This document discusses various channel estimation techniques for OFDM systems. It describes pilot structures like block, comb and lattice types and how they are suited for different channel conditions. It also explains training symbol based channel estimation techniques like LS and MMSE. DFT-based channel estimation aims to improve performance by eliminating noise outside the channel delay. Decision directed channel estimation updates the channel coefficients without pilots by using detected signal feedback.

1. Channel Estimation
Jay Chang
1

2. 2
Pilot Structure
Training Symbol-Based Channel Estimation
DFT-Based Channel Estimation
Decision-Directed Channel Estimation
Advanced Channel Estimation Techniques
Agenda

3. 3
Fig. Block diagram of transmitter and receiver in an OFDM system.
(S/P)
Pulse
shaping
(S/P)

4. 4
In an OFDM system, transmitter modulates → PSK/QAM symbols → IFFT on the symbols to convert them into time-domain
signals → channel. The channel effect must be estimated and compensated in the receiver.
Each subcarrier can be regarded as an independent channel, as long as no ICI (Inter-Carrier Interference) occurs, and thus
preserving the orthogonality among subcarriers. The orthogonality allows each subcarrier component of the received signal to
be expressed as the product of the transmitted signal and channel frequency response at the subcarrier.
The transmitted signal can be recovered by estimating the channel response just at each subcarrier.
Channel can be estimated by using a preamble or pilot symbols known to both transmitter and receiver, which employ various
interpolation techniques to estimate the channel response of the subcarriers between pilot tones.
Data signal as well as training signal, or both, can be used for channel estimation.
In order to choose the channel estimation technique for the OFDM system under consideration, many different aspects of
implementations, including the required performance, computational complexity and time-variation of the channel must be
taken into account.
Channel estimation

5. 5
Pilot Structure
Training Symbol-Based Channel Estimation
DFT-Based Channel Estimation
Decision-Directed Channel Estimation
Advanced Channel Estimation Techniques
Agenda
Depending on the arrangement of pilots, three different types of pilot structures
are considered:
block type, comb type, and lattice type

6. 時間選擇性衰落(快衰落)
頻率選擇性衰落
6
1
coherent
Doppler
T
f
∝
∆
1
: BW .
: ( )
coherent
spread
coherent
spread
B
t
B
t h t
∝
相干帶寬 在該 內信道衰落基本不變
時延擴展 信道沖激響應 持續時間
2個重要觀念個重要觀念個重要觀念個重要觀念

7. 7
Pilot Structure: Block Type
Pilot symbols are transmitted periodically for channel estimation.
Using these pilots, a time-domain interpolation is performed to estimate the channel along the time axis.
Let St denote the period of pilot symbols in time. In order to keep track of the time-varying channel characteristics, the pilot
symbols must be placed as frequently as the coherence time is.
Coherence time is inverse form of the Doppler frequency fDoppler in the channel, the pilot symbol period must satisfy the following
inequality:
Pros: pilot tones are inserted into all subcarriers of pilot symbols with a period in time, the block-type pilot arrangement is
suitable for frequency-selective channels.
Cons: for the fast-fading channels, incur too much overhead to track the channel variation by reducing the pilot symbol period.
Pilot symbols
1
coherent timet
Doppler
S
f
≤ =
Fig. Block-type pilot arrangement.

8. 8
Pilot Structure: Comb Type
Fig. Comb-type pilot arrangement.
Comb-type every OFDM symbol has pilot tones at the periodically-located subcarriers, which are used for a frequency-domain
interpolation to estimate the channel along the frequency axis.
Let Sf be the period of pilot tones in frequency. In order to keep track of the frequency-selective channel characteristics, the
pilot symbols must be placed as frequently as coherent bandwidth (BW) is.
Coherence bandwidth is determined by an inverse of the maximum delay spread σmax, the pilot symbol period must satisfy the
following inequality:
Pros: comb-type pilot arrangement is suitable for fast-fading channels.
Cons: Not for frequency-selective channels.
max
1
coherent BW
(delay spread)
fS
σ
≤ =

9. 9
Pilot Structure: Lattice Type
Fig. Lattice-type pilot arrangement.
Pilot tones are inserted along both the time and frequency axes with given periods. The pilot tones scattered in both time and
frequency axes facilitate time/frequency-domain interpolations for channel estimation.
Let St and Sf denote the periods of pilot symbols in time and frequency, respectively. In order to keep track of the time-varying
and frequency-selective channel characteristics, the pilot symbol arrangement must satisfy both equations
max
1 1
coherent time and coherent BW
(delay spread)
t f
Doppler
S S
f σ
≤ = ≤ =

10. 10
Pilot Structure
Training Symbol-Based Channel Estimation
DFT-Based Channel Estimation
Decision-Directed Channel Estimation
Advanced Channel Estimation Techniques
Agenda

11. 11
Training Symbol-Based Channel Estimation
Training symbols can be used for channel estimation, usually providing a good performance.
Transmission efficiencies are reduced due to the required overhead of training symbols such as preamble or pilot tones that are
transmitted in addition to data symbols.
The least-square (LS) and minimum-mean-square-error (MMSE) techniques are widely used for channel estimation when
training symbols are available.

12. 12
LS Channel Estimation: the following cost function (LS) is minimized:
X is assumed to be
diagonal due to the ICI-free condition
The mean-square error (MSE) of this LS channel estimate is given as:
Y = HX + Z
Note that the MSE in Equation is inversely proportional to the SNR , which implies that it may be subject to noise
enhancement, especially when the channel is in a deep null.
Due to its simplicity, the LS method has been widely used for channel estimation.
2 2
/x zσ σ
1
SNR
∝

13. 13
MMSE Channel Estimation: the following cost function (MSE) is minimized:
Fig. MMSE channel estimation.
MMSE method finds a better (linear) estimate in terms of W in such a way that the MSE in is minimized.ˆ( )J H
ˆ =H WHɶ
Hɶ
ˆ= −e H HH

14. 14
is the cross-correlation matrix between the true channel vector and temporary channel estimate vector in the
frequency domain.
HH
R ɶ

15. 15

16. 16
Fig. Time-domain correlation characteristic of channel

17. 17
function H_LS = LS_CE(Y,Xp,pilot_loc,Nfft,Nps,int_opt)
% LS channel estimation function
% Inputs:
% Y = Frequency-domain received signal
% Xp = Pilot signal
% pilot_loc = Pilot location
% N = FFT size
% Nps = Pilot spacing
% int_opt = 'linear' or 'spline'
% output:
% H_LS = LS channel etimate
Np = Nfft/Nps; % # of pilot
k = 1:Np;
LS_est(k) = Y(pilot_loc(k))./Xp(k); % LS channel estimation
if lower(int_opt(1)) == 'l',
method = 'linear';
else
method = 'spline';
end
H_LS = interpolate(LS_est,pilot_loc,Nfft,method); % Linear/Spline interpolation

18. 18
Pilot Structure
Training Symbol-Based Channel Estimation
DFT-Based Channel Estimation
Decision-Directed Channel Estimation
Advanced Channel Estimation Techniques
Agenda

19. 19
DFT-Based Channel Estimation
The DFT-based channel estimation technique has been derived to improve the performance of LS or MMSE channel estimation
by eliminating the effect of noise outside the maximum channel delay.
Fig. DFT-based channel estimation.
maximum channel delay L
must be known in advance.

20. 20
SNR = 20 dB
Illustration for performance improvement with DFT-based channel estimation.
https://github.com/oklachumi/octave-in-communications/blob/master/channel_estimation.m

21. 21
SNR = 20 dB
Received signal constellation diagrams before and after channel compensation.
https://github.com/oklachumi/octave-in-communications/blob/master/channel_estimation.m

22. 22https://github.com/oklachumi/octave-in-communications/blob/master/channel_estimation.m

23. 23
Pilot Structure
Training Symbol-Based Channel Estimation
DFT-Based Channel Estimation
Decision-Directed Channel Estimation
Advanced Channel Estimation Techniques
Agenda

24. 24
Fig. Block diagram of transmitter and receiver in an OFDM system.
(S/P)
Pulse
shaping
(S/P)
Review…

25. 25
Decision-Directed Channel Estimation
Fig. Block diagram for an OFDM receiver with
decision-directed channel estimation.
Once initial channel estimation is made with the preamble or pilots, the coefficients of channel can be updated with decision-
directed (DD) channel estimation, which does not use the preamble or pilots.
DD technique uses the detected signal feedback to track the possibly time-varying channel while subsequently using the channel
estimate to detect the signal.