A spherical near field to far field transform for large antenna arrays

The simulation or measurement of large antenna arrays requires a spherical near field to far field (NFFF) transform, which suffers from the underflow when calculating the high degree associated Legendre functions by double precision. This paper proposes to normalize the associated Legendre functions by the first non-zero term in the recursion and set the extremely small terms to zero. Numerical experiments show that the proposed method is much more accurate and stable than the commonly used SPHEREPACK library. Besides, the pattern of a linear array of 600 elements is evaluated by the proposed method with the truncation degree up to 985, which is validated against the Method of Moment (MoM).