Deterministic and Statistical Analysis of the DoF of Continuous Linear Arrays in the Near Field

This paper examines the number of communication modes, that is, the degrees of freedom (DoF), in a wireless line-of-sight channel comprising a small continuous linear intelligent antenna array in the near field of a large one. The framework allows for any orientations between the arrays and any positions in a two-dimensional space, assuming that the transmitting array is placed at the origin. Therefore, apart from the length of the two continuous arrays, four key parameters determine the DoF and are hence considered in the analysis: the Cartesian coordinates of the center of the receiving array and two angles that model the rotation of each array around its center. The paper starts with the calculation of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">deterministic</i> DoF for a generic geometric setting, which extends beyond the widely studied paraxial case. Subsequently, a stochastic geometry framework is proposed to study the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">statistical</i> DoF, as a first step towards the investigation of system-level performance in near field networks. Numerical results applied to millimeter wave networks reveal the large number of DoF provided by near-field communications and unveil key system-level insights. A comparison of the proposed method with the singular value decomposition-based method is illustrated to validate the proposed approach.