Frequency estimation for single-carrier and OFDM signals in communication and radar systems

Estimating the frequency of a signal embedded in additive white
Gaussian noise is one of the classical problems in signal
processing. It is of fundamental importance in various
applications such as in communications, Doppler radar,
synthetic aperture radar (SAR), array processing, radio
frequency identification (RFID), resonance sensor, etc.

The requirement on the performance of the frequency estimator
varies with the application. The performance is often defined
using four indexes: i). estimation accuracy, ii).
estimation range, iii). estimation threshold, and
iv). implementation complexity. These indexes may be in
contrast with each other. For example, achieving a low threshold
usually implies a high complexity. Likewise, good estimation
accuracy is often obtained at the price of a narrow estimation
range. The estimation becomes even more difficult in the presence
of fading-induced multiplicative noise which is considered to be
the general case of the frequency estimation problem. There have
been a lot of efforts in deriving the estimator for the general
case, however, a generalized estimator that fulfills all indexes
can be hardly obtained.

Focusing on communications and radar applications, this thesis
proposes a new generalized closed-form frequency estimator that
compromises all performance indexes. The derivation of the
proposed estimator relies on the nonlinear least-squares principle
in conjunction with the well known summation-by-parts formula. In
addition to this, several modified frequency estimators suitable
for non-fading or very slow fading scenarios, are also introduced
in this thesis.