Tremendous growing demand for high data rate services such as video, gaming and social networking in wireless cellular systems, attracted researchers' attention to focus on developing proximity services. In this regard, device-to-device (D2D) communications as a promising technology for future cellular systems, plays crucial rule. The key factor in D2D communication is providing efficient peer discovery mechanisms in ultra dense networks. In this paper, we propose a centralized D2D discovery scheme by employing a signaling algorithm to exchange D2D discovery messages between network entities. In this system, potential D2D pairs share uplink cellular users' resources with collision detection, to initiate a D2D links. Stochastic geometry is used to analyze system performance in terms of success probability of the transmitted signal and minimum required time slots for the proposed discovery scheme. Extensive simulations are used to evaluate the proposed system performance.

Heterogeneous networks (HetNets) as a combination of macro cells and small cells are used to increase the cellular network's capacity, and present a perfect solution for highspeed communications. Increasing area spectrum efficiency and capacity of HetNets largely depends on the high speed of backhaul links. One effective way which is currently utilized in HetNets is the use of full-duplex (FD) technology that potentially doubles the spectral efficiency without the need for additional spectrum. On the other hand, one of the most critical network design requirements is delay, which is a key representation of the quality of service (QoS) in modern cellular networks. In this paper, by utilizing tools from the stochastic geometry, we analyze the local delay for downlink (DL) channel, which is typically defined as the mean number of required time slots for a successful communication. Given imperfect self-interference (SI) cancellation in practical FD communications, we utilize duplex mode (half-duplex (HD) or FD) for each user based on the distance from its serving base station (BS). Further, we aim to investigate the energy efficiency (EE) for both duplexing modes, i.e., HD and FD, by considering local delay. We conduct extensive simulations to validate system performance in terms of local delay versus different system key parameters.

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