Quadratic Phase Generator for Accurate CAZAC Ranging Signals
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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, minimizing quantization errors.
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 quadratic phase generator is divided into multiple functional blocks: a numerically controlled oscillator (NCO) for generating base sequences, a switching mechanism for selecting between different phase progression values, and integrator stages for accumulating phase values. This segmentation allows each block to perform a specific function, achieving high measurement precision while keeping the overall circuit implementation manageable through modular design.
2Ease of manufacture
If digital-to-analog converters with finite bandwidth are used, then the circuit is practical and implementable, but band edges are disturbed and quantization errors occur
Solution Approach 1:
The quadratic phase generator performs preliminary interpolation of the CAZAC sequence before it reaches the digital-to-analog converter. By pre-calculating and storing the interpolated sequence values in digital form, the system compensates for the upcoming bandwidth limitations and band edge disturbances that will occur during analog conversion, thereby maintaining measurement precision while using practical DAC hardware.
3Measurement precision
If CAZAC sequence interpolation is performed, then distance estimation accuracy is improved, but the device complexity increases
Solution Approach 1:
The system changes the parameter of phase progression through the switching mechanism that selects between different values (q and q-M) based on the NCO output. This parameter change enables the generation of multiple distinct quadratic phase responses, creating a linear instantaneous frequency response without frequency outliers, thereby improving spatial ranging accuracy while maintaining a relatively simple circuit structure through parameter variation rather than structural complexity.
Data Source
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.