# Clustering Approach for Reliable Wireless Communication
## 2 Materials and Methods  
### MUSA Codes Selection  
The key role of multiple access techniques lies in facilitating multiple users to be active simultaneously. This must be achieved by maintaining the key performance indicators (KPIs), such as inter-user interference, at an acceptable level. With code-based approaches, users' signals can be separated by accessing perfectly orthogonal or low-correlated sequences, which can lower the IUI. In fifth-generation systems, spreading codes used for the MUSA technique are generated using values from two sets: \(\{1\), \(-1\}\) and \(\{-1\), \(0\), \(1\}\) or \(\{-2\), \(-1\), \(0\), \(1\), \(2\}\), for both real/imaginary parts. Possible combinations include, for example, \(\{1+\text{j},\,1-\text{j},\,-1+\text{j},\,-1-\text{j}\}\), or \(\{-2\), \(-2\text{j},\,-2-\text{j},\,-2+\text{j},\,-2-\text{j},\,-2+\text{j},\,-1- \text{j},\,-1+\text{j},\,-1-\text{j},\,-1+\text{j},\,-1,\text{j},\,0,\,j,\,1,\,1-\text{j},\,1+\text{j},\,2,\,1-\text{j},\,1-\text{j},\,2-\text{j},\,2+ \text{j},\,2\text{j},\,2-\text{j},\,2+\text{j}\}\), selected depending on the network's capacity. Considering \(L\), the length of the spreading code, and \(N\), the number of values in the set, there can be \(N^{L}\): \(4^{L}\), \(9^{L}\), or \(25^{L}\) spreading codes [50]. To appropriate the technical details related to the MUSA technique, the innovative aspect of this research relies on a unique design of MUSA complex spreading codes starting from the CDMA technique (an OMA technique) using real spreading codes and their grouping into \"clusters\". According to 3 GPP Specifications [51; 52], for multi-access signature classification, MUSA handles user equipment (UE) with low correlation sequences to separate different users at the symbol level. To maximize spectral efficiency, symbols can be chosen from binary phase shift keying (BPSK), QAM, or QPSK. For example, in the CP-OFDM waveform with BPSK, the combination \(\left\{\frac{1+\text{j}}{\sqrt{2}},\frac{-1-\text{j}}{\sqrt{2}}\right\}\) can be considered. Data processing comprising symbol-level spreading is depicted in Figure 1.  
According to Figure 1, the order of the transformations applied to users' data begins with coding and modulation, followed by symbol-by-symbol processing performed using spreading sequences. Basic elements of the spreading sequences can be drawn from quantized constellations such as QPSK and 9-QAM constellations (the total numbers of sequences are \(4^{L}\) and \(9^{L}\)). Four code sequences using a QPSK constellation are depicted in Figure 2.  
Figure 1: Processing steps with specific symbol-level spreading (transmitter level). Using low correlation spreading sequences, the multipath effects on individual user data are mitigated. For the signals to be effectively decoded, at the receiver's end, the same spreading sequences as those in the transmission part must be used for their identification. MUSA functionality assumes that each user randomly selects a certain spreading sequence from a large group of sequences. To minimize the undesired phenomena that may affect signals on the propagation channel and to improve the performance of the communication, the same approach is available for symbol spreading. Although MUSA sequences are low-correlation sequences, the randomness of the allocation can lead to neighboring sequences, or the same sequence being assigned to two users that have highly correlated channels. According to the authors of [53], when the elements of the spreading sequences are selected from 9-QAM constellations, e.g., \(\{-1,\,-1-\,j,\,-1+\,j,\,-j,\,0,j,\,1,\,1-\,j,\,1+\,j\}\), groups of three 4-length orthogonal codes (\(c_{1}\), \(c_{2}\), \(c_{3}\) in Equation (1)) can be obtained. \[c_{1}=[\;-j\qquad-j\qquad\quad j\qquad\quad j\;] \tag{1}\] \[c_{2}=[\;-j\qquad\quad j\qquad-1+j\qquad 1-j\;]\] \[c_{3}=[-1+j\qquad 1-j\qquad-1\qquad\quad 1\;]\]  
Similarly, up to 16 low correlation spreading codes can be designed [53].