Transcript www.sal.ufl.edu

Waveform design course
Chapters 7 & 8 from
Waveform Design for Active Sensing Systems
A computational approach
Cross ambiguity function (CAF)
CAF has more degrees of freedom compared
to that of the conventional ambiguity function,
a case where v(t) equals u(t)
.
Discrete-CAF synthesis
Under the assumptions that
It can be proved that
Design problem
Cyclic algorithm (CA) for discreteCAF synthesis
Using the following notations
CA contd..
C2 can be re-written as
CA steps
Discrete CAF with weights
Numerical examples
Numerical examples
Numerical examples
Numerical examples
Numerical examples
Continuous time CAF synthesis
Continuous time CAF synthesis
CA for CAF synthesis
Numerical example
Numerical example
Joint design of transmit sequence
and receive filter





In Radars/Sonars.
Conventional receiver : Matched filter (MF) (in
the case of Doppler shifts, a bank of filters).
MF maximizes the signal-to-noise ratio (SNR).
Apart from noise here one can also have
clutters.
Signal to clutter-plus interference ratio (SCIR)
Data model and problem formulation
MSE of the mis-matched filter
CREW (gra)

Minimization of MSE wrt to w

Concentrated MSE :

Minimization problem :
which can be tackled via gradient methods like
BFGS (Broyden-Fletcher-Goldfarb-Shanno)
method – requires only gradient.
A frequency domain approach
Contd..
Using the circulant parameterization
Contd..
Using the DFT matrices to diagonalize
the circulant matrices
CREW (fre)
The design problem can be re-written as
Minimizer over {hp}
Minimization over {εp}
CREW (fre)
Minimization over {zp} is convex, it can be solved using the
Lagrangian methods
Using Lagrangian multipliers
CREW (fre)
Once {|εp|} is obtained, x can be obtained via
which can be solved by a CA, unimodular and PAR constraints can be
imposed.
Lower bound on MSE
CREW (mat)
MSE for the matched filter
Minimization over {εp}
Numerical examples
Jamming scenarios
Numerical example
Barrage jamming
Robust design
Robust design