Cross-layer Design for Wireless Networks
Sanjay Shakkottai, Theodore S. Rappaport and Peter C. Karlsson
June 23, 2003
As the cellular and PCS world collides with Wireless LANs and Internet-based packet data, new networking approaches will support the integration of voice and data on the composite infrastructure of cellular base stations and Ethernet-based wireless access points. This paper highlights some of the past
accomplishments and promising research avenues for an important topic in the creation of future wireless
networks. In this paper, we address the issue of cross-layer networking, where the physical and MAC layer
knowledge of the wireless medium is shared with higher layers, in order to provide efficient methods of
allocating network resources and applications over the Internet. In essence, future networks will need to
provide ”impedance matching” of the instantaneous radio channel conditions and capacity needs with the
traffic and congestion conditions found over the packet-based world of the Internet. Further, such matching will need to be coordinated with a wide range of particular applications and user expectations, making
the topic of cross-layer networking an increasingly important one for the evolving wireless build-out.
There continues to be rapid adoption of wireless technology, and when coupled with the explosive growth of
the Internet, it is clear that there will be increasing demand for wireless data services . Traffic on future
wireless networks is expected to be a mix of real-time traffic such as voice, multimedia teleconferencing, and
games, and data-traffic such as WWW browsing, messaging and file transfers. All of these applications will
require widely varying and very diverse quality of service (QoS) guarantees for the different types of offered
traffic, and we are now in the early days of this eventual amalgamation. Various mechanisms have been
proposed and recently deployed to support data traffic over wireless media. This has ranged from Wireless
Local Area Networks (WLANs), mainly based on the IEEE 802.11b or HiperLAN standards, to wireless wide
area networks (WWANs) where data services are supported in the 2.5G and 3G system versions.
In this paper, we explore some key issues which will likely impact future cross-layer network design.
We begin with an overview of data services over networks (Section 2). In Section 3, we describe some
Shakkottai and Rappaport are faculty in the Wireless Networking and Communications Group (WNCG), Department of Electrical and Computer Engineering, The University of Texas at Austin, [email protected], [email protected] Peter C.
Karlsson is with the Wireless Solutions Group at Telia Research AB, Sweden, [email protected]
fundamental differentiators between wireline and wireless networks. Then, in Section 4, we consider the
gains that can be achieved by means of a cross-layer approach for wireless network design, where physical
layer information is passed to the higher layers, and discuss some of the standardization efforts in Section 5
that are beginning to move toward this integrated cross-layer approach. We finally conclude with a discussion
of future research challenges.
2 Network Service Types
The Internet today consists of thousands of access networks, which vary in scale from large wireline access
networks, such as campus wide area networks or Internet Service Providers, supporting tens of thousands of
users, to smaller wireless access networks supporting tens to hundreds of users. These access networks are
interconnected by core networks (such as AT&T, WorldCom, or Sprint backbone networks) which support
hundreds of millions of users. All of these networks primarily offer two types of services: guaranteed
service and best effort service.
In guaranteed service, the network provides some sort of service guarantee to individual users or groups
of users. These guarantees are often in the form of ensuring that the throughput for a group of users is greater
than some minimum value or that the delay experienced is smaller than some threshold. Often times, the
guarantee is offered in a statistical sense, e.g. providing a particular data rate x% of the time.
In best effort service, the network makes no promises. This service is typically used by elastic traffic. Elastic traffic consists of traffic where users do not necessarily have any minimum requirements, but
would like to get as much data through to their respective destinations as quickly as possible. Individual user
data flows react to congestion in the network and adapt their transmission rate with the aim of minimizing
congestion. Email service is often provided on a best effort basis.
3 Differences between Wireline and Wireless Networks
Both wireless and wireline networks need to support the different network data service types described in the
previous section. The focus of this paper is on supporting such services over wireless networks, and the gains
that can be accrued by cross-layer techniques which do away with the firm boundary that currently exists
between the PHY and MAC layers, and the higher layers of the Network protocol stack. Before studying
mechanisms by which data services can be supported over wireless networks, we briefly describe the characteristics of wireless systems. Based on limited frequency allocations and channel considerations, wireless
networks have peculiarities which distinguish them from conventional wireline networks.
(i) The wireless channel varies over time and space and has short-term (or small-scale) memory due to
multipath. These variations are caused either due to motion of the wireless device, or due to changes in
the surrounding physical environment, and lead to detector errors. This causes bursts of errors to occur
during which packets cannot be successfully transmitted on the link. Fast channel variations due to
fading are such that states of different channels can asynchronously switch from “good” to “bad” within
a few milliseconds and vice-versa. Further, very strong forward error correction codes (i.e. very low
rates) cannot be used to eliminate errors because this technique leads to reduced spectral efficiency.
(ii) In addition to small-scale channel variations, there is also spatio-temporal variations on a much greater
time-scale . Large-scale channel variation means that the average channel state condition depends
on user locations and interference levels. Thus, due to small-scale and large-scale changes in the channel, some users may inherently demand more channel access time than others based on their location
or mobile velocity, even if their data rate requirement is the same as or even less than other users.
In Section 4, we discuss the implications of these effects for supporting data services over wireless
4 Cross-layer Design for Supporting Data Services over Wireless Networks
In this section, we explore the gains that can be achieved by means of a cross-layer approach, where physical
layer information is passed to the higher layers. We first consider supporting TCP traffic over wireless links,
and then consider supporting data services in a multi-user wireless network. We finally discuss deployment
tools and practical issues facing the build-out of access points, based on network throughput requirements.
4.1 TCP over Wireless Links
The prevalent protocol for data transport over the Internet is Transmission Control Protocol (TCP). TCP is
a connection-oriented, end-to-end data transfer protocol. It has two objectives, namely (i) reliable end-toend transmission of data, achieved by error or loss detection and re-transmission, and (ii) congestion control
over the Internet. Routers in the network indicate congestion by dropping packets, which in turn causes the
source to adaptively decrease its sending rate. Future deployment of TCP is expected to include the Explicit
Congestion Notification (ECN) mechanism  which is used to notify the receiver whenever congestion
occurs in the network. This mechanism works in the following manner: included in a TCP packet’s header
is the ECN bit which is set to zero by the source. If the router detects congestion, it will set the ECN bit to
one, and the packet is said to be marked. The marked packet eventually reaches the destination, which in turn
informs the source about the value of the mark (i.e., the ECN bit value). The source adapts its transmission
rate depending on the value of the mark.
The current deployment of the TCP protocol interprets all losses as being congestion related. Whenever
losses occur over a wireless channel, the TCP source reacts to this as though it was due to congestion and thus
decreases the packet transmission rate, causing loss in network throughput. A solution that has been proposed
to mitigate this problem is to “smooth” the channel by suitable coding and link layer ARQ at a faster timescale than that of the TCP control loop  (additional references available in ). so that the wireless link
ideally is perceived as a constant channel, but with lower capacity. However, in practice, there is still the
problem that the TCP sender may not be fully shielded from wireless link losses. This can lead to the TCP
congestion control mechanism reacting to packet losses thus resulting in redundant retransmissions and loss
However, once ECN-enabled TCP is deployed, where the ECN bit can be used to mark packets to indicate
congestion, there is a means of differentiating between congestion related loss and wireless channel related
loss. Thus, the channel need not be smoothed because the ECN mechanism provides a means of explicitly
indicating congestion. In , it has been analytically shown that in a single user environment, if packets
are marked based solely on congestion information, there is no significant degradation of TCP performance
due to the time varying nature of the wireless channel. A similar idea based on explicit loss notification has
been discussed in , where simulations indicate improved throughput performance. Such an approach is an
example where a cross-layer view of physical layer information (channel conditions) is used at the network
layer to significantly improve network-layer throughput performance.
4.2 Data over Wireless in a Multi-user Context
We now discuss various issues related to supporting data services over cellular wireless networks. We illustrate
how channel-state dependent techniques (cross-layer methods) can lead to improved network throughput, and
survey some of the current related research.
Consider a conventional cellular system with a fixed base-station and a number of mobile users. Data
flows (packets) arrive from the wired Internet to the cell base station and are destined to the mobile users, with
the packets for each user being queued temporarily at the base station (a separate queue is maintained for each
user). The objective of the base station is to schedule these packets to various mobiles in a timely manner. In
this section, we restrict ourselves to just considering the forward-link problem, where the direction of the data
flow is from the base-station to the mobile user.
The earliest method used by the cellular industry to send data to a mobile user on a cellular network consisted of sending data over a circuit-switched voice channel by means of a modem (usually over
a FDMA/TDMA network). As data traffic is typically bursty, this method had the disadvantage that when a
user is not transmitting data, the bandwidth on the voice channel is wasted by the dedicated voice channel.
A more efficient way to use cellular spectrum is to dedicate some bandwidth for data transport and
allocate this bandwidth in a dynamic manner among various data users. For instance, time could be divided
into fixed size time-slots and users could be allocated time-slots in a dynamic manner. The simplest scheduling
algorithm is the round robin mechanism, where users are periodically allocated slots irrespective of whether
there is data to be sent to a particular mobile user. Note that this simple TDM scheme leads to wasted
bandwidth just as in the previous case. Further, it suffers from a more subtle problem, namely, this approach
is independent of the channel state (a channel state independent scheduling mechanism).
The 3G wireless systems exploit a built-in mechanism where the forward-link channel state information
for each user is fed back to the base-station. Examples of such systems include High Data Rate (HDR)
versions of CDMA2000  and enhanced general packet radio service (EGPRS) in the EDGE extension of
GSM . These proposals are essentially time-division overlays over the underlying physical-layer protocol
to enable data traffic, and have the flexibility of allowing smart scheduling mechanisms to improve efficiency
based on instantaneous user demand and channel states for each user.
In CDMA2000 HDR, the channel state is periodically measured by the user and fed back to the basestation once every 1.667 msec. As can be shown easily by computing the Doppler frequency of a mobile user
at 2GHz, this slot size is short enough so that each user’s channel quality stays approximately constant within
one time-slot. In each time-slot, one user is scheduled for transmission. Each user constantly reports to the
base station its “instantaneous” channel capacity, i.e., the rate at which data can be transmitted if this user
is scheduled for transmission. In an HDR system, a “good” scheduling algorithm should take advantage of
channel variations by giving some form of priority to users with instantaneously better channels.
Multiuser Diversity Gain: A Simple Illustration
We illustrate the significant gains due to channel state dependent scheduling algorithms by means of a simple
example. Consider a wireless system consisting of three users as in Figure 1. For this example, we consider
access time to be slotted, and the channels to be constant over a time-slot. We assume that the channels are
X 1 (t) ON/OFF
X 2(t) ON/OFF
X 3 (t) ON/OFF
Figure 1: Packet data flows arrive from the Internet to the base-station. The data is destined to mobile users,
and are temporarily buffered at the base-station. At each time t the scheduler transmits to one of the mobile
users based on the channel state X1 t X2 t X3 t with each component taking one of two values: ON or
either ON or OFF, equally likely, and the channels being independent of each user. Thus, in this system, there
are eight possible (instantaneous) channel states for the three independent users, ranging from (ON,ON,ON)
When a user’s channel is ON, one packet can be transmitted successfully to the mobile user during the
time-slot. The system is assumed to be a TDM system; thus, the base-station can transmit to only one user on
each time-slot. The associated scheduling problem is to decide which user is allowed access to the channel
during each particular time-slot.
A naive scheduling rule would be to employ the well-known round-robin mechanism. In such a scheme,
the users periodically are given access to the channel, with each user getting 1 3 of the slots over time. As the
channel of each user is equally likely to be ON or OFF in each time-slot, it follows that over time, on average,
each user will get a data rate of 1 6 packets/slot.
On the other hand, suppose that the base-station uses knowledge of the instantaneous channel state. Then,
a simple policy would be to schedule and transmit to a user whose channel is in the ON state. If more that
one user’s channel is in the ON state, then, the scheduler could pick a user randomly (equally likely) among
those users whose channel are ON, and send data to the selected user. This simple example assumes that all
the users have identical traffic demands. For the case where some users have greater needs than others, such
users would be assigned channel access with greater likelihood.
We observe that this policy ensures that no data is sent by the base-station if and only if all users’
channels are OFF (which occurs on average, only 1 8 of the time). Thus, the total data rate achieved by this
state dependent rule is 1 1 8 7 8 packets/slot. As this rule is symmetric across users, it follows that on
average, the data rate per user is 7 24 packets/slot, which is almost twice the throughput as the round-robin
scheme which provided 1 6 packets/slot. In addition, the base station does not radiate power during bad
channel conditions, thereby decreasing interference levels in the wireless network.
This gain achieved due to channel-state dependent scheduling is called the multi-user diversity gain
[8, 9]. This example illustrates the significance of multi-user diversity gain in network scheduling. However,
a central question is how to design on-line algorithms which achieve this gain, while also supporting diverse
quality of service requirements for various users for realistic channel scenarios. While this problem is not
yet completely answered, there has been extensive research on various aspects of this problem. Some recent
references include [10, 9, 11, 12, 13, 14, 15, 16]. Additional references are available in a longer version of
this paper .
Multiuser Gain with QoS
The previous sections illustrate gains that can be accrued based on cross-layer methods. In this section, we
discuss some of the important issues related to multiuser gain and briefly survey related current literature. In
particular, some important issues that will need to be addressed are:
(i) How can multiple real-time data users be supported simultaneously with good quality of service (QoS)
for all real-time users, namely, with packet delays not exceeding given thresholds with high probability?
(ii) How can a mixture of real-time and non-real-time users be supported simultaneously with real-time
users receiving their desired QoS and non-real-time users receiving the maximum possible throughput
without compromising the QoS requirements of real-time users?
(iii) How can bandwidth be fairly allocated among various users, especially when some users inherently
demand more channel access time than others, even if their data rate requirement is the same, or less
Though these questions have not been answered fully, there has been extensive research on various
aspects of the above problems. Below, we discuss some of the available results. Additional discussion is
available in a longer version of this paper .
In , optimal scheduling for a wireless system consisting of N queues and a single server is studied.
The arrival processes to each of the queues are assumed to be independent and identically distributed (i.i.d.)
Bernoulli processes. The channel perceived by each queue is also assumed to be an i.i.d. ON-OFF Bernoulli
process. The authors show that the policy which minimizes the total number of packets in the system, in a
stochastic ordering sense, is the one which serves the user whose channel is ON and has the longest queue
The authors in  were among the first to study wireless scheduling in a multi-user context, and explicitly characterize the multi-user diversity gain. In , the author proposed a scheduling rule called the
proportionally fair rule, which explicitly makes use of the channel state information and also provides fair
allocation of bandwidth across users. In [12, 17], the authors show that an online algorithm (the Exponential
rule) can be designed which can stabilize the user queues without explicit knowledge of the arrival rates or
channel statistics, and also discuss QoS properties of such a rule.
In , the authors consider opportunistic beam-forming, and multi-user scheduling based on the proportional fair rule , and show that significant gains can be accrued due to multi-user diversity. In ,
researchers consider a utility based approach which address fairness with multi-user gains. There has been
recent research on adaptively modifying the channel access time for individual users on an opportunistic basis
depending on the “goodness” of user channels in wireless LANs .
Supporting reverse link data services imposes additional constraints due to the distributed nature of
mobile users. Some recent work on supporting data services over the reverse link in a distributed manner
is available in .
4.3 Deployment of Wireless Network Access Points
In today’s cellular/PCS networks, site deployment is conducted through computer-aided modeling of propagation characteristics, as well as the anticipated user densities and the corresponding RF interference levels
. Except for some large public WLAN systems, today’s WLAN deployments are made by IT professionals
who are not accustomed to RF/interference issues. For efficient build-out for WLANs and 3G networks, site
specific methods of determining locations of access points and in-situ throughput performance measurement
of wireless modems offer promise [19, 20]. However, with so many different user classes and data rate requirements, future deployment and layout tools will need to “convert” from a wireless system design mindset
with a propagation emphasis, to a wireless network design mindset with a user throughput or QoS emphasis.
Early work shows that there are some first-order effects that relate well-known wireless propagation parameters, Signal to Noise Ratio (SNR) and Signal to Interference Ratio (SIR) to end-user network parameters
(throughput, delay), independent of modem manufacturer or user classes.
Consider a multi user network based on 802.11b access points. The upshot of Figures 2 and 3 (see 
Figure 2: SIR vs. throughput for 3COM WLAN 802.11b modem in an indoor environment. Throughput
was measured on a round-trip basis between two nodes, using LANFielder to generate random messages with
for more details) is that with knowledge of physical layer parameters, such as RSSI (Received Signal Strength
Indication) and CIR (Carrier to Interference Ratio), it is possible to map these to network layer parameters,
such as throughput.
This holds promise for network deployment CAD software tools that IT professionals can use without
knowledge of specific propagation issues, while incorporating such vital data in their deployment strategy.
SitePlanner and LANfielder are examples of commercial deployment and measurement tools that incorporate
a network-centric approach to wireless design .
Another key issue facing large-scale deployment of future wireless networks in and around buildings is
the need to track the location and on-going maintenance issues associated with the installed wireless equipment. Often, installers find it most desirable to hide the location of access points and antennas within buildings, primarily for aesthetic reasons, thereby making it difficult to find such equipment when providing upgrades or repairs. Unlike the early cellular telephone industry, where tall towers were easy to identify by sight,
the wireless networks of the future will be hidden – “embedded” within buildings and campuses, much like
building wiring, itself. There are products available today (such as those by ) that allow designers and
Figure 3: SNR vs. throughput for 3COM WLAN 802.11b modem in an indoor environment. Throughput
was measured on a round-trip basis between two nodes, using LANFielder to generate random messages with
managers of wireless networks to handle all engineering, maintenance, and cost accounting details using simple Computer Aided Design software. This approach enables a wide range of staff, such as building owners,
integrators, and vendors, to electronically share “as-built” design and measurement information that includes
visual details of the location of network infrastructure within buildings. This same data may be easily ported
to hand-held devices for use in the field by maintenance personnel.
5 Standardization Status for Cross-layer Design and Interoperability
As described earlier, wireless networks can be implemented as wireless LANs or cellular/WWANs. Coverage,
mobility support, and throughput differ significantly between these network architectures, and there is no
single system that currently stands out as a single best solution to mobile and nomadic users. The system
performance of future networks will be enhanced by cross-layer design between PHY, MAC and higher layer
protocols, as discussed in earlier sections. However, for a combination of services and applications demanded
by users in a variety of environments, each wireless network can provide an important piece in the large
mobile multimedia jigsaw puzzle. Standardization efforts are in progress to integrate various architectures.
The important co-design of physical layer, MAC and higher layers have been taken into account in
some of the latest standardization issues. As discussed in Section 4.2, 3G standards such as CDMA2000
have been designed with cross-layer issues in mind. The Data Link Control (DLC) and physical layer of
BRAN HiperLAN2 have been designed for high throughput, low latency and QoS support . The 2 msec
MAC frame with logical frame control channel, radio link control mechanisms, and scheduling provides a
layered resource management. In 3GPP, the enhancement High Speed Downlink Packet Access (HSDPA)
with hybrid ARQ (Automatic Repeat reQuest) and scheduling at the base-station have been introduced for
reduced latency. The important topic of cross-layer design has recently been considered in the Study Group on
Mobile Broadband Wireless Access Networks (MBWA) within IEEE, with the goal of improving throughput
and reduced latency both in downlink and uplink.
5.1 Interoperability between WLANs and cellular WWANs
Interoperability between standards of distinct networks is crucial both for user adoption and operator management in a wide scale deployment of products and services over wireless networks. At the time of this writing,
dozens of specialized applications and network protocols are being designed for dual use on IEEE 802.11a/b
and cellular/PCS networks . End user equipment for multi-mode terminals, such as PDAs, web phones and
smart-cards, are emerging on the market.
Successful integration of existing and emerging wireless systems is a demanding task. Inherently, several
standardization and regulatory bodies need to be involved, and the process is made difficult by the status of
each specification process. A first WLAN/WWAN standardization initiative was taken by the ETSI BRAN
project, which started the UMTS-HiperLAN2 interworking specification work. The scope has been generalized to include all WLAN standards with a loose coupling reference architecture based on the Internet
Engineering Task Force (IETF) protocols. The standardization work was adopted by 3GPP, where a phased
approach based on six scenarios ranging from common billing and access control toward seamless services
has been defined for future releases. A new Wireless Interworking Group (WIG) was established in 2002 as
a joint effort from the WLAN Community including ETSI BRAN, IEEE 802.11 and MMAC HiSWANa. The
scope of WIG is to solve the interworking issues by defining an interface behind the WLAN AP toward the
IP core network.
6 Conclusion and Future Research
This paper has attempted to provide an overview of the cross-layer paradigm shift that is beginning to take
place as wireless communications evolves from a circuit-switched infrastructure to a packet-based infrastructure. The advantages of cross-layer networking appear to be real, and will be increasingly important as
capacities offered through the wireless LAN interface approach the level of capacity that can be handled over
the Internet backbone. Based on our observations, it appears that the following research areas are important
for successful build-out of future broadband wireless networks. By no means, however, do we wish to suggest
that these are necessarily the best problems to solve, nor is this listing meant to be exhaustive, but it does
provide one viewpoint of the technical challenges and emerging research areas that will lead to new network
implementations that support the amalgamation of user services and QoS requirements.
(i) Fundamental properties of multiuser diversity: It has been shown (see Section 4.2) that multi-user
diversity gains can substantially improve wireless network throughput. However, given different types
of QoS constraints, how does the diversity gain grow with the number of users? The answer to this
question is of great relevance from a practical perspective. The associated design problem would be to
come up with good algorithms which make use of multiuser diversity gain. Finally, most of the studies
so far are confined to a single-cell scenario. Extending these studies to the multi-cell case would be of
(ii) Modeling network performance: Understanding the properties of mixed traffic and service types over
wireless networks in practical propagation environments will be crucial for deploying and analyzing
the performance characteristics of future scheduling approaches and protocols. Early progress has been
made (see Section 4.3) but much more work remains as the industry converts from a circuit switched
approach to a packet network. Creating models that translate actual channel characteristics, such as
path loss and interference, into useful models at the network layer and above, while benchmarking such
models with actual network field data will enable scheduling and traffic techniques to be developed
accurately and expeditiously. Adaptive control of wireless networks, on a building-by-building basis,
may also be needed to ensure proper scheduling and utilization of capacity as more access points and
users are added in unlicensed spectrum.
(iii) Design for multi-carrier systems: Most down-link scheduling algorithms today (for 3G wireless systems) are for a single-carrier (such as a shared time-division) system. Emerging WLANs and fourth
generation wireless systems are expected to be based on a multi-carrier scheme (OFDM) with hundreds
of carriers. In this scheduling and cross-layer networking context, an interesting area to explore is the
design of good algorithms with low complexity.
 T. S. Rappaport, A. Annamalai, R. M. Buehrer, and W. H. Tranter, “Wireless communications: Past events and a
future perspective,” IEEE Communications Magazine, vol. 40, pp. 148–161, May 2002.
 T. Rappaport, Wireless Communications: Principles and Practice. Upper Saddle River, NJ: Prentice Hall, 2002.
 S. Floyd, “TCP and explicit congestion notification,” ACM Computer Communication Review, vol. 24, pp. 10–23,
 H. Balakrishnan, V. Padmanabhan, S. Seshan, and R. H. Katz, “A comparison of mechanisms for improving TCP
performance over wireless links,” IEEE/ACM Transactions on Networking, December 1997.
 S. Shakkottai, T. S. Rappaport, and P. C. Karlsson, “Cross-layer design for wireless networks.” WNCG Technical Report TR-2003-04-00001, Wireless Networking and Communications Group, Department of Electrical and
Computer Engineering, The University of Texas at Austin. Available for download at http://www.wncg.org.
 S. Kunniyur and R. Srikant, “End-to-end congestion control: utility functions, random losses and ECN marks,” in
Proceedings of IEEE Infocom, vol. 3, (Tel Aviv, Israel), pp. 1323–1332, March 2000.
 P. Bender, P. Black, M. Grob, R. Padovani, N. Sindhushayana, and A. Viterbi, “CDMA/HDR: A bandwidth efficient
high speed wireless data service for nomadic users,” IEEE Communications Magazine, pp. 70–77, July 2000.
 R. Knopp and P. Humblet, “Information capacity and power control in single-cell multiuser communications,” in
Proceedings of the ICC, (Seattle, WA), June 1995.
 D. Tse, “Forward link multiuser diversity through proportional fair scheduling,” August 1999. Presentation at Bell
 L. Tassiulas and A. Ephremides, “Dynamic server allocation to parallel queues with randomly varying connectivity,” IEEE Transactions on Information Theory, vol. 39, pp. 466–478, March 1993.
 M. Andrews, K. Kumaran, K. Ramanan, A. L. Stolyar, R. Vijayakumar, and P. Whiting, “CDMA data QoS scheduling on the forward link with variable channel conditions,” April 2000. Bell Laboratories Tech. Rep.
 S. Shakkottai and A. Stolyar, “Scheduling for multiple flows sharing a time-varying channel: The exponential
rule,” American Mathematical Society Translations, Series 2, A volume in memory of F. Karpelevich, Yu. M.
Suhov, Editor, vol. 207, 2002.
 A. Eryilmaz, R. Srikant, and J. Perkins, “Stable scheduling policies for broadcast channels,” in Proceedings of
the IEEE Symposium on Information Theory, (Lausanne, Switzerland), July 2002. An earlier version appeared
in Modelling and Design of Wireless Networks, Proceedings of SPIE, E. K. P. Chong (editor), vol. 4531, pages
 X. Liu, E. K. P. Chong, and N. B. Shroff, “A framework for opportunistic scheduling in wireless networks,” To
appear in the Computer Networks Journal, 2002.
 M. J. Neely, E. Modiano, and C. E. Rohrs, “Power and server allocation in a multi-beam satellite with time varying
channels,” in Proceedings of IEEE Infocom 2002, (New York, NY), June 2002.
 B. Sadeghi, V. Kanodia, A. Sabharwal, and E. Knightly, “Opportunistic media access for multirate ad hoc networks,” in Proceedings of ACM MOBICOM 2002, (Atlanta, GA), September 2002.
 S. Shakkottai, R. Srikant, and A. L. Stolyar, “Pathwise optimality and state space collapse for the exponential rule,”
in Proceedings of IEEE Symp. on Info. Theory (ISIT), (Lausanne, Switzerland), July 2002.
 P. Viswanath, D. Tse, and R. Laroia, “Opportunistic beamforming using dumb antennas,” IEEE Transactions on
Information Theory, vol. 48, pp. 1277–1294, June 2002.
 B. Henty and T. S. Rappaport, “Throughput measurements and empirical prediction models for IEEE 802.11b
wireless LAN (WLAN) installations,” Tech. Rep. MPRG 01-08, Dept. of Electrical and Computer Engineering,
Virginia Tech, Blacksburg, VA, August 2001. http://scholar.lib.vt.edu/theses/available/etd-08142001-172523/.
 “Siteplanner, Wireless Valley Communications inc..”
6499006, 6493679, 6442507, and 6317599.
http://www.wirelessvalley.com. Also see US Patents
 A. Doufexi, S. Armour, P. Karlsson, M. Butler, A. Nix, D. Bull, and J. McGeehan, “A comparison of the HIPERLAN/2 and IEEE 802.11a wireless LAN standards,” IEEE Communications Magazine, vol. 40, pp. 172–180, May