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Sparse Channel Estimation and Its Application in Channel Equalization

Niazadeh, Rad | 2010

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 41375 (05)
  4. University: Sharif University of Technology
  5. Department: ELectrical Engineering
  6. Advisor(s): Babaie Zadeh, Massoud
  7. Abstract:
  8. Recently, sparse channel estimation, i.e. recovering a channel which has much less non zerotaps than its length using a known training sequence, has been a major area of research in the field of sparse signal processing. It can be shown that on the one hand, the underlying unique structure of such channels will make the possibility of estimating the channel taps with the extreme performance, i.e. achieving the Cram´er-Rao bound of the estimation. On the other hand, with an appropriate use of this structure, computational complexity of the receiver (both channel estimator and equalizer) can be reduced by an order. For achieving these goals in this thesis, firstly we have proposed an information theoretical analysis to our problem. In this investigation, by the use of random matrix theory and the concept of typical detection borrowed from Shannon‘s IT, we will generalize the results obtained by Babadi et al. around the subject of asymptotic achievability of Cram´er-Rao bound in our problem and will proof this achievability under our generalized conditions. After that, by the use of alternating minimization technique, we will propose a MAP-based algorithm that uses the MAP estimation of the non-zero channel taps locations at each iteration. for approximate MAP estimation, we will propose three different methods based on sparse CDMA problem. Additionally, an adaptive algorithm based on the concept of smoothed l? norm and the well-known LMS will be proposed for adaptive channel estimation. At the next step, we will use a powerful mathematical tool named as “Factor Graph” and the well-known “Massage Passing Algorithm” to find an exact solution for the MAP problem. In this way, we will propose a near optimal algorithm for sparse channel estimation, named as “OMAPFG” which can operate in polynomial time with respect to channel length. As an application of the proposed channel estimators, the problem of equalization of ISI in the case of Sparse ISI channels will be investigated. By use of the idea of parallel Viterbi equalizers and use of a re-shaper filter at the input of the receiver, we will propose an efficient equalizer named as “Pre-Filtered PVA” that approximately implements the sequence by sequence Viterbi equalizer. Finally, the concatenation of proposed sparse channel estimators and equalizers, in addition to their standalone performance will be examined by simulation
  9. Keywords:
  10. Cramer-Rao Bound ; Sparse Representation ; Sparse Channel Estimation ; Joint Typical Estimator ; Factor Graph ; Viterbi Equalizer

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