Optimal Power Control and Joint SourceChannel Coding for Delay Constrained Traffic

1
Optimal Power Control and Joint Source-Channel
Coding for Delay Constrained Traffic
Tim Holliday Depts of MSE and E.E. Stanford
University thollida_at_stanford.edu
Andrea Goldsmith Dept of E.E. Stanford
University andrea_at_ee.stanford.edu
Peter Glynn Dept of MSE Stanford
University glynn_at_stanford.edu
IEEE ICC 2002 New York, NY
2
Motivation

• Next Generation wireless systems will provide
  many new data services
• Voice over IP, Streaming Audio/Video, etc.
• These new services require tight constraints on
  system performance
• Delay, Probability of Data Loss, Audio/Video
  Quality
• Adaptive resource allocation is required to meet
  these requirements over wireless channels
• e.g. Power, Coding, Cross-Layer Adaptation

3
The Problem

• In standard link adaptation problems performance
  metrics are often computed as time averages
• Average throughput, delay, distortion
• When the metric varies substantially with the
  state of the wireless channel an average can
  often mask many important problems
• For example, suppose we want to minimize average
  delay subject to an average power constraint

4
Delay Vs. Data Rate For Different Power
Constraints
5
Delay Vs. Channel Gain For Different Power
Constraints
6
The Problem

• Averages do not accurately represent QoS when the
  metric of interest can vary substantially with
  the wireless channel
• Ideally we want to be able to constrain more
  relevant quantities e.g.
• Probability distributions
• Conditional expectations

7
A Solution

• In this paper we develop a dynamic programming
  algorithm for finding optimal joint
  source-channel coding policies for delay
  constrained traffic
• Rather than constrain average delay, we develop a
  set of constraints on the conditional expectation
  of delay
• This type of constraint will increase power
  consumption but optimal source-channel coding
  greatly mitigates this penalty

8
System Model

• A single mobile transmitting delay sensitive data
  to a base station
• In each time slot the mobile may generate a
  packet with some probability
• The source encoder must then decide how many bits
  to use to describe the packet
• When the packet is transmitted the mobile may
  choose a transmission power and channel code
• Our goal is to jointly select the source/channel
  codes and transmission power

9
Model for a Mobile Device
To the Wireless Channel
Source Traffic
Data Buffer
Encoder
Power Control Channel Coding
Note that we have queueing delay between source
coding and transmission
10
Dynamic Program Formulation

• Construct a Markov chain model for a wireless
  device (see the paper for details)
• Fading/shadowing channel models
• Markov modulated traffic
• Each choice of source/channel code and
  transmission power determines a transition matrix
  for the Markov chain
• We want to find the optimal transition matrix
  that meets our performance criteria

11
Transitions and Value Functions

• For any control policy g, we can define a
  transition matrix P(g) and an infinite horizon
  value function V(g)
• ?(g) is the steady-state distribution of P(g) and
  c(g) is the cost of g in one time slot (e.g.
  power)

12
Optimization

• The minimum value function and optimal control
  can be found via a linear program
• The function f denotes a set of performance
  constraints

13
Performance Constraints

• In order to constrain the performance of our
  mobile we can add any number of constraints to
  our linear program
• Expected Delay or Power
• Conditional Expectation of Delay or Power

14
Numerical ExamplePower and Joint Source-Channel
coding for EDGE

• Traffic arrives according to an On/Off DTMC
• Source can be coded into 56 byte or 112 byte
  packets with a deadline of 100 milliseconds
• Channel code options are MCS-5 and MCS-7 (Rate
  0.37 and .74 8PSK)
• Power 20mW to 800mW in 2 dB increments
• TU-50 channel model within a microcell shadowing
  environment

15
Delay Vs. Channel Gain For Different Power
Constraints
16
Power Vs. Data Rate with Constraints on
Conditional Expectation of Delay Power Control
Only
17
Power Vs. Data Rate with Constraints on
Conditional Expectation of Delay Power Control
and S-C Coding
18
Conclusions

• We have presented a general stochastic control
  formulation for solving optimal power and coding
  problems with delay sensitive traffic
• The contribution is not necessarily the example
  results we presented, but rather the method we
  used to solve for those results.
• The CDMA version requires a different problem
  structure and has been submitted for publication