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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

EVMdB = 20*log10 (EVMrms)

EVM of QPSK constellation

Higher EVMdB 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