Low PAPR permformance for Monochromatic Frequency signals

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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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