1. Optimal Channel Estimation
for Capacity Maximization in
OFDM Systems

2. Topics
– Objective
– Principle
– Motivation
– Benefits
– System Architecture
– Implementation
– List of work completed
– Errors in implementation
– Applications of OFDM
– Reference

3. Group Members
1. Rohan Lad
2. Manoj Gorde
3. Anirudh Mayekar
4. Aaditya Gawde
Project Guide: Prof. B. G. Shreegan

4. Objective
The capacity of OFDM systems can be achieved by:
1. Channel estimation and adaptive transmission
at each subcarrier.
2. Using various channel model we can tune
various parameters of channel estimation.
3. MMSE Channel Estimation.
4. Pilot Arrangement in OFDM Systems.

5. Principle
• BASIC IDEA : Channel bandwidth is divided into
multiple subchannels to reduce ISI and frequency-
selective fading.
• Multicarrier transmission : Subcarriers are orthogonal
to each other in frequency domain.

6. Motivation for OFDM
• Disadvantages of FDMA
– Bad Spectrum Usage
• Disadvantages of TDMA
– Multipath Delay spread problem

7. OFDM Definition
• OFDM = Orthogonal FDM
• Carrier centers are put on orthogonal frequencies
• ORTHOGONALITY - The peak of each signal coincides
with trough of other signals
• Subcarriers are spaced by 1/Ts

8. Benefits of OFDM
Benefits of OFDM:
• Higher data rates
– Overlap of subcarriers
• Lower bandwidth than spread spectrum.
– High spectral efficiency
• Lower multi-path distortion
– Usage of cyclic prefix

9. FDM  OFDM
• Frequency Division Multiplexing
• OFDM frequency dividing
EARN IN SPECTRAL EFFICIENCY

10. OFDM: Eliminating ISI
• Cyclic Prefix
– Prepend the last part of the signal to the beginning of
the signal
• Duration of the CP larger than multipath delay
spread
• Orthogonality of the carriers not affected.

11. FEC IFFT
DAC
Linear
PA
add cyclic extension
bits
fc
OFDM symbol
Pulse shaper
&
view this as a time to
frequency mapper
Generic OFDM Transmitter
Complexity (cost) is transferred back from the digital to the analog domain!
Serial to
Parallel
System Architecture-1

12. AGC
fc
VCO
Sampler FFT
Error
gross offset
Slot &
fine offset
Freq.
Offset
Estimation
Timing
Sync.
(of all tones sent in one OFDM symbol)
Generic OFDM Receiver
Recovery
P/S and
Detection

13.     
1,...,2,1,0 

Nn
kXIFFTnx
 
 
 





1,...,1,0,
1,...,1,,
Nnnx
NNnnNx
nx gg
f      nwnhnxy ff 
    1,...,1,0  Nnnyny f
    
1,...,2,1,0 

Nk
nyFFTkY
         
1,...,1,0 

Nk
kWkIkHkXkY    
 
1,...,1,0  Nk
kH
kY
kX
e
e
1
76
54
32
System Architecture-2
Input to Time Domain
Guard Interval Channel
Guard Removal Output to Frequency Domain
Output Channel EstimationICI AWGNChannel Estimated
Channel

14. Implementation

15. Define Parameters
START
Create a binary data stream
Bit to Symbol Mapping
MODULATION
Transmitted Signal
CHANNEL
DEMODULATION
Received Signal
Symbol to Bit Mapping
AWGN
BER Computation
END
compare the transmitted
& received signal for bit
errors & bit error rate

16. START
Define Parameters like type of
channel, No. Subcarriers, Cyclic Prefix
length, SNR, no. pilot carriers,
transmitting & receiving antenna, etc
Derive Channel Impuse Response
with the mathematical model.
If
Rayleigh: N=50, fm=100, B=20e3
find fd=(rand no.-0.5)*2*fm
theta= randn*2*pi
c = randn(1,n)
t=0: (fm/B): (10000*fm/B)
Define Tc & Ts as zero matrix of order t
For
define funcn
k as column vector
Tc=[c(k)*{cos(2*pi*fd(k)*t+theta(k)}] +Tc
Ts=[c(k)*{cos(2*pi*fd(k)*t+theta(k)}] +Ts
define r as unity matrix &
define a index vector with
round off values
End

17. Define a zero matrix
for estimating errors
Define estimating
errors for two Tx & Rx
antenaa
Go for Channel Estimation
compute estimation errors
with Tx, Rx, as well as No. of
sub-carriers
Plot the figures
1. Plot the H_act as result of FFT
2. Plot the H_estimation 1
3. Plot the H_estimation 2
4. Plot the errors 1
5. Plot the errors 2
on SNR v/s BER
END

18. Channel Impulse Response
In the absence of noise, the received signal can be expressed as
( ) ( ) ( ) ( ) ( )
where
( ) is the channel impulse resonse.
( ) is the transmitted signal.
( ) i
y t x t h t x h t d
h t
x t
y t
  


   
1
0
s the received signal.
After sampling, the discrete received signal is given by
[ ] [ ] [ ]
L
k
y n x k h n k


 

19. Equations
 BER (Bit Error Rate): It is the number
of bit errors divided by the total number
of transferred bits during a studied time
interval.
BER = number of errors / total
number of bits sent
 Rayleigh’s fading expression:

20. 20
The Matrix Form of Channel
• The wireless stationary channel impulse response is given
by , where L is the total number of
resolvable paths.
• We assume that each tap of the channel impulse
responses , are independently distributed
complex Gaussian random variables with zero-mean and
variance .
     [ 0 , 1 ,..., 1 ]T
h h h L h
 h l 0 1l L  
 
2
h l


21. Pilot Arrangement
• Block Type
– All sub-carriers
reserved for pilots with a
specific period
• Comb Type
– Some sub-carriers are
reserved for pilots for
each symbol

22. Task of pilot subcarriers
Pilot subcarriers contain
signal values that are known
in the receiver.
These pilot signals are used
in the receiver for
correcting the magnitude
(important in QAM) and
phase shift offsets of the
received symbols (see
signal constellation example
on the right).
Re
Im
Received symbol
Transmitted symbol

23. Matlab program

24. List of work completed
 Programs for Channel impulse response
including channel estimation.
 Programs for Rayleigh’s test.
 Programs for adding noise.
 Program of random bit modulation.

25. Errors in implementation
 Program syntax errors caused due to various
“functions” & undefined variables.
Error occuring during Matlab program
debugging.
Error occuring while saving the “. mat” file.

26. Future Work
 Program of MMSE & LSE for pilot arrangement not
developed due to insufficient mathematical models

27. Applications of OFDM
OFDM is used (among others) in the following systems:
• IEEE 802.11a&g (WLAN) systems
• IEEE 802.16a (WiMAX) systems
• ADSL (DMT = Discrete MultiTone) systems
• DAB (Digital Audio Broadcasting)
• DVB-T (Digital Video Broadcasting)
OFDM is spectral efficient, but not power efficient (due
to linearity requirements of power amplifier).
OFDM is primarily a modulation method; OFDMA is
the corresponding multiple access scheme.

28. Reference
 R. van Nee and R. Prasad, ”OFDM Wireless
Multimedia Communications,” Artech
House,Boston, 2000.
 Rohit Negi and John Coiffi,”Pilot tone selection for
channel estimation in a mobile OFDM system”, IEEE
Trans. on Consumer Electronics, vol.44, no.3, Aug.
1998.
Rappaport, T., Wireless Communication: Principles
and Practice. New Jersey: Prentice Hall, 1996.
 http://grouper.ieee.org/groups/802/11/.
 www.authorstream.com/channel estimation.
 www.slideworld.com/OFDM modulation.

29. Thank You
Any Queries?