Page 64 - Autonomous Mobile Robots

Millimeter Wave RADAR Power-Range Spectra Interpretation 47

man-made interference signals) and internally produced noise at the receiver
antenna and amplifiers in the system.
In the mixer, the received signal is mixed with a portion of the transmitted
signal with an analog multiplier.

v T (t)v R (t − τ) =[A T + a T (t)][A R + a R (t − τ)]

A b 2
× cos ω c t + t + φ(t)
2

A b 2
× cos ω c (t − τ) + (t − τ) + φ(t − τ) (2.3)
2
The output of the mixer, v out (t) is (using the trigonometric identity for the
product of two sine waves cos A cos B = 0.5[cos(A + B) + cos(A − B)])

[A T + a T (t)][A R + a R (t − τ)]
v out (t − τ) = [B 1 + B 2 ] (2.4)
2

2
where B 1 = cos[(2t − τ)(ω c − A b τ/2) + A b t + φ(t) + φ(t − τ)] and B 2 =
cos[(ω c − A b (τ/2 − t))τ + φ(t) − φ(t − τ)].
The second cosine term, B 2 , is the signal containing the beat frequency. The
output of the low pass filter consists of the beat frequency component, B 2 and
noise components with similar frequencies to the beat frequency, while other
components are filtered out. The beat frequency, f b , is directly proportional to
the delay time, τ which is directly proportional to the round trip time to the
target. The relationship between beat frequency and target distance is

cT s 1
R = f b (2.5)
2 f s

where R is the range of the object, c is the velocity of the electromagnetic wave,
T s is the frequency sweep period, and f s is the swept frequency bandwidth [18].

2.3.1 Noise in FMCW Receivers and Its Effect on Range
Detection

As described above, the low pass filter output at the RADAR receiver can be
represented by

A τ
v beat (t, τ) = cos ω c − A b − t τ + φ(t, τ) (2.6)
2 2

© 2006 by Taylor & Francis Group, LLC

FRANKL: “dk6033_c002” — 2006/3/31 — 17:29 — page 47 — #7