## 4 Numerical Results  
In this section, we present numerical results based on the average sum rate performance of the proposed optimization schemes and of the HDR based cooperative NOMA system in various parameter settings. The system model in Figure 1 is considered with the assumed statistical properties for the channel gains, where two relaying UTs and two NOMA users are served by an AP. For each curve in the simulations, ten thousand channels are generated independently to average out the sum rate over these channels. Furthermore, the noise power is normalized to one, and the signal power values are all relative to this noise power. The HDR-based scheme does the role of a baseline scheme, which requires only one relaying UT and two time slots for the cooperative NOMA transmission, and thus, it suffers no CRI, while it requires twice the spectral resources. Furthermore, it requires one SDR operation for the UT transmit beamforming for the two NOMA users. In Figure 2, the average sum throughput (bit per second per hertz; BPS) of the various schemes described in this paper are displayed over the relaying UT transmit power (\(P_{r}\)) with three different AP transmit power (\(P_{s}\)) cases. The number of antennas at the relaying UTs is set to three (\(M=3\)). This experiment shows how effectively the proposed schemes handle the CRI (as it depends on the relay transmit power \(P_{r}\)) and achieve better average throughput since the proposed schemes beat the HDR cases in all three cases and over  
Figure 1: Cooperative non-orthogonal multiple-access transmission system through successive relaying. the whole relay power range (\(P_{r}\)). As expected proposed two algorithms which exhibit their capability in handling CRI in all the three cases, while Algorithm 1 shows the extra benefit of NOMA beamforming gain obtained from the iterative applications of SDR in the algorithm, which is reflected in the additional throughput gain of Algorithm 1 over Algorithm 2. This gain of Algorithm 1 appears in the low-to-mid range of \(P_{r}\), though it diminishes as \(P_{r}\) increases further and dominates the performance. The two proposed SR schemes successfully mimic the full duplex operation by suppressing the CRI very well and surpassing the average sum throughput of HDR cases. Different from the case of Figure 2, where the AP power \(P_{s}\) is fixed and the relaying UT power \(P_{r}\) varies, Figure 3 tests the case where \(P_{s}\) varies while \(P_{r}\) is fixed for three different values. Again, the two proposed schemes take the advantage of the AP transmit power into the performance gain so that they excel the HDR in performance. The amount of advantage of two Algorithms diminishes as \(P_{r}\) reduces, and Algorithm 2 suffers more than Algorithm 1 in this respect. Now in Figure 4, the average sum throughput of proposed schemes over the number of relaying UT transmit antennas \(M\) are compared with three different sets of fixed \(P_{s}\) and \(P_{r}\) values. First, consider the case of \(P_{s}\) = 0 (dB) and \(P_{r}\) = 20 (dB) in black curves, which reminds us of the cases of Figure 2, where the advantage of Algorithm 1 over Algorithm 2 disappears as \(P_{r}\) becomes excessive and the suppression of CRI is challenging. Second, the case is reversed in red curves and that we set \(P_{s}\) = 20 (dB) and \(P_{r}\) = 0 (dB). The interpretation of this case needs the observations from Figure 3 as the performance of Algorithm 2 suffers in low \(P_{r}\) values. Here, Algorithm 2 performs even worse than the HDR case as \(M\) grows into large values, while the gain of Algorithm 1 is limited as well. Finally, the most interesting case of green curves corresponds to the setting of \(P_{s}\) = 10 (dB) and \(P_{r}\) = 10 (dB). Here, the curves of Algorithm 2 flatten and become degrading after \(M\) increases by more than 6. This weird event can be explained by the channel hardening property of the multiple antenna channel at the massive value of \(M\).