IEEE North Jersey Advanced Communications Symposium, 2014
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IEEE North Jersey Advanced Communications Symposium, 2014. Robust Multipath Channel Identification with Partial Filter Information Kuang Cai ﹡ , Hongbin Li ﹡ , Joseph Mitola III † ﹡ Department of Electrical and Computer Engineering, Stevens Institute of Technology, Hoboken, NJ 07030, USA

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Introduction

IEEE North Jersey Advanced Communications Symposium, 2014

Robust Multipath Channel Identification

with Partial Filter Information

Kuang Cai﹡, Hongbin Li﹡, Joseph Mitola III †

﹡Department of Electrical and Computer Engineering, Stevens Institute of Technology, Hoboken, NJ 07030, USA

†Mitola's STATISfaction, 4985 Atlantic View, St. Augustine, FL 32080, USA

Introduction

  • Cramér–Rao bound (CRB)

    • To benchmark performances of proposed estimators

    • The filter response becomes a random parameter with existence of the perturbation

    • Bayesian CRB

      • Write all data blocks in one equation

      • Compute Fisher information matrix (FIM)

      • Constraint is applied in blind estimation to eliminate ambiguity

      • Compute constrained CRB based on FIM

  • Expansion for slowly time-varying channels

    • Channel response does not have significant change over one data block duration

    • Compute an initial sample covariance matrix and update it when a new output data

      block is available

    • Applied estimation algorithms based on the time-varying sample covariance matrix

    • The second-order statistics of the channel output contain sufficient

      information for blind channel estimation due to the cyclostationarity

      of the channel output induced by a fractionally spaced sampling

    • A subspace-based multipath channel identification based on exploiting

      knowledge of the transmit/receive filter was presented and popular

      • Simplicity and good performance

      • Requires full knowledge of the filter

    • Transmit/receive filter response is often partially known due to perturbations

      • I/Q imbalance at the transmit/receive side

      • Physical distortions due to environmental factors (i.e., temperature, humidity)

    • To improve the estimation performance, two algorithms are proposed

      • Subspace method based Iterative channel identification (conventional estimation)

        when accuracy of the prior knowledge is unknown

      • Robust channel identification when accuracy of the prior knowledge is partially

        known (the statistical knowledge of the perturbation is available)

    : Forgetting factor,

    Numerical Results

    System Model

    • System model

      • Composite channel

      • Discrete time model

      • Filter perturbation model

    : Input information sequence

    :Channel noise (AWGN)

    : Transmit/receive filter

    : Multipath channel

    : th data block

    : Block Toeplitz channel matrix

    Fig.1

    Fig.2

    : Nominal filter response

    : Unknown perturbation error modeled as a random

    variable with zero mean and variance

    Channel Identification

    • Subspace decomposition of the sample covariance of channel output

    • According to the orthogonality between channel and noise, given the filter

      response, the channel estimate can be achieved by minimizing

    • Iterative channel identification

      • Accuracy of prior knowledge unknown

      • Given the channel response, the filter estimate can be achieved by minimizing

      • Use nominal filter response as an initial estimate of filter to initialize an iterative

        procedure that estimates the channel and filter response in a sequential fashion

    • Robust channel identification

      • Accuracy of prior knowledge partially known (statistical knowledge of perturbation)

      • Develop a knowledge-aided robust estimation algorithm

        • Define an ellipsoidal uncertainty bound for the difference between the filter response

          and its estimate

        • Estimate the filter within this bound

        • The estimation problem can be solved by the Lagrange multiplier methodology

      • Apply the iterative channel identification

        • Estimate the filter with the robust estimation

        • Estimate the channel with the subspace method

    : Eigenvectors span on the signal subspace

    : Eigenvectors span on the noise subspace

    : Sample covariance matrix

    Fig. 3

    Fig.4

    • Simulation settings

      • BPSK input

      • Raised-cosine pulse shaping

        filter with roll-off factor 0.1

      • Multipathchannel

        • Four ray (time-invariant channel)

        • Two ray (time-varying channel)

    : th Eigenvector belongs to the noise subspace

    : Block Toeplitz matrix formed by

    : Convolutional matrix formed by filter response

    • Results

      • Fig. 1 and 2 show the results for

        time-invariant channels

      • Fig. 3, 4 and 5 show the results

        for time-varying channels

    Fig.5

    Conclusions

    : Convolutional matrix formed by channel response

    • We examine two cases, in which the transmit/receive filter is affected by

      unknown perturbation, and propose the corresponding estimators

    • With the statistical knowledge of the perturbation, the robust estimation

      achieved better performance than the conventional estimation

    • Robust estimation algorithm also works for the slowly time-varying channels

    Future Work

    • Explore the application of robust channel identification in OFDM systems


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