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ISWCS’06, Valencia, Spain 1
Blind Adaptive Channel Shortening by
Unconstrained Optimization for Simplified UWB
Receiver Design
Authors: Syed Imtiaz Husain and Jinho Choi
Presenter: Syed Imtiaz Husain
ISWCS’06, Valencia, Spain 2
Presentation Outline
Problem StatementSolution and MotivationSystem ArchitectureProposed Channel Shortening AlgorithmSimulation ResultsConclusions
ISWCS’06, Valencia, Spain 3
Problem Statement
UWB channels are very dense in multipaths.To maintain a good SNR, a RAKE receiver with large number of fingers must be used.This makes the receiver structure and the rest of the signal processing very complex.Difficult from analysis and design perspectives and involves higher manufacturing costs.A simple and cost effective receiver structure is needed.
ISWCS’06, Valencia, Spain 4
The proposed solution is Channel Shortening: An equalization technique which compresses
the channel impulse response (CIR) within a small desired temporal window.
Mainly in use for MCM/OFDM systems. It is used to eliminate just few channel taps
beyond the cyclic prefix (CP) length. Available algorithms are MCM/OFDM system
specific, not general, except few. Mostly developed for wired line slowly varying
scenarios.
Solution and Motivation
ISWCS’06, Valencia, Spain 5
Solution and Motivation
UWB systems are different in: Working principles Architecture Channel models and many other things
Channel shortening appears in its extreme sense in UWB in contrast to MCM/OFDM systems: CIRs must be compressed to just few
multipaths eliminating a large number of channel taps.
Rapidly varying wireless scenarios.
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Solution and Motivation
New and modified channel shortening algorithms are needed to: Address specific needs of UWB systems. Make use of UWB parameters. Can work in dense multipath channels. Can handle the extreme nature of channel
shortening needed in UWB CIRs. Must be capable to adapt to channel
variations.
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System Architecture
Assuming time hopping pulse position modulated (TH-PPM) UWB system.Standardized UWB channel models (CM 1 to CM 4) for performance evaluation.A multiuser AWGN environment with Nu simultaneous active users.
) ( ) ( ) (1
t n t r t ru N
jj
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Proposed Channel Shortening Algorithm
Fundamental assumptions: In a single user AWGN environment, if a
single pulse is received, it quite accurately reveals the channel information.
This assumption is not quite valid in a multiuser environment, but still provides a basis to develop channel shortening equalizer (CSE).
A CSE which can shorten the received signal is also capable to shorten the channel, a property explicitly available in UWB systems.
ISWCS’06, Valencia, Spain 9
Proposed Channel Shortening Algorithm
Fundamental assumptions (continued): We propose block by block data
transmission. Two consecutive blocks should be separated
by at least 600 nS. A single pulse is transmitted between the
two blocks to calculate and update/adapt CSE.
The length of data block is variable and can be adjusted according to channel coherence time.
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Proposed Channel Shortening Algorithm
We assume: ,
is the received signal vector and ,is the channel shortening equalizer, such that
b<<q.
The effective channel (channel-CSE) is: ,where is the convolution matrix of .
Tbo www ][ 11 w
Tqo rrr ][ 11 r
wx r
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Proposed Channel Shortening Algorithm
Now we define using a row vector in as follows:
where
such that .
To obtain the optimum CSE, we define the following unconstrained optimization:
vvM T
M v
][ 11 bvvv rrr v bv
)(max Mwww
T
ISWCS’06, Valencia, Spain 12
Proposed Channel Shortening Algorithm
Hence, the optimum CSE is:
where is the maximum eigenvalue of and is
the corresponding eigenvector.
The effective channel can now be given as:
where ‘n’ is the length of CIR.
dw maxopt
max M d
][ 121 21 bn
owhannelWindShortenedC
nn
ISWCS’06, Valencia, Spain 13
Proposed Channel Shortening Algorithm
If: Signal bandwidth = W Time between maximum and minimum pulse amplitude = τp
then the shortened channel window length is This shortened window occurs from:
to
where ‘p’ is odd and represent the length of transmitted signal vector.
Wp2
2
1221
Wpbn p
2
1221
Wpbn p
ISWCS’06, Valencia, Spain 14
Simulation Results
Following simulation parameters were used: CSE Length = 50 Nu = 1 (Single User) and 20 (Multi
User) Channel Models = CM 1 to CM 4 Length of Shortened Channel = 2 taps
Performance of the proposed algorithm is evaluated in terms of: BER Vs. SINR Captured Energy Vs. SINR BER Vs. No. of users
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Simulation Results
BER performance degrades as the channel becomes more dense in multipaths or the number of interfering users increases.
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Simulation Results
As BER performance, the energy capture also exhibits the similar trends.
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Simulation Results
At a constant SINR of nearly 8 dB, increasing number of users does not show any significant effect. Only dense multipath channels degrade the performance.
ISWCS’06, Valencia, Spain 18
Conclusions
The proposed channel shortening algorithm:1. Exploits the UWB channel and system characteristics
to address the specific needs of UWB systems.2. This algorithm can blindly shorten the dense
multipath channels to just two significant taps with a CSE length of 50 and can still capture 55% of the channel energy.
3. The algorithm can be updated via proposed mechanism periodically at channel coherence time.
4. It greatly simplifies the UWB receiver structure, associated signal processing and reduces the manufacturing cost.