Graphics Programs Reference
In-Depth Information
176 MATLAB Simulations for Radar Systems Design
Finally, one can define the corresponding velocity resolution as
c f d
2 f 0
c
2 f 0 τ'
v
=
-----------
=
-----------
(3.140)
Again observation of Eqs. (3.138) and (3.116) indicate that the output of the
matched filter and the ambiguity function (when ) are similar to each
other. Consequently, one concludes that the matched filter preserves the wave-
form Doppler resolution properties as well.
τ
=
0
3.10.3. Combined Range and Doppler Resolution
In this general case, one needs to use a two-dimensional function in the pair
of variables ( ). For this purpose, assume that the complex envelope of the
transmitted waveform is
τ f d
,
ψ () u () e j f 0 t
=
(3.141)
Then the delayed and Doppler-shifted signal is
) e j f 0
(
–
f d
) t
(
–
τ
)
ψ' t
(
–
τ
)
=
ut τ
(
–
(3.142)
Computing the integral square error between Eqs. (3.142) and (3.141) yields
ε 2
2
ψ () 2
ψ () ψ' t
=
ψ () ψ' t
–
(
–
τ
)
d
=
2
d
–
2 Re
–
(
–
τ
)
d
(3.143)
–
–
–
which can be written as
2 Re e j f 0
(
–
f d
) e j f d t
ε 2
u () 2
u () u t
=
2
d
–
(
–
τ
d
(3.144)
–
–
Again, in order to maximize this squared error for
τ
0
one must minimize the
last term of Eq. (3.144).
Define the combined range and Doppler correlation function as
) e j f d t
u () u t
χτ f d
(
,
)
=
(
–
τ
d
(3.145)
–
In order to achieve the most range and Doppler resolution, the modulus square
of this function must be minimized for
and
. Note that the output of
τ
0
f d
0
Search WWH ::




Custom Search