Fixed-Point FFT Scaling for Radar and Sonar Signal Processing
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Solution Overview
Problem
Existing fixed-point Fast Fourier Transform (FFT) algorithms in radar and sonar systems face challenges in scaling to prevent overflow and maintain signal-to-noise ratio (SNR), particularly for complex exponential input signals, leading to reduced precision and increased noise.
Innovation Solution
Implementing a scaling mechanism where the output of every pair of consecutive butterfly stages in the FFT algorithm is scaled by a factor equal to twice the inverse of the growth factor for complex exponential input signals, allowing for adequate SNR and preventing overflow, while allowing signals to saturate.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If fixed-point FFT algorithms are used to process radar and sonar signals, then computational efficiency is improved, but overflow and precision loss occur due to signal growth through butterfly stages
Solution Approach 1:
The patent applies preliminary scaling at predetermined intervals through the butterfly stages rather than attempting to prevent overflow reactively. By pre-scheduling scaling operations at specific stages, the system proactively manages signal amplitude growth before overflow can occur, maintaining computational efficiency while ensuring reliability.
Solution Approach 2:
The patent dynamically changes the scaling parameter (scaling factor) based on the current stage number and signal characteristics. The scaling factor is calculated as a function of the stage number and the growth factor of the FFT algorithm, allowing the system to adapt the degree of scaling to the actual signal growth at each stage, thereby preventing overflow while minimizing precision loss.
2Reliability
If scaling is applied to prevent overflow in fixed-point FFT, then reliability is improved, but signal-to-noise ratio deteriorates due to additional noise introduction
Solution Approach 1:
The patent applies different scaling factors to different stages of the FFT algorithm rather than using a uniform scaling approach. Each stage receives scaling tailored to its specific signal growth characteristics, with the scaling factor calculated based on the stage number and growth factor. This localized scaling minimizes unnecessary noise introduction while maintaining overflow prevention where needed.
Solution Approach 2:
The patent applies scaling selectively at specific butterfly stages rather than at every stage. By choosing to scale only at predetermined intervals where signal growth is most problematic, the system prevents overflow while minimizing the total amount of scaling operations that would otherwise introduce noise. The scaling is applied partially rather than excessively.
3Reliability
If uniform scaling is applied at every butterfly stage, then overflow is prevented, but computational complexity and processing time increase
Solution Approach 1:
The patent extracts and removes unnecessary scaling operations from the FFT algorithm by identifying that not every butterfly stage requires scaling. By taking out only the essential scaling operations at predetermined stages where signal growth is most problematic, the system maintains overflow prevention while reducing computational complexity compared to uniform scaling at every stage.
Solution Approach 2:
The patent segments the FFT butterfly stages into groups, applying scaling at predetermined intervals rather than continuously at every stage. This segmentation divides the processing into scalable segments, reducing the overall number of scaling operations and thereby lowering computational complexity while maintaining reliability through strategic scaling at critical stages.
4Productivity
If no scaling is applied to allow maximum signal processing, then productivity is maintained, but signal saturation and distortion occur
Solution Approach 1:
The patent applies preliminary scaling at predetermined stages to prevent signal saturation before it occurs. By proactively scaling at strategic points through the butterfly stages, the system maintains signal accuracy while preserving processing throughput, avoiding the need for post-processing correction of saturated signals.
Solution Approach 2:
The patent dynamically adjusts the scaling parameter based on the stage number and signal growth characteristics, changing the scaling factor to match the actual signal conditions. This adaptive parameter change ensures scaling is applied only when and where necessary to prevent saturation, maintaining signal accuracy without unnecessarily reducing processing throughput.
Data Source
AI summary
Present disclosure describes an improved scaling mechanism for a multi-stage fixed-point FFT algorithm used to process signals received by radar or sonar systems. Proposed scaling includes scaling an output of every pair of consecutive butterfly stages of the FFT algorithm by a scaling factor equal to two times of the inverse of a growth factor for the pair of consecutive butterfly stages for the FFT algorithm for a purely complex exponential input signal. Besides this scaling, input signals are allowed to overflow by saturation. Such mechanism yields adequate performance of radar and sonar receivers implementing fixed-point FFTs for any types of input signals, from random to substantially complex exponential or sinusoidal signals. Proposed scaling achieves a balance between having signal to noise ratio (SNR) that is possible to obtain for a particular input signal and SNR that is needed to successfully process that signal for radar and sonar applications.