Cataloged from PDF version of article.Novel approaches for three classical signal processing problems in optimization
framework are proposed to provide further flexibility and performance improvement.
In the first part, a new technique, which uses Hermite-Gaussian (HG) functions,
is developed for analysis of signals, whose components have non-overlapping
compact time-frequency supports. Once the support of each signal component
is properly transformed, HG functions provide optimal representations. Conducted
experiments show that proposed method provides reliable identification
and extraction of signal components even under severe noise cases. In the second
part, three different approaches are proposed for designing a set of orthogonal
pulse shapes for ultra-wideband communication systems with wideband antennas.
Each pulse shape is modelled as a linear combination of time shifted and scaled
HG functions. By solving the constructed optimization problems, high energy
pulse shapes, which maintain orthogonality at the receiver with desired timefrequency
characteristics are obtained. Moreover, by showing that, derivatives
of HG functions can be represented as a linear combination of HGs, a simple
optimal correlating receiver structure is proposed. In the third part, two different
methods for phase-only control of array antennas based on semidefinite
modelling are proposed. First, antenna pattern design problem is formulated as
a non-convex quadratically constraint quadratic problem (QCQP). Then, by relaxing
the QCQP formulation, a convex semidefinite problem (SDP) is obtained.
For moderate size arrays, a novel iterative rank refinement algorithm is proposed
to achieve a rank-1 solution for the obtained SDP, which is the solution to the
original QCQP formulation. For large arrays an alternating direction method of
multipliers (ADMM) based solution is developed. Conducted experiments show
that both methods provide effective phase settings, which generate beam patterns
under highly flexible constraints.Alp, Yaşar KemalPh.D
