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Expansion for slowly time-varying channels

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

- 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)

- Subspace method based Iterative channel identification (conventional estimation)

: 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

- Define an ellipsoidal uncertainty bound for the difference between the filter response
- 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. 1 and 2 show the results for

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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