IQ-to-Phase Conversion Using Logarithmic 1-D Lookup Tables
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Solution Overview
Problem
Existing IQ to phase conversion methods face challenges in balancing circuit costs with high-speed and high-accuracy performance, particularly due to the computational delays and exponential growth in implementation size associated with inverse tangent calculations, especially in high-precision 4-quadrant arctan calculations.
Innovation Solution
The method involves converting input values into absolute and logarithmic values, using a subtractor module to generate a subtract value, and selecting a phase value from a storage unit based on this subtract value, which allows for efficient IQ to phase conversion using 1-D lookup tables instead of 2-D tables, reducing computational complexity and circuit size.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If CORDIC algorithm is used for inverse tangent calculation, then computational accuracy is improved, but computational delay increases and operational clock frequency decreases
Solution Approach 1:
The patent segments the inverse tangent calculation into two parts: a coarse estimation using a simplified method and a fine correction using a lookup table. This segmentation allows the system to achieve high accuracy without the full computational burden of traditional CORDIC algorithms, thereby reducing computational delay while maintaining precision.
Solution Approach 2:
The patent performs preliminary action by pre-calculating and storing inverse tangent values in a lookup table during the design phase. During runtime, the system only needs to perform a table lookup and simple arithmetic operations, eliminating the need for iterative calculations and significantly reducing computational delay.
2Measurement precision
If 2-D LUT is used for high precision 4-quadrant arctan calculations, then calculation accuracy is improved, but implementation size increases exponentially
Solution Approach 1:
The patent extracts the quadrant determination logic from the main LUT structure and handles it separately through sign detection and conditional processing. This allows the use of a smaller 1-D LUT for the magnitude calculation while handling the 4-quadrant requirement through external logic, thereby reducing the LUT size from exponential to linear growth.
Solution Approach 2:
The patent applies asymmetry by treating the magnitude calculation and quadrant handling as separate, asymmetric components. The 1-D LUT handles only the magnitude aspect with linear size growth, while quadrant information is processed through separate sign detection logic, breaking the symmetric exponential growth pattern of traditional 2-D LUTs.
3Measurement precision
If traditional inverse tangent calculation methods are used, then calculation accuracy is maintained, but circuit complexity and area consumption increase
Solution Approach 1:
The patent substitutes complex iterative mechanical calculation systems (CORDIC) with a combination of simple arithmetic operations and memory lookup. This replacement eliminates the need for complex iterative logic circuits, reducing circuit complexity and area consumption while maintaining calculation accuracy through the mathematical equivalence of the logarithmic transformation approach.
Data Source
AI summary
A method for cartesian (IQ) to polar phase conversion includes: converting a first input value into a first absolute value, and a second input value into a second absolute value; converting the first absolute value into a first logarithmic value by calculating a scaled logarithmic value of the first absolute value, and the second absolute value into a second logarithmic value by calculating a scaled logarithmic value of the second absolute value; subtracting the first logarithmic value from the second logarithmic value, to provide a subtract value; and selecting a phase value from a plurality of phase values stored in a storage unit. Each of the plurality of phase values corresponds to a respective index value, and the phase value is selected taking the subtract value as the index value.