# Low PAPR performance for Monochromatic frequency signals

I understand what is Monochromatic frequency signals from here, 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"?. (Note- topic for achieving Good PAPR(constant Envelope) for Radars)

The term monochromatic signal is really just a more complicated way of saying a sinusoid, a function that only contains spectral content at one frequency. Peak-to-average power ratio (PAPR) is a bit of a mushy term if you start to look for a theoretical definition, as power by definition is the time rate of delivery of energy over some period of time; the measurement period that you choose will affect the power value that you select.

For our purposes, let's just assume that the "instantaneous" delivered power is proportional to the square of the signal's amplitude (as if it was driving a resistive load). Let's assume the peak power of the signal, then, corresponds with the peak value of the sinusoidal signal $x(t)$:

$$x(t) = A \cos{\left(2\pi f t \right)}$$

$$P_{peak} \propto A^2$$

To find the average power delivered by the sinusoid, we use the RMS value of a sinusoidal signal:

$$A_{rms} = \frac{A}{\sqrt{2}}$$

$$P_{av} \propto \frac{A^2}{2}$$

The coefficient of proportionality is the same for both cases, so the ratio is:

$$\text{PAPR} = \frac{A^2}{\frac{A^2}{2}} = 2$$

This PAPR actually isn't that bad when compared to many modulated signal types. As an example, OFDM signals often have PAPRs of 10 dB or more, which can complicate the design of amplifiers that are suitable for driving said signals for transmission.

• Thank you for a clear explaination about PAPR. According to my understanding about PAPR, the value of PAPR increases when there is Amplitude variation (non-Constant or varying Envelope). But considering the case of Monochromatic signals, it is described as a signal with NO Phase and Amplitude Modulation. I am not clear about one point i.e.,- If there is NO Amplitude modulation in the Monochromatic Frequency signals, Why will the PAPR performance degrade ? – Gowthami Jun 8 '16 at 9:21