Aerospace and Electronic Systems Magazine January 2018 - 26

Malanowski et al.
The target with acceleration A changes bistatic velocity during the
integration time T by AT. If the echo remains in one bistatic velocity
resolution cell, the change of the velocity AT should be smaller than
ΔV, which leads to the following limitation of the integration time:
T<

Figure 3.

Measurement scenario geometry.

too long may lead to range cell migration or velocity cell migration
effect. The bistatic range resolution is calculated as:
ΔR =

c
,
B

(4)

where B is the signal bandwidth. In the case of a DVB-T signal,
the bandwidth is B ≈ 7.6 MHz, resulting in ΔR ≈ 40 m. During
the integration time T, the target moving with bistatic velocity V
changes bistatic range by VT. If this distance is greater than the
bistatic range resolution cell ΔR, range cell migration occurs. This
leads to the limitation of the integration time:
c
(5)
.
T<
BV
As it will be shown later, the observed rocket reached bistatic velocities up to 600 m/s, which limits the integration time to ca. 56 ms.
Let us next consider the velocity cell migration. The bistatic
velocity resolution cell can be calculated as:
ΔV =

λ
T

(6)

λ
A

(7)

In the experiments, the wavelength was equal to λ ≈ 45 cm, and
the observed rocket reached bistatic acceleration up to 400 m/s2. In
such case, the integration time is limited to ca. 33 ms.
It is worth noting that the considered limitations (5) and (7) can be
overcome by extending the crossambiguity function. One of the extensions consists in taking into the account the stretch of the envelope
of the signal [9], which is connected with limitation (5). Another extension takes into consideration quadratic term in the exponent of the
crossambiguity function [10], which is connected with compensating
the bistatic acceleration, thus relaxing limitation (7). In this article,
however, we assume that the basic version of the crossambiguity
function (3) is used, and the limitations (5) and (7) must be applied.
In practice, when a system operating in real time was considered, the
maximum bistatic velocity and acceleration of the target would have
to be specified, and the appropriate integration time applied.

EXPERIMENT SETUP
SCENARIO GEOMETRY
The measurement scenario geometry is shown in Figure 3. Three
DVB-T transmitters were used for target illumination. Each transmitter was rated at 100 kW (Effective Isotropic Radiated Power).
The distance to transmitters was Rb = 73 km, Rb = 44 km, and Rb =
90 km, for Tx1, T x2, and Tx3, respectively. The rocket launch site
was located ca. 200 m west from the radar receiver.

PASSIVE RADAR SETUP
The antenna setup during the experiment is shown in Figure 4. The
reference signal from three transmitters was received using three
separate high gain antennas (ca. 15 dBi), each pointed towards

Figure 4.

Antennas used for reference signal (a) and echo signal (b) reception.

IEEE A&E SYSTEMS MAGAZINE

JANUARY 2018

Table of Contents for the Digital Edition of Aerospace and Electronic Systems Magazine January 2018