Antenna Arrays for Multipath and Interference Mitigation In GNSS
Receivers
Universitat Politecnica De Catalunya, Department of Signal Theory
and Communications, (Juli 2000)Zusammenfassung
This thesis deals with the synchronization of one or several replicas
of a known signal received in a scenario with multipath propagation
and directional interference. A connecting theme along this work
is the systematic application of the maximum likelihood (ML) principle
together with a signal model in which the spatial signatures are
unstructured and the noise term is Gaussian distributed with an unknown
correlation matrix. This last assumption is key in obtaining estimators
that are capable of mitigating the disturbing signals that exhibit
a certain structure, and this is achieved without resorting to the
estimation of the parameters of those signals. On the other hand,
the assumption of unstructured spatial signatures is interesting
from a practical standpoint and facilitates the estimation problem
since the estimates of these signatures can be obtained in closed
form. This constitutes a first step towards the elimination of the
multidimensional searches required by many estimators, which is one
of the objectives pursued in this work. In the first part of the
thesis, the maximum likelihood solution to the general time delay
estimation problem for the case of noise with unknown spatial correlation
is derived. The resulting criterion for the delays is shown to be
consistent and asymptotically efficient; but it is highly non-linear
due to the presence of a matrix determinant operator, and does not
lead to simple optimization procedures. It is proven using systematic
and heuristic methods that the optimal ML criterion can be approximated
by a simpler and asymptotically equivalent cost function. Unlike
many other estimation problems, the asymptotic efficiency is not
maintained if the optimal criterion is approximated by its first
term in the Taylor series expansion. The interesting feature of the
new cost function is the fact that it depends linearly on the projection
matrix onto the subspace spanned by the signals, and hence it can
be minimized using the computationally efficient IQML algorithm.
Furthermore, the existence of simple yet robust against the interference
initialization schemes based on identity weightings and possibly
ESPRIT makes the approach viable for practical implementation. The
proposed cost function can be applied identically to the estimation
of the delay" in a FIR channel. In this case, the IQML algorithm
is modified in such a way that each iteration comes down to rooting
a polynomial whose order is equal to the length of the FIR channel.
The goal of the estimators presented in the second part of the thesis
is to take advantage of one particularity of the GNSS (Global Navigation
Satellite Systems) systems consisting in that the direction-of-arrival
of the line-of-sight signal may be known a priori. Resting on this
additional information and assuming that the antenna is calibrated,
a simplified and approximate model for the received signal is proposed.
It consists in gathering all the signals except for the direct one
into a equivalent term with unknown spatial correlation. The ML estimators
of the time delay and carrier phase of the line-of-sight signal derived
under the simplified model are analyzed. They largely reduce the
bias produced by multipath components and, as a matter of fact, their
RMSE is in many situations very close to or even better than the
best possible performance attainable with more detailed models of
the multipath channel. Two polynomial rooting algorithms for computing
the time delay estimate are presented. It is also shown that the
ML estimates can be obtained from the output signal of a hybrid beamformer.
Since the beamformer itself depends on the time delay and amplitude
estimates of the direct signal, an iterative algorithm arises naturally.
The hybrid beamformer provides insights into the ML estimators and
may be appropriate for a practical design. It is shown both analytically
and numerically that the proposed ML time delay estimator is robust
against errors in the a priori steering vector of the direct signal,
and an approach to extend the range of tolerable pointing errors
is presented. In the last part of the thesis, the synchronization
of a desired user transmitting a known training sequence in a DS-CDMA
communication system is addressed. A model in which the multiple-access
interference, the external interference and the noise are included
into an equivalent disturbance term with unknown and arbitrary space-time
correlation is considered. Starting from this model, a large-sample
ML code-timing estimator that operates in frequency non selective,
slowly fading channels is derived. It is a single-user and near-far
resistant method. The significance of the proposed estimator is that
it takes advantage of the structure of the signals in both the space
and time domains, so it contrasts with other methods put forward
up to date that, while also employing antenna arrays, only exploit
the structure of the signals in one of the domains. In a CDMA communication
system, the desired user is interfered by the signals of a generally
large number of users and by possible external interferers. In accordance
with this fact, numerical results show that the joint use of all
the spatial and temporal degrees of freedom is indispensable for
the correct acquisition and tracking of the synchronization parameters
in heavily loaded systems and/or in the presence of external interference.
