# Trellis Tone Modulation Multiple-Access for Peer Discovery in D2D Networks
## 2 System Model and Conventional FDMA-Based D2D Discovery
### FDMA-Based Discovery  
Figure 1 exhibits the timing diagram of repetitive LTE uplink frames with a peer discovery time slot [24]. This structure is based on the synchronized OFDM physical layer of the LTE uplink. The time interval for peer discovery is periodically allocated within the LTE uplink frame every 20 s. The UEs broadcast a discovery signal using time-frequency resources partially in this interval. Each UE can receive discovery signals from other UEs during a time when it does not transmit, due to the half-duplex nature of wireless communications.  
Figure 1 also shows the OFDM resource map that constitutes the discovery interval. The basic unit, a single subcarrier of one OFDM symbol, is called a resource element (RE). The basic resource configuration unit of the LTE standard is called the resource block (RB), which consists of 12 subcarriers and 14 symbols, thus containing 168 REs. The number of RBs in the frequency domain in the discovery interval is determined by the frequency bandwidth. When 10 MHz bandwidth is used for discovery, 44 RBs are packed in the band. Since one discovery-frame spans 64 RBs in time, 44 \(\times\) 64 RBs form a discovery-frame. Thus, one discovery interval has 64 discovery-frames.  
Each UE selects one RB for each discovery-frame and transmits a discovery signal over the RB. The frequency domain has 44 parallel RBs when 10 MHz bandwidth is used for discovery. The UEs select one RB and transmit the discovery signals through an exclusively assigned resource. Therefore, this scheme can be regarded as frequency division multiple-access (FDMA) on the OFDM resource grid from the perspective of a device that aims to detect all of the discovery signals. In this case, each UE must prevent its own discovery signal from overlapping with signals of other UEs; therefore, the UEs select an RB using a collision avoidance technique. Collision avoidance is conducted as follows. (1) A UE that intends to join a D2D network listens to the discovery signals of other UEs without transmitting its own discovery signal. (2) The UE then calculates the energy level for all RBs in an entire discovery interval. (3) The UE randomly selects one of the RBs of the bottom 5% in measured energy and transmits the discovery signal over the selected RB in the next discovery interval [24], which we call the \"minimum-energy-based selection rule\". This collision avoidance scheme approximately maximizes the distance between the UEs that use the same RB for discovery signal transmission.  
Due to the half-duplex constraint, the UE cannot receive the discovery signals of other UEs while transmitting its own discovery signal. Therefore, as shown in Figure 1, the UE transmits the same discovery message through RBs changed by a predetermined hopping pattern over time in several discovery-frames. For example, this hopping pattern is determined by Latin-square [27].  
Even if the UE uses the collision avoidance based on the minimum-energy-based selection rule, it cannot completely prevent proximate UEs from selecting the same RB because the collision avoidance is performed distributively. Therefore, each UE needs to monitor whether or not there is a nearby UE that uses the same RB. For this purpose, each UE listens to signals from other UEs in a discovery-frame without broadcasting a signal at a given time. If high energy is detected in the RB chosen by the UE, it is recognized as a collision and a resource is reselected by using a minimum-energy-based selection rule. This is a collision detection technique.