The enabling element of the CMCW-LiDAR is the cross-correlation process between the reference transmitted optical signal and the received optical signal. The cross-correlation of two deterministic signals returns information about the similarity between the signals. Formally, it is the convolution between the first signal and the time-reversed second signal. If the second signal is just the delayed version of the first signal, the cross-correlation will exhibit a clear peak corresponding to the time delay between the two signals. This is the basic concept used to measure the delay between the transmitted and received signals of the code-modulated LiDAR. There is a third element occurring in the cross-correlation process of the CM-LiDAR signal: the noise. How does noise impact the recognition of the cross-correlation outcome? There is a unique property of cross-correlation that makes this process particularly efficient under large noisy conditions. The convolution acts as a temporal averaging along the cross-correlation process effectively improving the signal-to-noise ratio at the output of the cross-correlation process. In principle, no matter large the additive noise is, a sufficiently long cross-correlation process can approach an infinite signal-to-noise ratio at the output. However, for practical purposes, the length of the cross-correlation process is fixed, determining a constant gain of the input signal-to-noise ratio, known as cross-correlation gain, which is the main topic of this chapter.

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Cross-Correlation of Signal and Noise

  • Stefano Bottacchi

摘要

The enabling element of the CMCW-LiDAR is the cross-correlation process between the reference transmitted optical signal and the received optical signal. The cross-correlation of two deterministic signals returns information about the similarity between the signals. Formally, it is the convolution between the first signal and the time-reversed second signal. If the second signal is just the delayed version of the first signal, the cross-correlation will exhibit a clear peak corresponding to the time delay between the two signals. This is the basic concept used to measure the delay between the transmitted and received signals of the code-modulated LiDAR. There is a third element occurring in the cross-correlation process of the CM-LiDAR signal: the noise. How does noise impact the recognition of the cross-correlation outcome? There is a unique property of cross-correlation that makes this process particularly efficient under large noisy conditions. The convolution acts as a temporal averaging along the cross-correlation process effectively improving the signal-to-noise ratio at the output of the cross-correlation process. In principle, no matter large the additive noise is, a sufficiently long cross-correlation process can approach an infinite signal-to-noise ratio at the output. However, for practical purposes, the length of the cross-correlation process is fixed, determining a constant gain of the input signal-to-noise ratio, known as cross-correlation gain, which is the main topic of this chapter.