Theory of GNSS Reflectometry - GNSS Remote Sensing: Theory, Methods and Applications - page 209

models against DM observables has been widely used to estimate some reflecting
surface parameters (mostly roughness) (e.g. Garrison et al. 2002 ; Cardellach et al.
2003 ; Komjathy et al. 2004 ).
Delay-Doppler waveform or Delay-Doppler Map (DDM) Output of the signal
correlation process, when conducted along a set of delay-bins and also a set of
central correlation frequencies, ıf : W.;ıf /. It can be given in amplitude/power
units or as complex values (phase/amplitude or I/Q). Examples of different uses
of DDM for surface roughness characterization can be found in Germain et al.
( 2004 ), Cardellach and Rius ( 2008 ), and Marchan-Hernandez et al. ( 2008 ).
Integrated spectrum and delay

Elfouhaily et al. ( 2002 ) shown that the

D R Dopplers DDM.; f /df ) and

frequency-integrated delay spread (IDM./

delay-integrated Doppler spread (IDS.f / D R Delays DDM.; f /d ) relate to
the roughness conditions of the scattering surface.
Specular group delay Observable obtained from the delay-derivative of the
delay-waveform, W 0 . / D @W . /=@ . The delay of the radio-link reflected
off the specular point, spec , is given by the delay-location of the peak of the
derivative:

@ 2 W
@ 2

j spec D 0 (8.58)

This observable was suggested in Hajj and Zuffada ( 2003 ) and proved in Rius
et al. ( 2010 ), where derivation and application details are given.
Scatterometric delay Delay of the peak of the delay waveform, with respect to
the specular delay, scatt D peak spec . The derivative of the waveform can be
used to estimate the peak's delay:

@W
@ j peak

D 0 (8.59)

It is called scatterometric because it contains information about the roughness of
the reflecting surface. Note that when the surface is smooth and the reflection
purely specular, the waveform is shaped as the modulation auto-correlation
function, and its peak location corresponds to the delay of the specular radio-
link. Then, scatt

D 0. It has been widely use, starting in Nogués-Correig et al.

( 2007 ).
Phase-delay Delay of the specular radio-link estimated using phase-information
out of the complex waveform. Note that only specular-like reflections (little dif-
fuse contribution) provide meaningful phase information. The main challenges of
phase-delay observations are the potential cycle slips present in the data, together
with the unwrapping of measured [ ; ) phases to obtain the dynamic delay.
Examples of different ways to extract and process phase-delay observables can
be found in e.g. Treuhaft et al. ( 2001 ), Martín-Neira et al. ( 2002 ), Semmling et al.
( 2011 ), and Fabra et al. ( 2011 ).