IEEE Solid-States Circuits Magazine - Spring 2022 - 50

Angular Resolution Expansion
Angular resolution defines the ability
of a radar to resolve targets with
different angular positions. Shown
in Figure 7, it is estimated by applying
reflection path length differences
between the targets and the
antennas in the array. Resolution is
inversely proportional to the aperture
of the array. Coherent MIMO
[10] exploits transmit waveform
orthogonality to construct a virtual
array with a larger aperture than
the physical array. Orthogonality
entails that signals from different
transmitters can be separated at the
receiver. The resolution depends on
the aperture of the virtual instead
of the physical array, which is much
smaller. This reduces system complexity
substantially. The array pattern
is determined by convolving
transmit and receive arrays. Multiple
transmitters also improve the
SNR. Angular resolutions well below
1c
require virtual arrays of 192 elements
or more, e.g., 12 transmitters
and 16 receivers operating concurrently
at the cost of complexity.
FMCW requires encoding in the
time, frequency, Doppler, range, or
code domains to achieve transmit
Physical Array
Direction
of Arrival
Different Distance to the
Reflector Results in Phase Shift
φ
Transmit
Antenna
Receive Antenna
Virtual Array
FIGURE 7: The detection of the angle of arrival using a virtual array.
signal orthogonality, as shown in Figure
8, requiring the sharing of physical
resources (bandwidth, cycle time, and
so on), introducing tradeoffs. TDMA
ensures transmit orthogonality but
trades angular resolution with maximum
unambiguous velocity; it limits
maximum velocity within the fixed
cycle time and compromises average
radiation power using one transmitter
only per FMCW ramp [11]. Doppler
division multiple access (DDMA)/
slow-time CDMA (ST-CDMA) and FDMA
[11] allow for simultaneous transmission,
trading angular resolution for
maximum velocity or range, and
introduce respective domain ambiguities.
Range division MA (RDMA) [12]
encodes signals in the range domain,
trading angular resolution for maximum
range, and introduces range
ambiguities. Channel coherency limits
waveform performance.
In other words, waveforms need
to stay close together in time, frequency,
and space; otherwise, targets
are not observed in the same way,
similar to the range migration that
was introduced earlier. Phase differences
are corrupted, which limits
angular dynamic range. In TDMA,
this occurs when targets move during
Time Division Multiple Access
Doppler and Slow-Time Code Division
Multiple Access
TX Sequentially Activated: 1, 2, 3, ... N
2
1
Time
Frequency and Range Division Multiple Access
TX: 1, 2, 3, ... N
11 1
-1 1-1
N
1
1
Fast-Time Code Division (Phase Coded)
Time
N
2
1
Time
FIGURE 8: MIMO-encoding waveforms.
50
SPRING 2022
IEEE SOLID-STATE CIRCUITS MAGAZINE
Time
10101..01 10101..01 10101..01
110010..0 110010..0 110010..0
00111..10 00111..10 00111..10
Time
11
-1
-1
1
-1
Wave Front
Frequency
Frequency
Frequency
Frequency
Frequency
TX Phase Node
Code
IEEE Solid-States Circuits Magazine - Spring 2022

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