Orthogonal Frequency Division Multiplexing (OFDM) was adopted by the fourth generation (4G) of mobile communication systems to guarantee high data rates with high terminal mobility. However, OFDM ensures strict synchronism and orthogonality, which reduces the throughput and energy efficiency of the communication networks. With the advent of 5G cellular wireless communication systems, the use of non-orthogonal multiplexing schemes, which preserves the OFDM benefits without requiring high-level synchronization, becomes an important research topic. Recently, the POPS algorithm [1] has been introduced as a powerful tool to efficiently design waveforms candidates for 5G. In this paper, we propose a new design of PHYDYAS waveforms namely POPS-PHYDYAS. It is based on the mix of the POPS algorithm and the PHYDYAS filter [2]. The results confirm the advantage behind the POPS-PHYDYAS algorithm in enhancing the performance compared to multicarrier systems using the original PHYDYAS waveforms, as they are conceived by Mirabbasi-Martin [3]. Simulations are given to support our clamis.