Aerospace and Electronic Systems Magazine April 2018 - 50

3D FMCW MIMO Radar System for Medium-Range Applications

Figure 5.

Exemplary timing of a MIMO cycle.

configuration, the system has an update rate of about 3 s. This is
mainly determined by the user datagram protocol data transfer (1.4
s) and the MATLAB radar processing, which represent the current
bottleneck of the system. These processes can be accelerated by
implementing the radar processing directly in the FPGA.

positions. To achieve the same angular
resolution with a conventional mechanically or electronically scanning radar,
256 RX antennas (16 × 16) and one TX
antenna are needed. With a rectangular
MIMO array configuration, the size of
the antenna array can be reduced by a
factor of two in both the x- and the ydimension compared to a conventional
phased array radar. Because of physical
placement constraints, there is one additional column in the y-direction, which
is unoccupied. For the empty column,
which appears in the center of Figure 6,
an interpolation of the data is performed,
according to what has previously been
described in [17]. This results in a virtual array, which has 16 elements in the
x-direction (Nvir,x) and 17 elements in the y-direction (Nvir,y). The
angular resolution defined as the 3-dB beamwidth of the main lobe
for this particular MIMO array can be calculated as
Δθ 3dBx ≈ 50°

λ0

N vir, x d x

= 50°

MIMO VIRTUAL ARRAY AND DIGITAL BEAMFORMING
In the following section, the advantages of a MIMO radar are
shown and the theoretical angular resolution is calculated. The
MIMO radar has 16 TX (NTX) and 16 RX (NRX) antennas, leading
to a total number of NTX + NRX = 32 antennas and Nvir = NTX NRX
= 256 virtual elements. The physical antenna placement and the
resulting virtual array are shown in Figure 6. It can be seen that the
antenna elements are placed along a rectangle, with 8 antennas per
edge. The virtual array (in purple) can be calculated as the discrete
convolution of all RX (in red) and TX (in blue) antenna element

Figure 6.

Schematic representation of the MIMO antenna configuration with the
physical array (left), showing the 16 TX antennas in blue and the 16
RX antennas in red, and the resulting virtual array (right). A unit in the
graph is equivalent to

50

d x and d y , respectively.
2
2

Δφ3dB y ≈ 50°

λ0

N vir, y d y

= 50°

(

λ0

)

2 N pop + 1 d x

λ0

2 N pop d y

≈ 4.5°

≈ 3.5°

(3)

(4)

with λ0 ≈ 18 mm as the wavelength, dx = 12 mm and dy = 16 mm as
the spacings between elements along the corresponding axis, and
Npop = 8 as the number of antenna elements used along each edge
of the rectangle.
The data structure for the MIMO processing is a real-valued
N
×N
×M
3D data matrix D ∈ IR vir,x vir, y , where Nvir,x × Nvir,y is the dimension of the resulting virtual array that represents all TX-RX combinations (including element interpolation). The elements in the first
two dimensions have to be ordered in the same way, because they
result from the convolution. The third dimension M results from
the chirp length (100 ms) and the sampling frequency (100 MHz)
of the ADC, which results in M = 10,000 samples for each TX-RX
combination.
The 3D reconstruction of the radar scenario is done with a 3D
fast Fourier transform (FFT) on the data matrix described earlier.
The FFT processing is very fast but requires a plane wavefront.
The first step is to perform an FFT along the third dimension M
of D. The D1 result is a complex-valued, range-compressed matrix
for every element of the virtual array. Now the direction of arrival
(DOA) of the targets can be estimated with two additional FFT. For
the azimuth angle extraction, an FFT across the second dimension
(Nvir,x) of the previously calculated matrix (D1) is performed. The
resulting matrix is D2. Similarly, the elevation angles can be determined via an FFT across the third dimension (Nvir,y) of matrix D2.
The next paragraph explains the link between the result of the
FFT and the DOA estimation. Here, just the calculations for the
azimuth angles are presented, but the same principle applies for the
elevation direction. For complex input samples (D1), the FFT re-

IEEE A&E SYSTEMS MAGAZINE

APRIL 2018



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