## 1 Introduction  
The exponential growth of IoT devices connected to a 6G network has led to an increased demand for non-orthogonal multiple access (NOMA) to efficiently share a limited spectrum, along with robust modulation schemes to cope with the multipath conditions of communication channels. The necessity to enhance performance through an innovative progressive pattern interleaver (PPI) utilized for user distinction in interleaved division multiple access (IDMA) schemes, recommended by the 3 GPP guidelines as a NOMA scheme for 6G and IoT networks, arises from several pivotal factors in the development and evolution of wireless communication networks. These factors include the scarcity of spectral and energy resources, the exponential proliferation of IoT devices, and the surge in data traffic within 6G networks, where spectrum is a finite and valuable resource. It is imperative to enhance spectral efficiency to accommodate a larger number of IoTdevices and deliver higher-quality services, given the growing demand for new applications and services requiring increased capacity. Consequently, the development of more efficient multiple access schemes capable of meeting these demands becomes essential. Signal fading resulting from multipath channels, coupled with the presence of numerous users in bandwidth-constrained networks, exacerbates the challenge of handling IoT scenarios [1, 2]. NOMA emerges as a solution [3, 4, 5] to achieve spectral and power-efficient networks in multi-user environments. Figure 1 illustrates the evolution of various NOMA schemes along with their limitations. Spread-spectrum multiple access, in the form of code-division multiple access (CDMA) [6, 7], was adeptly implemented in 3G networks to address fading channel communication scenarios. CDMA multi-user communication employs user-specific spreading codes to enable simultaneous user access. Multi-user detection (MUD) for CDMA signals is relatively straightforward to implement for a smaller number of users; however, as the user count increases in a network, the implementation complexity of CDMA-MUD also escalates exponentially [8]. Interleaved division multiple access (IDMA), proposed as a NOMA technique [1, 4], can also serve as a viable option to facilitate multiple access in fading channel environments. In multiple access scenarios, the CDMA scheme assigns a unique spreading code to each user, whereas the IDMA scheme employs a unique interleaving pattern. Chip-level interleaving in the IDMA scheme results in less complex MUD [9, 10, 11] with faster convergence for the required bit error rate (BER) outcomes compared to CDMA. Consequently, IDMA emerges as a favorable choice for future generations of networks. The IDMA scheme demonstrates superior and swifter convergence performance compared to the CDMA scheme; nonetheless, a severe multipath environment necessitates a more complex IDMA receiver with an increased number of paths [12]. Addressing this challenge, OFDM [13] has been integrated into 4G and 5G networks as a signal processing technique, offering significant resilience against multipath fading environments. Other authors such as those of [14] highlight the adaptability, performance evaluation and signal-processing capabilities of the OFDM system in DSP Platform for Various Purposes and Applications. Single-carrier modulation systems are not particularly effective in multipath channel environments, as receiver complexity increases with the number of paths in the channel. In contrast, multi-carrier orthogonal frequency-division multiplexing (OFDM) divides the entire channel bandwidth into orthogonal multiple narrow sub-channels. These narrow orthogonal sub-channels encounter nearly flat fading, which can be addressed with relatively simple frequency domain equalization (FDE) using a single tap. The required frequency domain equalization operation in a multi-carrier OFDM system is facilitated by fast Fourier transform (FFT) and inverse fast Fourier transform (IFFT) operations.