1. January 2003 Joe Kwak InterDigital Communications Corporation
IEEE /100r1
doc: IEEE /773r2
November 2003
EVM SIMULATIONS FOR OFDM EVM vs BER data plots and data tables to support PSNI premise
Joe Kwak
InterDigital Communications Corporation
Submission
Joe Kwak, InterDigital

2. OUTLINE Background for EVM Simulation Work EVM Measurement Notes
Public Domain Simulation Tool
EVM Calculations in Simulator
Simulation Setup/Assumptions
Plotted Simulation Results
Importance of EVM variance in Fading Channels
Conclusions
Joe Kwak, InterDigital
Submission

3. Background
r2-K-RCPI_PSNI_Measurements.ppt, presented at May meeting, proposed a single scalar measure (PSNI) as new signal quality indicator for all WLAN rates, modulations, FEC, and channel conditions.
PSNI to be based on internal demod parameter such as EVM, internal observed SNR paramter, or other param.
PSNI to be specified in AWGN for PER performance.
Validity of PSNI(or EVM) as quality indicator of BER was questioned in fading channels.
Dave Skellern and Joe Kwak agreed to study EVM.
Skellern argues EVM not valid indicator, Kwak argues EVM is adequate indicator of signal quality and BER.
Joe Kwak, InterDigital
Submission

4. Graphical Error Vector Magnitude
due to noise or
distortion
Transmitted symbol
(Io,Qo) I I
(Is,Qs) Q Q
Average power circle
EVM measure requires apriori knowledge of transmitted symbol, or must assume that closest constellation point is transmitted symbol. EVM is normalised to average power.
Joe Kwak, InterDigital
Submission

5. EVM Calculation in Transmitter
EVM has gained popularity as a figure of merit for transmitters.
EVM may be easily computed from a modulated signal because:
SNRs are extremely high so that the measured EVM represents transmitter constellation distortion, and not noise-induced signal distortion.
High SNRs for measurement means that nearest constellation point is always the transmitted constellation point, I.e BER = 0 for transmitter testing purposes.
The same technique, widely used for transmitters and specified for transmitters, does not directly apply to EVM measurement in receivers.
Joe Kwak, InterDigital
Submission

6. EVM Calculation in Receiver
Characterization of receivers is not limited to high SNRs; receivers are designed for operation in very low SNRs, where link distances are stretched to maximum.
At low SNRs, processed symbol (I,Q) may cross demodulation decision boundary and lead to demod errors.
Practical measurement of EVM in receivers has no apriori knowledge of transmitted symbol and so must assume closest constellation point.
This assumption leads to EVM error in low SNR: measured EVM is lower than actual EVM; measured Inverse EVM is higher than actual IEVM.
Joe Kwak, InterDigital
Submission

7. January 2003
IEEE /100r1
Inverse EVM
EVM in simulator is computed according to : ([(I-Io)2+(Q-Qo)2])1/ Nsubcsym * (Im2 + Qm2)1/ where (Io,Qo) is nearest constellation point, and (Im2 + Qm2)1/2 is the average signal power, and summation is taken over all packet subcarrier symbols.
The Inverse EVM is equivalent to SNR where,
IEVM = 20*log10( 1 / EVM )
Plots of IEVM vs SNR in AWGN shows simulator EVM produces expected results.
Joe Kwak, InterDigital
Submission

8. Matlab Simulation Tool
A publically available MATLAB simulation tool has been published in OFDM Wireless LANs: A Theoretical and Practical Guide, Juha Heiskala and John Terry, SAMS publishing, 2002.
This tool implements IEEE802.11a modulations and coding and uses AWGN channel or the IEEE exponentially decaying ray channel model to demonstrate WLAN capability.
This simulation tools calculates rawBER, data BER, PER on a packet by packet basis for any input SNR value and channel model using various ray decay time constants.
This tool was modified to also compute EVM average and EVM Sdev over a series of packets.
Joe Kwak, InterDigital
Submission

9. EVM Calculation in Simulation Tool Receiver
Matlab receiver.m code module directs processing; EVM calc is performed just prior to demodulation:
Packet Detection
Frequency Error estimation and correction
Fine time synchronization
Channel estimation
Phase error estimation and correction
Rx diversity processing
Amplitude normalization
EVM calculation
Soft decision demodulation
Deinterleaving
Depuncturing
Soft decision weighting with subcarrier amps
Viterbi soft decision FEC decoding
Joe Kwak, InterDigital
Submission

10. IEVM vs SNR in AWGN
Joe Kwak, InterDigital
Submission

11. IEVM Error at low SNRs
When EVM is computed for transmit constellation testing, the transmitted signal is always at high SNR and the transmitted constellation point is always the nearest constellation point.
EVM computation in a receiver also assumes that nearest constellation point is intended constellation point.
This leads to EVM error at low SNR values when high noise levels may cause signal to cross demod decision boundary, leading to raw bit errors.
Joe Kwak, InterDigital
Submission

12. EVM Error at low SNR Values
Joe Kwak, InterDigital
Submission

13. Simulation Setup at 6Mbps (BPSK, R=1/2)
Simulator has many real-world options which were not studied or used for this effort.
Simulator is setup to provide near-ideal receiver performance, with minimal implementation-dependant losses:
Ideal packet detection
Ideal synchronization algorithms: time, freq, phase
No PA distortions
No transmitter phase noise
Adequate channel estimation algorithm (unverified)
No TX or Rx diversity
Full precision calculations, no quantization errors
Simulator tested and shows expected theoretical performance.
Joe Kwak, InterDigital
Submission

14. Simulation Setup at 6Mbps (BPSK, R=1/2) (cont)
Each plotted simulation point consists of 1000 simulated packets with 1000 data bits per packet (10E6 bits per data point).
For each data point, the simulator calculated the IEVM mean, IEVM stddev, raw BER, data BER (after FEC decoding).
Data was collected using various channel models: AWGN, IEEE fading using 25, 50, 100, 200, and 400 nsec decay times.
For each channel model, SNR was varied for each data point from -6 to +20dB in 2 dB steps.
Joe Kwak, InterDigital
Submission

15. IEVM vs Raw BER for AWGN and Fading Channels
Joe Kwak, InterDigital
Submission

16. IEVM vs Data BER (after FEC decoding)
Joe Kwak, InterDigital
Submission

17. Variance of EVM as modifier of measured EVM
The standard deviation (Sdev) is computed for all IEVMs measured in the simulations.
The Sdev varies with the decay time constant of the exponentially decaying rays in the fading model, in IEVM range from -5 to 40db
It may be useful to use the Sdev value to modify the measured IEVM to make an adjustment to more closely align the IEVMs in fading channels with that of AWGN case for better indication of Data BER.
IEVM Sdev
0.10
3.59
3.91
4.55
5.33
5.94
Tdecay (nsec)
AWGN
400
200
100 50 25
Joe Kwak, InterDigital
Submission

18. IEVMmod: Adjusted IEVM measurement
Heuristically, we may search for Sdev-based adjustment factors to more closely align the IEVM results to the AWGN case for all channel conditions.
We structure IEVMmod so that:
IEVMmod = IEVM - FactorSlope(IEVM,Sdev) + FactorOffset(Sdev)
Reasonable alignment is achieved using:
FactorSlope = (IEVM + C1)*Sdev*C2 and
FactorOffset = (C3 - Sdev)*Sdev*C4 where
C1= 0.9, C2=0.135, C3=6.0, and C4=0.3
Joe Kwak, InterDigital
Submission

19. IEVMmod vs Data BER (after FEC decoding)
Joe Kwak, InterDigital
Submission

20. Similar Results for all OFDM Rates
Same procedure is repeated for other OFDM rates:
Simulations are run across wide SNR range for 6 channel models: runs per OFDM rate
1000 packets are simulated in each run and IEVM is measured for each packet
Mean and StdDev of IEVM in 1000 packets are calculated.
Mean IEVM vs Data BER is plotted
IEVMmod is calculated using IEVMmean and IEVMsd.
IEVMmod vs Data BER is plotted and coefficients are selected to align fading channels with AWGN
Since performance varies for each OFDM rate, the coefficients for IEVMmod also vary.
Joe Kwak, InterDigital
Submission

21. IEVM: BPSK, R=3/4
Joe Kwak, InterDigital
Submission

22. IEVMmod: BPSK, R=3/4
Joe Kwak, InterDigital
Submission

23. IEVM: QPSK, R=1/2
Joe Kwak, InterDigital
Submission

24. IEVMmod: QPSK, R=1/2
Joe Kwak, InterDigital
Submission

25. IEVM: QPSK, R=3/4
Joe Kwak, InterDigital
Submission

26. IEVMmod: QPSK, R=3/4
Joe Kwak, InterDigital
Submission

27. IEVM: 16QAM, R=1/2
Joe Kwak, InterDigital
Submission

28. IEVMmod: 16QAM, R=1/2
Joe Kwak, InterDigital
Submission

29. IEVM: 16QAM, R=3/4
Joe Kwak, InterDigital
Submission

30. IEVMmod: 16QAM, R=3/4
Joe Kwak, InterDigital
Submission

31. IEVM: 64QAM, R=2/3
Joe Kwak, InterDigital
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32. IEVMmod: 64QAM, R=2/3
Joe Kwak, InterDigital
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33. IEVM: 64QAM, R=3/4
Joe Kwak, InterDigital
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34. IEVMmod: 64QAM, R=3/4
Joe Kwak, InterDigital
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35. Study of Sample Size for Error Analysis
In fading channels, IEVM varies significantly from packet to packet.
How many packets need to be measured to get a useful IEVMmean and IEVMsd?
50nsec fading channel was simulated for all OFDM rates using different sample sizes of 10, 100, 1000 packets per measurement
Joe Kwak, InterDigital
Submission

36. Sample Size Study Results
Partial results for BPSK, R=1/2
Joe Kwak, InterDigital
Submission

37. Sample Size Study Results (cont)
Std Dev of IEVMmod measurements
Joe Kwak, InterDigital
Submission

38. Sampling error for IEVM
Based on these results we see that normal sample error may have significant effect on IEVMmod.
In AWGN-dominated channels, a single EVM measurement is adequate.
In fading channels where EVM variance is high, a large number of measurements are required to achieve accurate results:
When measured over 100 packets, IEVMmod results may vary over a +/- 2db range.
When measured over 1000 packets, IEVMmod results may vary over +/- .4dB range.
IEVMavg, IEVMsd and Sample Size are all needed for meaningful measurement.
Joe Kwak, InterDigital
Submission

39. Conclusions
Results clearly show that IEVM, when modified by the the std deviation of the IEVM measure, can provide a strong indicator of BER performance after FEC decoding for all channel conditions for all OFDM rates.
IEVM alone is not sufficient. IEVMavg and IEVMsd measured over a sufficient number of packets is required to characterize channel to indicate the QOS of the radio link.
PSNI premise still valid: EVM (with variance) is adequate basis for PSNI. But as Steve Pope indicated, other demod parameters may be preferred by certain manufacturers.
Specification of PSNI needs to consider sample size and sample error.
Joe Kwak, InterDigital
Submission

40. Sample Simulation Results
For BPSK, R1/2, AWGN
Complete results in -->
Joe Kwak, InterDigital
Submission

41. EVM Calculation Matlab Code
[j,k] = size(freq_data_syms);
%compute number of data symbols, excludes extra noise symbols
no_syms = j*(k-2);
%create array with data symbol values
temp0 = freq_data_syms(:);
temp1 = temp0(1:no_syms);
if ~isempty(findstr(sim_options.Modulation, 'BPSK'))
%take absolute value to place all symbols in (+,+) quadrant
temp2 = abs(real(temp1)) + i*(abs(imag(temp1)));
% subtract out constellation point (1.0, i0), leaving error vector
temp3 = (real(temp2)-1.0) + i*(imag(temp2));
elseif ~isempty(findstr(sim_options.Modulation, 'QPSK'))
% subtract out constellation point (.7071, i.7071), leaving error vector
temp3 = (real(temp2)-(sqrt(2)/2)) + i*(imag(temp2)-(sqrt(2)/2));
Joe Kwak, InterDigital
Submission

42. EVM Calculation Matlab Code (cont)
elseif ~isempty(findstr(sim_options.Modulation, '16QAM'))
%take absolute value to place all symbols in (+,+) quadrant
temp2 = abs(real(temp1)) + i*(abs(imag(temp1)));
%shift to decision threshhold in quadrant 1 for 16QAM
temp3 = (real(temp2) ) + i*(imag(temp2) );
temp2 = abs(real(temp3)) + i*(abs(imag(temp3)));
% subtract out constellation point (.3162, i.3162), leaving error vector
temp3 = (real(temp2) ) + i*(imag(temp2) );
elseif ~isempty(findstr(sim_options.Modulation, '64QAM'))
%shift to decision threshhold#1 in quadrant 1 for 64QAM
temp3 = (real(temp2) ) + i*(imag(temp2) );
%shift to decision threshhold#2 in quadrant 1 for 64QAM
temp3 = (real(temp2) ) + i*(imag(temp2) );
% subtract out constellation point (.1543, i.1543), leaving error vector
temp3 = (real(temp2) ) + i*(imag(temp2) );
end
Joe Kwak, InterDigital
Submission

43. EVM Calculation Matlab Code (cont)
%compute magnitude of error vectors
REvm = (real(temp3)).^2;
IEvm = (imag(temp3)).^2;
Evm = REvm + IEvm;
%compute EVM
EVMpkt = sqrt(sum(Evm) / no_syms);
%EVMpkt now contains EVM calc for all symbols in this packet
%Packet series processing loop for IEVMavg and IEVMstd
IEVM = 20 * log10( 1 / EVMpkt );
%IEvm array contains IEVM values for each packet in series
IEvm(packet_count) = IEVM;
EVMtot = EVMtot + EVMpkt;
% IEVMavg is scalar of average IEVM for all packets in series
IEVMavg = 20 * log10( 1 /( EVMtot / packet_count));
%IEVMstd is scalar of Standard Deviation of IEVM for all packets in series
IEVMstd = std(IEvm);
%Output values for IEVMavg and IEVMstd with other BER calcs
Joe Kwak, InterDigital
Submission