In this paper, we investigate the almost periodic frequency arrangement (APFA) asynchronous system for super-multi-access radio systems, and APFA configuration procedure on a frequency domain multiplex scheme by using almost periodic function (APF). We report on the relationship between the total number of prime numbers, the number of sub-carriers, and the normalized frequency standard deviation for a system with up to one million users. By using computer simulations, we show the multi-carrier modulation and asynchronous demodulation based on APFA, in which ICI interference by nonlinear elements is improved compared with the orthogonal frequency-division multiplexing (OFDM).