Distributed Rate Assignments for Broadband CDMA Networks Tara Javidi Electrical & Computer Engineering University of California, San Diego.

Distributed Rate Assignments for Broadband CDMA Networks

Tara JavidiElectrical & Computer Engineering

University of California, San Diego

Multi-Cell Single Hop CDMAMotivation

• Wideband CDMA network with variable rates

• Mobiles communicate directly with the base station

• Base stations are connected directly to the traditional IP network

Rate Assignment Problem

• Limited by congestion constraints in the wired network

• Limited by interference constraints in the wireless network

• Objective: Maximize the global network utility in a distributed adaptive manner

Philosophically Related WorksWired Networks

[1] F. Kelly. Mathematical Modeling of the Internet. B. Enquist and W. Schmid, editors. Mathematics Unlimited – 2001 and Beyond, pages 685-702. Springer-Verlaq, 2001.[2] J. Mo and J. Walrand. Fair End-to-End Window-Based Congestion Control. IEEE/ACM Transactions on Networking, 8(5):555-567, 2000.[3]S.H. Low and D.E. Lapsley. Optimization Flow Control I: Basic Algorithm and Convergence. IEEE/ACM Transactions on Networking, 7(6):861-874, 1999.

Wireless Networks

[3] T. Javidi Distributed Rate Assignment in Multi-sector CDMA. Global Telecommunications Conference, 2003.[4] M. Chiang and R. Man. Jointly Optimal Congestion Control and Power Control in Wireless Multihop Networks. Global Telecommunications Conference, 2003.[5] X. Lin and N.B. Shroff. The Impact of Imperfect Scheduling on Cross-Layer Rate Control in Wireless Networks. INFOCOM 2005.

Cross-Layer Design: One-Shot

• One-shot and joint design of a rate assignment protocol (merging MAC and transport layers)

• Wireless and wired networks generate feedback based on their respective system constraints

• This feedback allows for dynamic adaptation to slowly varying network conditions

Iterative Methods and Convergence

If the Lagrange multipliers are computed using a gradient projection method, the rate assignment

becomes an iterative algorithm that uses feedback from the network

Theorem: Given an appropriate choice of step-size, the distributed system will converge to the

solution to the primal problem (cross-layer optimal)

Related Work

[1] X. Lin and N.B. Shroff. Joint rate control and scheduling in multi-hop wireless networks. CDC’04

[2] M. Neely, E. Modiano, and C. Li. Fairness and Optimal Stochastic Control for Heterogeneous Networks. Infocom’05

+ Due to structure of the problem, we get truly distributed solutions (little overhead comm)

- Such solutions require a fundamental re-doing of the protocol stack in general and transport layer in particular

Cross-Layer Design: Modular

• MAC and transport layer protocols are separate • MAC chooses rate using feedback from wireless• The transport layer chooses rate based on end-end

feedback following a dual controller• Can this be optimal in a cross-layer sense?

• If no wired core, the answer is yes:[1] A. Eryilmaz and R. Srikant. Fair Resource Allocation in Wireless Using

Queue-based Scheduling and Congestion Control

Outline

• Motivation and Overview• One-Shot Rate Assignments• Modular Rate Assignments

• The Problem with Dual Methods• Practical Implementation & Cross-Layer

Coordination

• Observations, Conclusions, & Future Work

Notation

• CDMA uplink•dynamic power and spreading gain control

(distributed)

• Network Parameters•M: number of nodes: N of them wireless •L: number of sectors J: number of (wired) links • Cj: capacity of link j ψij: routing function

•W: chip bandwidth gil: channel power gain• K: acceptable interference b(i): mobile i’s sector

• Node Variables•Pi: transmit power for user i•αi: transmit rate for user i at MAC•xi: transmit rate for user i at transport

One-Shot Problem Formulation

subject to

Wired LinkCapacity

ROT-ControlledFeasible Rate Vector

Bench Mark: “cross-layer optimal”

Iterative Methods and Convergence

If the Lagrange multipliers are computed using a gradient projection method, the rate assignment

becomes an iterative algorithm that uses feedback from the network

Theorem: Given an appropriate choice of step-size, the distributed system will converge to the

solution to the primal problem (cross-layer optimal)

subject to

Modular Problem Formulation

Coordinate MAC and Transport Layers xi=αi

αi

αi

Dual Controller Fails

Question: What happens when we try to use the dual controller/gradient projection?

Answer: The dual controller fails to converge to solution of the optimization problem

We need to maximize a function that is strictly concave over all the primal variables

Modular Utility Functions

if i is a wired user

if i is a wireless user

A New Modular Problem Formulation

subject to

Economic Interpretation of the Dual

Price forLink j

Price forSector l

Individual ProfitMaximization

(Transport Layer)

Cross-LayerCoordination Signal

Iterative Methods and Convergence

If the Lagrange multipliers are computed using a gradient projection method, the rate assignment

becomes an iterative algorithm that uses feedback from the network

Theorem: Given an appropriate choice of step-size, the distributed system will converge to the

solution to the primal problem (cross-layer optimal)

Wired Network Prices• Individual Lagrange multipliers are generated

using gradient projection

• This has a well known physical interpretation: queuing delay!

• Aggregate price qi can be interpreted as end-to-end queuing delay, which can be measured by each user

if

if

Wireless Network Prices

• Individual Lagrange multipliers are generated using

gradient projection

• We can construct a signaling mechanism under which the

aggregate price pi becomes closely related to forward link

SINR on the pilot signal

• Again, individual Lagrange multipliers are

generated using gradient projection

• These equations are similar to the equations

representing delay in queues!

if

if

if

if

Cross-Layer Coordination Signal

• Each equality is broken into two inequalities• For each inequality two multipliers computed

Cross Layer Coordination Signal

• Two imaginary queues whose associated delays are υi

+ and υi-

• Queue 1 is our MAC-layer buffer, and Queue 2 is our token bucket

• Token bucket is not used to regulate service rate, but to keep track of the mismatch between transport and MAC layer rates

The Role of the New Buffers

• Non-zero delay in the MAC-layer buffer corresponds to a wireless bottleneck• The “price” from the actual link prevents the transport layer from

out-running the MAC layer

• Non-zero delay in the token bucket corresponds to a wired bottleneck• The “price” from the token bucket prevents the MAC layer from

out-running the transport layer

• Generally only one of the queues is nonempty (i.e. only one of the constraints is active) at a time

• Without the use of a token bucket, the solution will converge but not to the desired equilibrium when wired bottle-neck

Transport Layer Profit Maximization

• Information about the interference levels in the wireless network is now incorporated into the end-to-end queuing delay (qi+υi

+) minus the token bucket delay (υi

-)

• Allows the transport layer to take interference levels into account without any major modification of current protocols• add the token bucket delay to the propagation delay

Mac Layer Profit Maximization

• Wireless sources now receive “credit” for long data queues (i.e. large νi

+) and are penalized for long token buckets (i.e. large νi

-)

• Prioritize wireless users based on their backlog • (De)Prioritize wireless users based on received

service so far

Simulations

Dynamical Behavior

• Convergence• Since we wish to interpret the Lagrange multipliers as delay, the

step size must be chosen as Δt/C• Convergence is dependent upon the step size being “small

enough,” hence the algorithm being run “fast enough”

• Nested Feedback Loops• Decoupling of the MAC and transport layer allows for the

corresponding feedback loops to be run at different time scales – aid in convergence and/or robustness?

• Interaction of three separate feedback loops (MAC, transport, and power control) plays a significant role in dynamic situations

• Choice of parameters σ and K play an important role

Future Work

• Provide a stability analysis• Use the concept of Markov chain stability for queue

lengths

• Understand the impact of realistic arrival statistics on the system• How does statistical multiplexing impact the transient

behavior of the system?

• Determine whether these results can be extended to other MAC protocols• Does the addition of the MAC-layer queue and token

bucket provide sufficient coordination for other MAC schemes?