Channel Estimation Using Factor Graphs

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Channel Estimation Using Factor Graphs
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Purpose of Factor Graphs

• Suppose a function factors
• Marginalization w.r.t yields and takes
  Multiplications

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Lets exploit the distributive law

• factorable functions can be marginalized very
  efficiently

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Factor Graphs
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Factor Graphs
If Cycle free
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The Sum Product Algorithm
variable to local function
local function to variable
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The Sum Product Algorithm
variable to local function
local function to variable
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The Sum Product Algorithm
variable to local function
local function to variable
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Application to Channel Estimation
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Model
Multipath fading channel model
Gaussian noise
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Channel Estimation Approach

• Optimization Goal
• Solution Factor , generate factor
  graph and apply sum-product algorithm

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Channel Estimation Approach

• Solution Factor , generate factor
  graph and apply sum-product algorithm

Bayes
Independent codebits assumption (actually wrong)
Markov Model for channel u