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Submission Joe Kwak, InterDigital1
EVM SIMULATIONS FOR OFDM
EVM vs BER data plots and data tables to support PSNI premise
Joe Kwak
InterDigital Communications Corporation
doc: IEEE 802.11-03/638r0July 2003
Submission Joe Kwak, InterDigital2
doc: IEEE 802.11-03/638r0July 2003
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
Submission Joe Kwak, InterDigital3
doc: IEEE 802.11-03/638r0July 2003
Background 11-03-315r2-K-RCPI_PSNI_Measurements.ppt,
presented at last 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.
Submission Joe Kwak, InterDigital4
doc: IEEE 802.11-03/638r0July 2003
Graphical Error Vector Magnitude
I
Q
I
Q
Error Vector:due to noise or distortion
EVM measure requires apriori knowledge of transmitted symbol, or must assume that closest constellation point is transmitted symbol. EVM is normalised to average power.
Transmitted symbol
(Io,Qo)
(Is,Qs)
Average power circle
Submission Joe Kwak, InterDigital5
doc: IEEE 802.11-03/638r0July 2003
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 802.11 transmitters, does not directly apply to EVM measurement in receivers.
Submission Joe Kwak, InterDigital6
doc: IEEE 802.11-03/638r0July 2003
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.
Submission Joe Kwak, InterDigital7
doc: IEEE 802.11-03/638r0July 2003
Inverse EVM EVM in simulator is computed according to :
([(I-Io)2+(Q-Qo)2])1/2
--------------------------- Nsubcsym * (Im2 + Qm
2)1/2
where (Io,Qo) is nearest constellation point, and (Im2 + Qm
2)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.
Submission Joe Kwak, InterDigital8
doc: IEEE 802.11-03/638r0July 2003
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 mean and EVM Sdev over a series of packets.
Submission Joe Kwak, InterDigital9
doc: IEEE 802.11-03/638r0July 2003EVM 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
Submission Joe Kwak, InterDigital10
doc: IEEE 802.11-03/638r0July 2003
IEVM vs SNR in AWGNIEVM vs SNR
-20
-10
0
10
20
30
40
50
-20 0 20 40 60
SNR (dB)
IEV
M (
dB
)
BPSK. R=1/2 QPSK, R=1/2
16QAM, R=1/2 64QAM, R=3/4
Submission Joe Kwak, InterDigital11
doc: IEEE 802.11-03/638r0July 2003
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.
Submission Joe Kwak, InterDigital12
doc: IEEE 802.11-03/638r0July 2003
EVM Error at low SNR Values
IEVM Error vs SNR in AWGN
0
2
4
6
8
-20 -10 0 10 20 30SNR (dB)
IEV
M-S
NR
(d
B)
BPSK. R=1/2 QPSK, R=1/2
16QAM, R=1/2 64QAM, R=3/4
Submission Joe Kwak, InterDigital13
doc: IEEE 802.11-03/638r0July 2003
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.
Submission Joe Kwak, InterDigital14
doc: IEEE 802.11-03/638r0July 2003
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.
Submission Joe Kwak, InterDigital15
doc: IEEE 802.11-03/638r0July 2003
IEVM vs Raw BER for AWGN and Fading Channels
Raw BER vs IEVM (no FEC)
-8
-7-6
-5
-4
-3-2
-1
0
-2.00E+01
-1.00E+01
0.00E+00
1.00E+01
2.00E+01
3.00E+01
20*log10(1/EVM)
Raw
BE
R (
10-x
) BPSK, R=1/2, AWGN
BPSK, R=1/2, 100ns
BPSK, R=1/2, 50ns
BPSK, R=1/2, 400ns
BPSK, R=1/2, 200ns
BPSK, R=1/2, 25ns
Submission Joe Kwak, InterDigital16
doc: IEEE 802.11-03/638r0July 2003
IEVM vs Data BER (after FEC decoding)
Data BER vs IEVM (with FEC)
-8
-7-6
-5
-4
-3-2
-1
0
-2.00E+01
-1.00E+01
0.00E+00
1.00E+01
2.00E+01
3.00E+01
20*log10(1/EVM)BE
R(o
ut
of
FE
C d
eco
der
) (1
0-x)
BPSK, R=1/2, 100ns
BPSK, R=1/2, AWGN
BPSK, R=1/2, 25ns
BPSK. R=1/2, 400ns
BPSK, R=1/2, 200ns
BPSK, R=1/2, 50ns
Submission Joe Kwak, InterDigital17
doc: IEEE 802.11-03/638r0July 2003
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 0.1 3.6 3.9 4.6 5.3 6Tdecay (nsec) AWGN 400 200 100 50 25
Submission Joe Kwak, InterDigital18
doc: IEEE 802.11-03/638r0July 2003
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
Submission Joe Kwak, InterDigital19
doc: IEEE 802.11-03/638r0July 2003
IEVMmod vs Data BER (after FEC decoding)
Data BER vs IEVMmod
-8
-7
-6
-5
-4
-3
-2
-1
0
-1.00E+01
-5.00E+00
0.00E+00
5.00E+00
1.00E+01
1.50E+01
2.00E+01
2.50E+01
IEVMmod (dB)
BE
R(o
ut
of
FE
C d
eco
der)
(10-
x)
BPSK, R=1/2, 100ns
BPSK, R=1/2, AWGN
BPSK, R=1/2, 25ns
BPSK. R=1/2, 400ns
BPSK, R=1/2, 200ns
BPSK, R=1/2, 50ns
Variance across all channel conditions < +/-1.5dB
Submission Joe Kwak, InterDigital20
doc: IEEE 802.11-03/638r0July 2003
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 6Mbps OFDM.
EVM alone is not sufficient, as Dave Skellern has shown. Variance of EVM is required to characterize channel.
Additional simulations are needed for other OFDM rates and for DSSS mode.
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.
Expect Dave Skellern to critique these details in next meeting cycle.
Submission Joe Kwak, InterDigital21
doc: IEEE 802.11-03/638r0July 2003
Simulation Results
Model Trms SNR IEVMavg IEVMstdev raw BER data BER data PER logRBER logDBER IEVMmodAWGN 0 -6 -5.03E+00 1.09E-01 2.39E-01 4.59E-01 1.00E+00 -0.6216021 -0.33818731 -4.78E+00AWGN 0 -4 -3.13E+00 1.08E-01 1.86E-01 3.01E-01 1.00E+00 -0.73048706 -0.5214335 -2.91E+00AWGN 0 -2 -1.31E+00 9.89E-02 1.30E-01 3.83E-02 9.68E-01 -0.88605665 -1.41680123 -1.13E+00AWGN 0 0 4.60E-01 9.57E-02 7.87E-02 2.91E-04 6.30E-02 -1.10402527 -3.53610701 6.12E-01AWGN 0 2 2.24E+00 9.26E-02 3.79E-02 1.00E-07 0.00E+00 -1.42136079 -7 2.36E+00AWGN 0 4 4.08E+00 9.50E-02 1.25E-02 1.00E-07 0.00E+00 -1.90308999 -7 4.18E+00AWGN 0 6 6.02E+00 9.67E-02 2.47E-03 1.00E-07 0.00E+00 -2.60730305 -7 6.10E+00AWGN 0 8 8.00E+00 9.34E-02 1.91E-04 1.00E-07 0.00E+00 -3.71896663 -7 8.05E+00AWGN 0 10 1.00E+01 9.40E-02 3.48E-06 1.00E-07 0.00E+00 -5.45842076 -7 1.00E+01AWGN 0 12 1.20E+01 9.34E-02 1.00E-07 1.00E-07 0.00E+00 -7 -7 1.20E+01AWGN 0 14 1.40E+01 9.74E-02 1.00E-07 1.00E-07 0.00E+00 -7 -7 1.40E+01AWGN 0 16 1.60E+01 9.90E-02 1.00E-07 1.00E-07 0.00E+00 -7 -7 1.59E+01AWGN 0 18 1.80E+01 9.75E-02 1.00E-07 1.00E-07 0.00E+00 -7 -7 1.79E+01AWGN 0 20 2.00E+01 9.84E-02 1.00E-07 1.00E-07 0.00E+00 -7 -7 1.99E+01
Avg Sdev of IEVM = 9.78E-02
Submission Joe Kwak, InterDigital22
doc: IEEE 802.11-03/638r0July 2003
Simulation Results (cont)
Model Trms SNR IEVMavg IEVMstdev raw BER data BER data PER logRBER logDBER IEVMmod Decay 25 -6 -1.17E+01 5.91E+00 2.75E-01 4.07E-01 9.75E-01 -0.56066731 -0.39040559 -2.92E+00 Decay 25 -4 -1.02E+01 6.26E+00 2.31E-01 3.26E-01 8.72E-01 -0.63638802 -0.4867824 -2.83E+00 Decay 25 -2 -8.78E+00 6.26E+00 1.86E-01 2.41E-01 7.48E-01 -0.73048706 -0.61798296 -2.61E+00 Decay 25 0 -6.81E+00 5.98E+00 1.47E-01 1.65E-01 5.99E-01 -0.83268267 -0.78251606 -2.00E+00 Decay 25 2 -4.14E+00 5.92E+00 1.09E-01 1.03E-01 4.16E-01 -0.9625735 -0.98716278 -1.41E+00 Decay 25 4 -1.96E+00 5.72E+00 7.61E-02 4.99E-02 2.73E-01 -1.11861534 -1.30189945 -6.61E-01 Decay 25 6 -3.52E-01 5.92E+00 5.45E-02 2.67E-02 1.72E-01 -1.2636035 -1.57348874 -6.48E-01 Decay 25 8 1.83E+00 5.66E+00 3.46E-02 1.13E-02 7.80E-02 -1.4609239 -1.94692156 3.21E-01 Decay 25 10 3.35E+00 5.89E+00 2.42E-02 3.88E-03 3.70E-02 -1.61618463 -2.41116827 1.65E-01 Decay 25 12 5.07E+00 6.06E+00 1.72E-02 1.11E-03 2.00E-02 -1.76447155 -2.95467702 7.69E-02 Decay 25 14 7.27E+00 6.01E+00 1.06E-02 8.02E-04 9.00E-03 -1.97469413 -3.09582563 6.23E-01 Decay 25 16 9.23E+00 5.99E+00 6.28E-03 4.80E-05 2.00E-03 -2.20204036 -4.31875876 1.06E+00 Decay 25 18 1.17E+01 5.96E+00 3.91E-03 4.20E-05 1.00E-03 -2.40782324 -4.37675071 1.63E+00 Decay 25 20 1.37E+01 5.65E+00 2.25E-03 1.00E-07 0.00E+00 -2.64781748 -7 3.16E+00
Avg Sdev of IEVM = 5.94E+00
Submission Joe Kwak, InterDigital23
doc: IEEE 802.11-03/638r0July 2003
Simulation Results (cont)
Model Trms SNR IEVMavg IEVMstdev raw BER data BER data PER logRBER logDBER IEVMmod Decay 50 -6 -1.34E+01 5.73E+00 2.76E-01 4.30E-01 9.87E-01 -0.55909092 -0.36653154 -3.27E+00 Decay 50 -4 -1.13E+01 5.84E+00 2.30E-01 3.40E-01 9.33E-01 -0.63827216 -0.46852108 -2.82E+00 Decay 50 -2 -9.46E+00 5.55E+00 1.92E-01 2.44E-01 8.54E-01 -0.71669877 -0.61261017 -2.30E+00 Decay 50 0 -7.13E+00 5.56E+00 1.45E-01 1.33E-01 6.07E-01 -0.838632 -0.87614836 -1.72E+00 Decay 50 2 -5.02E+00 5.24E+00 1.10E-01 6.57E-02 3.98E-01 -0.95860731 -1.18243463 -9.11E-01 Decay 50 4 -2.99E+00 5.16E+00 7.61E-02 2.10E-02 2.07E-01 -1.11861534 -1.67778071 -2.34E-01 Decay 50 6 -1.13E+00 5.19E+00 5.33E-02 7.01E-03 9.30E-02 -1.27327279 -2.15428198 2.92E-01 Decay 50 8 7.13E-01 5.06E+00 3.64E-02 1.50E-03 3.60E-02 -1.43889862 -2.82390874 1.04E+00 Decay 50 10 2.33E+00 5.41E+00 2.40E-02 2.95E-04 1.10E-02 -1.61978876 -3.53017798 9.29E-01 Decay 50 12 4.81E+00 5.18E+00 1.36E-02 6.60E-05 1.00E-03 -1.86646109 -4.18045606 2.09E+00 Decay 50 14 6.98E+00 5.28E+00 8.85E-03 1.00E-07 0.00E+00 -2.05305673 -7 2.50E+00 Decay 50 16 8.75E+00 5.23E+00 5.70E-03 1.00E-07 0.00E+00 -2.24412514 -7 3.14E+00 Decay 50 18 1.09E+01 4.91E+00 3.79E-03 1.00E-07 0.00E+00 -2.42136079 -7 4.68E+00 Decay 50 20 1.25E+01 5.27E+00 2.48E-03 1.00E-07 0.00E+00 -2.60554832 -7 4.12E+00
Avg Sdev of IEVM = 5.33E+00
Submission Joe Kwak, InterDigital24
doc: IEEE 802.11-03/638r0July 2003
Simulation Results (cont)
Model Trms SNR IEVMavg IEVMstdev raw BER data BER data PER logRBER logDBER IEVMmod Decay 100 -6 -1.51E+01 4.94E+00 2.77E-01 4.57E-01 9.98E-01 -0.55752023 -0.3400838 -4.06E+00 Decay 100 -4 -1.18E+01 4.83E+00 2.33E-01 3.70E-01 9.80E-01 -0.63264408 -0.43179828 -3.00E+00 Decay 100 -2 -9.80E+00 4.79E+00 1.90E-01 2.38E-01 9.02E-01 -0.7212464 -0.62342304 -2.31E+00 Decay 100 0 -8.04E+00 4.86E+00 1.47E-01 1.14E-01 6.54E-01 -0.83268267 -0.94309515 -1.69E+00 Decay 100 2 -6.02E+00 4.65E+00 1.11E-01 3.82E-02 3.63E-01 -0.95467702 -1.41793664 -9.23E-01 Decay 100 4 -3.39E+00 4.35E+00 7.87E-02 8.72E-03 1.36E-01 -1.10402527 -2.05948352 2.26E-01 Decay 100 6 -1.55E+00 4.35E+00 5.28E-02 8.18E-04 2.90E-02 -1.27736608 -3.0872467 9.85E-01 Decay 100 8 7.76E-01 4.20E+00 3.54E-02 1.71E-04 5.00E-03 -1.45099674 -3.76700389 2.09E+00 Decay 100 10 2.51E+00 4.31E+00 2.26E-02 8.00E-06 2.00E-03 -1.64589156 -5.09691001 2.71E+00 Decay 100 12 4.13E+00 4.44E+00 1.48E-02 1.00E-07 0.00E+00 -1.82973828 -7 3.19E+00 Decay 100 14 5.27E+00 4.68E+00 9.29E-03 1.00E-07 0.00E+00 -2.03198429 -7 3.23E+00 Decay 100 16 8.47E+00 4.12E+00 5.77E-03 1.00E-07 0.00E+00 -2.23882419 -7 5.58E+00 Decay 100 18 1.02E+01 4.23E+00 4.06E-03 1.00E-07 0.00E+00 -2.39147397 -7 6.11E+00 Decay 100 20 1.06E+01 4.93E+00 2.64E-03 1.00E-07 0.00E+00 -2.57839607 -7 4.53E+00
Avg Sdev of IEVM = 4.55E+00
Submission Joe Kwak, InterDigital25
doc: IEEE 802.11-03/638r0July 2003
Simulation Results (cont)
Model Trms SNR IEVMavg IEVMstdev raw BER data BER data PER logRBER logDBER IEVMmod Decay 200 -6 -1.42E+01 4.28E+00 2.76E-01 4.67E-01 1.00E+00 -0.55909092 -0.33068312 -4.31E+00 Decay 200 -4 -1.21E+01 4.16E+00 2.33E-01 3.85E-01 9.96E-01 -0.63264408 -0.41453927 -3.51E+00 Decay 200 -2 -9.91E+00 3.94E+00 1.91E-01 2.39E-01 9.51E-01 -0.71896663 -0.6216021 -2.68E+00 Decay 200 0 -7.88E+00 3.99E+00 1.47E-01 8.43E-02 6.76E-01 -0.83268267 -1.07417243 -1.71E+00 Decay 200 2 -6.27E+00 4.20E+00 1.10E-01 1.75E-02 2.86E-01 -0.95860731 -1.75696195 -9.57E-01 Decay 200 4 -3.58E+00 3.83E+00 7.65E-02 1.53E-03 6.30E-02 -1.11633856 -2.81530857 2.99E-01 Decay 200 6 -2.14E+00 4.04E+00 5.35E-02 1.64E-04 6.00E-03 -1.27164622 -3.78515615 9.12E-01 Decay 200 8 -1.39E-01 3.84E+00 3.65E-02 4.00E-06 1.00E-03 -1.43770714 -5.39794001 1.95E+00 Decay 200 10 2.05E+00 3.65E+00 2.40E-02 1.00E-07 0.00E+00 -1.61978876 -7 3.17E+00 Decay 200 12 3.46E+00 4.01E+00 1.65E-02 1.00E-07 0.00E+00 -1.78251606 -7 3.49E+00 Decay 200 14 5.84E+00 3.55E+00 1.04E-02 1.00E-07 0.00E+00 -1.98296666 -7 5.22E+00 Decay 200 16 7.27E+00 3.77E+00 7.51E-03 1.00E-07 0.00E+00 -2.12436006 -7 5.63E+00 Decay 200 18 8.83E+00 3.83E+00 4.95E-03 1.00E-07 0.00E+00 -2.3053948 -7 6.29E+00 Decay 200 20 1.06E+01 3.63E+00 3.63E-03 1.00E-07 0.00E+00 -2.44009337 -7 7.55E+00
Avg Sdev of IEVM = 3.91E+00
Submission Joe Kwak, InterDigital26
doc: IEEE 802.11-03/638r0July 2003
Simulation Results (cont)
Model Trms SNR IEVMavg IEVMstdev raw BER data BER data PER logRBER logDBER IEVMmod Decay 400 -6 -1.42E+01 3.66E+00 2.81E-01 4.82E-01 1.00E+00 -0.55129368 -0.31695296 -5.06E+00 Decay 400 -4 -1.19E+01 3.68E+00 2.38E-01 4.18E-01 1.00E+00 -0.62342304 -0.37882372 -3.87E+00 Decay 400 -2 -9.87E+00 3.46E+00 1.98E-01 2.76E-01 9.85E-01 -0.70333481 -0.55909092 -3.04E+00 Decay 400 0 -9.48E+00 4.01E+00 1.56E-01 9.53E-02 7.76E-01 -0.8068754 -1.0209071 -2.44E+00 Decay 400 2 -6.98E+00 3.99E+00 1.17E-01 1.26E-02 3.01E-01 -0.93181414 -1.89962945 -1.30E+00 Decay 400 4 -4.52E+00 3.75E+00 8.57E-02 5.93E-04 4.30E-02 -1.06701918 -3.22694531 -1.56E-01 Decay 400 6 -2.55E+00 3.52E+00 6.21E-02 2.00E-05 4.00E-03 -1.2069084 -4.69897 8.53E-01 Decay 400 8 -9.37E-01 3.63E+00 4.37E-02 1.00E-07 0.00E+00 -1.35951856 -7 1.66E+00 Decay 400 10 3.35E-01 3.45E+00 3.33E-02 1.00E-07 0.00E+00 -1.47755577 -7 2.40E+00 Decay 400 12 1.86E+00 3.41E+00 2.42E-02 1.00E-07 0.00E+00 -1.61618463 -7 3.24E+00 Decay 400 14 2.51E+00 3.54E+00 1.98E-02 1.00E-07 0.00E+00 -1.70333481 -7 3.49E+00 Decay 400 16 3.51E+00 3.40E+00 1.59E-02 1.00E-07 0.00E+00 -1.79860288 -7 4.14E+00 Decay 400 18 4.40E+00 3.23E+00 1.38E-02 1.00E-07 0.00E+00 -1.86012091 -7 4.77E+00 Decay 400 20 4.13E+00 3.57E+00 1.25E-02 1.00E-07 0.00E+00 -1.90308999 -7 4.31E+00
Avg Sdev of IEVM = 3.59E+00
Submission Joe Kwak, InterDigital27
doc: IEEE 802.11-03/638r0July 2003
EVM Calculation Matlab Code% EVM calculation[j,k] = size(freq_data_syms);%compute number of data symbols, excludes extra noise symbolsno_syms = j*(k-2);%create array with data symbol valuestemp0 = 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')) %take absolute value to place all symbols in (+,+) quadrant temp2 = abs(real(temp1)) + i*(abs(imag(temp1))); % subtract out constellation point (.7071, i.7071), leaving error vector temp3 = (real(temp2)-(sqrt(2)/2)) + i*(imag(temp2)-(sqrt(2)/2));
Submission Joe Kwak, InterDigital28
doc: IEEE 802.11-03/638r0July 2003
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)-.632455532) + i*(imag(temp2)-.632455532); %take absolute value to place all symbols in (+,+) quadrant temp2 = abs(real(temp3)) + i*(abs(imag(temp3))); % subtract out constellation point (.3162, i.3162), leaving error vector temp3 = (real(temp2)-.316227766) + i*(imag(temp2)-.316227766);elseif ~isempty(findstr(sim_options.Modulation, '64QAM')) %take absolute value to place all symbols in (+,+) quadrant temp2 = abs(real(temp1)) + i*(abs(imag(temp1))); %shift to decision threshhold#1 in quadrant 1 for 64QAM temp3 = (real(temp2)-.6172134) + i*(imag(temp2)-.6172134); %take absolute value to place all symbols in (+,+) quadrant temp2 = abs(real(temp3)) + i*(abs(imag(temp3))); %shift to decision threshhold#2 in quadrant 1 for 64QAM temp3 = (real(temp2)-.3086067) + i*(imag(temp2)-.30860667); %take absolute value to place all symbols in (+,+) quadrant temp2 = abs(real(temp3)) + i*(abs(imag(temp3))); % subtract out constellation point (.1543, i.1543), leaving error vector temp3 = (real(temp2)-.15430335) + i*(imag(temp2)-.15430335);end
Submission Joe Kwak, InterDigital29
doc: IEEE 802.11-03/638r0July 2003
EVM Calculation Matlab Code (cont)
%compute magnitude of error vectorsREvm = (real(temp3)).^2;IEvm = (imag(temp3)).^2;Evm = REvm + IEvm;%compute EVMEVMpkt = sqrt(sum(Evm) / no_syms);%EVMpkt now contains EVM calc for all symbols in this packet
%Packet series processing loop for IEVMavg and IEVMstdIEVM = 20 * log10( 1 / EVMpkt );%IEvm array contains IEVM values for each packet in seriesIEvm(packet_count) = IEVM;EVMtot = EVMtot + EVMpkt;% IEVMavg is scalar of average IEVM for all packets in seriesIEVMavg = 20 * log10( 1 /( EVMtot / packet_count));%IEVMstd is scalar of Standard Deviation of IEVM for all packets in seriesIEVMstd = std(IEvm);
%Output values for IEVMavg and IEVMstd with other BER calcs