  This paper investigates wireless communications based on a new antenna array
architecture, termed modular extremely large-scale array (XL-array), where an
extremely large number of antenna elements are regularly arranged on a common
platform in a modular manner. Each module consists of a flexible/moderate
number of antenna elements, and different modules are separated with an
inter-module spacing that is typically much larger than the inter-element
spacing/signal wavelength for ease of deployment. By properly modelling the
variations of signal phase, amplitude and projected aperture across different
array modules/elements, we develop the new channel model and analyze the
signal-to-noise ratio (SNR) performance of the modular XL-array based
communications. Under the practical non-uniform spherical wave (NUSW) model,
the closed-form expression of the maximum achievable SNR is derived in terms of
key geometric parameters, including the total planar array size, module
separation distances along each dimension, as well as the user's location in
the three-dimensional (3D) space. Besides, the asymptotic SNR scaling laws are
revealed as the number of modules along different dimensions goes to infinity.
Moreover, we show that our developed near-field modelling and performance
analysis include the existing ones for the collocated XL-array, the far-field
uniform plane wave (UPW) model, as well as the one-dimensional (1D) modular
extremely large-scale uniform linear array (XL-ULA) as special cases. Extensive
simulation results are provided to validate our obtained results.
