Following article describes physical layer measurements for OFDM based systems viz. WLAN-11a/g/n/ac/ad, WiMAX-16d/16e and LTE. It covers very useful measurement such as power spectrum, transmit power,Error Vector Magnitude or EVM,CCDF,I-Q Constellation diagram,channel frequency response and spectral flatness.

Power Spectrum measurement

It is the Baseband transmitter power spectrum measured at the output of IFFT module. Following equation is used to determine value in dB. X axis represent frequency. The spectrum is the response of the power at various frequency bands. This helps design proper filter to take care of RF compliance requirement of the spectrum as per RF regulatory bodies.

Transmit Power:

It is the instantaneous power at the output of IFFT module in baseband transmitter. Baseband transmit power help power amplifier to design the system taking into consideration PAPR characteristics of the modulated spectrum of the system. This is mentioned in Equation below.
power equation

EVM per Sub carriers

EVM per sub carriers measurement is usually calculated after taking FFT in the de-mapper (before de mapping). The generic equation is mentioned below. Here 200 are the total carriers (data + pilots) in one symbol. Likewise EVM for all the symbols in LP packets and NF frames are calculated.
EVM equation
For example if OFDM frame is 10 symbols long and say each symbol has 192 data carriers then EVM is plotted for all the subcarriers across all the 10 symbols.

EVM per symbols

It provides the individual symbol EVMs for each subcarrier, at each symbol, for all symbol-times within the time domain frame. For Example if OFDM frame is 10 Symbol long and each symbol has 192 data carriers then the EVM per symbols measurement is plotted for all the symbols and each symbol will have 192 EVM values for all the data carriers within the symbol. This is called DATA RCE (Relative constellation error) also. The same can be plotted for pilot carriers also. This physical layer measurement is very useful to determine performance of the modem.


The CCDF i.e. complementary cumulative distribution function is a statistical power calculation and can only be performed on time-domain data.
Y axis- units of percent
X axis- power in dB
Power on the x-axis is relative to the signal average power, so 0 dB is the average power of the signal.
For example, 3 dB at 15 percent means there is a 15 percent probability that the signal power will be 3 dB or more above the average power. This physical layer measurement helps RF designers working on power amplifier design.

Constellation Diagram

I-Q constellation measurement is done the output of IQ mapper as mentioned below for X and Y axis.
X axis: In-Phase component in volts represented as I (V)
Y axis: Quadrature-Phase component in volts represented as Q (V)

Channel Frequency Response (CFR)

CFR is estimated after the frequency correction
H (f) = Y (f)/X (f) with simple linear interpolation
H (f) is CFR, Y (f) is the received preamble, X (f) is the reference preamble.
X axis is Carrier Index and Y axis is amplitude in dB.

Spectral flatness

Spectral flatness is Calculated after channel estimation by taking FFT for Preamble symbol.
spectral flatness
Where x (n) is the received signal
Where X axis is Carrier Index and Y axis is Power in dB.
This physical layer measurement helps in understanding channel characteristics the transmitted signal has traversed from far end to reach the receiver end.

There are more baseband measurements for physical layer other than the mentioned here such as AM-AM conversion, AM-PM conversion,IQ imbalanace, phase noise and so on.

Useful Links

AM-AM conversion
AM-PM conversion
Error Vector Magnitude
RF measurements tutorial

Test and Measurement Related Links

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Test and Measurement Signal Generator Companies
Test and Measurement Signal Analyzer Companies
Test and Measurement Signal generation and analysis article
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BER T&M equipment manufacturers
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