Statistical Analysis of Path Losses for Sectorized Wireless Networks

In modern mobile communication networks, such as 3G and 4G networks, sectorized antennas have been widely used to divide each cell into multiple sectors in order to improve coverage, spectrum efficiency, and quality of service. Large-scale path loss from a transmitting antenna to a receiving antenna should include: 1) propagation attenuation that depends on transmission distance; 2) shadowing that depends on surrounding environment; and 3) antenna loss that depends on a sectorized antenna pattern and transmission angle. An in-depth analysis of statistical characteristics of large-scale path losses involving with these three factors is crucial for the design, operation, evaluation, and optimization of modern sectorized wireless networks. In this paper, a sectorized antenna pattern is, for the first time, considered in the derivation of a closed-form expression of a probability density function (pdf) of large-scale path losses. Specifically, we first discover that the normalized pdf of propagation attenuation plus shadowing, which can be approximated by the Gaussian mixture model (GMM) with all system parameters, is fully determined by our newly defined metric 10/ln 10β/σ_s, namely, the attenuation exponent β to standard deviation of shadowing σs ratio (ASR). The convolution of GMM and antenna loss statistics is elaborately transformed to a series of differential equations. A closed-form pdf of large-scale path losses with sectorized antenna pattern can be obtained by solving these differential equations. To reduce the computational complexity, we further prove that the exciting sources of these differential equations can be tightly approximated by weighted Gaussian functions, and thus, the final solutions (i.e., pdf of path losses) can be derived in the form of Gaussian and Dawson functions. Our analytical results are verified by extensive numerical computation and Monte Carlo simulation results, e.g., the impact of ASR on the shape of pdf of propagation attenuation plus shadowing. Compared with traditional Gaussian-fitting approach, our newly derived pdf of large-scale path losses with sectorized antenna patterns is at least two orders of magnitude more accurate in terms of Kullback-Leibler divergence under typical propagation attenuation and shadowing conditions.