Conjugate Gradient Channel Estimation for ATSC DTV Receivers

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Solution Overview

Problem

Adaptive equalizers in ATSC DTV receivers face challenges with slow convergence and failure to adapt to changing channel conditions due to multipath interference and intersymbol interference, especially in severe multipath environments, where existing algorithms like LMS and blind decision feedback equalizers struggle with convergence and computational complexity.

Innovation Solution

The implementation of a conjugate gradient algorithm for channel estimation, which reduces computational complexity by avoiding the inversion of the input data auto-correlation matrix and utilizing FFTs to efficiently update channel estimates, allowing for faster convergence and improved tracking of channel variations.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If LMS algorithm is used for adaptive equalization, then the equalizer can adapt to channel conditions, but convergence is slow and may not be achieved during a single training sequence

Engineering Contradiction:

Improveconvergence reliabilityVSAvoidconvergence time

Core Design Contradiction:

ReliabilityVSLoss of time

Solution Approach 1:

The patent transitions from the LMS algorithm to the conjugate gradient algorithm, fundamentally changing the adaptation parameter update mechanism. The conjugate gradient algorithm uses a different mathematical approach (solving normal equations via conjugate directions) that provides faster convergence in fewer iterations, directly addressing the slow convergence issue of LMS while maintaining adaptive equalization capability

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent replaces the iterative gradient descent mechanism of LMS with the conjugate gradient optimization method. This substitution changes the underlying mathematical mechanism from simple gradient following to conjugate direction optimization, which converges faster for quadratic cost functions typical in equalization problems

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

2Adaptability or versatility

If blind and decision directed methods are added to adapt between training sequences, then tracking of channel variations is improved, but several data fields are required to achieve convergence

Engineering Contradiction:

Improvechannel tracking capabilityVSAvoidconvergence time

Core Design Contradiction:

Adaptability or versatilityVSLoss of time

Solution Approach 1:

The patent performs channel estimation using the conjugate gradient algorithm during the training sequence period, preparing the equalizer in advance before data transmission begins. This preliminary action during training sequences eliminates the need for slow convergence during data fields, allowing immediate tracking without requiring several data fields to converge

Inventive Principle:

Principle #10Preliminary action

3Reliability

If decision feedback equalizer is used in 8-VSB applications, then multipath signals can be handled, but computational complexity increases and convergence may fail under difficult multipath conditions

Engineering Contradiction:

Improvemultipath handling capabilityVSAvoidequalizer complexity

Core Design Contradiction:

ReliabilityVSDevice complexity

Solution Approach 1:

The patent replaces the complex decision feedback equalization mechanism with a channel estimation approach using conjugate gradient algorithm. This substitution simplifies the system by eliminating the need for decision-directed feedback loops and complex tap weight adjustments, while maintaining multipath handling capability through accurate channel impulse response estimation

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

4Reliability

If recursive least square algorithm is used to avoid convergence problems, then convergence reliability improves, but computational complexity increases due to matrix inversion

Engineering Contradiction:

Improveconvergence reliabilityVSAvoidcomputational complexity

Core Design Contradiction:

ReliabilityVSDevice complexity

Solution Approach 1:

The patent replaces the recursive least squares algorithm with the conjugate gradient algorithm. This substitution eliminates the need for explicit matrix inversion operations that plague RLS, instead using iterative conjugate direction searches that are computationally less intensive while maintaining convergence reliability and avoiding local minima problems

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

Data Source

PatentUS7327810B2Efficient conjugate gradient based channel estimator

Publication Date: 2008.02.05 ZENITH ELECTRONICS CORPORATION

AI summary

In forming a channel estimate, a received signal y is decoded to form data s, a convolution matrix Ŝ is formed from the data s, a matrix F is formed from the data s such that the matrix F results from the forming of the matrix Ŝ as a convolution matrix, and a conjugate gradient algorithm is performed to determine the channel estimate. The conjugate gradient algorithm is based on the received signal y, the matrix Ŝ, and the matrix F.