Low PAPR permformance for Monochromatic Frequency signals

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Monochromatic frequency signals, characterized as simple sinusoidal waves, exhibit a Peak to Average Power Ratio (PAPR) of 3 dB, which is relatively low. When modulation occurs, the signal's bandwidth increases, moving it away from being monochromatic, and can lead to higher PAPR values. Using a square wave can improve PAPR, but introduces spectral sidebands that complicate the trade-off between PAPR and spectral properties. Filtering these sidebands may further degrade PAPR performance. Ultimately, monochromatic signals demonstrate better PAPR characteristics compared to more complex signals like OFDM, which can exceed 12 dB.
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I understand what is Monochromatic frequency signals from https://www.physicsforums.com/threads/monochromatic-waves.570958/, but could somebody kindly give a brief explanation about "why does a monochromatic frequency signal result in poor PAPR (Peak to average Power Ratio) performance"?.

Thank You.
 
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Maybe I'm misunderstanding the question, but I don't think that claim is necessarily true.

A monochromatic signal is essentially just a simple, unmodulated sinusoidal wave. That gives a PAPR of 3 dB.

Once you start modulating that signal, in frequency, phase or amplitude, its bandwidth will increase, but at that point it's no longer monochromatic.

You can improve PAPR by starting with a square wave (and modulate its phase or frequency if you choose to modulate it), but the fact that a square wave is involved introduces spectral sidebands (the power spectral density of a square wave is sinc squared function). So at least in this respect, there is a trade-off between PAPR and spectral properties. Filtering off the sidebands can worsen PAPR properties.

All that said, compare a monochromatic signal with a PAPR of 3 dB to a typical OFDM (orthogonal frequency division multiplxing) signal which can have a PAPR in excess of 12 dB. The narrowband, monochromatic signal has much better PAPR properties.
 
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