Abstract
In time delay estimation the correlator or, equivalently,
matched filter estimator is widely used. Examples of its usage can
be found in the global positioning system (GPS), radars and code
division multiple access (CDMA) communication systems. Although
widely used its performance is not studied in general case until
recently. Partially this study is done in this thesis. If interfering
signals like multipath or multiple access signals exist in addition
to additive white Gaussian noise, as in GPS and CDMA, the correlator
is not a maximum likelihood (ML) estimator. However, it is known
that the correlator produces consistent estimates in the existence
of multipath interference if the delay separation is larger than
the correlation time of the signal (in direct sequence spread spectrum applications
such as GPS and CDMA, the correlation time approximately equals
the chip duration of the spreading code). It also performs well
in the existence of multiple access interference (MAI), if the powers
of the MAI signals are equal to the power of the desired signal.
In this thesis the asymptotic distribution of the correlator
estimator is derived in multisignal environments. Using the result,
it can be analytically shown, that in these benign interference
cases the exact ML estimator and the correlator estimators perform
equally well in the sense that their asymptotic covariance matrices
are equal. The thesis also verifies the well known result that if
the signals are orthogonal, then the correlator and ML estimators
perform equally. In addition, the correlator's asymptotic
performance is investigated also in the inconsistent case by slightly
extending the earlier results found in the literature. Also the
resolution of the correlator estimator is investigated. It is numerically
shown that the correlator estimator can produce consistent estimators
even if the delay separation is less that the chip duration, which
is commonly believed to be the resolution limit of the correlator.
This can happen in fading channels where the multipath amplitudes
are uncorrelated or just slightly correlated. This result seems
to be fairly unknown.
In addition to the classical ML estimator, where all the unknowns
are assumed to be deterministic, also an improved ML estimator is
investigated. This other ML estimator is obtained by assuming that the
amplitudes are Gaussian distributed. It is an improved estimator
in the sense that its asymptotic covariance, say CML,
is less positive definite than that of the classical ML estimator
CCML, i.e., CCML-CML is
positive semidefinite. More importantly, this result is valid independent
of the fact are the amplitudes really deterministic or Gaussian.
This well known result is shown in this thesis to be valid also
if the signals contain more than one unknown parameter, which occurs,
for example, in direction-of-arrival estimation when two angles
per arrival are to be estimated.
| Identifer | oai:union.ndltd.org:oulo.fi/oai:oulu.fi:isbn951-42-5684-0 |
| Date | 09 June 2000 |
| Creators | Saarnisaari, H. (Harri) |
| Publisher | University of Oulu |
| Source Sets | University of Oulu |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/doctoralThesis, info:eu-repo/semantics/publishedVersion |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess, © University of Oulu, 2000 |
| Relation | info:eu-repo/semantics/altIdentifier/pissn/0355-3213, info:eu-repo/semantics/altIdentifier/eissn/1796-2226 |
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