Underlay Device to Device Communication with Imperfect Interference Channel Knowledge

Abstract

Device-to-device (D2D) communication underlying cellular networks is an important technology to enhance spectrum efficiency in next generation wireless networks. One main challenge in this technology is the power control of D2D transmitter in order to preserve a certain level of transmit rate for cellular users. This challenge would be even more critical if there is imperfect knowledge on the interference channel to cellular users. To address this challenge, in this paper, D2D power control schemes including stochastic optimization, robust optimization, and a game theoretic approach are proposed. These schemes aim to maximize the achieved rate of an underlay D2D pair while satisfying a given transmit rate for a cellular user. Numerical results demonstrate the effectiveness of the proposed schemes. In particular, the results of the game theoretic approach match the case when there is perfect knowledge on the interference channel gain. Following this observation, the game theoretic approach is also extended for the case of multiple D2D pairs. Simulations reveal the performance degradation of the cellular user with the increase in the number of D2D pairs.

Appendix

The constraint (5b) can be rewritten as

$$\sum\limits_{i} {\left( {\pi_{i} \log_{2} \left( {1 + \frac{{g_{ce} p_{c} }}{{g_{de}^{i} p_{d} + \sigma_{n}^{2} }}} \right)} \right)} \ge r_{c}^{T} .$$

(12)

The function $\log_{2} \left( {1 + \frac{{g_{ce} p_{c} }}{{g_{de}^{i} p_{d} + \sigma_{n}^{2} }}} \right)$ is a convex function of $g_{de}^{i}$. Based on the properties of convex functions, we can write [21]

$$\sum\limits_{i} {\left( {\pi_{i} \log_{2} \left( {1 + \frac{{g_{ce} p_{c} }}{{g_{de}^{i} p_{d} + n}}} \right)} \right) \ge \log_{2} \left( { 1 { + }\frac{{{\text{g}}_{\text{ce}} {\text{ p}}_{\text{c}} }}{{\sum\nolimits_{i} {\pi_{i} } {\text{g}}_{de}^{i} {\text{p}}_{\text{d}} { + }\sigma_{n}^{2} }}} \right)} .$$

(13)

Based on this inequality, we can substitute constraint (12) by

$$\log_{2} \left( { 1 { + }\frac{{{\text{g}}_{\text{ce}} {\text{ p}}_{\text{c}} }}{{\sum\nolimits_{i} {\pi_{i} } {\text{g}}_{de}^{i} {\text{p}}_{\text{d}} { + }\sigma_{n}^{2} }}} \right) \ge r_{c}^{T} .$$

(14)

Indeed, we replaced the right hand-side of (12) with a smaller value function in (14) that is monotonically decreasing in $p_{d}$. Indeed, with a given $r_{c}^{T}$, the feasible power in (14) is a lower bound on the feasible power in (12).