Quadratic Phase Generation Circuitry for Precise CAZAC Ranging Chirps
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Solution Overview
Problem
Conventional generation of Zadoff-Chu sequences for spatial ranging operations in electronic devices with wireless circuitry often results in quantization errors and inaccuracies in distance estimation due to finite bandwidth of digital-to-analog converters.
Innovation Solution
Incorporating a quadratic phase generator with a switch and numerically controlled oscillator to produce an interpolated constant amplitude zero autocorrelation (CAZAC) sequence, which is then adjusted using a weighting factor to ensure accurate transmission with variable bandwidth, reducing frequency outliers and enhancing the linear instantaneous frequency response.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional Zadoff-Chu sequence generation is used, then the circuit implementation is simpler, but quantization errors occur and distance estimation accuracy deteriorates
Solution Approach 1:
The patent implements a dynamic quadratic phase generator that continuously adjusts phase values based on a linear frequency modulation law. The system uses a numerically controlled oscillator (NCO) that dynamically updates phase increments to generate chirp signals with continuously varying frequency, thereby eliminating quantization errors inherent in static conventional generators while maintaining reasonable circuit complexity through efficient digital implementation.
Solution Approach 2:
The patent changes the fundamental parameters of sequence generation by introducing quadratic phase progression instead of conventional linear phase. The system modifies the phase parameter φ[n] = 2π(αn² + βn)/N where α and β are dynamically adjusted parameters that control the chirp characteristics. This parameter transformation enables perfect interpolation properties and eliminates frequency outliers, significantly improving distance estimation accuracy.
2Measurement precision
If digital-to-analog converter with finite bandwidth is used, then the hardware is practical and cost-effective, but band edges are disturbed and measurement precision deteriorates
Solution Approach 1:
The patent applies preliminary windowing and interpolation functions to the CAZAC sequence before digital-to-analog conversion. By pre-processing the signal with a window function that tapers the band edges smoothly, the system prevents spectral leakage and distortion that would otherwise occur at the finite bandwidth boundaries. This preliminary action ensures that the signal is optimally conditioned for the practical DAC hardware, maintaining measurement precision without requiring unlimited bandwidth.
3Adaptability or versatility
If fixed DAC sampling frequency is used, then the hardware implementation is simpler, but variable bandwidth chirp transmission cannot be achieved
Solution Approach 1:
The patent implements dynamic bandwidth control by varying the chirp rate parameter α in the quadratic phase function while maintaining fixed DAC sampling frequency. The system dynamically adjusts the frequency sweep range and duration by modifying the phase increment parameters, enabling flexible bandwidth adaptation without changing the hardware sampling rate. This dynamic parameter adjustment achieves variable bandwidth capability through software-controlled signal generation.
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AI summary
An electronic device may include wireless circuitry. The wireless circuitry may include a quadratic phase generator for outputting a perfectly interpolated constant amplitude zero autocorrelation (CAZAC) sequence for a transmit path. The quadratic phase generator may include a numerically controlled oscillator, a switch controlled based on a value output from the numerically controlled oscillator, a first integrator stage, and a second integrator stage connected in series with the first integrator stage. The numerically controlled oscillator may receive as inputs a chirp count and a word length. The switch may be configured to switchably feed one of two input values that are a function of the chirp count and the word length to the first integrator stage. The quadratic phase generator may output full-bandwidth chirps or reduced-bandwidth chirps. Bandwidth reduction can be achieved by scaling the two input values of the switches.