Adaptive Channel Estimation in Wireless Communications - Adaptive Signal Processing in Wireless Communications - page 50

ˆ

H QY

H = argmin H () H , (2.47)

|| ||=1 H

where Q ( Y ) is a positive definite matrix constructed from the observation. Asymptoti-
cally (as either the sample size increases to infinity or the noise variance approaches
zero), these estimates converge to true channel parameters.

2.3.3 Semiblind Approaches
Semiblind approaches utilize a combination of training-based and blind approaches.
Here we present a brief discussion about the idea and refer the reader to a recent survey
[ 7 ] for details. The objective of semiblind channel estimation (and equalization) is to
exploit the information used by blind methods as well as the information exploited by
the training-based methods. Semiblind channel estimation assumes additional knowl-
edge of the input sequence. Specifically, part of the input data vector is known. Both
the statistical and deterministic maximum likelihood estimators remain the same
except that the likelihood function needs to be modified to incorporate the knowledge
of the input. However, semiblind channel estimation may offer significant performance
improvement over either the blind or the training-based methods, as demonstrated in
the evaluation of the Cramer-Rao lower bound in [7].
There are many generalizations of blind channel estimation techniques to incorpo-
rate known symbols. In [6], Cirpan and Tsatsanis extended the approach of Kaleh and
Vallet by restricting the transition of the hidden Markov model. In [30], knowledge of
the known symbol is used to avoid the local maxima in the maximization of the likeli-
hood function. A popular approach is to combine the objective function used to derive
the blind channel estimator with the least squares cost in the training-based channel
estimation. For example, a weighted linear combination of the cost for blind channel
estimator and that for the training-based estimator can be used [16, 29, 33].

2.3.4 Superimposed Training-Based Approaches
In the superimposed training (hidden pilots)-based approach, one takes

sn bn cn () =+, () () (2.48)

where { b ( n )} is the information sequence and { c ( n )} is a nonrandom periodic training
(pilot) sequence. Exploitation of the periodicity of { c ( n )} allows identification of the
channel without allocating any explicit time slots for training, unlike traditional train-
ing methods. There is no loss in data transmission rate. On the other hand, some useful
power is wasted in superimposed training that could have otherwise been allocated to
the information sequence. This lowers the effective signal-to-noise ratio (SNR) for the
information sequence and affects the bit error rate (BER) at the receiver.
Superimposed training-based approaches have been discussed in [19, 20] and [38] for
SISO systems. A block transmission method has been proposed in [10] and [11] where