Multicarrier Modulation Scaling for FFT Overflow Control
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Solution Overview
Problem
Multicarrier modulation systems, particularly OFDM, face challenges due to arithmetic processing limitations, such as round-off noise and arithmetic overflow in fixed-point DSP implementations, which affect the accuracy of IFFT and FFT operations, leading to suboptimal performance in terms of bit error rate and computational complexity.
Innovation Solution
The method allows a predetermined amount of saturation in the IFFT and FFT structures, using scaling factors that balance clipping and rounding errors based on the statistical properties of signals, optimizing the trade-off between these errors to minimize the overall noise power across all outputs, thereby reducing the number of bits required for processing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Use of energy by moving object
If fixed-point DSP approach is used to reduce cost and power consumption, then device complexity and energy usage are reduced, but arithmetic processing accuracy deteriorates due to round-off noise and overflow
Solution Approach 1:
The patent changes the scaling parameters of fixed-point numbers within the FFT/IFFT structure. By adjusting the scaling factors and quantization levels at different stages of the transform, the system optimizes the balance between fixed-point precision and computational accuracy, reducing round-off noise while maintaining acceptable performance
Solution Approach 2:
The patent introduces dynamic scaling and quantization strategies that adapt to the signal characteristics at different stages of the FFT/IFFT computation. The scaling factors are adjusted based on the cumulative distribution of signal values, allowing the system to optimize precision where needed while accepting lower precision where the impact is minimal
2Reliability
If scaling is applied to maintain numbers within active window to avoid saturation, then arithmetic overflow is prevented, but rounding errors increase due to limited dynamic range
Solution Approach 1:
The patent optimizes scaling parameters to achieve the desired balance. By carefully selecting scaling factors that allow a predetermined amount of saturation while maintaining most numbers within the active window, the system reduces rounding errors compared to aggressive scaling, while still preventing overflow through controlled design
Solution Approach 2:
The patent converts the harmful effect of saturation into a beneficial design constraint. By allowing controlled saturation at low probability while optimizing scaling, the system transforms the potential harm of overflow into a design guideline that balances precision and reliability, using the statistical properties of signals to their advantage
3Measurement precision
If higher bit length is used to reduce rounding errors, then arithmetic processing accuracy is improved, but device complexity and computational burden increase
Solution Approach 1:
The patent changes the bit length parameters dynamically throughout the FFT/IFFT structure. Different stages use different bit lengths and scaling factors, optimizing the balance between precision and complexity. This allows the system to use lower bit lengths where precision requirements are relaxed while using higher bit lengths only where necessary
Solution Approach 2:
The patent applies different precision requirements to different parts of the computation. By analyzing the cumulative distribution of signal values at each stage, the system applies higher bit length and more precise arithmetic only where the signal statistics require it, while using lower precision where the impact on overall performance is minimal
Data Source
AI summary
The invention provides a new approach which is better suited to FFT design as applied to multicarrier modulation systems such as OFDM. The signals are scaled so that overflow, rather than being completely avoided, occurs with low probability throughout the IFFT and FFT structures. The size of the error that results from an overflow depends on how overflow is handled in the DSP. To minimize the degradation, overflow should result in saturation of the value at the maximum positive or negative value option. This is equivalent to clipping the signal. Using the new technique, signals within the FFT structure are scaled to balance the effect of clipping and round-off. Clipping may result in comparatively large errors in a few signal values but because of the spreading effect of the FFT and because OFDM systems typically include error coding/correction, system performance depends on the total error or, in other words the total noise power, across all of the FFT outputs rather than on any individual value.