Non-Iterative PPM Waveform Generation for Lidar
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Solution Overview
Problem
Current methods for generating Pulse Position Modulated (PPM) waveforms in lidar systems are computationally intensive and limited in applicability, leading to range ambiguity and waveform quality issues due to iterative processes and post-collection processing limitations.
Innovation Solution
A non-iterative method for generating cyclically optimal PPM waveforms by obtaining prime numbers, calculating pulse modulations, and determining nominal pulse timings, resulting in a waveform that can be indefinitely repeated without degradation in peak-to-maximum-sidelobe-ratio (PMSLR), thus improving waveform quality and reducing computational time.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If iterative processes are used to calculate PPM elements, then waveform quality (PMSLR) is improved, but computational time and complexity increase significantly
Solution Approach 1:
The patent applies preliminary action by pre-calculating and storing prime numbers and their modular arithmetic results before waveform generation. The prime number list and pre-computed modular values are stored in lookup tables, allowing the waveform generation process to simply query pre-computed results rather than performing iterative calculations during runtime, thus achieving both high waveform quality and fast generation speed
Solution Approach 2:
The patent replaces the mechanical iterative optimization process with a mathematical closed-form solution based on number theory. Instead of iteratively adjusting PPM elements to optimize waveform quality, the invention directly computes optimal values using prime numbers and modular arithmetic formulas, substituting the iterative mechanical process with a direct mathematical calculation that achieves the same quality metric much faster
2Loss of time
If pulses are transmitted at higher frequency, then integration time is reduced, but time of flight calculation becomes ambiguous
Solution Approach 1:
The patent applies parameter changes by dynamically adjusting the PPM waveform parameters (pulse positions, modulation depths) based on the chosen pulse repetition frequency. The closed-form solution computes optimal PPM elements that are specifically tailored to the given PRF, ensuring that the waveform structure adapts to the transmission frequency to maintain unambiguous time of flight measurements while achieving the desired integration time
Solution Approach 2:
The patent introduces the PPM encoding as an intermediary mechanism between the pulse transmission and time of flight measurement. The PPM modulation creates a coded waveform structure that acts as a signature, allowing the system to distinguish between multiple pulses and accurately measure time of flight even at high repetition frequencies where simple pulse timing would be ambiguous
3Manufacturing precision
If waveform length is increased, then waveform quality is improved, but generation complexity and computational load increase
Solution Approach 1:
The patent applies preliminary action by pre-computing and storing prime numbers and their modular arithmetic results in lookup tables before waveform generation. When generating long waveforms, the system simply queries pre-computed values from these tables rather than performing complex calculations for each pulse position, allowing efficient generation of long waveforms with high quality without proportional increase in computational complexity
Solution Approach 2:
The patent applies segmentation by dividing the waveform generation process into discrete, independent steps based on prime number properties. The closed-form solution breaks down the complex waveform generation into modular arithmetic operations on prime-based indices, allowing the system to construct long waveforms by systematically applying simple rules rather than using complex iterative optimization across the entire waveform
Data Source
AI summary
A lidar for generating a cyclically optimal Pulse Position Modulated (PPM) waveform includes: a memory for storing a list of prime numbers; a processor for obtaining a list of prime numbers up to a predetermined maximum code length; selecting a largest prime number p* that is less than or equal to a ratio of a timing system bandwidth to the predetermined pulse repetition frequency (PRF), from the list of the prime numbers; constructing a list of pulse indices, m=0: p*−1 for the cyclically optimal PPM waveform; calculating a list of pulse modulations, dJs=mod(m2, p*)−(p*−1)/2, wherein dJs are modulation values; calculating a list of nominal pulse timings T, as T=m×ceil(TPRI/Δj), where Δj is a predetermined modulation resolution, and TPRI is the reciprocal of the PRF; calculating pulse timings t0 of the cyclically optimal PPM waveform as t0=Δj×(T+dJs); and generating the cyclically optimal PPM waveform from the pulse timings t0.