IEEE Circuits and Systems Magazine - Q4 2022 - 20

TTD arrays and their rainbow codebooks can be leveraged to spatially
allocate a small fraction of frequency resources to
each served user.
for the rainbow beam-training as shown in Fig. 19(b)
which shows the efficacy of the proposed algorithm.
Additional measurement details for these plots are
captured in [89]. The automated test process further
minimizes the human errors in the manual process. In
addition, this enables benchmarking entire system from
the antenna to the higher network layers combined with
machine learning algorithms in future.
VI. Future Work
A. 3D Rainbow Beam with Planar TTD Array
In principle, the frequency dependent beam steering
can be extended into the planar TTD array. In our
recent work [90] we studied beamforming codebooks
with the uniform delay steps 99
 , introduced in
xy,
the antenna elements in the x−y plane before combining,
i.e., the received signal in the (i,j)-th element is delayed
by ijxy
11
99
 . We showed that uniform
delay spacing can create 3D beams such that different
frequency components are steered toward a unique
spherical direction s,. Further, the entire 3D angular
space can be covered by at least one beam. Fig. 20
presents the frequency dispersing steering for 10 frequency
components. However, this preliminary study
also reveals a number of design challenges from both
circuits and system perspectives. On the one hand, the
required maximum delay range is increased. For planar
array with a total N elements, the required delay range
Overall gain constraint G(θaz
100
120
140
160
180
60
80
20
40
-80
-60-40 -20 020406080
Azimuth angle (degrees)
Figure 20. the simulated 3 dB beam contour of frequency
dependent steering from a planar ttd array. Nx = 4, Ny = 2,
M = 10 subcarriers, 99

20
IEEE cIrcuIts and systEms magazInE
xy
22
1/ BW;7/BW.
, θel, fm) ≥ (1 - ε)NR
f1 = 57.54GHz
f2 = 58.09GHz
f3 = 58.63GHz
f4 = 59.18GHz
f5 = 59.72GHz
f6 = 60.27GHz
f7 = 60.82GHz
f8 = 61.36GHz
f9 = 61.91GHz
f10 = 62.45GHz
B. TTD Rainbow Beam Enabled Multiple Access
Beam training is not the only application of the TTD array
dispersive rainbow beam. In [91], a novel orthogonal frequency
division multiple access scheme was proposed.
In low-mobility line-of-sight scenarios, TTD arrays and
their rainbow codebooks can be leveraged to spatially
allocate a small fraction of frequency resources to each
served user. There are a number of advantages that
make such scheme appealing for the future IoT application.
Firstly, the hardware bandwidth of each user can
be much smaller than that of the infrastructure. This
facilitates a power- and cost-friendly design for the terminals.
Secondly, the conventional time division beam
switching can be eliminated, because different users
are simultaneously served using different frequency
resources, which are allocated based on the corresponding
rainbow beam directions. It is worth noting
that the frequencyto-angle mapping in rainbow codebooks
is deterministic, i.e., TTD arrays cannot independently
tune frequencies to arbitrary angles. However,
it is possible to exploit phase shifters in different RF
chains of TTD arrays to rotate the entire mapping and
enable the spatial reuse of frequencies. The TTD-based
massive access scheme can also reduce the beam management
overhead to support IoT applications with
strict latency requirements [91]. To this end, designing
a frame structure and synchronization procedure that
are compatible with existing standard represents one of
the most important challenges.
C. Compatibility of TTD Beam Training with 5G
Standard
Exhaustive beam sweeping with synchronization is the
main part of the IA procedure in 5G New Radio Standard.
It is performed using periodic bursts of up to
64SS blocks, each associated with a different steering
Fourth quartEr 2022
is at least 2(N−1)/BW, a factor of 2 larger than its linear
array counterpart. On the other hand, as compared to
the rainbow beam using a linear TTD array, the 3D rainbow
beam using planar array has some unique characteristics.
More specifically, beams from some frequency
component experience a reduced gain as compared to
others. There is non-trivial challenge to calibrate the
beam pattern and design beam training algorithm tailored
for this non-ideality.
Elevation angle (degrees)
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