IEEE Circuits and Systems Magazine - Q4 2022 - 8

mode, intentional beam squint is introduced to achieve
accurate but fast beam-training significantly reducing
the search latency in existing analog PAAs. To realize
these different SSP modes in a TTD PAA, it is important
to understand the trade-offs between the delay range,
delay resolution, and modulated bandwidth as shown
in Fig. 2. Higher delay resolutions and moderate bandwidth
are needed for beamnulling (independent interference
cancellation [52]) whereas large delay range,
moderate resolution, and large bandwidths are needed
for beam-training. The SSP mode for independent interference
cancellation is a corollary of the beamforming
SSP and thus will not be studied in this article.
A. Mitigating Beam-Squint for Data
Communications Mode
To alleviate the beam squint effect, the PAA is required to
compensate inter-element signal delays before any SSP is
done as illustrated in Fig. 3. Assuming a half-wavelength
antenna spacing, the delay difference between the received
signals in two consecutive antennas ∆T can thus be modeled
as 9Td c
2 sin  / , which can be also expressed as
a frequencydependent phase shift difference 9A in the
frequency domain through the following expression:
9A 2 229
fT
sin
f
fc
(1)
where f is frequency. If the signal of interest is narrowband,
i.e., ff/ c ≈1 , the required TTD element can
be replaced with a frequency-flat phase shifter (PS).
This approximation is the basis of large portion of the
SOTA SSP systems [19], [27][45]. A generalized implementation
of phase shifting based SSP unit is shown
in Fig. 4.
Figure 3. Beamforming in an N-element linear array with ttd
elements.
As for any approximation, replacing a TTD element
with a PS imposes performance limitations. These limitations
can be described both in the angular domain and the
frequency domain. In the angular domain, PS-based implementation
causes the intended angle-of-arrival (AoA) to
be frequencydependent. To be more specific, the intended
AoA, for the both beamforming and beam-nulling cases,
varies with the signal of interest frequency as in:
T sin
1 cf
f
§
©
¨
')
S
·
¹
¸
(2)
At the center frequency of the band, the PS-based and
the TTD-based AoAs are the same and the beam is formed/
nulled. As the frequency moves away from the center, the
approximation of TTD with a PS becomes less valid and
there will be an error between the actual and real intended
AoA. This error can be formulated as follows:
'T nsin
si ')
SS
11cf
f
§
©
¨
')
·
¹
¸
§
©
¨
·
¹
¸
(3)
This error depends on the actual AoA and the relative
frequency of the interest. The maximum error happens
Figure 2. trade-offs in different ssP modes: data communications,
beamtraining, and independent
cancellation.
8
IEEE cIrcuIts and systEms magazInE
interference
Figure 4. generalized Ps-based implementation in an
N-element Paa.
Fourth quartEr 2022
IEEE Circuits and Systems Magazine - Q4 2022

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