1. Robust Multipath Channel Identification
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
Multipath channel
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