1. Relations Between EVM, ρ, SNR and Phase Noise
Renshou Dai
July 20, 1999
1 Relations between EVM, ρ and SNR
EVM (RMS value of error-vector-magnitude), ρ (linear-correlation-coefficient-squared) and SNR
(signal-to-noise-ratio) all measure the same thing except in different manner.
1.1 EVM and SNR
The RMS value of EVM is related to SNR by:
SNR =
1
EV M2
RMS
EV MRMS =
1
√
SNR
(1)
1.2 ρ and SNR
ρ =
SNR
1 + SNR
δρ = 1 − ρ =
1
1 + SNR
(2)
SNR =
1 − δρ
δρ
=
ρ
1 − ρ
(3)
1.3 EVM and ρ
EV MRMS =
1 − ρ
ρ
ρ =
1
1 + EV M2
RMS
(4)
2 Relating to Phase Noise RMS Values
When there is only phase noise, then all these three parameters are different measure of phase noise
RMS value. Designate the phase noise RMS value as Φdeg (in degree) or Φrad (in radian), then the
following relations are true:
1

2. 2.1 EVM and phase noise Φ
EV MRMS = Φrad = Φdeg ×
π
180
(5)
2.2 ρ and Φ
ρ =
1
1 + Φ2
rad
δρ = 1 − ρ =
Φ2
rad
1 + Φ2
rad
(6)
3 Some Numerical Results
Table 1 lists the corresponding EVM (in percentage), δρ and SNR (dB) for various phase noise
ranging from 0 to 3 degrees in RMS value.
Φdeg EVM(×100) δρ × 10−3 SNR(dB)
0 0 0 ∞
0.2000 0.3491 0.0122 49.1419
0.4000 0.6981 0.0487 43.1213
0.6000 1.0472 0.1097 39.5994
0.8000 1.3963 0.1949 37.1007
1.0000 1.7453 0.3045 35.1625
1.2000 2.0944 0.4385 33.5788
1.4000 2.4435 0.5967 32.2399
1.6000 2.7925 0.7792 31.0801
1.8000 3.1416 0.9860 30.0570
2.0000 3.4907 1.2170 29.1419
2.2000 3.8397 1.4722 28.3140
2.4000 4.1888 1.7515 27.5582
2.6000 4.5379 2.0550 26.8630
2.8000 4.8869 2.3825 26.2193
3.0000 5.2360 2.7341 25.6200
Table 1: EVM,δρ and SNR values for various phase noise RMS values
4 Implications for the IS-97 CDMA Radio Receiver
IS-97 specifies the ρ accuracy to be δρ < 5 × 10−4. Judging from Table 1, this requires a phase
noise to be less than 1.28 deg in RMS value. If we need to perform 10 times better (δρ < 5×10−4),
this requires the phase noise RMS value to be less than 0.4 deg.
2