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 forcomplex 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(H) =‖ Y − XH ‖22

X =

x1 . . . 0...

. . ....

0 . . . xp

, H =

h1...

hp

, Y =

Y1...

Yp

Analytical Solution HLS = X−1Y



Least Squares

least squares estimatation minimizes the L2 norm, or in other order the

euclidean distance between the received signal and the original signal


∴ HLS =

Y1X1...

Yp

Xp

X : Matrix of transmitted pilots diag(X ) for p = 0, . . . , lNp − 1Y : Received pilot signals.

H 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(H) = E{‖ H − H ‖22

}= E {‖ e2 ‖22}

Figure: MMSE block diagram



Minimum Mean Square Error

MMSE solution

min J(H) = E{‖ H − H ‖22

}= E {‖ e2 ‖22}

Analytical Solution hMMSE = RhY R−1YY Y

ˆHMMSE = F ˆhMMSE

F =

W 00N . . . W 0(N−1)

N...

. . ....

W (N−1)0N . . . W (N−1)(N−1)

N

, F : DFT matrix

ˆHMMSE = (RHH + σ2w(XXH)H)−1︸︷︷︸W

HLS



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 4010

−6

10−5

10−4

10−3

10−2

10−1

100

101

Eb/No (dB)

Channel M

SE

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 4Group no.12 Advanced Communications Systems 2014 23 / 26


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 σ2i .



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

Engineering

ofdm systems group

channel statistics

pilot arrangements group

pilots group

mmse block diagram group

snr group

pilot arrangements figure

pilot signals