# Trellis Tone Modulation Multiple-Access for Peer Discovery in D2D Networks
## 5 Performance Evaluation
Unlike the FDMA-based scheme, the receiving UE doesn't performs the SIC operation. Since the number of resources used in the TTMMA scheme is about 5.4 times greater than that of the FDMA-based scheme for a single discovery signal, for a fair comparison, UEs are configured to select one of six DRU1s and transmit a discovery signal in the FDMA-based scheme. That is, in the TTMMA scheme, all \(n\) UEs generate a signal using one DRU2 that includes 912 Res; while in the FDMA-based scheme, \(n\) UEs select one of the six DRU1s, in which each DRU1 includes 168 REs, through which the signal is transmitted. In the FDMA-based scheme, we assume two cases of resource allocation. One is the ideal resource allocation so that each DRU1 experiences the same level of congestion. Another is randomly selected resource allocation so that each DRU1 experiences different levels of congestion. Simulations are performed on two different channel models, which are shown in Table 1. The result is based on the average obtained over 50,000 independent experiments. The performance metric is the average number of discovered UEs versus the number of multiple-access UEs. Average number of discovered UEs means average number of discovery signals passed the CRC check per an independent experiment. Figures 7 and 8 show the results in block Rayleigh fading channel. In Figure 7, the FDMA-based scheme can discover up to 4.5 UEs without SIC in case of ideal resource allocation, while the TTMMA scheme can discover up to 6 UEs, even though it uses fewer resources and does not perform the SIC. In Figure 8, the FDMA-based scheme can discover more UEs due to applying the SIC. However, the performance is still less than the TTMMA, even though it uses fewer resources and does not apply the SIC. Figure 7: Average number of discovered user equipment (UEs) according to the number of multiple-access UEs in block Rayleigh fading channel without applying successive interface cancellation (SIC). In Figure 10, the FDMA-based scheme can discover more UEs due to applying the SIC. In particular, the performance of the FDMA-based scheme is better than that of the TTMMA scheme in cases of more than 11 Multiple-Access UEs. However, the FDMA-based scheme should apply SIC and assume an ideal resource allocation for this performance. The computational complexities the FDMA-based scheme and TTMMA are compared in terms of the number of additions in Table 2. The decoding in the FDMA-based scheme is composed of the demodulation and polar code successive cancellation list (SCL) decoding [34], but the TTMMA decoding is a sole multi-user demodulation whose complexity is calculated by (12). In Table 2, \(N_{modsym}\) is the number of modulated symbols, \(N_{constel}\) is the number of constellations, \(N_{DRUI}\) is the number of DRU1, \(L\) is the list size for SCL decoding, \(N_{mc}\) is the mother code size of polar code, and \(N_{UE}\) denotes the number of multiple-access UEs. The complexity for SCL decoding of polar codes is evaluated for the simplified LLR-based SCL decoding [35; 36]. We compare the complexities of both schemes for our performance evaluation scenario. The parameter values for the scenario are given in Table 3. In Table 4, the complexity evaluation is shown for the FDMA-based scheme with or without SIC and for the proposed scheme. In the FDMA-based scheme, the resource region is composed of 6 DRUs. Because knowledge of the number of UEs that share the same resource region is not assumed, a receiver needs to try to decode discovery