SubmissionJoe Kwak, InterDigital1 EVM SIMULATIONS FOR OFDM EVM vs BER data plots and data tables to support PSNI premise Joe Kwak InterDigital Communications

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


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


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.


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


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.


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.


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.


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.


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


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


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.


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


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.


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.


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


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


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


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


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


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.


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


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


doc: IEEE 802.11-03/638r0July 2003


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



doc: IEEE 802.11-03/638r0July 2003


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



doc: IEEE 802.11-03/638r0July 2003


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



doc: IEEE 802.11-03/638r0July 2003


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



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));


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


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

Documents

SubmissionJoe Kwak, InterDigital1 EVM SIMULATIONS FOR OFDM EVM vs BER data plots and data tables to support PSNI premise Joe Kwak InterDigital Communications