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In this paper, we derive spatial correlation functions of linear and circular antenna arrays for three types of angular energy distributions: a Gaussian angle distribution, the angular energy distribution arising from a Gaussian spatial distribution, and uniform angular distribution. The spatial correlation functions are investigated carefully. The spatial correlation is a function of antenna spacing, array geometry and the angular energy distribution. In order to emphasize the research and their applications in diversity reception, as an example, performance of the antenna arrays with MRC in correlated Nakagami fading channels is investigated, in which analytical formulas of average BER for the spatial correlation are obtained.

Channel models are vital for theoretical analysis, performance evaluation, and system deployment of the communication systems between the transmitter and receivers. For six-generation (6G) wireless networks, channel modeling and characteristics analysis should combine different technologies and disciplines, such as high-mobility, multiple mobilities, the uncertainty of motion trajectory, non-stationary nature of time/frequency/space domains. In this paper, we begin with an overview of the salient characteristics in the modeling of 6G wireless channels. Then, we discuss the advancement of the channel modeling and characteristics analysis for next-generation communication systems. Finally, we outline the research challenges of channel models and characteristics in 6G wireless communications.

In this article, we provide a novel improved model-free temporal-difference control algorithm, namely, Expected Sarsa(λ), using the average value as an update target and introducing eligibility traces in wireless communication networks. In particular, we construct the update target using the average action value of all possible successive actions, and apply eligibility traces to record the historical access of every state action pair, which greatly improve the model's convergence property and learning efficiency. Numerical results demonstrate that the proposed algorithm has the advantage of high learning efficiency and a higher learning-rate tolerance range than Q Learning, Sarsa, Expected Sarsa, and Sarsa(λ) in the tabular case of a finite Markov decision process, thereby providing an efficient solution for the study and design wireless communication networks. This provides an efficient and effective solution to design further artificial intelligent communication networks. INDEX TERMS Model-free reinforcement learning, Sarsa, Q learning, eligibility traces. I. INTRODUCTION