## 2 System Model of Upgraded Multi-Carrier OGFDM  
Following the successful launch of the multi-carrier OGFDM system [18], in this paper, an extended design of the OGFDM waveform is explored physically and mathematically. The developed system aims to increase the number of subscribers yet keeping each user with a high level of channel capacity. As such, despite the enlarged number of the subcarriers, the introduced system aims to sustain the specified bit-rate for each client by expanding the utilized BW, particularly, after achieving good progress in terms of the BW efficiency of the OGFDM [16; 18; 20; 21]. As is clear in Figure 1, on the transmitter side of the multi-carrier OGFDM system, mainly, at the modulation level, the complex numbers of the frequency domain can be generated via applying different sizes of bit token (N) on an input stream of digital data. By adopting such a hybrid modulation with an enhanced channel state, an extra number of bits can be allocated for each employed subcarrier at the acceptable limit of errors. Consequently, the key downside of the conventional bit loading schemes can be mitigated by alternatively employing an adaptive modulation format. Figure 1: Transmitter design of the orthogonal generalized frequency division multiplexing (OGFDM) including the two key parts of the upgraded level. After that, at the allocation level where the first part of upgrading is applied, the obtained complex numbers are distributed among the utilized frequency subcarriers in accordance with their variance ability to carry data. It is worth noting that, the number of used frequency subcarriers is doubled at this level of processing which in turn can increase the number of network subscribers at the upgraded OGFDM. At the oversampling level, a dual set of the modulated subcarriers is flexibly handled. Thus, the working frequency subcarriers can be up-sampled by a factor of \(K\), or \(2K\) according to the system requirements that always tend to achieve a high channel capacity even in worse transmission statuses. The number of assigned copies for each frequency subcarrier is decided by the oversampling stage which represents a significant base for the upcoming stage (filtration level). Moving to the filtration level where a double assembly of the up-sampled subcarriers is efficiently managed. At this vital stage of processing, every two adjacent subcarriers of frequencies are filtered by the shaping filters of the Hilbert pair and perpendicularly assigned for a similar _fc_. Thus, the cosine and sine parts of the Hilbert filters are employed effectively to orthogonally multiplex the processed subcarriers. The convoluted subcarriers are collected digitally employing a proper electrical adder and input as one sequence of data to the digital-to-analog converter (DAC). At the acceleration level where the second part of upgrading is applied, the promoted \(\mathrm{F_{DAC}}\) size is utilized to mitigate the impact of system expansion where doubled subcarriers participate in the same resource space. Hence, to avoid sharing limitations, the BW size is amended herein to be compatible with the developed system requirements. Accordingly, the \(\mathrm{F_{DAC}}\) limit should be expanded to keep supplying a high level of bit-rate for each utilized subcarrier. The output of this operation is an analog signal that is ready for transmission by a suitable antenna. As is seen in Figure 2, on the receiver side of the multi-carrier OGFDM system where the wireless signal is recognized, inverse processes are performed to recover the originally transmitted data. At the acceleration level (the second part of upgrading), the promoted analog-to-digital converter (ADC) is used to convert the analog signal to the digital domain. Then, at the filtration level, the doubled set of the matching filters are employed to extract each intended subcarrier of every elected _fc_.