Junjik Bae

Sequential Bandwidth and Power Auctions for Distributed Spectrum Sharing

We study a sequential auction for sharing a wireless resource (bandwidth or power) among competing transmitters. The resource is assumed to be managed by a spectrum broker (auctioneer), who collects bids and allocates discrete units of the resource via a sequential second-price auction. It is well known that a second price auction for a single indivisible good has an efficient dominant strategy equilibrium; this is no longer the case when multiple units of a homogeneous good are sold in repeated iterations. For two users with full information, we show that such an auction has a unique equilibrium allocation. The worst-case efficiency of this allocation is characterized under the following cases: (i) both bidders have a concave valuation for the spectrum resource, and (ii) one bidder has a concave valuation and the other bidder has a convex valuation (e.g., for the other useriquests power). Although the worst-case efficiency loss can be significant, numerical results are presented, which show that for randomly placed transmitter-receiver pairs with rate utility functions, the sequential second-price auction typically achieves the efficient allocation. For more than two users it is shown that this mechanism always has a pure strategy equilibrium, but in general there may be multiple equilibria. We give a constructive procedure for finding one equilibrium; numerical results show that when all users have concave valuations the efficiency loss decreases with an increase in the number of users.

On the Uplink Capacity of an 802.16j System

A multihop relay extension for IEEE 802.16e systems is the subject of ongoing standardization activities within the IEEE 802.16j Task Group. The emerging IEEE 802.16J standard enhances the 802.16e PHY and MAC to enable support of multihop routes between a mobile station and a base station through intermediate relay stations. Since it is believed that the capacity of a single-hop 802.16e system is uplink-limited, this paper evaluates potential capacity gains attained with the relay enhancement of the 802.16e uplink. The capacity here denotes either cumulative throughput for data traffic or total number of users for voice traffic supported, under certain system-specific constrains detailed below. We first develop a simplified one-dimensional model of a relay-enhanced 802.16e system and estimate the capacity gains via analysis and numerical optimization. Motivated by the capacity gains predicted by this first-order analysis, simulation results obtained from a full two-dimensional simulator modeling a realistic deployment of a relay-enhanced system are then presented. Based on the simulation results, a parametric analysis of relay deployment cost vs. the capacity gain is also presented.

Spectrum Markets for Wireless Services

It has been widely recognized that the current under-utilization of spectrum across many bands could be alleviated through the application of spectrum markets. So far, discussions of market mechanisms for spectrum allocations have focused primarily on secondary markets, which are managed by licensees. Here we explore the consequences of lifting current restrictions on allocations and ownership, and allowing more extensive markets for allocating spectrum across locations, times, and diverse sets of applications (e.g., broadcast, cellular, broadband data, emergency, etc). To motivate our discussion we first estimate the achievable rate per user that could be provided by sharing a large portion of the spectrum suitable for cellular and broadcast types of services. Our results suggest that in general the demand for spectrum may exceed supply implying that market mechanisms are needed to avoid a tragedy of the commons (i.e., associated with an alternative commons model). We then discuss a two- tier spectrum market structure for wireless services in which licenses for spectrum assets at particular locations are traded as commodities. Spectrum owners can choose to rent or lease their spectrum assets via spot markets at particular locations. Such an approach may lower barriers to entry into the wireless services market thereby facilitating competition and the introduction of new services.

High quality type II InAs/GaSb superlattices with cutoff wavelength ∼3.7 μm using interface engineering

We report the most recent advance in the area of type II InAs/GaSb superlattices that have cutoff wavelength of ∼3.7 μm. With GaxIn1−x type interface engineering techniques, the mismatch between the superlattices and the GaSb (001) substrate has been reduced to <0.1%. There is no evidence of dislocations using the best examination tools of x-ray, atomic force microscopy, and transmission electron microscopy. The full width half maximum of the photoluminescence peak at 11 K was ∼4.5 meV using an Ar+ ion laser (514 nm) at fluent power of 140 mW. The integrated photoluminescence intensity was linearly dependent on the fluent laser power from 2.2 to 140 mW at 11 K. The temperature-dependent photoluminescence measurement revealed a characteristic temperature of one T1=245 K at sample temperatures below 160 K with fluent power of 70 mW, and T1=203 K for sample temperatures above 180 K with fluent power of 70 and 420 mW.

Type II InAs/GaSb superlattices for high-performance photodiodes and FPAs

The authors report the most recent progress in Type II InAs/GaSb superlattice materials and photovoltaic detectors developed for focal plane array applications with a cutoff wavelength of ~8 μm. No turn-on of tunneling current was observed even at a reverse bias of -3 V for a 3 μm thick p-i-n photodiodes. The thermally-limited zero bias detectivity under 300 K 2 π FOV was 2~3×1011 cm•Hz1/2/W at liquid nitrogen temperature, with a current responsivity of 2~3 A/W and a mean quantum efficiency of ~50%. Initial passivation using SiO2 has shown to decrease the dark current by ~30% at a reverse bias of -1 V. The same detector structure was used for focal plane arrays with silicon readout integrated circuit. Concept proof of imaging was demonstrated with a format of 256×256 at liquid nitrogen temperature.

On the efficiency of sequential auctions for spectrum sharing

In previous work we have studied the use of sequential second price auctions for sharing a wireless resource, such as bandwidth or power. The resource is assumed to be managed by a spectrum broker (auctioneer), who collects bids and allocates discrete units of the resource. It is well known that a second price auction for a single indivisible good has an efficient dominant strategy equilibrium; this is no longer the case when multiple units of a homogeneous good are sold in repeated iterations. Previous work attempted to bound this inefficiency loss for two users with non-increasing marginal valuations and full information. This work was based on studying a setting in which one agents valuation for each resource unit is strictly larger than any of the other agents valuations and assuming a certain property of the price paid by such a dominant user in any sub-game. Using this assumption it was shown that the worst-case efficiency loss was no more than e−1. However, here we show that this assumption is not satisfied for all non-increasing marginals with this dominance property. In spite of this, we show that it is always true for the worst-case marginals for any number of goods and so the worst-case efficiency loss for any non-increasing marginal valuations is still bounded by e−1

Efficiency bounds for sequential resource allocation auctions

Market-based mechanisms such as auctions have been widely considered for various network resource allocation problems. We consider such a mechanism motivated by dynamic spectrum sharing applications. In this model multiple homogeneous units of a given resource are to be allocated to two agents. We study a sequential second price auction for allocating these resource units. It is well known that such auctions can have inefficient equilibria. For the case of two bidders, we show that the value of the allocation obtained in the unique subgame perfect equilibrium is at least 1 - e-1 of the value of the efficient allocation. Furthermore, we show that this bound is asymptotically tight as the number of goods increases.

Incentives and Resource Sharing in Spectrum Commons

It has been suggested that light regulation in the form of etiquette protocols, device design and bargaining amongst users will suffice to mitigate a tragedy of the commons in unlicensed spectrum. In this paper we propose a game theoretic model to examine this claim. In this game, each user decides whether or not to set up an access point, which operates on a particular (single) band. The effect of regulation is modeled in reduced form through transfers. A user who sets up an access point, provides payments to each neighbor who does not and suffers a disutility depending on the number of interfering access points. A user who does not set up an access point, receives payments from each neighbor that does. For a suitable model of payoffs, the game is a potential game and best response updates converge to a Nash equilibrium of the game. For any interference parameters, there is a suitable transfer resulting in a Nash equilibrium which is efficient. However, all Nash equilibria may not be efficient.

Power Allocation, Rate, and Coverage for Relay-Assisted Downlink Data Transmission

The coverage of a base station terminal (BST) in a cellular network can generally be increased through the use of a relay node within the cell boundary. We consider the downlink for a single, one-dimensional cell with a relay node, or access point (AP), which serves a separate set of (non-cellular) users (e.g., corresponding to a WiFi system). The BST and AP jointly allocate available power across users and the BST-AP link to maximize the sum data rate across all cellular and AP users. Two relay schemes are considered: (i) the information flows to the cellular users served by the relay are jointly encoded and transmitted from the BST to the AP; and (ii) the preceding information flows are transmitted in parallel from the BST to the AP. We give an upper bound on the increase in rate provided by the AP, which depends on the relative powers and bandwidths available to the BST and AP. Although the increase in total rate provided by sharing AP resources is typically modest, it can provide a more equitable rate distribution across cellular users, and extend the coverage of the BST.

Efficiency of Sequential Bandwidth and Power Auctions With Rate Utilities

We study a sequential second-price auction for allocating wireless resources between two non-cooperative users. This mechanism requires relatively little computation and information exchange among agents, but does not always achieve an efficient allocation. This is a continuation of previous work in which the worst-case efficiency is evaluated, assuming each user has full knowledge of the other users utility function. Here we assume that the users are randomly placed within a region, and evaluate the associated efficiency via simulation. Sequential auctions for bandwidth (with fixed power) and for power (with fixed bandwidth) are considered, where each user utility is the achievable rate, and interference is treated as background noise. Our results show that the sequential auction typically achieves the efficient (utility-maximizing) allocation. We also relate observed improvements in the worst-case efficiency to constraints on the size of the marginal utilities associated with each resource.