In communication systems transmitting data through unknown fading channels, traditional
detection techniques are based on channel estimation (e.g., by using pilot signals),
and then treating the estimates as perfect in a minimum distance detector. In this thesis,
we derive and investigate an optimal detector that does not estimate the channel explicitly
but jointly processes the received pilot and data symbols to recover the data. This optimal
detector outperforms the traditional detectors (mismatched detectors). In order to approximate
correlated fading channels, such as fast fading channels and frequency-selective
fading channels, basis expansion models (BEMs) are used due to high accuracy and low
complexity.
There are various BEMs used to represent the time-variant channels, such as
Karhunen-Loeve (KL) functions, discrete prolate spheroidal (DPS) functions, generalized
complex exponential (GCE) functions, B-splines (BS), and the others. We derive the
mean square error (MSE) of a generic BEM-based linear channel estimator with perfect
or imperfect knowledge of the Doppler spread in time-variant channels. We compare the
performance and complexity of minimum mean square error (MMSE) and maximum likelihood
(ML) channel estimators using the four BEMs, for the case with perfect Doppler
spread. Although all BEM-based MMSE estimators allow achievement of the optimal
performance of the Wiener solution, the complexity of estimators using KL and DPS
BEMs is significantly higher than that of estimators using BS and GCE BEMs. We then
investigate the sensitivity of BEM-based estimators to the mismatched Doppler spread.
All the estimators are sensitive to underestimation of the Doppler spread but may be robust
to overestimation. The results show that the traditional way of estimating the fading
statistics and generating the KL and DPS basis functions by using the maximum Doppler
spread will lead to a degradation of the performance. A better performance can be obtained by using an overestimate of the Doppler spread instead of using the maximum
Doppler spread. For this case, due to the highest robustness and the lowest complexity,
the best practical choice of BEM is the B-splines.
We derive a general expression for optimal detection for pilot-assisted transmission
in Rayleigh fading channels with imperfect channel estimation. The optimal detector is
specified for single-input single-output (SISO) Rayleigh fading channels. The slow (timeinvariant)
fading channels and fast (time-variant) fading channels following Jakes’ model
are considered. We use the B-splines to approximate the channel gain time variations
and compare the detection performance of the optimal detector with that of different mismatched
detectors using ML or MMSE channel estimates. Furthermore, we investigate
the detection performance of an iterative receiver implementing the optimal detector in
the initial iteration and mismatched detectors in following iterations in a system transmitting
turbo-encoded data. Simulation results show that the optimal detection outperforms
the mismatched detection with ML channel estimation. However, the improvement in the
detection performance compared to the mismatched detection with theMMSE channel estimation
is modest. We then extend the optimal detector to channels with more unknown
parameters, such as spatially correlated MIMO Rayleigh fading channels, and compare
the performance of the optimal detector with that of mismatched detectors. Simulation results
show that the benefit in detection performance caused by using the optimal detector
is not affected by the spatial correlation between antennas, but becomes more significant
when the number of antennas increases.
This optimal detector is extended to the case of orthogonal frequency-division multiplexing
(OFDM) signals in frequency-selective fading channels. We compare the performance
and complexity of this optimal detector with that of mismatched detectors using
ML and MMSE channel estimates in SISO and MIMO channels. In SISO systems,
the performance of the optimal detector is close to that of the mismatched detector with
MMSE channel estimates. However, the optimal detector significantly outperforms the
mismatched detectors in MIMO channels.
