Relay Incentive Mechanisms Using Wireless Power Transfer in Non-Cooperative Networks

TL;DR

This paper proposes a protocol based on a reverse auction that enables the source to determine which candidate UE to select as the relay and the amount of energy to be transferred as payment, even when the channel quality between the candidates and the destination is unknown to the source.

Abstract

This paper studies the use of a multi-attribute auction in a communication system to bring about efficient relaying in a non-cooperative setting. We consider a system where a source seeks to offload data to an access point (AP) while balancing both the timeliness and energy-efficiency of the transmission. A deep fade in the communication channel (due to, e.g., a line-of-sight blockage) makes direct communication costly, and the source may alternatively rely on non-cooperative UEs to act as relays. We propose a multi-attribute auction to select a UE and to determine the duration and power of the transmission, with payments to the UE taking the form of energy sent via wireless power transfer (WPT). The quality of the channel from a UE to the AP constitutes private information, and bids consist of a transmission time and transmission power. We show that under a second-preferred-offer auction, truthful bidding by all candidate UEs forms a Nash Equilibrium. However, this auction is not incentive compatible, and we present a modified auction in which truthful bidding is in fact a dominant strategy. Extensive numerical experimentation illustrates the efficacy of our approach, which we compare to a cooperative baseline. We demonstrate that with as few as two candidates, our improved mechanism leads to as much as a 76% reduction in energy consumption, and that with as few as three candidates, the transmission time decreases by as much as 55%. Further, we see that as the number of candidates increases, the performance of our mechanism approaches that of the cooperative baseline. Overall, our findings highlight the potential of multi-attribute auctions to enhance the efficiency of data transfer in non-cooperative settings.

Figures (6)

• Figure 1: Overview of problem scenario. A source UE must offload data to the AP, but the LOS path is blocked, resulting in poor link quality. The source must induce a candidate UE to cooperate with a payment in the form of WPT.
• Figure 2: System setup for the WPT-enabled relaying scenario. The orange dot gives the location of the source, $q_s$, the black dots give the locations of the candidates, $q_i$, and the AP is at the origin. The large black circle in the center indicates the blockage, and the gray region indicates the area where the channel to either the source or the AP is NLOS. The arrows represent channels, with the green arrows representing channels used if UE $i$ acts as the relay. The channels are labeled with corresponding channel power variables.
• Figure 3: Numerical results for a sample blockage scenario. (a) and (b): The probability that a candidate at each point could act as a relay in the cooperative case for (a) lognormal and (b) Rayleigh fading, i.e., $p_{\text{out},c}$ from Eq. (\ref{['eq:candidate_op']}) conditioned on candidate placement. Areas which do not have a LOS path to both the AP and the source are crosshatched. (c) and (d): The outage probability of the MWA, VWA, and cooperative baseline for (c) lognormal and (d) Rayleigh fading. The cooperative baseline outage probability is calculated using the expression for the minimal outage probability in Eq. (\ref{['eq:vick_p_out']}), while the MWA and VWA outage probabilities are determined empirically from the numerical experiments. The outage probability under the MWA is greater than it is for the VWA, which matches the minimum outage probability. For both the VWA and MWA, the outage probability decays exponentially. (e): The outage probability gap between the Vickrey and Myerson auction. This gap decays exponentially in the number of candidates. (f) and (g): The average source transmit power under the VWA and MWA, as well as for the cooperative baseline introduced in Section \ref{['sec:auction']}, for (f) lognormal and (g) Rayleigh fading. Energy usage for the MWA is less than it is under the VWA, and energy efficiency converges as the number of candidates increases. See color PDF for optimal viewing.
• Figure 4: Average net energy harvested for the scenario depicted in Fig. \ref{['fig:fixed_exp_setup']}.
• Figure 5: Numerical results for the blockage scenario shown in (a) under Rayleigh fading. (a): The probability that a candidate at each point could act as a relay in the cooperative case,i.e., $p_{\text{out},c}$ from Eq. (\ref{['eq:candidate_op']}) conditioned on candidate placement. Areas which do not have a LOS path to both the AP and the source are crosshatched. (b): The empirical outage probability of the MWA and VWA, and the analytical outage probability of cooperative baseline, calculated using Eq. (\ref{['eq:vick_p_out']}). (c): The average source transmit power under the VWA and MWA, as well as for the cooperative baseline introduced in Section \ref{['sec:auction']}. See color PDF for optimal viewing.

Theorems & Definitions (13)

• Definition 1
• Lemma 1
• proof
• Definition 2
• Theorem 1
• proof
• Definition 3
• Corollary 1
• proof
• Theorem 2