Variable Modulus Algorithm Blind Equalization
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Solution Overview
Problem
Existing blind equalization techniques, such as the Constant Modulus Algorithm (CMA), face limitations when dealing with unknown modulation schemes and constellation densities, requiring significant computational resources and relying on approximate knowledge of modulation parameters, which hinders effective equalization across various modulation schemes.
Innovation Solution
The Variable Modulus Algorithm (VMA) iteratively adapts the modulus parameter γ using a stochastic gradient descent algorithm, minimizing a cost function based on the equalized samples, allowing for blind equalization without prior knowledge of the modulation type or constellation order, and converges faster than CMA in similar conditions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If the Constant Modulus Algorithm (CMA) is used for blind equalization, then equalization can be performed without training sequences, but the algorithm requires significant computational resources and relies on approximate knowledge of modulation parameters
Solution Approach 1:
The patent transforms the fixed modulus parameter γ in CMA into a variable parameter that adapts based on the equalized signal statistics. By computing γ dynamically from the equalized samples using the relationship γ = E[|yn|^4]/E[|yn|^2], the algorithm automatically adjusts to different modulation schemes without requiring prior knowledge of modulation parameters, thereby reducing computational complexity while maintaining versatility
Solution Approach 2:
The algorithm makes the equalization process self-adapting by having it automatically determine the appropriate modulus parameter from the signal itself. The system uses the equalized output to compute the modulus parameter, creating a self-service mechanism that eliminates the need for external training sequences or prior knowledge of modulation characteristics
2Adaptability or versatility
If the Constant Modulus Algorithm (CMA) is used for blind equalization, then equalization can be performed without training sequences, but the convergence speed is slow
Solution Approach 1:
The patent introduces feedback by using the equalized signal yn to continuously update the modulus parameter γ. This feedback mechanism allows the algorithm to rapidly adapt to the actual signal characteristics, significantly improving convergence speed compared to the fixed-parameter CMA approach
Solution Approach 2:
The algorithm transitions from a static parameter approach (fixed γ in CMA) to a dynamic parameter approach where γ evolves with the signal statistics. This dynamics enables the algorithm to quickly track and adapt to different modulation schemes, reducing convergence time while maintaining the ability to operate without training sequences
3Adaptability or versatility
If the Constant Modulus Algorithm (CMA) is used, then equalization can be performed on various modulation schemes, but the residual distortion is high
Solution Approach 1:
By changing the modulus parameter from a fixed approximate value to a dynamically computed value based on signal statistics, the algorithm achieves higher equalization accuracy. The computed parameter γ = E[|yn|^4]/E[|yn|^2] accurately reflects the actual modulation scheme being used, thereby reducing residual distortion while maintaining compatibility with different modulation types
Data Source
AI summary
A system, method and memory medium for performing blind equalization. A block {un} of the baseband samples is received. A function J of a vector f is minimized to determine a minimizer fMIN. The function J depends on vector f according to J(f)=Σ(|yn|2−γ)2. The summation Σ corresponds to a sequence {yn} of equalized samples. The sequence {yn} of equalized samples is related to the block {un} according to a convolution relation {yn}={un}*f. Parameter γ is a current modulus value. The current modulus value γ is updated to equal a ratio of a fourth moment of the sequence {yn} to a second moment of the sequence {yn}. The minimization and parameter update operations are repeated for a series of received blocks of baseband samples. The minimizer fMIN from a last of the repetitions is used to determine final equalized samples.