# Transmission Power Adaption for Full-Duplex Relay-Aided Device-to-Device Communication
## 1 Introduction
In [21], the authors outline an HD relaying-based D2D scheme by operating on the same frequency band as cellular user in frequency domain by splitting a frame into double transmitting phases in the time domain. In this scheme, because the BS transmit signal to the cellular user takes place in one half of a frame, the achievable transmission rate is dimidiated in this mode. Then to compensate for the cellular users' capacity loss, the D2D relay has to allocate almost all of its transmitting power to forward cellular signals when the direct link between the BS and cellular users is good. Then this scheme will degenerate to a conventional relaying mode. In contrast, when the direct link is in deep fading or shadowing, it also cannot give a significantly increasing transmission rate. Furthermore, the authors describe explicitly that the BS and the D2D relay should use maximum transmitting power as they can maintain the transmit capacity of the cellular user, which leads to low energy efficiency for the system. Alternatively, the FD mode as explicitly described in [27; 28; 29] relays cellular signals and the D2D component to the respective receiver simultaneously. Unfortunately, the self-interference cannot be eliminated perfectly and, consequently, the potential existence of residual interference is not negligible. The work that has been done in [27] advocates a new FD mode, in which the aggregate power of the system is defined as a constant. That makes the D2D relay much more able to use transmitting power than one when the power is normalized. By this means, they can get a significant capacity increase and a closed form of expression of the optimal power at BS and D2D relay by adding a power equation. However, it is more realistic to consider the BS and D2D relay with their own transmission power constraint. In contrast to the aforementioned works, the contributions of this paper are summarized as follows:  
1. The main contribution of the article is to draft a novel D2D relaying-aided scheme to improve the transmitting rate of a cellular user who is in deep fading or shadowing. Unlike the works that have been done before, our scheme guarantees cellular user' quality of service in terms of the minimum rate requirement. This means that the performance of the cellular user is improved rather than deteriorated or just maintained, as done in [13; 21]. 2. We consider an independent power constraint for the BS and D2D relay respectively rather than under the aggregate power constraint as in [27]. Although we use two inequalities to replace one equation, we also derived a closed form expression of the optimal allocated power and the power split factor. 3. By making comparisons with traditional direct communication of cellular mode and HD relaying mode, the FD mode we proposed could use the minimum transmitting power to make sure the cellular' rate requirement with also achieve the D2D rate as far as possible. It also has been demonstrated that the approach we proposed is more prominent in terms of spectral efficiency and power efficiency, in the situation that the residual loopback interference generating the D2D relay is controlled at a tolerable level. The rest of the paper is organized as follows: we describe the system model and scheme of the proposed FD relaying assisted D2D communication by underlaying the downlink frequency resource of a cellular network in Section 2. The optimal power adaption strategies for guaranteeing the rate requirement of cellular user versus benchmark HD mode are evaluated in Section 3. Simulations have been obtained are presented in Section 4. Finally, the conclusions are drawn in Section 5.