In this letter, a mathematical characterization for the cascaded double Beaulieu-Xie (BX) fading model is presented. Exact and new expressions are determined for the probability density function (PDF) and for the cumulative distribution function (CDF) of the random variable that models the envelope of the cascaded double BX fading, and for the PDF and the CDF of the instantaneous signal-to-noise ratio received. Expressions are obtained for the moment generating function, higher order moments, average channel capacity, outage capacity, outage probability, amount of fading, channel quality estimation index and symbol error probability, for different modulation schemes, of the channel model considered. Several curves, corroborated by simulations performed with Monte Carlo method, are presented for different parameters that characterize the fading model.

Ultra densification of the number of antennas combined with the use of large bandwidths in the millimeter wave (mmWave) spectrum is considered one of the main methodologies to achieve the quality of service requirements for future generations of wireless communications. Massive multiple-input multiple-output (mMIMO) cell-free (CF) systems have a large number of access points (APs) distributed in the coverage area, serving simultaneously a smaller number of users consuming the same time-frequency resources. In order to support realistic CF networks designs, this work proposes a performance analysis based on ray tracing simulations. The propagation modeling considers reflection, diffraction, diffuse scattering, atmospheric molecular absorption and foliage and rainfall losses. CF networks with APs equipped with multiple antennas operating in the 26 GHz, 38 GHz and 73 GHz bands are evaluated. From the simulation results, the communication channel is characterized and parameterized. Different performance analysis of CF networks are performed, based on downlink spectral efficiency. In addition, the performance of CF networks in rainy environments is evaluated, and it has been observed that this architecture promotes resistance to the effect of rain attenuation.

A new, exact and closed-form expression is presented for the Beaulieu-Xie (BX) phase-envelope joint distribution. In addition, bivariate statistics are also determined for the BX distribution: the bivariate probability density function (PDF) of the envelope, the bivariate PDF of the instantaneous signal to noise ratio (SNR) and the generalized joint moment of the envelope, with and without correlation between the in-phase and quadrature components. Theoretical curves are plotted for different parameter values that characterize the fading.

In this paper we derive a general and closed- form expression for the bit error probability of square M-ary quadrature amplitude modulation (M-QAM) for a Rayleigh fading channel.

In this letter, new and simple expressions are presented for the outage probability (OP) of the product of two Beaulieu-Xie, -, - or - random variables. The OP expressions obtained in this work are determined using the Gauss-Laguerre quadrature and are corroborated by computational simulations performed with the Monte Carlo method. Several theoretical and simulated OP curves are shown, with a great adherence between the curves, considering different values of the parameters that characterize the fading distributions.

Future wireless communication systems depend on the network’s ultra-densification, on the application of massive multiple-input multiple-output (mMIMO) techniques and on the use of higher frequency bands to satisfy the ever-increasing demands for capacity. The operation of cell-free (CF) networks in the millimeter wave (mmWave) spectrum combines those principles, because they are composed of multiple access points (APs) distributed over a geographic region which serve a small number of users. Despite the extensive available bandwidth, the mmWave spectrum imposes high path losses and significant atmospheric molecular absorption to the links. In addition, in this frequency range, rain attenuation can notably degrade communications. Therefore, this article presents a study of the impact of rain attenuation on CF networks operating in the mmWave spectrum, this is in the 26 GHz, 38 GHz and 73 GHz frequency bands, based on site-specific ray tracing simulations. The propagation simulation is characterized under the effects of reflection, diffraction, diffuse scattering, atmospheric molecular absorption, vegetation losses and rain attenuation. The channel model is characterized using a hybrid approach, with the large-scale parameters determined by ray tracing in an environment subject to random Rician small-scale fading. The system performance is measured by the sum spectral efficiency (SSE) and energy efficiency (EE). According to the results, it was observed that AP densification protects the network against the effect of rain attenuation. Furthermore, even in sparse networks, the CF system has low sensitivity with respect to the precipitation rate, resulting in relatively small reductions in the average SSE and EE.