UWB????(channel estimation)

1
UWB????(channel estimation)

• Speaker??? (Yu-Fan Chen)
• ??2005.07.31

2
Outline

• Introduction to DS-UWB Systems
• System Model
• Receiver Structure
• UWB Indoor Channel Model
• The Application of Channel Estimation Technique
  on DS-UWB Systems
• The Expectation-Maximization (EM) Algorithm
• The Application of EM Algorithm on DS-UWB Systems
• The Application of Adaptive Filter on DS-UWB
  Systems
• Conventional LMS Adaptive Filter
• Fuzzy Step Size LMS Adaptation
• The Application of Adaptive Filter on DS-UWB
  Systems
• Joint EM Algorithm and Adaptive Filter for DS-UWB
  Systems
• Conclusion

3
Introduction to DS-UWB Systems

• System Model

The transmitted base band signal xk(t) for user k
is obtained by spreading a set of BPSK data bits
dki, onto a spreading waveform sk(t). That is,
4

• UWB Indoor Channel Model

The UWB indoor channel model is based on the
Saleh-Valenzuela (S-V) approach 1 where the
impulse response is composed of the exponential
decay clusters to model the dense multipath
components. The UWB indoor channel model is shown
as follows 3
5
The channel impulse response of the IEEE model
can be expressed as follows
where X is the shadowing effect, and
are the channel amplitude gain, Tl is the
delay of the lth cluster, is the delay
of the mth ray in cluster l, Lk denotes the total
number of propagation paths for user k and
is the multipath delay.
The channel coefficient can be defined
as follows
where and is a
log-normal distributed channel coefficient of ray
m belonging to cluster l. The term can
thus be expressed as follows
6
where is assumed to be a Gaussian random
variable with mean and standard deviation
. Variable , in particular, can
be further decomposed as follows
where and are two Gaussian
random variable that represent the fluctuations
of the channel coefficient on each cluster and on
each ray, respectively.
Besides, the total energy of the multipath
transmission signal must be normalized to unity,
that is
7

• The characteristics of UWB channel model.

averaged from 1000 times
8
Discrete time channel impulse response for UWB
channel model 2 NLOS (0-4m).
Discrete time channel impulse response for UWB
channel model 1 LOS (0-4m).
Discrete time channel impulse response for UWB
channel model 4 extreme NLOS.
Discrete time channel impulse response for UWB
channel model 3 NLOS (4-10m).
9

• Channel Model

For the multi-user transmission, the received
signal is shown as
where Nu is the number of transmission users,
n(t) is the AWGN.
10

• Receiver Structure

For user k, the MRC Rake receiver block diagram
is shown as follows
The finger of the Rake receiver is regular
delayed by Tc to synchronize the multipath
signals, and the finger number is properly
designed to received the 85 of total transmitted
energy.
11

• At the output of the dispreading device, the
  estimated channel coefficient
• is multiply at each rake, we assume that the
  estimated channel coefficient
• is perfectly estimated and the equation is
  shown as

Ref.1
12
At the receiver, we use MRC Rake receiver to
receiver the multipath signals, for user k, the
MRC Rake receiver block diagram is shown as
follows
13

• For Channel Estimation
• The Expectation-Maximization (EM) Algorithm
• Fuzzy Step Size LMS adaptive filter

14
The Application of Channel Estimation Technique
on DS-UWB Systems

• The Expectation-Maximization (EM) Algorithm 2

Consider a wireless communication in which t
transmit antennas send date to r received
antennas. The data is unity-energy, BPSK
modulated onto a pulse waveform of duration T.
Assume that the signal is transmitted through jth
transmit antenna and is received by the antenna
i. At the output of the Match Filter whose sample
rate is 1/T, the received signal is given by
15
In an equivalent matrix form, we can write
where
16

• Pilot-Symbol-Assisted Modulation

For the multipath fading channel, the author
considers that the channel fading is constant
during each package, which contains both data and
training symbols 2. The transmitted data matrix
for each package can be written as
where P denotes the training symbol matrix and
is the transmitted data information matrix. At
the receiver, we assume that the initial channel
coefficient can be estimated by means of the
training symbols.
17

• Receiver Structure

The EM Algorithm is a general procedure for the
iterative computation of maximum likelihood (ML)
parameter estimates. The EM-based iterative
receiver scheme is shown as follows
18
To derive the p(HY,C), we need to consider the
following pdfs
We employ the Baeys rule and combine the above
pdfs to obtain
Ref.2
19
Eventually, the pdf p(HY,C) can be shown as
follows
Since the p(YH,C), p(YC), and p(HC) are
Gaussian pdf, the p(HY,C) is also a joint
Gaussian pdf with mean
and row-covariance
20
now we assume that
Given Y and Ci , the step is named as the
expectation step (E-step) of the EM algorithm.
21
We notice that each iteration of the EM algorithm
consists of two parts

• channel estimation

• data detection

The initial conditions for the iteration will
generally be derived from small number of
training symbols. If P denotes the block of
training symbols and Yp is the corresponding
received sequence, then the initial conditions are
22
These figures show the (a) BER simulation and (b)
channel tracking ability of EM algorithm under
Rayleigh fading channel with space-time technique
(2Tx., 1Rx.). The package length is 10 bit, and
the Rayleigh fading channel is assumed to be
constant during each package.
(b)
(a)
23

• The Application of EM Algorithm on DS-UWB Systems

• For user k, the combination of MRC Rake receiver
  and EM algorithm block diagram is shown as
  follows

• The EM algorithm block diagram is showing as
  fallow

24

• Using the Bayes rule

25
Suppose that the channel coefficient in the rth
finger is estimated by the EM algorithm, denoted
as . We multiple the estimated channel
coefficient to the received signal captured by
each finger, respectively. Then the summation of
each finger is operated and is shown as follows
Then, the received data for user k can be
detected by the decision device and denoted as
26

• Performance analysis with UWB indoor channel
  model

The simulation of single user and multi-user
transmission for DS-UWB systems that employ EM
algorithm is investigated in the following pages.
We assume that the package length is 30 bits
which contain both 10 bits training symbol and 20
bits data information. Besides, the channel
impulse response is fixed during each package.
27

• The simulation of BER for DS-UWB systems that
  employ EM algorithm with (a) UWB
• CM1, 6 fingers, (b) UWB CM4, 18 fingers,
  and single user transmission.

(b)
(a)
28

• The simulation of BER for DS-UWB systems that
  employ EM algorithm with (a) UWB
• CM1, 6 fingers, (b) UWB CM4, 18 fingers,
  and 5 user transmission.

(b)
(a)
29

• Summary

• Simulation results show that the application of
  the EM algorithm to the MRC Rake receiver for
  channel estimation can perform an attractive
  performance
• with only a few number of iterations.
  However, under the multi-user
• transmission environment, the multi-user
  interference will severely affect the system
  performance and eventually cause a poor channel
  estimation for EM
• algorithm.
• Therefore, in order to reduce the multi-user
  interference, a novel fuzzy step size
• LMS adaptive filter is proposed which
  adopts a variable step size for the interference
  cancellation. The detailed discussion can be seen
  in next chapter.

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The Application of Adaptive Filter on DS-UWB
Systems

• Conventional LMS adaptive filter

31
(No Transcript)
32

• Fuzzy step size LMS adaptation

• Introduction

For the conventional LMS algorithm
Proposed fuzzy step size LMS algorithm
33

• Fuzzy Step Size LMS Adaptation

The block diagram for the FSSD-LMS and FSPU-LMS
algorithm is shown as follows
34

• For example

• MSE large (L) , ?MSE large (L)
• ? Step size large (L)

• MSE small (S) , ? MSE large (S)
• ? Step size small (S)

35
Design Method for FSS-LMS Adaptation
In the FIS, the membership functions (MBFs) about
inputs and outputs are illustrated in the
following figures
36
The step size adjustment table for FSSD-LMS
algorithm.
To derive the variable , the Centroid
Calculation of is employed, which
returns the center of area under the aggregate
MBFs curve, as follows
where q is the output numbers of the Membership
Function, is the step size obtained
from the Table 4.1 and Table 4.2.,
is the Membership Function value of x.
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Design method for FSSD-LMS algorithm

• MSE 0.8M , 0.2S

• ?-MSE 0.7L , 0.3M

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3.Design method for FSS_LMS algorithm

• MSE 0.8M , ?- MSE 0.7L ? 0.8 M

39

• Fuzzy Sequential Partial Update LMS Adaptation

The tap-weights estimate of the fuzzy sequential
partial update LMS (FSPU-LMS) filter at the
(i1)th iteration is written as 5
Therefore, only coefficients of the
vector w(i) are updated at each iteration.
The sequential partial update adjustment table
for FSSD-LMS algorithm is shown below
40

• The application of adaptive filter on DS-UWB
  systems

For user k, the MRC Rake receiver combine with
adaptive filter block diagram is shown as follows
41

• Joint Fuzzy Adaptive Filter for DS-UWB System

For user k, the MRC rake receiver combine with
fuzzy step size LMS adaptive filter block
diagram is shown as follows
42

• Performance analysis with UWB indoor channel
  model

Simulation Environment The simulation of
single user and multi-user transmission for
DS-UWB systems that adopt the fuzzy step size LMS
adaptive filter for the interference cancellation
is demonstrated in the following pages. We assume
that the package length is 30 bits which contain
both 10 bits training symbols and 20 bits data
information, the SNR is 20dB, and the channel
impulse response is assumed to be fixed during
each package.
43

• The simulation of MSE for DS-UWB systems that
  employ adaptive filter with (a) UWB CM1, 6
  fingers,
• (b) UWB CM4, 18 fingers, and single user
  transmission.

(b)
(a)
44

• The simulation of MSE for DS-UWB systems that
  employ adaptive filter with (a) UWB CM1, 6
  fingers,
• (b) UWB CM4, 18 fingers, and 5 user
  transmission.

(b)
(a)
45
The simulation of Partial Update Parameter (L)
for DS-UWB systems that employ fuzzy sequential
partial update LMS (FSPU-LMS) adaptive filter
with CM1, 6 fingers, and the user number is 1, 5,
10, respectively.
46
Joint EM Algorithm and Fuzzy Adaptive Filter for
DS-UWB Systems

• Introduction

• The application of EM algorithm on DS-UWB
  systems

• The application of fuzzy adaptive filter on
  DS-UWB systems

When under the single user transmission with no
MPI and no MUI, the optimum of fuzzy adaptive
filter on DS-UWB systems is the same as the
channel coefficient in each finger. Therefore,
the joint of EM Algorithm and Fuzzy Adaptive
Filter for DS-UWB Systems is proposed.
47

• The system block of MRC Rake receiver that joint
  EM algorithm and fuzzy step LMS
• adaptive filter.

48

• Performance analysis with UWB indoor channel
  models

Simulation Environment The simulation of single
user and multi-user transmission for DS-UWB
systems that joint EM and fuzzy adaptive filter
is investigated in the following pages. We assume
that the package length is 30 bits, the SNR is
20dB, and the channel impulse response is fixed
during each package.

• The simulation of MSE for DS-UWB systems that
  joint adaptive filter and EM algorithm
• with CM1, 6 fingers, and single user
  transmission.

49

• The simulation of MSE for DS-UWB systems that
  joint adaptive filter and EM algorithm
• with CM4, 18 fingers, and single user
  transmission.

50

• The simulation of MSE for DS-UWB systems that
  joint adaptive filter and EM algorithm
• with CM1, 6 fingers, and 5 user transmission.

51

• BER Performance analysis for DS-UWB indoor
  channel models

Simulation Environment The simulation of single
user and multi-user transmission for DS-UWB
systems that joint EM and fuzzy adaptive filter
is investigated in the following pages. We assume
that the package length is 30 bits, and the
channel impulse response is fixed during each
package.

• The simulation of BER performance for DS-UWB
  systems that joint fuzzy adaptive filter and
• EM algorithm with CM1, 6 fingers, and single
  user transmission.

52

• The simulation of BER performance for DS-UWB
  systems that joint fuzzy adaptive filter and EM
• algorithm with (a) CM1, 6 fingers, (b) CM4,
  18 fingers, and single user transmission.

(b)
(a)
53

• The simulation of BER performance for DS-UWB
  systems that joint fuzzy adaptive filter and EM
• algorithm with (a) CM1, 6 fingers, (b) CM4,
  18 fingers, and 5 user transmission.

(b)
(a)
54

• The simulation of BER versus number of user for
  DS-UWB systems that joint fuzzy
• adaptive filter and EM algorithm with CM1,
  6 fingers. The SNR is 10 dB.

55

• Joint EM Algorithm and Fuzzy Adaptive Filter for
  DS-UWB System with space-time technique.

Adaptive Weight Control
EM Algorithm
EM Algorithm
Matched Filter
EM Algorithm
Fuzzy Inference System (FIS)
Delay
Adaptive Weight Control
EM Algorithm
EM Algorithm
Matched Filter
EM Algorithm
Fuzzy Inference System (FIS)
Delay
56

• The simulation of BER performance for DS-UWB
  systems that joint fuzzy adaptive filter
• and EM algorithm with space-time technique
  (1Tx., 2Rx.) under CM4, 18 fingers, and
• single user.

57

• The simulation of BER performance for DS-UWB
  systems that joint fuzzy adaptive filter
• and EM algorithm with space-time technique
  (1Tx., 2Rx.) under CM4, 18 fingers, and
• 5 users.

58
Conclusions

• This thesis demonstrates the joint of channel
  estimation technique and adaptive filter for the
  DS-UWB systems. With the adaptation of
  expectation-maximization algorithm proposed by
  2, the channel coefficient can be estimated the
  with iterative steps.
• For the multi-user transmission, the multi-user
  interference will cause a poor channel estimation
  operated by EM algorithm. Hence, a novel fuzzy
  step size LMS adaptive filter which adopts a
  variable step size for the interference
  cancellation is proposed for the DS-
• UWB systems.
• Therefore, with the joint of EM algorithm for
  channel estimation and fuzzy adaptive filter for
  interference cancellation, the DS-UWB systems can
  perform an astonishing
• performance even for the multi-user
  transmission.

59
Reference

• 1 A. A. Saleh and R. A. Valenzuela, A
  Statical Model for Indoor Multipath Propagation,
  IEEE J. Select. Areas Commun., vol. 5, pp.
  128-137, Feb. 1987.
• 2 C. Cozzo, L. Brain, Joint Detection and
  Estimation in Space-Time Coding and Modulation,
  1999 IEEE
• 3 M. G. D. Benedetto, G. Giancola,
  Understanding Ultra Wide Band - Radio
  Fundamentals, Prentice Hall PTR, 2004
• 4 H. Y. Lin, C. C. Hu, Y. F. Chen, J. H. Wen,
  An adaptive robust LMS employing fuzzy step size
  and partial update, IEEE Signal Processing
  Letters, vol. 12, NO. 8, Aug. 2005
• 5 J. Sanubari, Fast convergence LMS adaptive
  filters employing fuzzy partial updates,
  Conference on Convergent Technologies for
  Asia-Pacific Region, vol. 4, pp. 13341337, Oct.
  2003.

60

• Thanks For Your Attention

61
Appendix
Ref.1

• For the MRC RAKE receiver, after passing through
  the match filter whose sample rate is
• 1/Tc, the received signal for the kth user can be
  obtain by passing through the dispreading
• device, the steps are shown as follows

For user ks data passing through the match
filter, and accumulating a package duration of
Tp, denoted as z, where TpfTb and f is the
package length. The received signal z for the
user k is shown as follows
62

• When passing through the Rake receiver, we
  assume that Nk paths are
• synchronized by Nk fingers, where
  , for the rth finger, the
• equation is formulated as

63

• We can express the in a vector form,
  i.e.

where is the extended spreading code for
user k in the jth path,
and is the noise vector corresponding to
the ith bit,
64

• In the dispreading step, after passing through
  the dispreading device , the
• dispread signal is

65
Ref.2
To evaluate the p(HY,Ci), we employ the Baeys
rule and combine the above pdfs to obtain
The expression inside the trace can be written
as
66
assume that
therefore, the above equation can be simplified
as follows