Exploiting diversity of usage to enhance user equipment energy efficiency in LTE networks

Abstract

Energy efficiency is widely recognized as an important factor for future cellular networks. For mobile devices, energy efficiency leads to extended battery life. Existing works consider battery to be equally important for all users at all time. We recognize that the value of a device’s battery depends on the user’s target usage. In particular, we introduce the notions of valueless and valued battery, as being the available battery when the user does or does not have access to a power source, respectively. We argue that user experience only depends on valued battery. We propose a cooperative system to help raise the overall amount of valued battery in the network. Our system makes use of device-to-device communications underlaying LTE to create cooperative relay links between users. Users who expect to have a large amount of valueless battery help relay traffic for users with a small amount of valued battery. We develop our system as a proximity service for future LTE releases. We propose a framework to study utility functions to evaluate the value of battery. We show that with appropriate utility functions, a set of thresholding cooperative rules ensure network performance improvement. We illustrate this improvement through simulation. Our simulator source code is made available to the public.

Appendices

Appendices

Proof of Lemma 1

Since the consumption process $\zeta _L(\cdot )$ is non-negative, and the utility function is monotonically non-decreasing in $B$, the helper will never gain utility after a cooperative session

$$\begin{aligned} u_j(B_j&- \zeta _{L_j}(T_c), T_j \!-\! T_c, L_j) \nonumber \\&- u_j(B_j \!-\! \zeta _{L_j}(T_c) \!-\! \varDelta B_{ji}, T_j \!-\! T_c, L_j) \ge 0. \end{aligned}$$

(57)

From (4)

$$\begin{aligned} u_i(B_i&- \zeta _{L_i}(T_c) + \varDelta B_{ji} - \delta _{ji}, T_i - T_c, L_i) \nonumber \\&- u_i(B_i - \zeta _{L_i}(T_c), T_i - T_c, L_i) \ge 0. \end{aligned}$$

(58)

(5) follows from property (1) of the utility function. $\square$

Expected valued usage time for Gaussian consumption process

We want to calculate the expected valued usage time $\mathbb E[T_V]$ for the case the consumption process $\zeta _L(t)$ is Gaussian. As seen in (20), the time until outage $T_O$ is approximated as a Gaussian random variable $\mathcal N(\mu ,\sigma ^2)$. From (10)

$$\begin{aligned} \mathbb E[T_V]&= T - \int _0^T (T-\tau ) \frac{1}{\sqrt{2\pi \sigma ^2}} e^{-\frac{(\tau -\mu )^2}{2\sigma ^2}} d\tau \nonumber \\&= T - (T-\mu ) \int _0^T \frac{1}{\sqrt{2\pi \sigma ^2}} e^{-\frac{(\tau -\mu )^2}{2\sigma ^2}} d\tau \nonumber \\&\quad + \int _0^T (\tau -\mu ) \frac{1}{\sqrt{2\pi \sigma ^2}} e^{-\frac{(\tau -\mu )^2}{2\sigma ^2}} d\tau . \end{aligned}$$

(59)

Since $T_O \ge 0$, for the approximation $T_O \sim \mathcal N(\mu ,\sigma )$ to hold we need $\varPhi (\frac{-\mu }{\sigma }) \approx 0$. This is true for sufficiently large $\mu$. Consequently, we have

$$\begin{aligned} (T-\mu ) \int _0^T \frac{1}{\sqrt{2\pi \sigma ^2}} e^{-\frac{(\tau -\mu )^2}{2\sigma ^2}} d\tau \approx (T-\mu ) \varPhi \left( \frac{T-\mu }{\sigma }\right) \!. \end{aligned}$$

(60)

To compute the last term of (59), we make the change of variable $u = \frac{(\tau -\mu )^2}{2\sigma ^2}$. We have $(\tau -\mu )d\tau = \sigma ^2 du$. Therefore,

$$\begin{aligned}&\int _0^T (\tau -\mu ) \frac{1}{\sqrt{2\pi \sigma ^2}} e^{-\frac{(\tau -\mu )^2}{2\sigma ^2}} d\tau \nonumber \\&\quad = \int _{\frac{\mu ^2}{2\sigma ^2}}^{\frac{(T-\mu )^2}{2\sigma ^2}} \frac{\sigma }{\sqrt{2\pi }} e^{-u} du \nonumber \\&\quad = \frac{\sigma }{\sqrt{2\pi }} \left( e^{-\frac{\mu ^2}{2\sigma ^2}} - e^{-\frac{(T-\mu )^2}{2\sigma ^2}} \right) . \end{aligned}$$

(61)

Finally (59) becomes

$$\begin{aligned} \mathbb E[T_V]&= T - (T-\mu ) \varPhi \left( \frac{T-\mu }{\sigma }\right) \nonumber \\&\quad + \frac{\sigma }{\sqrt{2\pi }} \left( e^{-\frac{\mu ^2}{2\sigma ^2}} - e^{-\frac{(T-\mu )^2}{2\sigma ^2}} \right) . \end{aligned}$$

(62)