## EVM-Error Vector Magnitude

This page describes EVM(Error Vector Magnitude) basics,EVM equation and mention its significance in wireless system.

**EVM** or Error vector magnitude provides insight into quality of the modulated signal/symbol.
This modulated signal originates when bits are mapped to symbols in a complex modulation systems
such as QPSK, 16-QAM, 64-QAM etc. It is also referred as RCE (Relative Constellation Error).

Error Vector magnitude for a symbol is described in fig.1 where P1 is the
ideal constellation point and P2 is the measured constellation point with some impairments.
Impairments may be of different types in RF and baseband chain. It include IQ mismatch
(gain, phase, DC offset), frequency offset, phase noise, AM-AM distortion, AM-PM distortion,
AWGN, multipath fading (fixed, time varying), interference etc. From the figure it is imperative
that M and Φ are magnitude and phase errors respectively between two constellation points.

### EVM Equation

Where, P1= I1+j*Q1 is the ideal/reference symbol vector

P2= I2+j*Q2 is the measured symbol vector

**WiMAX EVM Equation:**

Here **Error Vector Magnitude** is calculated for all the frames (Nf) and all packets (Lp) in each frame and all the symbols
(total data and pilots carriers in each symbol are 200) in each packet.
Then it is averaged to obtain rms value of the EVM as shown in the EVM equation.

EVM per subcarriers and EVM per symbols for OFDM physical layer as per fixed wimax specifications described in IEEE 802.16-2004 standard is
explained in physical layer measurements page.

### EVM conversion

EVM_{dB} = 20*log_{10 } (EVM_{rms})

Download Error Vector Magnitude conversion excel sheet.

### EVM of QPSK constellation

Higher EVM_{dB} results in closer constellation points as shown in fig. 2b and lesser EVM(dB) results in scattered constellation points as shown in fig. 2a for QPSK constellation diagram.

Fig.2 EVM constellation for two different Error Vector Magnitude values

### Useful links

Various impairments for baseband chain MATLAB code

AM-AM conversion

AM-PM conversion

### What is Difference between

difference between FDM and OFDM

Difference between SC-FDMA and OFDM

Difference between SISO and MIMO

Difference between TDD and FDD

Difference between 802.11 standards viz.11-a,11-b,11-g and 11-n

Bluetooth vs zigbee

Bluetooth vs zigbee

Fixed wimax vs mobile

wibro vs mobile wimax

Microcontroller vs microprocessor

FDM vs TDM

CDMA vs GSM

OFDM vs OFDMA

wimax vs lte

RF heterodyne versus homodyne receiver