# Trellis Tone Modulation Multiple-Access for Peer Discovery in D2D Networks
## 5 Performance Evaluation  
This section compares and evaluates the discovery performance of the conventional FDMA-based scheme and the TTMMA scheme based on the 3 GPP LTE uplink system. Their computational complexities are also compared. We consider a situation where a total of \(n\) transmitting UEs transmit a discovery signal using given DRUs in a circular network with a radius of 500 m, which is the set-up for convenience of evaluation. Each transmitting UE broadcasts 150 bits of discovery message, which includes 16 bits of CRC code for error detection. The positions of transmitting UEs are determined uniformly at random in the given region and the receiving UE is located at the origin. Table 1 shows the simulation assumptions in detail. As shown in Table 1, we use the D2D outdoor-to-outdoor model [15] as propagation model and two channel models. One channel model is Block Rayleigh fading and another channel model is TDL-A [32]. Even though channel models in [32] are designed for above 6 GHz carrier frequency, these channel models are also generally considered for all evaluations in 3 GPP standards including below 6 GHz carrier frequency. Especially, TDL-A 30 ns is the most common channel model considered for 5G link level simulations such as Ultra-Reliable Low Latency Communication (URLLC) and NOMA. In the FDMA-based scheme, a UE transmits a discovery signal using a DRU1 that consists of 12 subcarriers and 14 symbols. One symbol of DRU1 is used for transmission-reception switching and another one symbol of DRU1 is used for Demodulation Reference Signal (DMRS). Therefore, each UE can use 12 \(\times\) 12 = 144 REs. Each UE encodes a 150 bits message using polar codes [33], which shows the best performance in short-length and adopted in the 5G standardization, to produce a 288 bits codeword, and modulates the 288 bits codeword into 144 QPSK symbols, which are then loaded onto 144 REs. At this time, the transmission power is evenly distributed to the 12 subcarriers. The DMRS for channel estimation are generated by a Hadamard sequence of length 8. That is, the collision probability is 1/8. The interference in pilots are fully interfered if the sequence is collided with 1/8 probability, and are partially interfered with 1/8 power if the sequence is not collided with 7/8 probability. Since two or more UEs can use the same DRU, the receiving UE performs channel estimation and a general SIC operation accordingly. We assume the ideal channel estimation. In the TTMMA scheme, each UE uses a DRU2 that consists of 12 subcarriers and 76 symbols. Since one symbol is used for transmission-to-reception switching in the same way as the FDMA-based scheme, each UE generates a TTMMA signal on 12 \(\times\) 75 REs. Because the transmit power is focused on one tone per symbol, single-tone transmission gain of 10.7 dB and the PAPR gain of 6 dB is considered in this simulation. The 150 bits of the discovery message are mapped to 2 bits from the first symbol to a single-tone position and 148 bits to a tone-transition between 75 symbols. No pilots or collision detection techniques are used. The receiving UE performs demodulation using a message-passing \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Bandwidth & 10 MHz \\ FFT size & 2048 \\ Subcarrier spacing & 15 kHz \\ Transmission power per symbol & 23 dBm \\ Noise power & \(-174\ dBm/Hz\) \\ Noise figure & 9 dB \\ Channel model I & Block Rayleigh fading \\ Channel model II & TDL-A \\ Delay spread for Channel II & 30 ns \\ Propagation model & D2D outdoor-to-outdoor model \\ Carrier frequency & 2.4 GHz \\ Height of antenna & 1.5 m \\ Mobile speed for Channel II & 5 km/h \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Evaluation Assumptions. process by adding the tone-space expansion and the pre-prediction. In the message-passing process, the maximum iteration number is fixed at 3. Even if only one candidate codeword is not found, the receiving UE increases the threshold value two-fold and further attempts demodulation up to three times.