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Abstract-This paper investigates the asymptotic uniform power allocation capacity of frequency nonselective multiple-input multiple-output channels with fading correlation at either the transmitter or the receiver. We consider the asymptotic situation, where the number of inputs and outputs increase without bound at the same rate. A simple uniparametric model for the fading correlation function is proposed and the asymptotic capacity per antenna is derived in closed form. Although the proposed correlation model is introduced only for mathematical convenience, it is shown that its shape is very close to an exponentially decaying correlation function. The asymptotic expression obtained provides a simple and yet useful way of relating the actual fading correlation to the asymptotic capacity per antenna from a purely analytical point of view. For example, the asymptotic expressions indicate that fading correlation is more harmful when arising at the side with less antennas. Moreover, fading correlation does not influence the rate of growth of the asymptotic capacity per receive antenna with high 0 . Index Terms-Correlated fading, free probability, multipleinput multiple-output (MIMO) capacity, random matrix theory.

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Abstract-Distributed consensus algorithms for estimation of parameters or detection of events in wireless sensor networks have attracted considerable attention in recent years. A necessary condition to achieve a consensus on the average of the initial values is that the topology of the underlying graph is balanced or symmetric at every time instant. However, communication impairments can make the topology vary randomly in time, and instantaneous link symmetry between pairs of nodes is not guaranteed unless an acknowledgment protocol or an equivalent approach is implemented. In this paper, we evaluate the convergence of the consensus algorithm in the mean square sense in wireless sensor networks with random asymmetric topologies. For the case of links with equal probability of connection, a closed form expression for the mean square error of the state along with the dynamical range and the optimum value of the link weights that guarantee convergence are derived. For the case of links with different probabilities of connection, an upper bound for the mean square error of the state is derived. This upper bound can be computed for any time instant and can be employed to compute a link weight that reduces the convergence time of the algorithm.Index Terms-Asymmetric links, mean average consensus, mean square convergence, random topology, wireless sensor networks.

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