7/27/2019 EVM With Phase Noise

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EVM with phase noise

by Krishna Sankar on July 9, 2012 Analog

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The previous post on phase noise discussed about finding theroot mean square phase noise for a

given phase noise profile. In this post let us discuss about the impact of phase noise on the error

vector magnitude (evm) of a transmit symbol.

Error Vector Magnitude due to constant phase offset

Consider a system model introducing a constant phase offset and thermal noise as shown in

the figure.

Figure : System model with phase noise and thermal noise

The received symbol is,

,

where

is the phase distortion in radians,

is the transmit symbol and

is the contribution due to thermal noise

Expanding into real and imaginary components,

.

Representing in matrix algebra,

The power of the error vector is,

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.

Finding the average error over many realizations,

.

The individual terms can be simplified as,

i)

as .

ii)

as and are uncorrelated.

iii) .

iv) , the variance of the noise.

Applying (i), (ii) , (iii) and (iv), the error term simplifies to

.

EVM due to random phase offset

The above equation derives the evm when the system is affected by a constant phase offset .

Assume that the phase is Gaussian distributed with zero mean and variance radians^2

having a probability density function as,

.

The conditional error power for a given phase is,

.

Computing the average over all realization of phase,

.

The integral term is,

(Note : proof will be discussed in another post)

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Then the error vector power is,

and the error vector magnitude is,

Using Taylor series, and assuming that the is small,

,

Figure : Example constellation plot (Es/N0=30dB, =5 degrees)

Matlab/Octave example

Attached script computes the evm of a QPSK modulated symbol versus Es/N0 for different values

of rms phase noise.

% Script for simulating the error vector magnitude (evm) of a QPSK% modulated symbol affected by phase noise and thermal noise

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Figure : EVM vs Es/N0 for different values of rms phase noise

Summary

As a quick rule of thumb, for a system with rms phase noise of1 degree, the evm due to phase

noise alone is -35.16dB and rises by 6dB per octave (or 20dB per decade).

The phase noise profile used in this simulations assumes a Gaussian distributed flat spectrum,

which is not the case in typical phase noise profiles. The EVM with a classical phase noise profile

will be discussed in another post.

References

[1] Georgiadis, A.; , Gain, phase imbalance, and phase noise effects on error vector

magnitude,Vehicular Technology, IEEE Transactions on , vol.53, no.2, pp. 443- 449, March 2004

doi: 10.1109/TVT.2004.823477URL:http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1275708&isnumber=28551

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