Closed‐form expressions for spatial correlation parameters for performance analysis of fluid antenna systems

Abstract

The emerging fluid antenna technology enables a high‐density position‐switchable antenna in a small space to obtain enormous performance gains for wireless communications. To understand the theoretical performance of fluid antenna systems, it is important to account for the strong spatial correlation over the different positions (referred to as ‘ports'). Previous works used a classical, generalised correlation model to characterise the channel correlation among the ports but were limited by the lack of degree of freedom of the model to imitate the correlation structures in an actual antenna. In this letter, it is proposed to use a common correlation parameter and to choose it by setting the correlation coefficient of any two ports to be the same as the average correlation coefficient of an actual fluid antenna taking up a linear space. A closed‐form expression for the spatial correlation parameter is first derived assuming that the number of ports is large, and it is illustrated that the correlation parameter depends only on the size of the fluid antenna but not the port density. Simpler expressions are then obtained for small and large sizes of fluid antenna. The resulting model is finally used to study the performance of fluid antenna systems. Simulation results based on the proposed model are provided to confirm the promising performance of fluid antenna in single and multiuser environments.

MIMO Evolution Beyond 5G Through Reconfigurable Intelligent Surfaces and Fluid Antenna Systems

“…Recently, in[142], it was proposed to set all the {µ k } to be equal so that the correlation between any two ports can be better modeled.…”

On the Diversity and Coded Modulation Design of Fluid Antenna Systems

“…It is well-known that the diversity defines the slope of the outage probability's curve and the outage gain represents the "distance" to the vertical axis [22], i.e., the smaller the value G o , the better. From (19), we can observe that correlation negatively affects the outage gain. It follows that the achieved diversity is independent of the FA's topology but the employed topological space characterizes the achieved outage gain.…”

“…Note that alternative spatial correlation models were recently proposed in[19],[20] which differ slightly from the one used in this paper. It would be an interesting future work to extend the work of this paper using the new models.…”

Extra‐large MIMO enabling slow fluid antenna massive access for millimeter‐wave bands

“…In [6, 9], the channel, $$g^{(\tilde{u},u)}_k$$, is modelled based on the generalized correlation model in [10] via the correlation parameter μ, that is $$$$\begin{align} {g}_{k}=\mathrm{\Omega}\left(\sqrt{1-{\mu}^{2}}{x}_{k}+\mu {x}_{0}\right)+j\mathrm{\Omega}\left(\sqrt{1-{\mu}^{2}}{y}_{k}+\mu {y}_{0}\right),\nonumber\\[-4pt] \text{for}\;k=1,2,\ldots ,N, \end{align}$$$$where $$x_0,x_1,\dots ,x_N,y_0,y_1,\dots ,y_N$$ are all independent and identically distributed (i.i.d.) Gaussian random variables with zero mean and variance of 0.5, and the parameter, μ, can be obtained using [9, Theorem 1]. Note that in (), the superscript $$(\tilde{u},u)$$ is omitted for conciseness.…”

“…Channel model: In [6,9], the channel, g ( ũ,u) k , is modelled based on the generalized correlation model in [10] via the correlation parameter μ, that is…”