Magnetworks: how mobility impacts the design of Mobile Networks

In this paper we study the optimal placement and optimal number of active relay nodes through the traffic density in mobile sensor ad-hoc networks. We consider a setting in which a set of mobile sensor sources is creating data and a set of mobile sensor destinations receiving that data. We make the assumption that the network is massively dense, i.e., there are so many sources, destinations, and relay nodes, that it is best to describe the network in terms of macroscopic parameters, such as their spatial density, rather than in terms of microscopic parameters, such as their individual placements. We focus on a particular physical layer model that is characterized by the following assumptions: i) the nodes must only transport the data from the sources to the destinations, and do not need to sense the data at the sources, or deliver them at the destinations once the data arrive at their physical locations, and ii) the nodes have limited bandwidth available to them, but they use it optimally to locally achieve the network capacity. In this setting, the optimal distribution of nodes induces a traffic density that resembles the electric displacement that will be created if we substitute the sources and destinations with positive and negative charges respectively. The analogy between the two settings is very tight and have a direct interpretation in wireless sensor networks

Random Matrix Products in Wireless (Multiantenna) Sytems

Modeling a multiantenna wireless channel via a product of independent random matrices captures the main geometrical and electromagnetic features of the communication link. Upon a proper tuning of the various parameters (e.g. marginal distribution of each matrix entry, size of each matrix factor, etc.) the product model, early introduced by Mu ̈ller [1], is suitable to model different scenarios, across several generations of wireless systems. Among the various applications of random matrix theory in the performance analysis of wireless systems represented by product models, we focus hereinafter on a finite-blocklength setting. Specifically, we evaluate the so-called channel dispersion, a metric useful to determine the impact of channel dynamics and antenna selection rules on the communication rate, for an isotropic (i.e. unitarily invariant in law) channel. Then, we provide the statistics of the mutual information corresponding to non-isotropic product channels, paving the way to the characterization of the dispersion in more realistic scenarios

Closed-form Output Statistics of MIMO Block-Fading Channels

The information that can be transmitted through a wireless channel, with multiple-antenna equipped transmitter and receiver, is crucially influenced by the channel behavior as well as by the structure of the input signal. We characterize in closed form the probability density function (pdf) of the output of MIMO block-fading channels, for an arbitrary SNR value. Our results provide compact expressions for such output statistics, paving the way to a more detailed analytical information-theoretic exploration of communications in presence of block fading. The analysis is carried out assuming two different structures for the input signal: the i.i.d. Gaussian distribution and a product form that has been proved to be optimal for non-coherent communication, i.e., in absence of any channel state information. When the channel is fed by an i.i.d. Gaussian input, we assume the Gramian of the channel matrix to be unitarily invariant and derive the output statistics in both the noise-limited and the interference-limited scenario, considering different fading distributions. When the product-form input is adopted, we provide the expressions of the output pdf as the relationship between the overall number of antennas and the fading coherence length varies. We also highlight the relation between our newly derived expressions and the results already available in the literature, and, for some cases, we numerically compute the mutual information, based on the proposed expression of the output statistics.Comment: 16 pages, 5 figure

Output Statistics of MIMO Channels with General Input Distribution

The information that can be conveyed through a wireless channel, with multiple-antenna equipped transmitter and receiver, crucially depends on the channel behavior as well as on the input structure. In this paper, we derive analytical results, concerning the probability density function (pdf) of the output of a single-user, multiple-antenna communication. The analysis is carried out under the assumption of an optimized input structure, and assuming Gaussian noise and a Rayleigh block-fading channel. Our analysis therefore provides a quite general and compact expression for the conditional output pdf. We also highlight the relation between such an expression and the results already available in the literature for some specific input structure

Toward an efficiently computable formula for the output statistics of MIMO block-fading channels

The information that can be conveyed through a wireless channel, with multiple-antenna equipped transmitter and receiver, crucially depends on the channel behavior as well as on the input structure. In this paper, we present very recent analytical results, concerning the probability density function (pdf) of the output of a single-user, multiple-antenna communication. The analysis is carried out under the assumption of an optimized input structure, and assuming Gaussian noise and block-fading. A further simplification of the output pdf expression presented in our last paper is derived, without the need for resorting to involved integration rules over unitary matrices. With respect to the former result, presented at the main track of this conference, the newly derived formula has the appealing feature of being numerically implementable with open access Matlab codes developed at MIT for the evaluation of zonal polynomial