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Millimeter Wave RADAR Power-Range Spectra Interpretation 57

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µ = 9.612 dB and variance, σ = 28.239 dB . These ranges have been selec-
ted arbitrarily to show the noise distributions for shorter (<45 m) and longer
ranges (45 < range < 200).
Therefore, to predict the power noise in the predicted power–range spectra,
for ranges above approximately 45 m, Equation (2.9) can be used with the con-
stant Weibull parameters determined at a range of 100 m. For ranges below this
value, an exponential distribution is assumed, which uses a standard deviation
value which is related to range as in Figure 2.6b.

2.4.3.2 Power-noise estimation in target presence

The receiver noise will also affect the signal when there is a target present.
The resultant distribution is the convolution of both the signal and noise and
is distributed normally [11]. The histogram in Figure 2.8a shows an approx-
imately normal distribution obtained experimentally for 5000 observations of
a RADAR retro-reflector at 10.25 m (the distance and the number of observa-
tions were selected arbitrarily). The experiment has been repeated for obtaining
the distribution from a wall at a distance of 150 m approximately. This is
shown in Figure 2.8b. The two histograms are approximately normally distrib-
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uted and have variances of 4.07 and 5.76 dB , respectively. It is evident from
Figure 2.8a, b and from Figure 2.5a that the noise variances affecting the signal
during target presence are similar.
For an FMCW RADAR, features close to the RADAR give beat frequency
signals with lower frequency and distant features give high frequency signals.
By attenuating lower frequencies and amplifying higher frequencies, it is pos-
sible to achieve a constant returned power for an object with a particular RCS
at all ranges. The graph shown in Figure 2.9 shows the calculated received
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power from two objects with RCS values of 1000 and 0.001 m for all range
values without the high pass filter effect. These have been calculated from the
simple RADAR equation, using the parameters of the particular RADAR used
here. The typical inverse range to the fourth power is still obtained even as
the RCS of the target reduces significantly. Hence in practice, even the small
signal reflections from atmospheric particles combined with the noise generated
inside the RADAR’s internal electronics will produce power–range relations of
this form (such as, e.g., Figure 2.10). Therefore, an ideal high pass filter will
give an approximately constant power noise variance for all ranges, for both
target presence and target absence [11]. From the noise variances under sig-
nal absence and presence conditions shown above, it is evident that the high
pass filter is close to its ideal state. (The power noise variance during target
absence and target presence are similar irrespective of ranges.) The estimation
of the noise statistics is helpful in accurately interpreting the range spectra as
well as predicting the RADAR spectra for feature location prediction in robot
navigation.

© 2006 by Taylor & Francis Group, LLC

FRANKL: “dk6033_c002” — 2006/3/31 — 17:29 — page 57 — #17