Approximate Square Root Demodulation Circuit for Digital Signals
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Solution Overview
Problem
Existing methods for demodulating a square root in VLSI digital systems and signal communication systems require extensive hardware, leading to poor performance and high production costs due to large error ratios, especially in communication systems with narrow error tolerance.
Innovation Solution
A method using the formula aX+bY to find an approximate square root, where X=|I| and Y=|Q|, with coefficients A and B, and a compare/compensate circuit to simplify the hardware structure by converting floating-point computation to fixed-point computation, reducing the number of comparators and improving accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If hardware circuits are used to obtain accurate square root values, then accuracy is improved, but hardware complexity and production cost increase
Solution Approach 1:
The patent divides the coordinate plane into multiple sectors based on angle ranges. Each sector has its own simplified calculation formula with specific coefficients. By segmenting the calculation space, the patent achieves acceptable accuracy across all angles while using simple hardware operations (addition, subtraction, bit shifting) rather than complex square root circuits.
Solution Approach 2:
The patent changes the calculation parameters by using different coefficients (a, b) for different angular sectors. Instead of using a universal accurate square root formula, it employs sector-specific linear approximations where the coefficients are optimized for each angular range, enabling accurate enough results with simple hardware.
2Device complexity
If coordinate slicing theory is used to obtain approximate square root, then hardware complexity is reduced, but error ratio increases
Solution Approach 1:
The patent further segments each coordinate slice into multiple angular sectors. Within each sector, specific optimized coefficients are applied to reduce the error ratio. This multi-level segmentation (both by coordinate slices and angular sectors) allows the patent to maintain simple hardware while significantly improving accuracy compared to uniform approximation methods.
Solution Approach 2:
The patent applies the principle of local quality by using different calculation formulas and coefficients for different angular sectors. Each sector has locally optimized parameters that are specifically tailored to minimize error in that angular range, rather than using a single global approximation formula.
3Measurement precision
If floating-point computation is used, then calculation accuracy is improved, but hardware structure complexity increases
Solution Approach 1:
The patent substitutes floating-point computation with fixed-point computation. By representing numbers in fixed-point format and using integer arithmetic operations (addition, subtraction, bit shifting), the patent eliminates the need for complex floating-point hardware units while maintaining sufficient calculation accuracy for the application.
4Measurement precision
If many comparators are used to obtain square root solution, then accuracy is improved, but production cost increases
Solution Approach 1:
The patent segments the calculation into multiple angular sectors, each handled by a simple comparator that checks angular range and applies the corresponding formula. This segmentation replaces the need for many comparators in traditional methods with a small number of comparators that work in conjunction with simple arithmetic operations, reducing production cost while maintaining accuracy.
Data Source
AI summary
A method of demodulating a square root for processing digital signals is disclosed. The demodulation includes the following steps. First, define |l arg e| to be the larger one between the absolute value of two input values I and Q and define |small| to be the smaller one between the absolute value of the two input values I and Q. Next, define a first determining form by the inequalities 16|small≦16|l arg e|≦18|small| and 16|l arg e|=16|small|. In addition, define a second determining form by the inequalities 16|small|≦16|l arg e|≦18|small| and 16|l arg e|≠|small|. When the relation between |l arg e| and |small| conforms to the first determining form, the approximate root-mean-square value of the two input values I and Q is |l arg e|+2−5|l arg e|. When the relation between |l arg e| and |small| conforms to the second determining form, the approximate root-mean-square value of the two input values I and Q is |l arg e|+2−6|l arg e|.