Extremely large aperture arrays operating in the near-field regime unlock additional spatial resources, which can be exploited to simultaneously serve multiple users even when they share the same angular direction. This work investigates the distance-domain degrees of freedom (DoF), defined as the DoF when a user varies only its distance to the base station and not the angle. To obtain the distance-domain DoF, we study a line-of-sight (LoS) channel with a source representing a base station and an observation region representing users, where the source is a large two-dimensional transmit (Tx) array with arbitrary shape and the observation region is an arbitrarily long linear receive (Rx) array with collinearly aligned elements located at different distances from the Tx array. We assume that both the Tx and Rx arrays have continuous apertures with an infinite number of elements and infinitesimal spacing, which establishes an upper bound for the distance-domain DoF in the case of a finite number of elements. First, we analyze an ideal case where the Tx array is a single piece and the Rx array is on the broadside of the Tx array. By reformulating the channel as an integral operator with a Hermitian convolution kernel, we derive a closed-form expression for the distance-domain DoF via the Fourier transform. Our analysis shows that the distance-domain DoF is predominantly determined by the extreme boundaries of both the Tx and Rx arrays rather than their detailed interior structure. We further extend the framework to non-broadside configurations by employing a projection method that converts the problem to an equivalent broadside case. Finally, we extend the analytical framework to modular arrays and show the distance-domain DoF gain over a single-piece array under a fixed total physical length.

翻译：在近场区域运行的极大孔径阵列释放了额外的空间资源，这些资源可用于同时服务多个用户，即使这些用户共享相同的角度方向。本文研究了距离域自由度（DoF），即当用户仅改变其与基站的距离而不改变角度时的自由度。为获得距离域自由度，我们研究了一个视距（LoS）信道，其中源代表基站，观测区域代表用户。源是一个具有任意形状的大型二维发射（Tx）阵列，观测区域是一个任意长的线性接收（Rx）阵列，其元素共线排列且与Tx阵列距离不同。我们假设Tx和Rx阵列均具有连续孔径，包含无限多个元素且间距无限小，这为有限元素情况下的距离域自由度建立了上界。首先，我们分析理想情况：Tx阵列是单块结构，且Rx阵列位于Tx阵列的侧向。通过将信道重构为具有埃尔米特卷积核的积分算子，我们利用傅里叶变换推导出了距离域自由度的闭式表达式。分析表明，距离域自由度主要由Tx和Rx阵列的极端边界决定，而非其内部详细结构。我们进一步通过投影方法将框架扩展到非侧向配置，将问题转化为等效的侧向情况。最后，我们将分析框架扩展到模块化阵列，并展示了在固定总物理长度下，相比单块阵列所获得的距离域自由度增益。