Distributed Learning Policies for Power Allocation in Multiple Access Channels

We analyze the problem of distributed power allocation for orthogonal multiple access channels by considering a continuous non-cooperative game whose strategy space represents the users' distribution of transmission power over the network's channels. When the channels are static, we find that this game admits an exact potential function and this allows us to show that it has a unique equilibrium almost surely. Furthermore, using the game's potential property, we derive a modified version of the replicator dynamics of evolutionary game theory which applies to this continuous game, and we show that if the network's users employ a distributed learning scheme based on these dynamics, then they converge to equilibrium exponentially quickly. On the other hand, a major challenge occurs if the channels do not remain static but fluctuate stochastically over time, following a stationary ergodic process. In that case, the associated ergodic game still admits a unique equilibrium, but the learning analysis becomes much more complicated because the replicator dynamics are no longer deterministic. Nonetheless, by employing results from the theory of stochastic approximation, we show that users still converge to the game's unique equilibrium. Our analysis hinges on a game-theoretical result which is of independent interest: in finite player games which admit a (possibly nonlinear) convex potential function, the replicator dynamics (suitably modified to account for nonlinear payoffs) converge to an eps-neighborhood of an equilibrium at time of order O(log(1/eps)).Comment: 11 pages, 8 figures. Revised manuscript structure and added more material and figures for the case of stochastically fluctuating channels. This version will appear in the IEEE Journal on Selected Areas in Communication, Special Issue on Game Theory in Wireless Communication

Energy Efficient and Reliable Wireless Sensor Networks - An Extension to IEEE 802.15.4e

Collecting sensor data in industrial environments from up to some tenth of battery powered sensor nodes with sampling rates up to 100Hz requires energy aware protocols, which avoid collisions and long listening phases. The IEEE 802.15.4 standard focuses on energy aware wireless sensor networks (WSNs) and the Task Group 4e has published an amendment to fulfill up to 100 sensor value transmissions per second per sensor node (Low Latency Deterministic Network (LLDN) mode) to satisfy demands of factory automation. To improve the reliability of the data collection in the star topology of the LLDN mode, we propose a relay strategy, which can be performed within the LLDN schedule. Furthermore we propose an extension of the star topology to collect data from two-hop sensor nodes. The proposed Retransmission Mode enables power savings in the sensor node of more than 33%, while reducing the packet loss by up to 50%. To reach this performance, an optimum spatial distribution is necessary, which is discussed in detail

Spectrum Policy Reform and the Next Frontier of Property Rights

The scarcity of wireless spectrum reflects a costly failure of regulation. In practice, large swaths of spectrum are vastly underused or used for low value activities, but the regulatory system prevents innovative users from gaining access to such spectrum through marketplace transactions. In calling for the propertyzing of swaths of spectrum as a replacement for the current command-and-control system, many scholars have wrongfully assumed the simplicity of how such a regime would work in practice. In short, many scholars suggest that spectrum property rights can easily borrow key principles from trespass law, reasoning that since property rights work well for land, they can work well for spectrum rights as well. But as we explain, spectrum is not the same as land, and a poorly designed property rights regime for spectrum might even be worse than the legacy model of spectrum regulation. This Article addresses three central questions that confront the design and implementation of property rights in spectrum. First, it suggests how policymakers must develop a set of rights and remedies around spectrum property rights that reflect the fact that radio signals defy boundaries and can propagate in unpredictable ways. In particular, if policymakers simply created rights in spectrum and enforced them like rights in land (i.e., with injunctions for trespass), they would invite strategic behavior: spectrum speculators would buy licenses for the sole purpose of suing other licensees when their transmission systems created interference outside the permissible boundary (i.e., act as spectrum trolls). Second, it rejects the suggestion that policymakers establish a unitary property right for spectrum, arguing that policymakers should zone the spectrum by establishing different levels of protection against interference (i.e., an ability to transmit signals with more latitude) in different frequency bands. Finally, this Article discusses what institutional strategy will best facilitate the development of the property right and its enforcement, concluding that an administrative agency - be it a new one or a reformed FCC - is better positioned than a court to develop and enforce the rules governing the use of spectrum so as to facilitate technological progress and prevent parties with antiquated equipment from objecting to more efficient uses of spectrum