate with one another and which are uniformly and randomly distributed, one set within a confined area, a hot spot, on the plane, and the other with a different density over the rest of the plane: an inverse power law with lognormal shadowing is assumed for attenuation. Communication is assumed to be possible if the attenuation of a signal transmitted from one point, say a mobile telephone, does not exceed some specified value by the time it reaches the other, say a base station. The probability distribution of the number of base stations which can hear such a signal from a given mobile is found, taking account of the effect of the hot spot. The conditional distribution of the number of such base stations within the hot spot, given the total number over the whole plane, is deduced, and this result is applied in an example to finding the blocking probability for a directed retry algorithm. The results also apply to the number of mobiles within range of a base station and, in an ad hoc network, to the number of nodes within range of a given node.

In this paper we present an analytical model for the estimation of the blocking probability as a function of the offered traffic per user in a cellular environment, where capacity is determined by hard blocking and the average number of users per cell is small. By the term "hard" capacity we mean the maximum number of users that can be served by a base station. Using a statistical model, the paper shows that the number of mobiles audible to a base that have that base as the strongest one has a Poisson distribution whose mean is given in terms of the mean densities of mobiles and base stations and the parameters of the attenuation law. The model proposed here does not represent a tool for detailed network planning, but it is a helpful (and from the computational viewpoint simple) means for network dimensioning.

This paper considers the effects of base station diversity on the capacity of a cellular CDMA system. Closed loop power control is assumed to maintain the received power constant at the base station receiving the second or third strongest signal for dual or triple diversity, as opposed to the strongest for conventional CDMA. The probability distributions of the power ratios between signals received at two such base stations (ranked in descending order of received signal strength) are obtained, and these lead to a measure of the reduction in the overall capacity of a system brought about by high power interferers affecting one base station but controlled by a neighbouring one.

This paper uses some computational results to show that the peak envelope power (PEP) of orthogonal frequency-division multiplex (OFDM) waveforms can be reduced very substantially by coding to select only those messages with low peak factor as valid codewords in the scheme. It is shown that the asymptotic limit of the PEP is between two and three, and that only four bits of redundancy are necessary to limit the PEP to within 10% of this optimum value as the number of carriers becomes large.