Error Vector Magnitude Phase Noise
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Error Vector Magnitude Equation
Editors STEM Starter Tournament Pop Quizzes Engineering Bracket Challenge CompaniesCompany Directory Part Search Advertisement Home > Learning Resources > Engineering Essentials > Understanding Error Vector Magnitude Understanding Error Vector Magnitude This measure of modulation quality may be a better predictor of wireless reliability than BER. Oct 10, 2013 Lou Frenzel | Electronic Design EMAIL Tweet Comments 0 Learn the meaning and importance of error error vector magnitude pdf vector magnitude measurements. Download this article in .PDF format This file type includes high resolution graphics and schematics when applicable. Error vector magnitude (EVM) is a measure of modulation quality and error performance in complex wireless systems. It provides a method to evaluate the performance of software-defined radios (SDRs), both transmitters and receivers. It also is widely used as an alternative to bit error rate (BER) measurements to determine impairments that affect signal reliability. (BER is the percentage of bit errors that occur for a given number of bits transmitted.) EVM provides an improved picture of the modulation quality as well. Related 3G Transceiver Consumes 30% Less Power And Delivers 50% Better EVM VSA App Adds Multi-Measurement Signal Analyzer Capability Understanding Cell-Aware ATPG And User-Defined Fault Models A Multi-Level Approach Makes Understanding Motor Control Easier EVM measurements are normally used with multi-symbol modulation methods like multi-level phase-shift keying (M-PSK), quadrature phase-shift keying (QPSK), and multi-level quadrature amplitude modulation (M-QAM). These methods are widely used in wireless local-area networks (WLANs), broadband wireless, and 4G cellular radio systems like Long-Term Evolution (LTE) where M-QAM is combined with orthogonal frequency division multi
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phase noise discussed about finding the root mean square phase noise for a given phase noise profile. In this post let us discuss about http://www.dsplog.com/2012/07/09/evm-phase-noise/ 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 error vector 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, . 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 vector magnitude 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) 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 % ---------------------------------------------------------- clear;close all; N = 10^5 % number of bits or symbols Es_N0_dB = [15:3:40]; % multiple Eb/N0 values phi_rms_deg_vec = [0:1:5]; for ii = 1:length(Es_N0_dB) for jj = 1:length(phi_rms_deg_vec) % Transmitter ip_re = rand(1,N)>0.5; % generating 0,1 with equal probability
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