Time Delay and Frequency Offset Calculation Using Cross-Correlation
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Solution Overview
Problem
Existing signal processing systems face challenges in accurately calculating time delay and frequency offset between signals, particularly when signals are delayed in time and frequency due to motion or noise, leading to difficulties in synchronization and data retrieval in communication systems.
Innovation Solution
A system and method that utilize auto-product functions, discrete Fourier transforms, and cross-correlation to calculate time delay and frequency offset by identifying a global maximum value of a delay optimization function, allowing for precise synchronization and data processing in various communication systems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional signal processing methods are used to calculate time delay and frequency offset, then the system structure is simple, but the measurement precision deteriorates when signals are delayed in time and frequency due to motion or noise
Solution Approach 1:
The patent segments the signal processing task into distinct functional modules: auto-product function generation, discrete Fourier transform processing, cross-correlation generation, delay optimization function generation, and maximum value detection. Each module processes a specific aspect of the signal analysis, allowing complex calculations to be broken down into manageable steps that improve precision without overwhelming system complexity
Solution Approach 2:
The patent introduces intermediate functions (auto-product functions and delay optimization functions) as mediators between the input signals and the final time delay/frequency offset calculations. These intermediate functions transform the raw signals into forms that are more amenable to precise measurement, acting as bridges that enhance calculation accuracy while maintaining manageable system complexity
2Measurement precision
If advanced signal processing techniques are implemented to improve calculation accuracy, then measurement precision improves, but the processing time increases
Solution Approach 1:
The patent performs preliminary signal processing by generating auto-product functions and applying discrete Fourier transforms before the main cross-correlation and optimization steps. This preliminary preparation of the signals in the frequency domain facilitates faster and more accurate subsequent processing, reducing the overall computation time while maintaining high precision
Solution Approach 2:
The patent transforms the signal processing from the time domain to the frequency domain using discrete Fourier transforms. This dimensional change allows for more efficient processing of time-delayed signals and enables the use of frequency-domain correlation techniques that are computationally faster and more precise for detecting time delays and frequency offsets
3Adaptability or versatility
If the system processes signals with noise and motion-induced delays, then the adaptability improves, but the measurement precision deteriorates
Solution Approach 1:
The patent converts the harmful effects of noise and motion-induced delays into beneficial information by using them as inputs to the cross-correlation and delay optimization functions. The system is designed to detect and measure these disturbances rather than simply filtering them out, transforming the problem of noisy, delayed signals into an opportunity to extract precise time delay and frequency offset measurements that characterize the signal degradation
Data Source
AI summary
Time delay and frequency offset calculation systems and related methods. System implementations include modules coupled together configured to calculate a time delay and a corresponding frequency offset of a second signal delayed in time relative to a first signal with the maximum value of a magnitude of a delay optimization function. Implementations of a method for calculating a time delay and frequency offset calculate the maximum value of the delay optimization function by generating the cross-correlation of one or more adjacent discrete Fourier transformed blocks corresponding to the first signal and second signal, respectively, of two or more discrete Fourier transformed blocks. The maximum value of the delay optimization function is then identified. Implementations of the method may compare the identified maximum value of the magnitude of the delay optimization function with a threshold to determine whether to continue processing for additional adjacent discrete Fourier transformed blocks.