Blind Adaptive Channel Shortening by Unconstrained Optimization for Simplified UWB Receiver Design

1
Blind Adaptive Channel Shortening by
Unconstrained Optimization for Simplified UWB
Receiver Design

• Authors
• Syed Imtiaz Husain and Jinho Choi
• Presenter
• Syed Imtiaz Husain

2
Presentation Outline

• Problem Statement
• Solution and Motivation
• System Architecture
• Proposed Channel Shortening Algorithm
• Simulation Results
• Conclusions

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.

4
Solution and Motivation

• 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.

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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.

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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.

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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
  bltltq.
• The effective channel (channel-CSE) is
• 
  ,
• where is the convolution matrix of .

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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

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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.
  

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Proposed Channel Shortening Algorithm

• If Signal bandwidth W
• Time between maximum and minimum pulse
  amplitude tp
• 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.

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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.

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Conclusions

• The proposed channel shortening algorithm
• Exploits the UWB channel and system
  characteristics to address the specific needs of
  UWB systems.
• 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.
• The algorithm can be updated via proposed
  mechanism periodically at channel coherence time.
• It greatly simplifies the UWB receiver structure,
  associated signal processing and reduces the
  manufacturing cost.