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This paper presents a theoretical analysis for estimating the coverage probability in two-dimensional (2D) and three-dimensional (3D) peer-to-peer (P2P) millimeter-wave (mmWave) wireless networks. The analysis is carried out by adopting suitable link state models and realistic propagation conditions, involving path-loss attenuation, angular dispersion, mid-and small-scale fading, which comply with recent channel measurements. The presented framework accounts in detail for the actual shape of the transmitting/receiving antenna patterns and for the spatial statistic that describes the node location, by considering the widely adopted Poisson point process, the uniform distribution, and the random waypoint mobility model. Analytical expressions for the statistic of the received power and simple integral formulas for the coverage probability in the presence of interference and noise are derived. The accuracy of the obtained estimations and of the introduced approximations is checked by independent Monte Carlo validations. As possible applications in the 3D mmWave context, the conceived mathematical theory is used to discuss the impact of the interference model on the reliability of the noise-limited approximation, and to estimate the average link capacity of an interfered P2P communication.

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Low density parity check (LDPC) codes are still intensively studied investigating their iterative decoding convergence performance. Since the probability distribution function of the decoder's log‐likelihood ratio messages was observed to be approximately Gaussian, a variety of low‐complexity approaches to this investigation were proposed. One of them was presented in Chung et al.'s 2001 paper, involving the function ϕfalse(xfalse), therein specified, and its inverse. In this Letter, a new approximation of the function ϕfalse(xfalse) is given, such that, unlike the other approximations found in the literature, it is defined by a single expression (i.e. it is not piecewise defined), it is explicitly invertible, and it has less relative error in any x than the other approximations.

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This paper presents a mathematical framework for including the angular domain beside the radial one in the theoretical modeling of wireless networks, in which spatial reuse enables the coexistence of multiple single-hop peer-to-peer communications inside a finite region. The proposed model analyzes a scenario where the transmitting sources are uniformly distributed over a disk and the communications are subjected to path-loss attenuation and multipath-fading, considering the actual location of each destination and its antenna system. Different from most of the previous theories in which the coverage probability of a destination is estimated assuming that the destination itself is positioned at the center of the network, in the proposed analysis, the destination location is generic. This generalization, together with the consideration of the spatial channel model and of the actual receiving pattern, allows one to investigate the influence of the angular domain on the statistic of the interference power and on the coverage probability. The conceived theory, which is further verified by Monte Carlo validations, is finally exploited to derive the network transmission capacity, with the purpose to illustrate the possible advantages that may derive from a reliable modeling of the non-isotropic context, in which each destination has to operate realistically.

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