Generalized framework for the application of fast fourier transforms to radio system sharing and compatibility studies

In the area of radio spectrum management, understanding the co-existence of radio services within the same or adjacent frequency bands is of prime importance for maximizing efficient utilization of spectrum. This necessitates comprehensive studies to assess the likelihood of interference from one particular radio system to another. Many radio systems (e.g., mobile cellular systems, radar systems, and Earth exploration satellite systems) operate with two-dimensional (2D) planar array-based active antenna systems (AAS). For such systems, accurate assessment of sharing and compatibility between radio services requires accurate modeling of the involved, often complex, AAS radiation patterns. In many co-existence studies, cumulative effect of interference arises and affects several radio devices turning them into victim receivers. In most cases, these sources of interference behave as independent random variables. This paper presents a novel framework in two different domains often met in sharing and compatibility studies. The first one is leveraging two-dimensional (2D) fast (discrete) Fourier Transforms (FFTs) to efficiently characterize AAS radiation patterns. Unlike previously, we demonstrate the applicability of 2D-FFTs to drastically reduce the computational complexity of canonical AAS array factor (AF) calculus from order O(MN⁴) to O(3MN² + N² log ₂(N)) (where M and N are scalar integers), irrespective of the type of tapering applied to the array. This enables the equivalent amount of computer savings to be made. Furthermore, we extend our framework to efficiently compute single-entry (from a single interference source) and aggregate interference (from multiple interference sources), highlighting its versatility in handling complex interference scenarios. For single-entry interference scenarios, we propose an efficient six-step procedure based on 2D-FFTs for reducing computational complexity in Monte Carlo simulations involving AAS. The second one put the stress on the computer saving for aggregate interference scenarios, where we address challenges related to convolution of multiple independent random variables, reflecting multiple sources of interference, by applying successive circular convolutions of the involved discrete set of probability density functions. Different to previous studies, this paper fills a critical gap in the literature by providing a systematic approach to leverage FFTs for an efficient and accurate characterization of AAS radiation patterns as well as the aggregation of independent interference components, for a faster computation advanced radio service co-existence studies.