Physical layer abstraction forLTE downlink

PRESENTED BY RAJ PATEL

Introductionlink level simulator simulates a single radio link

system level simulator takes into accounta complete cell: time consuming

Physical layer abstraction : process of modeling the performance of the physical layer based on the current channel state and the physical layer parameters

IntroductionAWGN

MCS -> CQI

target SNR – 10% BLER

Plots : Target SNR vs CQI / MCS - linear

IntroductionExtrapolation of Reference curve to get effective SNR

choose MCS values belonging to same constellation.

Get the Target SNR value

•Calc. difference between the T.SNR values

We note down the effective code rate for the MCS used.

We use the reference curves to get the values of SNRusing the effective code rate of that MCS

•Calc. the difference between the SNR values

Observationsotheoretical difference and the difference calculated using interpolation are not the same

oPossible reason: C* = (TBS + CRC) / G. G: bits transmitted per second; C: Code Rate

o 40 <= Code Block Size(= TBS + CRC) <= 6144 ; CRC = 24 bits

oEg: 6126 bits TBC6120 + 24 // 6 + 24 + 10 ; 10 : padding

Delta SNR from

Lookup table values

C = TBS / G

4.237 4.3203 1.4398 2.8805 4.7258 6.6409 2.6672 3.9737

Delta SNR from look

up table using

C* = (TBS + CRC) / G

4.1689 4.3423 1.4366 2.9057 4.7415 6.684 2.6877 3.9963

Delta SNR from log

BLER curve2.86 3.446 0.788 2.668 4.2 3.742 2.412 2.33

Frequency Selective FadingCoherence Bandwidth

Signal Bandwidth

Flat fading: Just attenuation, no distortion

Frequency Selective (much more realistic): Distortion

If the attenuation happens in different amounts for the different parts of the signal, it is a distortion.

Condition: Coherence Bandwidth < Signal Bandwidth

Frequency selective fading channel model

Eg.: EPA

EPA : Extended Pedestrian A modelomultiple paths

osame signal copies arrive at the receiver delayed and different attenuations

o-g E –M1 –R1 –N 100 –n 10000

o-M1: Abstraction flag keeps channel coefficients constant over SNR range

o-R1: to reduce simulation time

o-g E: fading model

o-n: number of packets

o-N: number of channel realizations

oOUTPUT format:SNR, 50 channel coefficients, BLER1

Abstraction TechniquesEESM

MIESM

EESM: Exponential Effective SINR Mapping𝛾eff = 𝛽1 𝐼

−1 1

𝑁 𝑛=1𝑁 𝐼

𝛾𝑛

𝛽2

𝐼 𝛾𝑛 = 1 − exp (−𝛾𝑛) ; 𝛾𝑛 is the instantaneous SNR

Aim: to calculate SINR effective

Noise_var = 1 / SNR_linear; inst_snr = 10*log10 (h^2/Noise_var);

1. Calculate the instantaneous SNR corresponding to each value of channel realization

2. Use the I function with the instantaneous SNR and average it over N

3. Use the inverse function of I to calculate the effective SNR

PLOTS - EESM

MIESMMutual Information Effective SINR Mapping

No closed form expression

Calculate the instantaneous SNR

Using lookup tables, calculate normalized capacity for each instantaneous SNR

Calculate average normalized capacity per SNR

Calculate the effective SNR using average normalized capacity with lookup table

PLOTS MIESM

MSE calculation𝛾eff = 𝐼−1

1

𝑁 𝑛=1𝑁 𝐼(𝛾𝑛)

*N stands for the number of valuesof channel coefficients per SNR.

SNR interp: image of SNR effective on AWGN curve

𝑀𝑆𝐸=1

𝑁 𝑛=1𝑁

𝛾𝑖𝑛𝑡𝑒𝑟𝑝 BLER𝑐ℎ −𝛾eff𝛾𝑖𝑛𝑡𝑒𝑟𝑝 BLER𝑐ℎ

2

*N here, stands for the number of SNR values.

MSE resultsMCS MSE EESM using

'linear','extrap'

NORMALIZED

Linear, log

MSE_MIESM

'linear','extrap'

NORMALIZED

Linear, log

3 58.695, 0.3663 108.92, 0.2975

15 1.5247, 0.4958 0.3202, 0.3395

15 _n = 1000, N =1000 1.1699, 1.3596 0.3403, 1.9242

20 * 0.3869, 0.2304 0.1067, 0.5900

23 0.2551, 0.4954 0.0823, 0.3636

25 0.0897, 0.7444 0.0672, 0.7858

MSE – With 𝛽1, 𝛽2𝛾eff = 𝛽1 𝐼

−1 1

𝑁 𝑛=1𝑁 𝐼

𝛾𝑛

𝛽2

𝑀𝑆𝐸argmin𝛽1,𝛽2

=1

𝑁 𝑛=1𝑁

𝛾𝑖𝑛𝑡𝑒𝑟𝑝 BLER𝑐ℎ −𝛾eff 𝛽1,𝛽2𝛾𝑖𝑛𝑡𝑒𝑟𝑝 BLER𝑐ℎ

2

MSE Results – With 𝛽1, 𝛽2

MCS B values MSE EESM

calibrated

3 [0.0334,0.6226] 0.7683

15 [3.975e+02,4.7833e+03] 0.0037

15 _n = 1000, N

=1000

[3.991e+02,5.581e+03] 0.0041

20 (erroneous) [41.3997,58.1240] 0.0466

23 [6.862e+02,1.241e+04] 1.64e-04

25 [7.469e+02,1.318e+04] 1.20e-04

MCS B values MSE MIESM

calibrated

3 [0.2051,17.348] 0.9835

15 [0.7490,0.6111] 0.2887

15 _n = 1000, N

=1000

[0.7903,0.7440] 0.3339

20 (erroneous) [0.6041,0.7456] 0.0430

23 [0.8813,0.7282] 0.0567

25 [0.8398,0.8028] 0.0645

EESM – calib.

MCS- color3-Red, 15- Yellow, 20*- Sky blue,23- Blue, 25- Pink

Conclusions and Observations

Calibration factors work better with EESM

The resultant MSE after using calibration factor with EESM are around 10^3 times better

Where as for MIESM, it is 10 times better.

MCS 25: EESM MIESM

MSE Without calibration 0.7444 0.7858

MSE With calibration 1.20e-04 0.0645

Conclusions and ObservationsCalculations done in the log scale don’t make

𝑀𝑆𝐸argmin𝛽1,𝛽2

=1

𝑁 𝑛=1𝑁

𝛾𝑖𝑛𝑡𝑒𝑟𝑝 BLER𝑐ℎ −𝛾eff 𝛽1,𝛽2𝛾𝑖𝑛𝑡𝑒𝑟𝑝 BLER𝑐ℎ

2

Division in log scale?MCS MSE EESM using

'linear','extrap'

NORMALIZED

Linear, log

MSE_MIESM

'linear','extrap'

NORMALIZED

Linear, log

3 58.695, 0.3663 108.92, 0.2975

15 1.5247,0.4958 0.3202, 0.3395

20 (erroneous) 0.3869, 0.2304 0.1067, 0.5900

23 0.2551, 0.4954 0.0823, 0.3636

25 0.0897, 0.7444 0.0672, 0.7858

NOTE: Calculations in Linear scale show a gradual Decrease in MSE value, unlike the log scale

Thus operate with linear valuesif we are using Normalization

But why does Lower MCS have weird MSE values?

Conclusions and ObservationsIssues with the lower MCS values any ideas??

Working on Linear scale, why is it that the Lower MCS has higher values of MSE compared to higher MCS values?

Reason: Normalization while calculating MSE

𝑀𝑆𝐸argmin𝛽1,𝛽2

=1

𝑁 𝑛=1𝑁

𝛾𝑖𝑛𝑡𝑒𝑟𝑝 BLER𝑐ℎ −𝛾eff 𝛽1,𝛽2𝛾𝑖𝑛𝑡𝑒𝑟𝑝 BLER𝑐ℎ

2

𝛾𝑖𝑛𝑡𝑒𝑟𝑝 BLER𝑐ℎ − 𝛾eff 𝛽1, 𝛽2 : more or less remains the same, say around 5-10 dB

But, 𝛾𝑖𝑛𝑡𝑒𝑟𝑝 BLER𝑐ℎ changes according to MCS value, stays close to -2 to 2 dB

Conclusions and Observations

Conclusions and ObservationsMCS MSE EESM using

'linear','extrap'

NORMALIZED

Linear

MSE_MIESM

'linear','extrap'

NORMALIZED

Linear

3 58.695 108.92

15 1.5247 0.3202

15 _n = 1000, N =1000 1.1699 0.3403

20 (erroneous) 0.3869 0.1067

23 0.2551 0.0823

25 0.0897 0.0672

Table with the calculations done in Linear scale.

Conclusions and ObservationsFor 15 _n = 1000, N =1000 case, the calculations are not in synchronization with the other cases.

Reason: too many values: may be it gives us a better estimate.

MCS B values MSE EESM

calibrated

3 [0.0334,0.6226] 0.7683

15 [3.975e+02,4.7833e+03] 0.0037

15 _n = 1000, N

=1000

[3.991e+02,5.581e+03] 0.0041

20 (erroneous) [41.3997,58.1240] 0.0466

23 [6.862e+02,1.241e+04] 1.64e-04

25 [7.469e+02,1.318e+04] 1.20e-04

MCS B values MSE MIESM

calibrated

3 [0.2051,17.348] 0.9835

15 [0.7490,0.6111] 0.2887

15 _n = 1000, N

=1000

[0.7903,0.7440] 0.3339

20 (erroneous) [0.6041,0.7456] 0.0430

23 [0.8813,0.7282] 0.0567

25 [0.8398,0.8028] 0.0645

Note: The MSE of EESM is lower than the MSE of MIESM

NOTE: Calculations in Linear scale show a gradual Decrease in MCS value

Conclusions and ObservationsNote: The MSE of EESM is lower than the MSE of MIESM

Reason? High values of Beta using EESM?

MCS B values MSE EESM

calibrated

3 [0.0334,0.6226] 0.7683

15 [3.975e+02,4.7833e+03] 0.0037

15 _n = 1000, N

=1000

[3.991e+02,5.581e+03] 0.0041

20 (erroneous) [41.3997,58.1240] 0.0466

23 [6.862e+02,1.241e+04] 1.64e-04

25 [7.469e+02,1.318e+04] 1.20e-04

MCS B values MSE MIESM

calibrated

3 [0.2051,17.348] 0.9835

15 [0.7490,0.6111] 0.2887

15 _n = 1000, N

=1000

[0.7903,0.7440] 0.3339

20 (erroneous) [0.6041,0.7456] 0.0430

23 [0.8813,0.7282] 0.0567

25 [0.8398,0.8028] 0.0645

Issues and Future WorkThe calibration factors are a bit high for some MCS values for EESM!

WHY!?

Is that the only reason why we see the performance of EESM is better than MIESM??

Thank You!Questions if any

LTEOFDM

OFDMA

Cyclic Prefix

ISI

RE

RB

OAIEurecom

Physical layer stimulations

Resource Elements Allocation•N_PILOTS = 6*N_RB*TM

•N_RB - by default set to 25

•N_RE = (OFDM symbols – Prefix length) * (N_RB*sub-carriers per block) - N_PILOTS

•Example: -x1 –y1 –z1 ; Normal cyclic prefix

•N_RE= (14-1)*(25*12) – (6*25*1) = 3750

Map CQI --> MCS•CQI – feedback

•MCS – chosen

CQI (1-15) MCS(1-28)

3 3

8 15

10 20

13 25 (with extended prefix)

AWGN reference curves•BLER vs SNR plots

•Monte Carlo stimulations

•Step size

•SNR range

•Interpret .csv

•Target SNR

Plots•Target SNR vs CQI

•Target SNR vs MCS

•Target SNR vs Code rate

•Observation

Extrapolation of curves•ΔSNR (db) = f -1(r2) – f-1(r1)

•Normalized capacity is the

effective code rate

•Code rate/ bits per symbol

Extrapolation method•Choose MCS values belonging to same constellation.

•Stimulate for those MCS values and get the Target SNR value. Target SNR is the SNR value for log BLER= -1

•ΔSNR value of two MCS schemes from stimulation

•We note down the effective code rate for the MCS used.

•We use the reference curves to get the values of SNR using the appropriate curve (taking into consideration the Modulation scheme used for that MCS)

•ΔSNR values found from the reference curves by extrapolation

Conclusions•Extrapolation important

•Needs to be improved