IEEE Circuits and Systems Magazine - Q4 2022 - 16

distance between the BS and UE. Power spectral
density of the noise is denoted as N0, while
99
BW 2 H
represents the subcarrier
spacing. Note that the SNR per subcarrier is Mtot/M
times larger than with a fully loaded OFDM waveform.
Since the proposed DSP algorithm considers
only M loaded subcarriers with high SNR, angle estimation
in (12) is not noise-limited. Further, due to
a lower number of used subcarriers, the proposed
OFDM waveform for TTD beam training results in
a more than 2 GB lower PAPR than a fully loaded
OFDM waveform, as presented in Fig. 14, where we
assumed the same simulation parameters as in the
previous subsection. We used a cyclic prefix of 128
samples and assumed that subcarriers are loaded
either with binary phase shift keying (BPSK) or
quadrature phase shift keying (QPSK) symbols.
Although the proposed frequency-dependent beamtraining
can benefit from a higher SNR per subcarrier,
the supported distances between the BS and UE are
reduced compared to the PAA beam sweeping approach.
This is because the UE has a lower total received signal
power. Specifically, with the codebook in Fig. 10, which
probes D different directions, roughly 1/D of the signal
power is received per direction. The received signal
power corresponds to the subcarriers that probe the
dominant AoA. To evaluate the impact of a lower received
signal power on the beam-training performance, we
compared the AoA RMSE of TTD-based algorithms
and PAA-based beam sweeping at different distances
between the BS and UE. We assumed a non-line-ofsight
scenario and modeled the path loss according to
mmMAGIC channel [77]. We considered two array sizes
at the UE, including NR = 16 and NR = 32. With NR = 16,
D = 32 directions are probed, while with NR = 16, D = 32
directions are probed. Other parameters are the same
as in the previous subsection. The comparison results
are presented in Fig. 15, where we highlighted the distances
that the compared beam training algorithms
can support. PAA-based beam sweeping combines the
entire signal bandwidth in each probed direction and
thus achieves a high received signal power and reliable
angle estimation at different distances. Nevertheless, it
requires large overheads of 32 and 64 OFDM symbols
to do so when NR = 16 and NR = 32, respectively. Subarray
based PAAs can reduce the overhead by sweeping
multiple beams at the same time, but this comes at
the cost of a lower beamforming gain and thus a lower
supported distance, as shown in Fig. 15 for 4 sub-arrays,
i.e., 4 and 8 antenna elements per sub-array. TTD beam
training algorithms are based on a single OFDM symbol
and their angle estimation accuracy is comparable to
that of exhaustive PAA beam sweeping. However, TTDbased
algorithms have the smallest supported distances
among the compared approaches. We note that with a
more sophisticated detection algorithm that exploits the
waveform structure, beam training capabilities and supported
distances of TTD arrays could increase. We leave
a more detailed theoretical study of supported distances
and better detection algorithms for future work.
V. Reconfigurable Discrete-time TTD SSP
Hardware Design Considerations
Figure 12. Impact of delay error on performance of two ttd
beam training algorithms [76].
In this section, we describe the design and hardware
implementation of reconfigurable time delay units in the
Figure 13. Illustration of oFdm power allocation in (a) conventional beam training and (b) ttd beam training.
(a)
(b)
16
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