Modeling OFDM Radio Channel

Sachin Adlakha

EE206A

Spring 2001

Modeling Multi carrier Systems

SNR for different Carrier is different. Adaptive Bit Loading

Optimizing Constellation Size and Transmit Power requires knowledge of each sub channel SNR .

Higher Layers like Link layer and MAC Layer require channel state information Adapt Retransmission and Error Control Schemes Adapt Frame Length Defer Transmission Channel State dependent Scheduling

Thus Simple model of Loaded Multi Carrier is Thus Simple model of Loaded Multi Carrier is imperativeimperative. .

Basic Multi Carrier System

INPUT

BITSTREAM S/P P/SEn-

Code

De-

Code OUTPUT

BITSTREAM

N-Parallel

Channels

X +

)(ki )(kni

)(kxi )(kyi

Performance Expressions

Assuming each sub carrier to be Quadrature Amplitude Modulated (QAM) we have

Here is the constellation size, A is the loss propagation factor, is the channel gain factor and represents transmit and

noise power.

2/2

11.4

..

12.3.

bii

n

i

ii

bi

i

i

ii

K

AP

PSNR

SNRQ

b

KBER

ib

ni PP ,

Single parameter model

To optimize the number of bit on each channel a Lagrange Multiplier based optimization technique is used Also called Water filling Assign bits to each sub channel so that performance is same on

each channel Using this technique and pervious equations we get

Here is the average constellation size and is the average power

N

i

i

n

av

bavav

KN

K

P

PAQ

b

KBER

1

1

.1

.2

..3.

avb avP

Single parameter model (contd..)

Thus the multi carrier system is completely modeled in terms of a single parameter , which depends on the knowledge of bit assignments and channel gains.

This parameter is independent of SNR, and thus characterize the entire BER-SNR curve.

Any higher layer can now perfectly characterize the current state of the channel through this parameter.

Encode DecodeX +INPUT OUTPUT

)(k )(kn

Model Verification

SNR (dB)

BER

Applications

Channel state dependent Scheduling Takes into account channel state The receivers calculate their parameters and send it back to

the transmitter. Since this parameter represents the channel state, the transmitter

can perform scheduling using this parameter.

Frame Length Adaptation The optimal frame length is dependent on the BER. Since fully specifies the BER, the link layer can perform frame

length adaptation.

Stochastic Modeling

The previous model was deterministic i.e. given channel gain factors the model compresses the channel state to single parameter.

However this parameter can also be generated as a random variable to simplify simulation of loaded multi carrier systems

The distribution of logarithm of is derived using chi-square distribution for channel gains

This distribution is derived for water filling case only and is approximated for practical bit loading algorithms

Mean

bav

2log

Variance

N

2log2

Statistics for practical Loading Algorithms

• The distribution for for water filling case is log-normal distribution

• For practical loading algorithm the mean is augmented to take into account the deviations for practical algorithms

• The variance however remains approximately same

Conclusions

• A loaded multi carrier system can be regarded as a single carrier one with single flat fading parameter.

• The overall system performance is governed by this parameter for different SNR.

• The distribution of this parameter is also obtained allowing easy modeling of multi carrier system for the purpose of simulation

• This modeling allows for compact interaction between physical layer and higher layer

Reference

• The entire presentation is based on following papers– “Model of Loaded Multi carrier system for Simulation and

Channel State Aware Protocols” by Curt Schurgers and Mani B Srivastava.

– “Single Parameter Model for Loaded Multi carrier Systems” by Curt Schurgers and Mani B Srivastava.

Thanks to Curt Schurgers for providing the graphs used in the presentation