Analyzing Multi-Antenna Wireless Systems: Distribution Functions, Integral Identities, and Performance Metrics

This work develops a novel framework for the performance evaluation of communication systems with receive diversity, in which the probability density function (PDF) statistic is formulated as a combination of power, exponential, and confluent hypergeometric functions. First, we establish the distribution function of the signal-to-noise ratio in the context where the receiver implements maximal ratio combining. Then, we propose closed-form solutions for integral identities involving this PDF and different functions, namely, algebraic, exponential, complementary error, generalized Q, and logarithmic. We further illustrate the suitability of the proposed formulation for different practical channel models, namely, shadowed κ-μ, extended ημ, and shadowed Beaulieu-Xie. In this context, we also derive various physical and data-link layer metrics, such as outage probability, average symbol error probability, optimal rate adaptation capacity, channel inversion with fixed rate capacity, and effective capacity, considering these practical fading models and different types of additive noises, including generalized Gaussian noise, Gaussian noise, Laplacian noise, and Gamma noise. Asymptotic analysis of the said metrics and of the diversity order of the system is also presented. The analytical results are validated using simulation results for various scenarios relevant to realworld applications.