Revisiting Spatial Block-Correlation Model for Fluid Antenna Systems: From Constant to Variable Correlations

Fluid antenna systems (FAS) have emerged as a promising technology to achieve high spatial diversity by dynamically reconfiguring multiple closely spaced <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> antenna ports. However, the inherent spatial correlation among these ports poses significant challenges for accurate performance analysis. Traditional block-correlation modeling algorithms, which partition the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> × <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> Toeplitz-structured correlation matrix into independent <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</i> blocks with constant correlation coefficients, often yield substantial approximation errors to block-correlation models, especially in scenarios with limited ports. In this paper, we revisit the spatial block-correlation model for FAS and introduce a novel block-correlation modeling algorithm in tuning the model parameters, which realizes the variable block-correlation model in practice. Our proposed approach derives closed-form expressions for the optimal block-specific correlation coefficients and develops a low-complexity heuristic algorithm that reduces the computational complexity from exponential <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D^N–D</i> to linear (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> – <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</i>) × <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</i> searches, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">thereby achieving significantly lower approximation error compared to constant correlation models</i>. To validate the effectiveness of our variable block-correlation modeling algorithm, we first apply it to point-to-point FAS communications with closely spaced ports, deriving analytical expressions for the joint probability density function (PDF) of channel amplitudes and outage probability. Our analysis shows that the proposed algorithm offers tractable performance evaluation and superior accuracy, particularly when the number of ports is small (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> < 20). Furthermore, we extend our framework to classical FAS-assisted reconfigurable intelligent surface (FAS-RIS) communications, where the interplay between direct and RIS-assisted links complicates the channel statistics. By integrating the central limit theorem (CLT) with variable block-correlation model, we derive tractable outage probability expressions that capture the coupling effects among different channel coefficients. Extensive numerical simulations under various system configurations demonstrate that variable block-correlation model not only outperforms conventional constant-correlation approaches in terms of approximation accuracy and robustness, but also provides reliable performance prediction in threshold-sensitive and challenging propagation environments. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">These results underscore the practical value of our approach for the design and optimization of next-generation FAS-based wireless networks</i>.