Transcript Single Correlator Based UWB Receiver Implementation

Single Correlator Based UWB
Receiver Implementation
through Channel Shortening
Equalizer
By
Syed Imtiaz Husain and Jinho Choi
School of Electrical Engineering and Telecommunications
University of New South Wales, Sydney.
Why Channel Shortening in UWB Receivers?
• UWB channel impulse responses have following features:
1.
Very long as compared to UWB pulse width.
2.
Dense in multipaths.
3.
Quasi-static.
• Due to fine resolution of UWB pulses, multipaths are resolvable and receiver
is implemented through RAKE.
• Complexity and cost of UWB receiver depends upon the number of fingers in
the RAKE.
• Channel shortening can help in reducing the number of fingers in RAKE and
eventually simplify the complexity and reduce the associated cost.
Channel Shortening – Introduction and Existing
Applications
Introduction:
• It is an equalization technique to reduce the channel impulse response within a
desired window of time.
• It is also known as Time Domain Equalization (TEQ).
Existing Applications:
• Channel shortening was first introduced in 1970s to reduce the complexity in
sequence estimation – Reduced State Sequence Estimation (RSSE).
• In 1990s, this technique reappeared for MCM/DMT systems to reduce the
channel delay spread as compared to the length of CP.
• A similar idea has been proposed to suppress scalar channels in a multiuser
environment for effective detection.
• Most of the recent applications for MCM/DMT systems are developed for
wired line channels with less multipaths and intend to maximize bit rate or
channel capacity.
Channel Shortening – Our Approach
•
•
•
In this paper, we design and apply a new channel shortening algorithm for
wireless UWB channels with dense multipaths.
We show that the proposed algorithm can shorten any UWB channel to just
one significant tap.
We also prove that the proposed algorithm performs better than its existing
variants in terms of energy capture and SINR improvement.
System Model
• Standard channel models suggested by IEEE 802.15 Study Group 3a, namely
CM 1 to CM 4, are used for performance evaluation.
• A time hopping pulse position modulated (TH-PPM) UWB system is
considered.
• Following realistic system parameters are assumed for comparative analysis:
Table 1: System Parameters
Pulse Width
2 nSec
No. of Repetitions ‘N’
3
Pulse Repetition Period ‘Tf ’
30 nSec
Modulation Index ‘D’
5 nSec
Sampling Rate
2 GHz
Centre Frequency
1.5 GHz
Bandwidth
> 2 GHz
Power Spectral Density
< -40 dBm
System Model (Continued….)
• The impulse response of the channel is ‘h’ whereas channel shortening
equalizer (CSE) weight vector is ‘w’. Hence, the combined channel-CSE
response ‘x’ is:
x = h*w
or
x = Hw
where H is channel convolution matrix.
• We assume that the receiver has complete knowledge of channel through a
channel estimator.
Previous Approaches
Maximum Shortening Signal to Noise Ratio (MSSNR) Algorithm:
• In this algorithm, a window within combined channel-CSE response vector
‘x’ is defined. This window represents the shortened channel. The energy
within and outside the window can be given as:
Energy within shortened channel window = Er = wTHrTHrw = wTH1w
Energy outside shortened channel window = Es = wTHsTHsw = wTH2w
• The algorithm works to maximize the energy within shortened channel
window with constrained outside window energy, i.e.
max (wTH1w)
such that
wTH2w = 1
• Hence, the optimum CSE can be obtained as follows:
wopt = {H21/2}-1 a
where ‘a’ is the eigenvector corresponding to maximum eigenvalue ‘amax’ of
the matrix:
A = (VD1/2)-1H1(D1/2V)-1
where V and D are the matrices containing eigenvectors and eigenvalues of
H2 respectively.
Previous Approaches (Continued….)
Target Impulse Response (TIR) Based Minimum Mean Squared Error
(MMSE) Algorithm:
• This algorithm generates the optimum CSE by exploiting the error statistics
between a predefined TIR and combined channel-CSE response.
• It defines the following optimization problem:
min (wT[Ryy – RTxy Rxy]w)
such that
wT RTxy Rxy w = 1
where Rxy is the input-output cross correlation matrix and Ryy is the output
auto correlation matrix.
• This optimization can be solved to yield optimum CSE.
• The performance of this algorithm is same as that of previous one.
Proposed Algorithm
• In our proposed algorithm, we define an unconstrained optimization
problem.
• This algorithm works to maximize the energy of a single tap in the combined
channel-CSE response. Hence, the optimization problem can be stated as:
max (wThLT hLw)
where hL is the Lth row of H and represents the tap to be maximized.
• Hence, the optimum CSE is the eigenvector ĥ associated to maximum
eigenvalue hmax of hLT hL..
wopt = ĥ
• This CSE is less complicated to evaluate and shortens the channel to just
single tap.
Simulation Results and Comparative Analysis
• Simulations are performed in a multiuser environment with 50 simultaneous
active users for CM1, CM2, CM3 and CM4 scenarios.
• Length of the shortened channel is assumed to be 10 taps maximum. Higher
values contradict to the problem definition.
• Performance of each algorithm is evaluated and compared on the basis of
Captured Energy, SINR Improvement and BER.
• Standard deviation in captured energy is used to determine the consistency of
each algorithm in successfully shortening the channel.
• Extensive simulations provided following results:
Energy Capture Performance in CM 1
CM 1
Energy Captured and Standard Deviation (%)
80
70
60
50
MSSNR/MMSE Energy Capture
Proposed Energy Capture
MSSNR/MMSE Std. Dev.
Proposed Std. Dev.
40
30
20
10
0
0
10
20
30
40
50
60
No. of CSE Taps
70
80
90
100
Energy Capture Performance in CM 2
CM 2
Energy Captured (%)/Standard Deviation
60
50
40
30
20
MSSNR/MMSE Energy Capture
Proposed Energy Capture
MSSNR/MMSE Std. Dev.
Proposed Std. Dev.
10
0
0
20
40
60
80
No. of CSE Taps
100
120
140
Energy Capture Performance in CM 3
CM 3
Energy Captured (%)/Standard Deviation
60
50
MSSNR/MMSE Energy Capture
Proposed Energy Capture
MSSNR/MMSE Std. Dev.
Proposed Std. Dev.
40
30
20
10
0
0
20
40
60
80
100
No. of CSE Taps
120
140
160
180
Energy Capture Performance in CM 4
CM 4
Energy Captured (%)/Standard Deviation
60
50
40
MSSNR/MMSE Energy Capture
Proposed Energy Capture
MSSNR/MMSE Std. Dev.
Proposed Std. Dev.
30
20
10
0
0
50
100
150
No. of CSE Taps
200
250
Comments
•
•
MSSNR/MMSE algorithms gather slightly more energy as compared to the
proposed one only in CM 1 environment, but:
–
They are more inconsistent as shown by the higher standard deviation
values.
–
Shortened channel is 10 taps long and they are completely unsuccessful
in shortening the channel to below this limit.
–
Whereas proposed algorithm shortens the channel to one significant tap
only.
–
And it can be implemented with less number of equalizer weights and
involves less computations.
In case of dense multipath environments, like CM 3 and CM 4, the
proposed algorithm performs well above MSSNR/MMSE algorithms in any
aspect.
SINR Improvement
15
10
Ouput SINR(dB)
5
0
-5
-10
MSSNR/MMSE (CM4)
Proposed (CM4)
MSSNR/MMSE (CM3)
Proposed (CM3)
MSSNR/MMSE (CM2)
Proposed (CM2)
MSSNR/MMSE (CM1)
Proposed (CM1)
-15
-20
-25
-20
-15
-10
Input SINR(dB)
-5
0
5
BER Analysis
0
10
-1
10
-2
BER
10
-3
10
-4
10
MSSNR/MMSE (CM4)
Proposed (CM4)
MSSNR/MMSE (CM3)
Proposed (CM3)
MSSNR/MMSE (CM2)
Proposed (CM2)
MSSNR/MMSE (CM1)
Proposed (CM1)
-5
10
-25
-20
-15
-10
Input SINR(dB)
-5
0
5
Conclusion
• BER analysis shows that MSSNR/MMSE algorithms are not suitable for
UWB environment. The proposed algorithms outperforms both of these
algorithms.
• The proposed algorithm enables a simple, cost effective and single correlator
based implementation of UWB receiver.
• Due to single correlator design, transmitted pulse shape can be used as
receiver template which further reduces the burden of on-line template
evaluation from the receiver.
• Future targets include testing of this algorithm in further dense multipath
environments and modifying it to a blind and adaptive design.
– Note: For theoretical BER analysis, please refer to section IV(D) of the
paper.
Thanks very much for your
patience.
Any Questions??