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# Performance Analysis of Relayed D2D Communications under Power Control

Farah Yassine, Oussama Bazzi, Youssef Nasser

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Farah Yassine, Oussama Bazzi, Youssef Nasser. Performance Analysis of Relayed D2D Communications under Power Control. 2020 43rd International Conference on Telecommunications and Signal Processing (TSP), Jul 2020, Milan, France. pp.377 - 381, 10.1109/tsp49548.2020.9163520. hal-05344798

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HAL
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# Performance Analysis of Relayed D2D Communications under Power Control

Farah Yassine, Oussama Bazzi, Youssef Nasser

► To cite this version:

Farah Yassine, Oussama Bazzi, Youssef Nasser. Performance Analysis of Relayed D2D Communications under Power Control. 2020 43rd International Conference on Telecommunications and Signal Processing (TSP), Jul 2020, Milan, France. pp.377 - 381, 10.1109/tsp49548.2020.9163520. hal-05344798

HAL Id: hal-05344798

https://hal.science/view/index/docid/5344798

Submitted on 4 Nov 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

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Open licence - etalab
# Performance Analysis of Relayed D2D Communications under Power Control

Farah Yassine, Oussama Bazzi

Department of Physics and Electronics

Lebanese University

Hadat, Lebanon

farahya@outlook.com, obazzi@ul.edu.lb

Youssef Nasser

Department of Electrical and Computer Engineering

American University of Beirut

Beirut, Lebanon

yn17@aub.edu.lb

**Abstract**—In this paper, we consider a relay-aided device-to-device (RA-D2D) communication link operating within a cellular network. The underlay mode where the D2D users share the uplink frequency resources of the cellular link is considered. An optimal algorithm for allocating the appropriate D2D transmit powers that maximize the ergodic capacity of the D2D link while ensuring the cellular communication requirements is proposed. The performance of the proposed scheme is then analyzed in terms of the ergodic capacity of the RA-D2D link. The improvement in the spectral efficiency is compared with the half-duplex (HD) and the full-duplex (FD) modes of D2D communications. Results show that the relay-aided system outperforms the HD system and even the FD system above a certain threshold of self-interference.

**Index Terms**—D2D, ergodic capacity, power control, relay-aided communications.

## I. INTRODUCTION

With the rapid increase in the number of user equipments and the new emerging applications such as multimedia and social networks, the demand for local traffic load and higher data rate transmission is increasing. Device-to-device (D2D) communications have thus been proposed as one of the promising techniques for increasing the throughput in the future 5G cellular networks [1]. In D2D communications, proximity user equipments (UEs) can communicate directly without passing through the base station (BS). This would improve the spectral efficiency (SE), reduce the latency and lower the required energy per bit.

Generally, based on the spectrum allocation for the D2D communication, two main modes of D2D operation are distinguished: the underlay mode where cellular users and D2D users share the same radio resources and the overlay mode where D2D users are given dedicated cellular resources. Despite the interference that exists between D2D users and cellular users in the underlay mode, this latter mode has attracted large interest since it can significantly improve the SE [2]. This is achieved through appropriate power control mechanisms to mitigate the existing interference [2],[3].

As for the D2D signal transmission, different techniques have been considered and evaluated in literature mainly the half duplex (HD) and the full duplex (FD) transmission [4-7]. These techniques are reviewed in this paper.

This work was supported by the Lebanese University research program.

In order to further improve the D2D performance, relay-aided D2D systems have also attracted interest [8-10]. Relay-aided communication was known in general, in cellular networks, for its capability to highly enhance the system transmission capacity and coverage [11]. In relay-aided D2D communication, an additional terminal, the relay node, is added between the D2D pair for helping in the transmission. In particular, the two-way relay channel (TWRC), also named bidirectional relaying, allows the two terminals to exchange simultaneously their messages through the relay, and thus enhances the spectral efficiency [10]. Relay protocols are broadly divided into amplify-and-forward (AF) and decode-and-forward (DF) based on the signal management procedure at the relay node [12]. Employing AF protocol causes the amplification of the interference with the expected signal together ending up with a low SINR at the receiver side. However, relay employed with DF protocol works on eliminating the interference before forwarding the message to the receiver side and hence achieves better performance.

In [8], the authors present an energy efficient power allocation for RA-D2D communications for a single way relay. Power allocation in a two-way AF RA-D2D was studied in [9], however the interference from the primary network on the D2D link was not considered. A DF RA-D2D system was considered in [10] and the ergodic capacity was derived, however transmit powers were considered equal for the D2D and cellular user (CU) and the power control was only applied to the relay transmission.

Compared to the above works, our contributions in this paper are as follows: the two-way DF RA-D2D link in the underlay mode is considered where an optimal power control of not only the relay but also of the D2D and the CU transmit powers is applied. A power allocation algorithm is proposed. The performance achieved in the RA-D2D system in terms of spectral efficiency is then compared to that obtained in for HD and FD techniques allowing setting the D2D design capabilities and limitations of the RA-D2D under different conditions.

The rest of this paper is organized as follows. In Section 2, the D2D system model operation is presented. The three communication techniques: HD, FD and RA-D2D are described and the optimisation problem for each technique is reviewed.
In Section 3, we derive an optimal power allocation strategy for RA-D2D communication. In Section 4, the simulation results are presented and discussed. Finally, Section 5 concludes the paper.

## II. SYSTEM MODEL

A D2D communication system underlaying a based wireless cellular network is shown in Fig. 1. An isolated cell scenario consisting of one pair of D2D users ($DU_1$ and $DU_2$), one cellular user CU and one base station (BS) is considered. The D2D pair communicates with each other using the same uplink frequency-time resource allocated to the CU. This gives rise to some mutual interference between the cellular link and the D2D link as shown in Fig. 1. It is worth noting that, in the uplink resource sharing (UL), the interference in D2D communications will only affect the BS. This interference can be reduced and mitigated in practice through BS coordination [2].

In the relay-assisted (RA) mode, an additional terminal, the relay node (RN), is added between the D2D pair, as shown in Fig. 1, to assist and enhance the D2D communications.

<figure><img src="image_5.png" /><figcaption>Fig. 1. Two-way directional RA-D2D Communication</figcaption></figure>

Due to the interference, the optimal operation of the D2D system that maximizes the transmission rate of the D2D link is obtained in general through a control of the transmit powers of D2D users under the constraint of satisfying the quality-of-service (QoS) requirement of CU. The formulation of this optimization problem for three different D2D communication modes is reviewed below.

### A. HD-D2D Mode (Without Relay)

In this mode, at a time, one of the D2D users (e.g $DU_1$) plays the role of transmitter, and the other one ($DU_2$) plays the role of a receiver.

The channel-to-interference-plus-noise-ratios (CINR's) of D2D and cellular links are then given respectively as

$$ \gamma_d = \frac{g_{d1,d2}}{P_c \cdot g_{c,d2} + NW} \qquad (1) $$

$$ \gamma_c = \frac{g_{c,bs}}{P_d \cdot g_{d1,bs} + NW} \qquad (2) $$

Where $g_{d1,d2}$, $g_{c,bs}$, $g_{c,d2}$ and $g_{d1,bs}$ denote the channel gains from $DU_1$ to $DU_2$, CU to BS, CU to $DU_2$ and $DU_1$ to BS respectively. $P_c$ and $P_d$ are the transmit powers of CU and DU's respectively. $N$ is the additive white noise power spectral density and $W$ is the transmission bandwidth.

The transmission capacities of $DU_1$ and CU are given respectively as

$$ R_d^{HD} = W \log_2(1 + P_d \cdot \gamma_d) \qquad (3) $$

$$ R_c^{HD} = W \log_2(1 + P_c \cdot \gamma_c) \qquad (4) $$

The optimization problem in this case is expressed as

$$ \begin{array}{ll} \max_{(P_c, P_d)} & R_d^{HD} \\ \text{s.t} & R_c^{HD} \ge R_c^{min} \\ & 0 \le P_c \le P_c^{max} \\ & 0 \le P_d \le P_d^{max} \end{array} \qquad (5) $$

Where $R_c^{min}$ is the minimal constraint on the CU capacity. $P_c^{max}$ and $P_d^{max}$ are respectively the maximal limits on the transmit powers of CU and DU's.

The optimization problem above is simple to solve using linear programming methods. The analytical solution is given by [6] as

$$ P_d^* = \min\{P_d^{max}, \frac{g_{c,bs}}{\mu \cdot g_{d1,bs}} \cdot (P_c^{max} - \frac{NW\mu}{g_{c,bs}})\} \qquad (6) $$

$$ P_c^* = \frac{\mu}{g_{c,bs}} \cdot (P_d^* \cdot g_{d1,bs} + NW) \qquad (7) $$

$$ \text{Where } \mu = 2^{(R_c^{min}/W)} - 1 \qquad (8) $$

### B. FD D2D Communication Mode (Without Relay)

Full-Duplex (FD) communication allows the simultaneous transmit and receive of signals between D2D users using the same frequency band. Under full ideal duplex mode the obtained data throughput would be highly increased (expected to double) as compared to the half-duplex mode. However, FD communication in practice suffers from the existence of self-inference which affects the optimization problem and which can severely limit the system performance [5]. Although different self-interference mitigation techniques exist, self interference cannot be totally eliminated.

The CINR's of the D2D links is given in this case as

$$ \gamma_{d_i, d_j} = \frac{g_{d_i, d_j}}{P_c \cdot g_{c, d_j} + P_{d_i} \cdot \eta_i + NW} \qquad (9) $$

Where $(i, j) \in \{(1,2), (2,1)\}$ and $\eta_i$ is the residual self-interference coefficient at $DU_i$ which is comprised between 0 and 1.

The CINR of the CU link is given by

$$ \gamma_c = \frac{g_{c,bs}}{P_{d_1} \cdot g_{d_1,bs} + P_{d_2} \cdot g_{d_2,bs} + NW} \qquad (10) $$

The capacities of each D2D link in the FD mode can be written as

$$ R_{d_i}^{FD} = W \log_2(1 + P_{d_i} \gamma_{d_i}) \qquad (11) $$
with $i \in \{1, 2\}$ The capacity of CU will have the same form as in (4) with $\gamma_c$ being replaced by its expression in (10).

The optimization of the power control problem in the FD mode is formulated as

$$ \begin{array}{l} \max_{(P_c, P_{d_1}, P_{d_2})} R^{FD} \triangleq R_{d_1}^{FD} + R_{d_2}^{FD} \\ \text{s.t} \quad R_c^{HD} \ge R_c^{min} \\ \qquad 0 \le P_c \le P_c^{max} \\ \qquad 0 \le P_{d_1}, P_{d_2} \le P_d^{max} \end{array} \quad (12) $$

Different approaches were considered in literature to solve this optimization problem which is non-convex. In [6], the problem was converted into a convex problem using approximations and was then solved using standard algorithms. In [7] the power allocation sub-problem was solved by means of the monotonic optimization theory.

### C. RA-D2D Communication Mode

In this scheme, the D2D users exchange messages with each other through a decode-and-forward (DF) relay node located between the D2D pair. The D2D transmission is divided into two phases or time slots as shown in Fig. 1. During the first time slot (TS), both $DU_1$ and $DU_2$ users transmit their encoded messages to the relay node (RN). After the decoding process, the relay re-encodes the messages and retransmits them to D2D terminals ($DU_1$ and $DU_2$) in the second phase.

The expressions of the SINRs ratios for the different links will then take different forms depending on the interference. For the first TS, the channel-to-interference-plus-noise-ratios (CINRs) for the links from $DU_1$ to RN and from $DU_2$ to RN are expressed as

$$ \gamma_{d_i,r} = \frac{g_{d_i,r}}{P_c \cdot g_{c,r} + NW} \quad (13) $$

for $i=1$ and 2 respectively. $g_{d_1,r}$, $g_{d_2,r}$ and $g_{c,r}$ are the channel gains from $DU_1$ to RN, $DU_2$ to RN and CU to RN respectively.

$$ SNR_{MAC} = P_{d_1}\gamma_{d_1,r} + P_{d_2}\gamma_{d_2,r} \quad (14) $$

For the second TS, the CINRs for the $RU-DU_1$ and the $RU-DU_2$ links respectively are expressed as

$$ \gamma_{r,d_i} = \frac{g_{r,d_i}}{P_c \cdot g_{c,d_i} + NW} \quad (15) $$

Where $i \in \{1, 2\}$, $g_{r,d_1}$, $g_{r,d_2}$, $g_{c,d_1}$, and $g_{c,d_2}$ are the channel gains from RN to $DU_1$, RN to $DU_2$, CU to $DU_1$, and CU to $DU_2$ respectively.

The expression of the two-way RA-D2D channel rate [12], denoted by $R_{sum}^{DF}$, is given by

$$ R_{sum}^{DF} = \min(R_{MAC}, R_1 + R_2) \quad (16) $$

Where

$$ R_1 = \log_2(1 + \min(P_{d_1}\gamma_{d_1,r}, P_{r_2}\gamma_{r,d_2})) \quad (17) $$

$$ R_2 = \log_2(1 + \min(P_{d_2}\gamma_{d_2,r}, P_{r_1}\gamma_{r,d_1})) \quad (18) $$

$$ R_{MAC} = \log_2(1 + SNR_{MAC}) \quad (19) $$

Where $P_{r_1}$ and $P_{r_2}$ are the relay transmit powers in the second TS directed to $DU_1$ and $DU_2$ respectively.

As for the CU transmission, it occurs in both TSs but will be subject to different forms of interference. At the BS side, the received CINR, allowing to obtain the data rate of cellular link, can be written as

$$ \gamma_c = \begin{cases} \frac{g_{c,bs}}{P_{d_1} \cdot g_{d_1,bs} + P_{d_2} \cdot g_{d_2,bs} + NW}; & 1^{\text{st}} \text{ TS} \\ \frac{g_{c,bs}}{P_r \cdot g_{r,bs} + NW}; & 2^{\text{nd}} \text{ TS} \end{cases} \quad (20) $$

Where $g_{r,bs}$ denote the channel gains of links RN to BS, and $P_r$ is the total transmit power of the relay in the second TS.

$$ P_r = P_{r_1} + P_{r_2} \quad (21) $$

Thus, the optimization problem in the RA-D2D system is expressed as

$$ \begin{array}{l} \max_{(P_c, P_{d_1}, P_{d_2}, P_{r_1}, P_{r_2})} R_{sum}^{DF} \\ \text{s.t} \quad R_c^{DF} \ge R_c^{min} \\ \qquad 0 \le P_c \le P_c^{max} \\ \qquad 0 \le P_{d_1}, P_{d_2}, P_{r_1}, P_{r_2} \le P_d^{max} \end{array} \quad (22) $$

In the following section, we provide a sub-optimal analytical approach for solving the problem above. An optimal algorithm for power control is also proposed.

### III. POWER CONTROL IN RA-D2D COMMUNICATIONS

#### A. Analytical Derivation of a Sub-Optimal Solution

By analyzing the problem in (22), it can be noticed that to get the maximum of the objective function, the lower bound of $R_c^{DF}$ must be achieved meaning that

$$ R_c^{min} = \begin{cases} W \log_2(1 + \frac{P_c \cdot g_{c,bs}}{P_{d_1} \cdot g_{d_1,bs} + P_{d_2} \cdot g_{d_2,bs} + NW}); & 1^{\text{st}} \text{ TS} \\ W \log_2(1 + \frac{P_c \cdot g_{c,bs}}{P_r \cdot g_{r,bs} + NW}), & 2^{\text{nd}} \text{ TS} \end{cases} \quad (23) $$

In the sake of simplifying the power control at CU, we consider in (23) the worst case corresponding to the maximal interference on the BS that is caused by $DU_1$, $DU_2$ or RN. This allows writing

$$ R_c^{min} = W \log_2(1 + \frac{P_c^{opt} \cdot g_{c,bs}}{\max\{(P_d^{max} \cdot g_{d_1,bs} + P_d^{max} \cdot g_{d_2,bs}), 2P_d^{max} \cdot g_{r,bs}\} + NW}) \quad (24) $$

And will lead to a sub-optimal power allocation in the system.

The sub-optimal transmit power at CU side is obtained from solving (24) as

$$ P_c^* = \left( \frac{\mu}{g_{c,bs}} \cdot \left( \max\{(P_d^{max} \cdot g_{d_1,bs} + P_d^{max} \cdot g_{d_2,bs}), 2P_d^{max} \cdot g_{r,bs}\} + NW \right) \right) \quad (25) $$
As for the D2D transmission, and depending on the CINRs of the four links defined in II.C, four cases are distinguished:

1) Case 1: $(\gamma_{d_1,r} \le \gamma_{r,d_2})$ and $(\gamma_{d_2,r} \le \gamma_{r,d_1})$

In this case, the quality of the two links $DU_1-DU_2$ and $DU_2-DU_1$ passing through the relay will be limited respectively by the lowest CINRs $\gamma_{d_1,r}$ and $\gamma_{d_2,r}$.

In order to achieve maximal energy efficiency, $P_{d_1}$, $P_{d_2}$, $P_{r_1}$, and $P_{r_2}$ are allocated such that SINRs are equal i.e.:

$$P_{d_1} \cdot \gamma_{d_1,r} = P_{r_2} \cdot \gamma_{r,d_2} \quad \text{and} \quad P_{d_2} \cdot \gamma_{d_2,r} = P_{r_1} \cdot \gamma_{r,d_1} \quad (26)$$

implying the following power allocation solution:

$$\begin{aligned} P_{d_1} &= P_d^{\max} \quad \text{and} \quad P_{d_2} = P_d^{\max} \\ P_{r_2} &= P_d^{\max} \cdot \frac{\gamma_{d_1,r}}{\gamma_{r,d_2}} \quad \text{and} \quad P_{r_1} = P_d^{\max} \cdot \frac{\gamma_{d_2,r}}{\gamma_{r,d_1}} \end{aligned} \quad (27)$$

For the remaining three cases, the suboptimal power control for the D2D link is obtained in a similar way as listed below:

2) Case 2: $(\gamma_{d_1,r} \le \gamma_{r,d_2})$ and $(\gamma_{d_2,r} \ge \gamma_{r,d_1})$

$$\begin{aligned} P_{d_1} &= P_d^{\max} \quad \text{and} \quad P_{r_1} = P_d^{\max} \\ P_{r_2} &= P_d^{\max} \cdot \frac{\gamma_{d_1,r}}{\gamma_{r,d_2}} \quad \text{and} \quad P_{d_2} = P_d^{\max} \cdot \frac{\gamma_{r,d_1}}{\gamma_{d_2,r}} \end{aligned} \quad (28)$$

3) Case 3: $(\gamma_{d_1,r} \ge \gamma_{r,d_2})$ and $(\gamma_{d_2,r} \le \gamma_{r,d_1})$

$$\begin{aligned} P_{r_2} &= P_d^{\max} \quad \text{and} \quad P_{d_2} = P_d^{\max} \\ P_{d_1} &= P_d^{\max} \cdot \frac{\gamma_{r,d_2}}{\gamma_{d_1,r}} \quad \text{and} \quad P_{r_1} = P_d^{\max} \cdot \frac{\gamma_{d_2,r}}{\gamma_{r,d_1}} \end{aligned} \quad (29)$$

4) Case 4: $(\gamma_{d_1,r} \ge \gamma_{r,d_2})$ and $(\gamma_{d_2,r} \ge \gamma_{r,d_1})$

$$\begin{aligned} P_{r_2} &= P_d^{\max} \quad \text{and} \quad P_{r_1} = P_d^{\max} \\ P_{d_1} &= P_d^{\max} \cdot \frac{\gamma_{r,d_2}}{\gamma_{d_1,r}} \quad \text{and} \quad P_{d_2} = P_d^{\max} \cdot \frac{\gamma_{r,d_1}}{\gamma_{d_2,r}} \end{aligned} \quad (30)$$

## B. Proposed Algorithm for Optimal Power Allocation

Based on the derivation above, and in the sake of obtaining the optimal power allocation, we propose the following iterative algorithm. The algorithm consists in reducing the initially assumed suboptimal value $P_c^*$ in (25) which was considered in the extreme case of maximal transmit powers of interfering devices. The new value $P_c^*$ is obtained by replacing the maximal device powers by the suboptimal values found in III. A.

## IV. SIMULATION RESULTS

In order to evaluate the performance of the RA-D2D mode, we use a numerical simulation of the power control scheme derived in III and compute the ergodic capacity of the D2D link. We then compare the obtained results with those obtained under HD and FD modes for different parameters (separation distance between D2D pair, distance between CU and BS, and the self-interference coefficient in FD mode).

A single cellular wireless network is considered with a radius of 350 m in the simulation. The RN is located at midway between D2D users. The simulation parameters are specified in Table I.

### Algorithm 1: Optimal power control algorithm

**Data:** $\epsilon = 0.1 \text{mWatt}$, $P_{d_1}^* = P_{d_2}^* = P_{r_1}^* = P_{r_2}^* = P_d^{\max}$

**Output:** $P_c^*, P_{d_1}^*, P_{d_2}^*, P_{r_1}^*$, and $P_{r_2}^*$

1. compute $P_c^*$ according to (25)

2. Obtain the power control ($P_{r_1}^*, P_{r_2}^*, P_{d_1}^*, P_{d_2}^*$) based on the derivation in III.A

3. $P_{cold} \leftarrow P_c^*$

4. Compute again the optimal $P_c^*$ by substituting the new sub-optimal solutions obtained from step 2 in equation (25)

5. **if** $(P_{cold} - P_c^*) > \epsilon$ **then**

6. **return** to step 2

7. **else**

8. **return** $P_c^*, P_{d_1}^*, P_{d_2}^*, P_{r_1}^*$, and $P_{r_2}^*$

<table><caption>TABLE I
SIMULATION PARAMETERS</caption><thead><tr><th>Parameter</th><th>Value</th></tr></thead><tbody><tr><td>Cell Radius</td><td>350m</td></tr><tr><td>Distance from D2D to BS</td><td>300m</td></tr><tr><td>Maximum Power of CU</td><td>24dBm</td></tr><tr><td>Maximum Power of DU</td><td>22dBm</td></tr><tr><td>White Noise Power Spectral Density</td><td>-174dBm/Hz</td></tr><tr><td>Channel Bandwidth</td><td>1 MHz</td></tr><tr><td>Rate Requirement of CU</td><td>3 Mbps</td></tr><tr><td>Path Loss Exponent</td><td>3</td></tr></tbody></table>

The channel power gain between transmitter i and receiver j is computed as: as $g_{i,j} = h \cdot d_{i,j}^{-n}$ where h represents the channel fading assumed to follow a Rayleigh distribution with unit mean, $d_{i,j}$ is the distance between the transmitter i and the receiver j and n is the path loss exponent.

A number of 1000 realizations is used in the simulations. In each iteration, the optimal powers allocated to HD, FD, and RA-D2D users are computed along with the D2D rate in each case. At the end, the ergodic capacity for each mode is determined. Fig. 2 and Fig. 3 show the variations of the D2D ergodic capacity in HD and in RA-D2D systems when the distances between CU and BS and between the D2D pair are increased respectively. As it could have been expected, it is clear that the use of the two-way relay in the D2D communication increases efficiently the ergodic capacity as compared to the simple HD mode. This is mainly due to the fact that, with the presence of the relay, D2D transmission distances will be reduced allowing for a better achieved capacity. The results for suboptimal and optimal power control in RA-D2D are also compared in Fig. 2. In Fig. 4, we compare the HD and RA-D2D capacities with the FD mode whose performance is governed by the self-interference reduction coefficient. It can be seen that as long as the self-interference is mitigated to a level below -65 dB, FD D2D communication outperforms the RA-D2D and the HD modes. However, beyond this value, the performance of FD sharply decreases and the RA-D2D mode takes its advantages.
<figure><img src="image_6.png" /><figcaption>Fig. 2. D2D ergodic capacity as function of the distance between CU and BS with D2D user separation d=20m.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Fig. 3. D2D ergodic capacity as function of the separation between D2D users with the CU located at 60m from BS.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 4. D2D ergodic capacity as function of the self-interference coefficient.</figcaption></figure>

V. CONCLUSION

This paper focuses on the analysis of the performance of the RA-D2D underlaying a cellular network in terms of ergodic capacity. Power control of all users and of the relay is proposed with the constrained objective of maximizing the ergodic capacity of the D2D link while guaranteeing the cellular user requirements. A suboptimal analytical solution of the power allocation is presented along with an optimal algorithm.

The performance of the RA-D2D link is obtained from numerical simulation and is compared to the HD and FD modes of D2D communications. It is shown that RA-D2D may offer a significant gain even when compared to FD if the self interference coefficient is above a certain threshold.

This work is to be extended in the future to cover the multi D2D pairs and multi cells. In addition, the FD relay mode of operation can also be considered.

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