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From a single pulse to precise detection: What is the secret of pulse compression?
Pulse compression is a signal processing technology widely used in radar, sonar and ultrasonic detection. The purpose of this technique is to improve range resolution when pulse length is limited, or to improve signal-to-noise ratio when the peak power and bandwidth of the transmitted signal are limited. Pulse compression technology accomplishes this by modulating a transmitted pulse and then correlating the received signal with the transmitted pulse.
Signal description of simple pulses
The most basic pulse radar or sonar signal model is a truncated sine pulse with amplitude A and carrier frequency f0, which is truncated by a rectangular function with width T. The pulse is transmitted periodically, but this article focuses on the case of a single pulse rather than the periodicity of the pulse. This signal can be expressed in plural form.
Range resolution
It is critical to understand the range of resolutions that can be achieved with this signal. The return signal r(t) is an attenuated and time-shifted copy of the original transmitted signal. In practice, noise is also present in the received signal, which in reality generally uses a bandpass filter as the first stage of the receive chain. Matched filters are often used to detect incoming signals, which are the best way to detect known signals amidst normally distributed additive noise. This process involves performing cross-correlation operations on the received signals.
The essence of pulse compression technology is to achieve the best balance between higher signal resolution and signal-to-noise ratio through specific signal design.
Signal energy and signal-to-noise ratio
The instantaneous power P(t) of the received pulse can be calculated by the square modulus. The energy E of the input signal is equal to the energy of the transmitted pulse. In the case of a receiver, the signal-to-noise ratio (SNR) changes as the pulse duration T changes, which introduces a tradeoff: increasing T improves SNR but reduces resolution, and vice versa.
Pulse compression with linear frequency modulation (or chirp)
So, how to obtain a long enough pulse without losing resolution while maintaining a good signal-to-noise ratio? This is when pulse compression comes in. The basic principle is to emit a sufficiently long signal that is designed so that, after matching filtering, the width of the cross-correlated signal is smaller than the width of a standard sinusoidal pulse. In radar and sonar applications, linear chirps are the most commonly used signals to achieve pulse compression.
Pulse compression allows us to obtain information from long pulses without losing resolution, which is critical for a variety of applications.
Conclusion
Pulse compression technology undoubtedly plays a vital role in various fields such as radar, sonar and medical imaging. It can not only significantly improve the range resolution of the signal, but also improve the signal-to-noise ratio of the received signal. However, in the process of improvement, how to achieve the best balance between resolution and signal-to-noise ratio is still a topic worth pondering.
