Short survey for Channel estimation using OFDM systems

Channel estimation using OFDM systems
Group no.12
Advanced Communications Systems 2014
Group no.12 Advanced Communications Systems 2014 1 / 26

Motivation
OFDM technique is used to split a
high-rate data stream into a number of
lower rate streams that are transmitted
simultaneously over a number of
subcarriers.
Figure: Spectrum of OFDM subcarriers

Motivation
Each subcarrier is multiplied by a
constant gain.
OFDM eases the equalization process
of received signals. No need for
complex equalizers
Figure: Parallel Subchannel Model

Motivation
For equalization, receiver should have a
Channel Estate Information (CSI)
Different channel estimation techniques
are developed.
Figure: IEEE 802.11g receiver

Conceptual view: Channel estimation
The transmitter side sends a kown signal to the receiver side∗
. The received
signal is then in frquency domain analysis (with noise free claim in this section)
Y(f ) = X(f )H(f ) , Where:
Y(f): Spectrum of received signal (know at Rx).
X(f): Spectrum of reference signal (known at Tx and Rx).
H(f): Frequency response of the channel(un known).
However, the estimated channel ˆH(f ) = H(f ) ± δ , where δ is
contaminated by noise effect.
Suggested techniques of estimation are investigated to reduce this value (δ).
∗
Basic point to point communications case

Pilot arrangements
Figure: Pilot arrangements

Pilot arrangements
There are two basic types of pilot arrangments :
Block type: All sub-carriers reserved for pilots wit a specific period.
used for slow fading channels.
Figure: Block type of pilot arrangement

Pilot arrangements
There are two basic types of pilot arrangments :
Comb type: Some sub-carriers are reserved for pilots for each symbol.
used for fast fading channels.
Figure: Comb type of pilot arrangement

Block type pilot channel estimation
Least Squares
least squares estimatation minimizes the L2 norm, or in other order the
euclidean distance between the received signal and the original signal
Least squares solution
min J( ˆH) = Y − X ˆH 2
2
X =



x1 . . . 0
...
...
...
0 . . . xp


 , ˆH =



ˆh1
...
ˆhp


 , Y =



Y1
...
Yp



Analytical Solution ˆHLS = X−1
Y

Least Squares
least squares estimatation minimizes the L2 norm, or in other order the
euclidean distance between the received signal and the original signal
∴ ˆHLS =





Y1
X1
...
Yp
Xp





X: Matrix of transmitted pilots diag(X) for p = 0, . . . , lNp − 1
Y: Received pilot signals.
ˆH Estimated Channel Frequency Response (CFR) at pilots

Minimum Mean Square Error
The MMSE estimator employs the second order statistics of channel conditions
to minimize the MSE.
MMSE solution
min J( ˆH) = E H − ˆH 2
2 = E { e2 2
2}
Figure: MMSE block diagram

Minimum Mean Square Error
MMSE solution
min J( ˆH) = E H − ˆH 2
2 = E { e2 2
2}
Analytical Solution ˆhMMSE = RhY R−1
YY Y
ˆHMMSE = F ˆhMMSE
F =



W00
N . . . W
0(N−1)
N
...
...
...
W
(N−1)0
N . . . W
(N−1)(N−1)
N


 , F : DFT matrix
ˆHMMSE = (RHH + σ2
w(XXH
)H
)−1
W
ˆHLS

LS performance
Advantages:
Very low complexity.
No dependency on channel statistics.
Disadvantages:
Suffer from high MSE between the actual channel gain and
estimated version. MSE =
1
SNR

MMSE performance
Advantages:
Better perfromance than LS, since it dependes on minimizing the
MSE.
Disadvantages:
High complexity, it depends on the channel statistics.
Suggested technique called Modified MMSE to reduce the complexity of MMSE
estimator.

LS vs MMSE performance
Performance characterization in terms of MSE.
0 5 10 15 20 25 30 35 40
10
−6
10
−5
10
−4
10
−3
10
−2
10
−1
10
0
10
1
Eb/No (dB)
ChannelMSE
Simulated−LS
Simulated−MMSE
Theory−LS
Theory−LMMSE
Figure: LS vs MMSE - 16 QAM

Comb type pilot channel estimation
Two basic techniques are used:
LS estimator
Hp(k) = Yp(k)
Xp(k), p = 0, . . . , Np − 1
p: Pilot index.
Np: Number of pilot signals uniformly inserted in X(k).
Hp(k): Channel frequency response at pilot sub-carrirers.
Xp input at the kth pilot sub-carrier.
Yp output at the kth pilot sub-carrier

LMS estimator: type of Adaptive filtering
Apply an iterative algorithm till a certain acceptable error.
Figure: LMS estimator

LMS estimator: type of Adaptive filtering
Apply an iterative algorithm till a certain acceptable error.
Figure: Convergence LMS estimator over number of iterations

Interpolation for Comb type
In comb type, Some sub-carriers are reserved for pilots for each symbol.
We need channel interpolation for the channel gain affecting on the data.
Figure: Pilots and Data symbols spectrum

Different types of interpolation techniques are used.
Linear interpolation
Second order interpolation
Low pass interpolation
Figure: Channel Interpolation

LS vs Kalman performance
Performance characterization in terms of BER.
Figure: LS vs Kalman - 16 QAM

Effect of mobility
Performance characterization in terms of BER.
Figure: Doppler spread effect

Channel estimation in MIMO - OFDM system
Pilot arrangment
Figure: Pilot arrangemnt MIMO channel for 2 x 2 and 4 x 4

Figure: MIMO channel model
Hĳ(n, k) is the Channel Frequency Response (CFR) between transmitting
antenna i to receiving antenna j.
Ni is the additive Gaussian noise with zero mean and variance σ2
i .

Tx Beamforming
Figure: Dynamic Digital Beamforming in a 4x4 MIMO System with Two Data Streams in WiFi 802.11
n/ac
Transmitter have no CSI, so tx can’t compute the beamforming weights.
In new WiFi standards, channel estimation is turned into the users.
Feedback channel concept.
Any imperfection causes performance degradation.

Thank you !

Short survey for Channel estimation using OFDM systems

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Short survey for Channel estimation using OFDM systems