This article has been accepted for publication in a future issue of this journal, but has not been

fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JLT.2016.2620146, Journal of
Lightwave Technology
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Photonic True-Time-Delay Beamformer for a

Phased Array Antenna Receiver based on Self-
Heterodyne Detection
Vanessa C. Duarte, Student Member, OSA, Miguel V. Drummond, Member, IEEE, Member, OSA, and
Rogério N. Nogueira, Member, IEEE, Senior Member, OSA

 ensures that the progressive phase shifts experienced by all

Abstract— In this paper, we propose a novel photonic true-time frequencies are correct, thereby avoiding beam squinting.
delay beamforming system for a phased array antenna receiver. Consequently, TTD beamforming systems rely on tunable
The beamformer relies on simple tunable optical delay lines and delay lines. Tunable electrical delay lines present some
also on self-heterodyne coherent detection. Each tunable delay line
drawbacks such as having increasing losses at high frequencies
is implemented by a Mach-Zehnder delay interferometer with
tunable coupling ratio, which allows varying the delay from 0 up and presenting a considerable footprint [1][4]. These drawbacks
to the delay of the interferometer. Self-heterodyne coherent have been addressed by bringing photonic techniques into play,
detection allows achieving maximum sensitivity inherent to as these have unique advantages such as low loss, large
coherent detection, and also laser phase noise cancellation, bandwidth, immunity to electromagnetic interference and light
photonic RF phase shifting and photonic RF frequency weight [5].
downconversion. The proposed system is analytically described
Different photonic TTD beamforming systems based on
and numerically validated. Numerical results show that,
considering a beamsteering range of ±𝟑𝟎𝐨 , the system is able to different tunable optical delay lines (TODLs) have been
beamform the signals received by 𝑵 antenna elements with reported [6]–[13]. The first proposed systems were based on
negligible distortion, thereby proving to be very promising for bulky switchable delay matrices, in which discrete delays are
high-end phased array antenna receivers operating at high RF implemented with fibers of different lengths [6]. More compact
frequencies. and continuously tunable photonic beamforming systems based
on dispersive devices were then proposed in [8]–[10], in which
Index Terms — Phased-array antenna, Photonic true-time delay
beamforming, Mach-Zehnder delay interferometer. the delay given to a signal depends on its wavelength and/or on
the center wavelength of the dispersive device. With the advent
of photonic integrated circuits, new techniques have been
I. INTRODUCTION proposed for photonic beamforming systems, inspired in
integrated digital finite and infinite impulse response (FIR and
H igh-end wireless communication systems such as radar [1],
satellite communications [2] and 5G cellular networks [3]
all require flexible and efficient transmission of spectrally rich
IIR) all-pass filters. A photonic beamforming system based on
optical ring resonator IIR filters and also on self-coherent
detection was proposed in [11], [12]. Each ring operates as a
radio signals. Such requirement has brought a close attention to
TODL, in which the time delay is configured by controlling the
phased-array antennas (PAAs), which have a unique capability
power coupling ratio between the waveguide and the ring. In
of efficiently generating arbitrary radiation diagrams.
[13], we proposed a TODL based on a Mach-Zehnder delay
The operational bandwidth of a PAA system depends not
interferometer (MZDI) FIR filter. The time delay is configured
only on the bandwidth of its antenna elements (AEs), but also
by controlling the power coupling ratio between the arms of the
on the operational bandwidth of the beamforming system
MZDI. By using a dispersive medium as delay in the MZDI, a
responsible for processing the signals generated by or fed to the
tunable dispersive device was first proposed in [14]. The same
AEs. Broadband beamforming systems cannot rely on phase
operation principle, however with a non-dispersive delay in the
shifters, since these have an operational bandwidth restricted to
MZDI, was employed in [13] as a TODL in a photonic
a single frequency. True-time delay (TTD) beamforming must
beamforming system for a PAA transmitter. Both approaches
therefore be employed [4]. In a TTD beamforming system, the
based on IIR and FIR filters have a tradeoff among time delay,
signals are effectively delayed instead of phase shifted. This
bandwidth and footprint. Nonetheless, as IIR filters are based

This paragraph of the first footnote will contain the date on which you V. C. Duarte is with Instituto de Telecomunicações and Physics Department,
submitted your paper for review. This work is co-funded by FCT/MEC through University of Aveiro, 3810-193 Aveiro, Portugal (e-mail: vanessaduarte@
national funds and when applicable co-funded by FEDER – PT2020 partnership av.it.pt).
agreement under the project UID/EEA/50008/2013 and also supported by the M. V. Drummond is with Instituto de Telecomunicações, University of
European Commission through the project BEACON (FP7-SPACE-2013-1- Aveiro, 3810-193, Aveiro, Portugal (e-mail: mvd@av.it.pt).
607401). R. N. Nogueira is with Instituto de Telecomunicações, University of Aveiro
and Watgrid Lda., 3810-193, Aveiro, Portugal (e-mail: rnogueira@av.it.pt).

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on resonant operation they require tighter fabrication tolerances

and also a good control of the power coupling ratio [15].
In this paper, we propose a novel photonic beamforming
system for a PAA receiver. The system relies on MZDI-based
TODLs and on self-heterodyne coherent detection. The TODLs
have a simple, potentially fast tuning mechanism, thereby
enabling dynamic TTD beamforming. In addition to offering (a)
maximum sensitivity, self-heterodyne coherent detection
enables phase noise cancellation, photonic RF phase shifting
and also photonic RF frequency downconversion. The latter
advantage is very important for relaxing the bandwidth of the
electrical circuitry of the receiver. Furthermore, thanks to self- (b)
heterodyne coherent detection and unlike the system proposed
Fig. 1. (a) Basic architecture of the proposed photonic beamforming
in [13], the maximum delay of the TODLs can be defined system for a PAA comprising a single AE. (b) Schematics of the
independently of the RF frequency. optical spectra at different points of the system.
This paper is organized in four sections. Section II presents
an analytical derivation of the proposed system. Such analysis
frequency-shifted version of the input CW laser signal, coherent
also addresses the distortion imposed by several impairments
detection is in fact self-heterodyne detection. In the following
related with modulation, optical local oscillator (OLO)
lines, an analytical model of this system is derived.
generation and heterodyne detection. Section III presents a
numerical validation of the system. The input RF signal
A. Modulation
parameters were chosen to be in line with those of a return user
signal received by a satellite receiver, complying with the The input laser signal is given by
frequency plan presented in [16]. The system performance is
𝐸in (𝑡) = √𝑃in exp (𝑗(𝜔o 𝑡 + 𝜙PN (𝑡))), (1)
assessed for a single and for multiple AEs, with the objective of
estimating a worst-case performance limit for a PAA where 𝑃in is the laser power, 𝜔o is the angular frequency, and
comprising a given number of AEs. In section IV the main 𝜙PN (𝑡) represents the laser phase noise. The modulated optical
conclusions are presented. signal is given by
1 𝜋
II. ANALYTICAL MODEL 𝐸(𝑡) = 𝐸in (𝑡) ⋅ [exp (𝑗 (𝑣1 (𝑡) + 𝑉B1 )) +
2√2 𝑉𝜋
The basic architecture and signals of the photonic
(2)
beamforming system for processing a single AE signal are 𝜋
𝑘ER exp (𝑗 (𝑣2 (𝑡) + 𝑉B2 ))],
depicted in Fig. 1. A continuous wave (CW) signal provided by 𝑉𝜋
a single laser source is split by two paths. Signal modulation is
performed in the upper path, whereas the frequency-shifted where 𝑉𝜋 is the half-wave voltage of the MZM, 𝑣1 (𝑡) is the
OLO (FSOLO) is generated in the lower path. alternated-current (AC) coupled electrical signal fed to the
In the upper path, the amplified RF signal generated by one upper electrode of the modulator, 𝑉B1 is the bias voltage of the
of the AEs drives a Mach-Zehnder modulator (MZM) biased at upper electrode, and 𝑣2 (𝑡) and 𝑉B2 are the corresponding
the minimum transmission point. The modulated optical signal parameters of the lower electrode. The constant 𝑘ER , in which
is then amplified by an optical amplifier, phase shifted by 𝛽, 0 < 𝑘ER ≤ 1, models the extinction ratio (ER) of the MZM
and delayed by the TODL. A phase shifter 𝛽 is required to such that
adjust the phase of each modulated optical signal, such that in a 1 + 𝑘ER
system with multiple AEs all signals add up with the correct ER [dB] = 20 log10 ( ). (3)
1 − 𝑘ER
phase. The TODL is a MZDI with a time delay of 𝜏 and with
tunable coupling ratio. The power coupling ratio between the Considering that the MZM is operating in push-pull mode, one
arms of the MZDI can be tuned by the phase shifter 𝜙, whereas has 𝑣1 (𝑡) = −𝑣2 (𝑡) = 𝑣(𝑡), and also 𝑉B1 = −𝑉B2 = 𝑉B . In
𝛾 allows centering the frequency response of the TODL with order to produce amplitude modulation, 𝑉𝐵 should be set to
𝑉 𝜋
the input optical signal. − 𝜋 ⋅ , leading to
𝜋 2
In the lower path, the input CW signal is modulated by an IQ
modulator (IQM), driven by a sinusoidal tone with a frequency 1 𝜋
𝐸(𝑡) = 𝐸in (𝑡) ⋅ [(1 + 𝑘ER ) sin ( 𝑣(𝑡)) − 𝑗(1 −
𝑓LO , and biased in order to produce an optical carrier suppressed 2√2 𝑉𝜋

single sideband (OCS-SSB) output signal. Hence, the output (4)

𝜋
optical signal is a frequency-shifted version of the input CW 𝑘ER ) cos ( 𝑣(𝑡))],
𝑉𝜋
signal, which serves as a FSOLO. The modulated optical signal
is combined with the amplified FSOLO and coherently detected where 𝑣(𝑡) is the input RF signal, which be modeled as
using a balanced photodiode (BPD). Since the OLO is a

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𝑣(𝑡) = 𝑎(𝑡) sin(𝜔RF 𝑡 + 𝜃(𝑡)), (5) where 𝐸MZDI (𝑓) is the delayed output optical signal, 𝑀(𝑓) is
the second output optical signal, which can be used for
where 𝑎(𝑡) and 𝜃(𝑡) are the amplitude and phase variation of operation monitoring, 𝜏(𝑓) is the transfer function of the optical
the input RF signal, respectively. For a matter of simplicity, let delay line and 𝐸(𝑓)𝑒𝑗𝛽 is the input optical signal. Without loss
us consider infinite ER, i.e., 𝑘ER = 1, and an RF signal with of generality, the amplitude and group delay responses of the
reduced amplitude, such that the MZM operates in its linear TODL can be derived by setting 𝛾 = 𝜋⁄2, as the variation of 𝛾
domain. Equation (4) can be simplified to only results in a displacement of the frequency response along
1 𝜋 the frequency. Such responses are given by
𝐸(𝑡) = 𝐸in (𝑡) ⋅ 𝑣(𝑡). (6)
√2 𝑉𝜋 1
‖𝐻(𝑓)‖2 = (sin(𝜙) cos(2𝜋𝑓𝜏) + 1), (9)
2
B. Tunable Optical Delay Line 𝜏 sin 𝜙 cos(2𝜋𝑓𝜏)−cos 𝜙+1
𝜏𝑔 (𝑓) = ( ). (10)
After being phase shifted by 𝛽, the modulated optical signal 2 sin 𝜙 cos(2𝜋𝑓𝜏)+1
is delayed by the TODL. The TODL output signals are given
by Fig. 2 shows the amplitude and group delay responses for
different values of 𝜙. Both responses have a periodical behavior
𝐸 (𝑓) 1 1 𝑗 𝑒𝑗𝜏(𝑓) 0 ] [1 𝑗 𝑒𝑗𝜙 0] [1 𝑗 ]
[ 𝑀𝑍𝐷𝐼 ] = [ ][ ][ with a period of 1/𝜏. The amplitude response is identical for
𝑀(𝑓) 2√2 𝑗 1 0 𝑒𝑗𝛾 𝑗 1 0 1 𝑗 1
(7) supplementary values of 𝜙, whereas the group delay response
𝑗𝛽
⋅ [𝐸(𝑓)𝑒 ] , increases with 𝜙, proving that the delay imposed by the MZDI
0
depends on the power coupling ratio between the arms of the
resulting in MZDI.
𝐸 (𝑓) 1 𝑒𝑗𝜏(𝑓) (𝑒𝑗𝜙 − 1) − 𝑒𝑗𝛾 (𝑒 𝑗𝜙 + 1) As depicted in inset C of Fig. 1, the modulated optical signal
[ MZDI ] = [ ] ⋅ 𝐸(𝑓)𝑒𝑗𝛽 , (8) has two sidebands, one of which is heterodynally detected.
𝑀(𝑓) 2√2 𝑗𝑒 𝑗𝜏(𝑓) (𝑒 𝑗𝜙 − 1) + 𝑗𝑒 𝑗𝛾 (𝑒 𝑗𝜙 + 1)
Without loss of generality, it is assumed that such sideband is
the one at the highest frequency. In order to have the MZDI
correctly operating as a TODL, one must center such sideband
at a maximum of the amplitude response, i.e., 𝑓RF ∙ 𝜏 = 𝑛,
where 𝑛 is an integer. If such is the case, the delayed optical
signal can be approximated by

𝐸MZDI (𝑡) = 𝛼(𝜙) ⋅ 𝐸 (𝑡 − 𝜏𝑔 (𝜙)), (11)

where 𝛼(𝜙) is the attenuation imposed by the MZDI and 𝜏𝑔 (𝜙)

is the configured delay. These functions can be derived from (9)
(a) and (10), by setting 𝑓 ∙ 𝜏 = 𝑛, where 𝑛 is an integer. Such
functions are shown in Fig. 3.
For a matter of simplicity, the TODL is considered to be ideal
in the following analytical derivations. The impact of its non-
ideal frequency response on the photonic beamforming system
is numerically assessed in Section III.

C. Frequency-shifted Optical Local Oscillator

As observed in Fig. 1 (a), input laser signal is modulated by
a dual-parallel MZM (DP-MZM), which can be modeled as
(b)
1 𝜋
Fig. 2. Amplitude (a) and group delay (b) responses of the MZDI for 𝐸OLO (𝑡) = 𝐸in (𝑡) ⋅ [cos ( (𝑣up (𝑡) + 𝑉B,up )) +
2√2 𝑉𝜋,up
different values of 𝜙 and 𝛾 = 3𝜋⁄2.
(12)
𝜋 𝜋
0 1 exp (𝑗 𝑉B,PS ) cos ( (𝑣low (𝑡) + 𝑉B,low ))],
𝑉𝜋,PS 𝑉𝜋,low
0.8
|| ()||2 [dB]

-1 where 𝑉𝜋,up , 𝑣up (𝑡) and 𝑉B,up are the half-wave voltage, RF
 () / 

0.6
0.4 input signal and bias voltage of the upper MZM, respectively,
g

-2
and 𝑉𝜋,low , 𝑣low (𝑡) and 𝑉B,low are the same variables of the
0.2
lower MZM. 𝑉𝜋,PS and 𝑉B,PS are the half-wave voltage and bias
-3 0
0 50 100 150 voltage of the optical phase shifter. Considering VB,up =
 [deg] 𝑉𝜋 𝜋 𝜋 𝜋
𝑉B,low = − ⋅ , 𝑉 = , 𝑉𝜋,up = 𝑉𝜋,low = 𝑉𝜋,IQ , and
Fig. 3. Attenuation and group delay response of the TODL as a 𝜋 2 𝑉𝜋,PS B,PS 2
function of 𝜙. assuming reduced a modulation index, (12) results in

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1 𝜋 system. In this section, the impact of the most relevant

𝐸OLO (𝑡) = 𝐸in (𝑡) ⋅ (𝑣up (𝑡) + 𝑗𝑣low (𝑡)), (13)
2√2 𝑉𝜋,IQ impairments is assessed. Starting with modulation, let us first
address harmonic generation. Considering an infinite ER, the
which represents the typical response of an IQM. In order to
frequency-shift the input optical signal by 𝜔LO , the RF input RF signal (5), and applying the Jacobi-Anger expansion, (4)
signals should be given by 𝑣up (𝑡) = 𝐴IQ cos(𝜔LO 𝑡) and becomes
𝑣low (𝑡) = 𝐴IQ sin(𝜔LO 𝑡), where 0 ≤ 𝐴IQ ≤ 𝑉𝜋 ⁄2. This results 𝜋
𝐸(𝑡) = 𝐸in (𝑡) ⋅ √2 ∑∞
𝑛=1 𝐽2𝑛−1 ( 𝑎(𝑡)) ⋅ sin ((2𝑛 −
in 𝑉𝜋
(20)
1 𝜋 1)(𝜔RF 𝑡 + 𝜃(𝑡))) ,
𝐸OLO (𝑡) = 𝐸in (𝑡) ⋅ 𝐴IQ exp(𝑗𝜔LO 𝑡). (14)
2√2 𝑉𝜋,IQ where 𝐽𝑛 (𝑧) is the Bessel function of first kind of order 𝑛.
Equation (20) shows that, besides the desired tone at 𝜔RF ,
D. Coherent Detection undesired harmonics at (2𝑛 − 1)𝜔RF are also produced. Using
The optical signals at the input of the BPD are given by a similar analysis, it can be shown that the generation of the
FSOLO also produces multiple tones, located at (2𝑛 − 1)𝜔LO .
𝐸BPD,1 (𝑡) 1 1 𝑗 𝐺sig ⋅ 𝐸MZDI (𝑡) Consequently, coherent detection produces tones at (2𝑛1 −
[ ]= [ ][ ] (15)
𝐸BPD,2 (𝑡) √2 𝑗 1 𝐺OLO ⋅ 𝐸OLO (𝑡) 1)𝜔RF ± (2𝑛2 − 1) 𝜔LO , 𝑛1 , 𝑛2 = 1,2, …. In order to avoid
where 𝐺sig and 𝐺OLO represent the combination of amplification that undesired tones fall at ±(𝜔RF − 𝜔LO ), thereby enabling to
reject them using band-pass filtering, one must have
and losses given to the optical signal and to the OLO,
respectively. The current produced by the BPD is given by (2𝑛1 − 1)𝜔RF ± (2𝑛2 − 1) 𝜔LO ≠ ±(𝜔RF − 𝜔LO ) (21)
𝐼(𝑡) = 𝐼1 (𝑡) − 𝐼2 (𝑡) for all values of 𝑛1 and 𝑛2 except for 𝑛1 = 𝑛2 = 1. For instance,
𝜔
R 2 this rules out 𝜔LO = RF.
= (|𝐺sig 𝐸MZDI (𝑡) + 𝑗𝐺OLO 𝐸OLO (𝑡)| (16) 2
2 Realistic modulators have a finite, non-negligible ER, which
2
− |𝑗𝐺sig 𝐸MZDI (𝑡) + 𝐺OLO 𝐸OLO (𝑡)| ), must be considered. Considering (4) and a RF signal (5) with a
reduced amplitude, the modulated optical signal is given by
where R is the responsivity of the photodiodes. The
1 𝜋
simplification of (16) results in 𝐸(𝑡) ≈ 𝐸in (𝑡) ⋅ [(1 + 𝑘ER ) 𝑎(𝑡) ⋅ sin(𝜔RF 𝑡 + 𝜃(𝑡)) −
2√2 𝑉𝜋
(22)
1 𝜋2 𝑗(1 − 𝑘ER )].
𝐼(𝑡) = − 𝑅𝐺sig 𝐺OLO 𝐴 𝑣(𝑡)
2 𝑉𝜋 𝑉𝜋,IQ IQ
∗ (𝑡)𝑒 −𝑗𝛽
⋅ ℑ{𝐸in 𝐸in (𝑡)𝑒 𝑗𝜔IF𝑡 } (17) Besides the expected tones at 𝜔o ± 𝜔RF , the modulated optical
1 𝜋2 signal now also has a residual tone at 𝜔o . By considering (22)
=− 𝑅𝐺sig 𝐺OLO 𝑃in 𝐴IQ 𝑣(𝑡) ⋅ sin(𝜔LO 𝑡 − 𝛽),
2 𝑉𝜋 𝑉𝜋,IQ in (16), one can derive the output current as
where ℑ{𝑥} is the imaginary part of 𝑥. Equation (18) shows that 1
𝐼(𝑡) = − 𝑅𝐺sig 𝐺OLO 𝑃in
𝜋 1+𝑘ER 𝜋
𝐴IQ . [ 𝑎(𝑡) ⋅
∗ 4 𝑉𝜋,IQ 2 𝑉𝜋
there is laser phase noise cancelation, as 𝐸in (𝑡)𝐸in (𝑡) = 𝑃in .
(cos((𝜔RF − 𝜔LO )𝑡 + 𝜃(𝑡) + 𝛽) − cos((𝜔RF + 𝜔LO )𝑡 + (23)
Using (5) in (17) and also trigonometric identities, the 𝜋
photocurrent becomes 𝜃(𝑡) − 𝛽)) + (1 − 𝑘ER ) sin (𝜔LO 𝑡 − 𝛽 − )].
2

1
𝐼(𝑡) = − 𝑅𝐺sig 𝐺OLO 𝑃in
𝜋2
𝐴IQ 𝑎(𝑡) ⋅ (cos((𝜔RF − Equation (23) shows that besides the desired tone at 𝜔RF − 𝜔LO
4 𝑉𝜋 𝑉𝜋,IQ (18) and the undesired tone at 𝜔RF + 𝜔LO , there is now another
𝜔LO )𝑡 + 𝜃(𝑡) + 𝛽) − cos((𝜔RF + 𝜔LO )𝑡 + 𝜃(𝑡) − 𝛽)). undesired tone at 𝜔LO . In order to avoid such that tone falls at
The undesired tone at the highest frequency of 𝜔RF + 𝜔LO can 𝜔RF + 𝜔LO , one must have
be filtered out through low-pass filtering, leading to
𝜔RF − 𝜔LO ≠ 𝜔LO , (24)
1 𝜋2 𝜔RF
𝐼(𝑡) = − 𝑅𝐺sig 𝐺OLO 𝑃in 𝐴 𝑎(𝑡) which, once again, rules out 𝜔LO = . An identical analysis
4 𝑉𝜋 𝑉𝜋,IQ IQ (19) 2
⋅ cos((𝜔RF − 𝜔LO )𝑡 + 𝜃(𝑡) + 𝛽). can be performed for the IQM, in which a finite ER results in
the OLO having a residual tone also at 𝜔o . After coherent
Equation (19) shows that the original RF signal is frequency detection, besides the tones at 𝜔RF ± 𝜔LO and at 𝜔LO , there is
converted from 𝜔RF down to 𝜔RF − 𝜔LO . It also shows that the another very weak undesired tone at DC. Such tone can be
optical phase shifting of 𝛽 is translated into an identical RF easily filtered out using bandpass filtering.
phase shifting due to the rejection of the received highest Besides harmonic generation and finite ER, one must also
frequency tone. consider the unavoidable drifting of the bias voltage of a
modulator, which cannot be neglected even when it is kept
E. Impairments under control. Small but realistic drifts can be straightforwardly
The model derived above assumes an ideal behavior of all modeled in (6) as
devices. In practice, the impairments caused by them need to be
1 𝜋
taken into account in order to determine the robustness of the 𝐸(𝑡) = 𝐸in (𝑡) ⋅ 𝑣(𝑡) + Δ𝑉B , (25)
√2 𝑉𝜋

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where Δ𝑉B is the deviation of the bias voltage of the MZM from The first term introduces undesired tones at DC and 2𝜔RF . The
the ideal value. This term, after coherent detection, produces an second term only produces a tone at DC, whereas the third term
undesired tone at 𝜔LO , similarly to the one produced due to the represents the tones at 𝜔RF ± 𝜔LO . Consequently, in order to
MZM having a finite ER. The same analysis is valid for drifts suppress the first and second terms one must have 𝜔RF −
in bias voltages of the IQM. Therefore, by carefully choosing 𝜔LO ≠ 0.
𝜔IF in compliance with (21) and (24), third-order harmonic Self-heterodyne detection has the advantage of enabling
generation, finite ER of the modulators, and drifting of the bias phase noise cancellation, as observed in (17). However, in the
voltages of modulators do not impair the output signal, as the derivation of (17) is assumed that the TODL does not delay the
resulting spurious tones can be rejected by bandpass filtering. modulated optical signal. However, the modulated optical
In order to achieve ideal frequency shifting of the input laser signal is delayed by 𝜏𝑔 (𝜙), 0 ≤ 𝜏𝑔 (𝜙) ≤ 𝜏, and therefore
signal using a DP-MZM, it is required that all electrical and
∗
optical signals are perfectly balanced, which is unrealistic. In 𝐸in (𝑡 − 𝜏𝑔 (𝜙)) 𝐸in (𝑡) = 𝑃in exp (𝑗 (𝜔o 𝜏𝑔 (𝜙) + 𝜙PN (𝑡) −
practice, even though most power is located at the desired tone (31)
𝜔o + 𝜔LO , there is a residual tone at 𝜔o − 𝜔LO that cannot be 𝜙PN (𝑡 − 𝜏𝑔 (𝜙)))).
fully suppressed. The presence of the residual tone at 𝜔o − 𝜔LO
can be modeled by generalizing (14) to The first term results in a constant phase shift, and can be easily
1 𝜋 accounted for by adjusting the optical phase shift 𝛽. The second
𝐸OLO (𝑡) = 𝐸in (𝑡) and third terms show that ideal phase noise cancellation is not
2√2 𝑉𝜋,IQ
⋅ 𝐴IQ (𝑘SBR exp(𝑗𝜔IF 𝑡)
(26) achieved, as in practice 𝜙PN (𝑡) − 𝜙PN (𝑡 − 𝜏𝑔 (𝜙)) ≠ 0.
+ (1 − 𝑘SBR ) exp(−𝑗𝜔LO 𝑡)), Consequently, the worst-case scenario corresponds to having
the highest possible delay, i.e., 𝜏(𝜙) = 𝜏. Instead of resorting
where 𝑘SBR is related with the ratio between the amplitudes of
to a complex statistical assessment of 𝜙PN (𝑡) − 𝜙PN (𝑡 −
the upper and lower sidebands, 0 ≤ 𝑘SBR ≤ 1, and ideally
𝑘SBR = 1. After coherent detection and low-pass filtering, the 𝜏𝑔 (𝜙)), a simple insight can be obtained using the concept of
output current is given by laser coherence time. The coherence time is the time during
1 𝜋2
which the laser signal may be considered coherent, and is given
𝐼(𝑡) = − 𝑅𝐺sig 𝐺OLO 𝑃in 𝐴IQ 𝑎(𝑡) ⋅ by
4 𝑉𝜋 𝑉𝜋,IQ
(𝑘SBR cos((𝜔RF − 𝜔LO )𝑡 + 𝜃(𝑡) + 𝛽) − (1 − (27)
1
𝑘SBR ) cos((𝜔RF − 𝜔LO )𝑡 + 𝜃(𝑡) − 𝛽)). 𝜏CT = , (32)
Δ𝜈
Equation (27) shows that the residual tone of the OLO directly where Δ𝜈 is the linewidth of the laser source. Therefore, it can
impacts the output signal, as it promotes fading whose be assumed that 𝜙PN (𝑡) − 𝜙PN (𝑡 − 𝜏𝑔 (𝜙)) ≈ 0, as long as
relevance depends on 𝑘SBR and 𝛽. The worst case occurs for 𝜏𝑔 (𝜙) < 𝜏CT . For realistic lasers, the linewidth can be safely
𝑘SBR = 0.5, as
assumed to be lower than 10 MHz, leading to a coherence time
1 𝜋2 of 100 ns. As shown in section III, such value is much higher
𝐼(𝑡) = 𝑅𝐺sig 𝐺OLO 𝑃in 𝐴IQ 𝑎(𝑡) ⋅ sin((𝜔RF − 𝜔LO )𝑡 +
4 𝑉𝜋 𝑉𝜋,IQ (28) than typical values of 𝜏.
𝜃(𝑡)) sin(𝛽).
F. Power budget
In this case, instead of translating into RF phase shifting, optical
In order to calculate the power budget of the proposed
phase shifting only produces pure fading.
Concerning coherent detection, the most relevant impairment beamforming system, let us first consider Fig. 4, which presents
of the BPD is the imbalance between its photodiodes. This can a trivial extension of the basic architecture shown in Fig. 1 from
be modeled in (16) as
𝐼(𝑡) = 𝐼1 (𝑡) − 𝑏BPD 𝐼2 (𝑡)
𝑅 2
= (|𝐺sig 𝐸MZDI (𝑡) + 𝑗𝐺OLO 𝐸OLO (𝑡)|
2 (29)
− 𝑏BPD |𝑗𝐺sig 𝐸MZDI (𝑡)
2
+ 𝐺OLO 𝐸OLO (𝑡)| ),

where 𝑏BPD models the imbalance of the photodiodes, and

ideally 𝑏BPD = 1. Using a single-ended detector instead of a
BPD can be modeled simply by considering 𝑏BPD = 0. Solving
(29) results in
𝑅 2 |𝐸 2
𝐼(𝑡) = ((1 − 𝑏BPD )𝐺sig MZDI (𝑡)| + (1 −
2
𝑏BPD )|𝐸OLO (𝑡)|2 ) − (1 + (30)
∗
𝑏BPD )2𝑅𝐺sig 𝐺OLO ℑ{𝐸MZDI (𝑡)𝐸OLO (𝑡)}. Fig. 4. Proposed beamforming system for 𝑁 antenna elements.

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one to 𝑁 AEs, again considering a single laser source. Using a PAA receiver of a satellite receives multiple return user beams
single laser source has the advantage that a single OLO and within a frequency range of 27.5 GHz to 30 GHz and with a
coherent detector are needed for multiple AEs. The maximum spectral bandwidth of 1 GHz of bandwidth. The
disadvantage is that the power of the laser source must be modulation format is typically chosen from the Digital Video
shared among all AEs. Therefore, for a large number of AEs, Broadcasting - Satellite - Second Generation (DVB-S2)
one should consider more laser sources, for example by using standard, which supports various amplitude and phase-shift
multiple beamforming systems such as the one of Fig. 4, and keying (PSK) formats.
combining their outputs either by electrical or digital means. An ideal CW laser with an average output power of 100 mW
The laser signal is split by a 1:2 splitter, in which the upper was generated. A 1 GBd quadrature PSK (QPSK) data signal
output is in turn split by 𝑁 paths, once per AE, and the lower pulse-shaped by a root-raised cosine (RRC) filter with a roll-off
output is used for OLO generation. The output signal of the 𝑛th factor of 𝛽RRC = 0.5 was generated with length of 29 symbols.
MZM is given by the generalization of (6) to The data signal was modulated onto an ideal carrier with a
𝜋 frequency of 𝑓RF = 30 GHz. Such signal is overdemanding for
𝐸𝑛 (𝑡) = 𝐸in (𝑡) ⋅ √𝑘1 𝑘2 𝑣𝑛 (𝑡), (33)
𝑉𝜋 the considered scenario, and thus provides a conservative
performance evaluation of the system. 𝑁 copies of such RF
where 𝑘1 and 𝑘2 are the splitting ratios of the 1:2 and 1: 𝑁
splitters. Concerning the generation of the OLO, (14) becomes signal were produced, individually delayed, and fed to the 𝑁
MZMs. A modulation index of 25% relatively to 𝑉𝜋 was
1 𝜋
𝐸OLO (𝑡) = √1 − 𝑘1 𝐸in (𝑡) ⋅ 𝐴IQ exp(𝑗𝜔LO 𝑡). (34) considered. The delay given to each copy was defined
2 𝑉𝜋,IQ
according to the following PAA specifications. The steering
Since the final purpose of the beamforming system is to range of the PAA was limited to |Θ| ≤ 30o , and the distance
constructively combine the contributions from all AEs, for a between adjacent AEs was of 𝑑 = 0.85𝜆, where 𝜆 is the
matter of simplicity let us assume ideal TODLs such that wavelength of the input radio signal. The time interval between
𝐸MZDI,𝑛 (𝑡) = 𝐸𝑛 (𝑡) = 𝐸(𝑡). The low-pass filtered output the radio signals received by two adjacent AEs is given by 𝛿 =
current amplitude is given by the generalization of (19) to 𝑑 sin(Θ)⁄𝑐 , where 𝑐 is the speed of light. Hence, 𝛿 varies
𝑅 𝜋2 between ±𝛿max, where 𝛿max = 14.17 ps, and thus the copy of
𝐼 = −𝑁 𝐺sig 𝐺OLO 𝑃in √𝑘1 (1 − 𝑘1 )𝑘2 𝑘3 𝐴IQ 𝐴sig, (35)
4 𝑉𝜋 𝑉𝜋,IQ the RF signal fed to the 𝑛th AE is delayed by (𝑛 − 1)𝛿, where
where 𝑘3 is the coupling ratio of the 𝑁: 1 combiner. As 𝑘2 = 𝑛 = 1, … , 𝑁.
⌈log2 𝑁⌉ Regarding the value of 𝜏, even though the operation principle
𝑘 3 = 2− 2 , for ⌈log 2 𝑁⌉ = log 2 𝑁 (35) becomes of the TODL is analogous to the one presented in [13], in the
𝑅 𝜋2 present case it is not necessary to define 𝜏 according to equation
𝐼 = − 𝐺sig 𝐺OLO 𝑃in √𝑘1 (1 − 𝑘1 ) 𝐴 𝐴 . (36)
4 𝑉𝜋 𝑉𝜋,IQ IQ sig (7) of [13]. As only one of the sidebands is detected, there is
only the need to center one of them at a maximum of the
The average output electrical power is given by TODL’s amplitude response. Therefore, the minimum required
1 value of 𝜏 only depends on 𝛿max and on 𝑁, and is given by
𝑃avg = 𝐼2 ⋅ 𝑅Ω
2 𝜏 = 𝛿max ∙ (𝑁 − 1). (39)
2 (37)
𝑅2 2 2 3
𝜋2 2
= 𝑘1 (1 − 𝑘1 )𝐺sig 𝐺OLO 𝑅Ω ( ) . 𝑃in 𝑃IQ 𝑃sig , The phase shifters 𝛽1 , … , 𝛽𝑁 , were adjusted such that all delayed
8 𝑉𝜋 𝑉𝜋IQ
optical signals were constructively added, thereby maximizing
where 𝑅Ω is the output load, 𝑃IQ is the electrical power fed to the output electrical power . The phase shifters of the TODL
the IQM, and 𝑃sig is the electrical power fed to each MZM. 𝛾1 , … , 𝛾𝑁 were set by default to an ideal value, enabling a
Therefore, the power budget of the system is given by perfect alignment of the input optical signals with the frequency
response of the MZDIs.
2
𝑃out 𝑅2 2 2
𝜋2 (38) Concerning the generation of the OLO, the IQM was fed with
2 = 𝑘1 (1 − 𝑘1 )𝐺sig 𝐺OLO 𝑅Ω3 ( ) .
𝑃in 𝑃IQ 𝑃sig 8 𝑉𝜋 𝑉𝜋IQ

This result shows that for a fixed set of input powers the output
power is constant and independent of the number of AEs. It also
shows that the best strategy to increase the output power is
increasing the gain of the optical amplifiers associated with 𝐺sig
and 𝐺OLO , and also increasing 𝑃in .

III. NUMERICAL ASSESSMENT

The performance degradation caused by one or multiple
TODLs comprising a beamforming network cannot be modeled
by simple analytical expressions. Hence, a numerical system
simulation model was developed for an arbitrary number of Fig. 5. Degradation imposed by laser phase noise for different values
AEs. The simulation scenario is based on [16], in which the of 𝜏 in system comprising a single AE.

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a purely sinusoidal signal with 𝑓LO = 20 GHz with a

modulation depth of 25%. All optical amplifiers were set with 55
a unitary gain. The responsivity of the BPD was of 1 A/W. The

OIP3 [dBm]
detected signal was match-filtered by an RRC filter. The 50
filtered signal was finally demodulated by a typical QPSK
45
demodulator, however without any carrier phase recovery
technique nor algorithm.
40
Other than laser phase noise, no noise was considered at any 10 20 30 40 50
point of the system, meaning that signal degradation only IQ modulation index[%]
stemmed from phase noise, third-order intermodulation Fig. 6. OIP3 for different modulation indexes of the IQM.
distortion (IMD3), and non-ideal frequency response of the
TODLs. The error vector magnitude (EVM) [17] was the only 180
figure of merit used, as for slightly distorted signals the bit error 4
rate is consistently zero. 160 6

2
140 10

4
A. Laser Phase Noise 8
As observed in (31), in practice, laser phase noise is not 120

12
ideally cancelled, and therefore its impact should be assessed.

6
 [degrees]
A system with a single AE was considered. In order to consider 100

10
the worst-case scenario, the TODL was set to its maximum

2
80
delay, i.e., 𝜏𝑔 (𝜙) = 𝜏, meaning that degradation was caused

14
8
only by non-ideal phase noise cancellation. 60
12
As shown in Fig. 5 the EVM increases both with Δ𝜈 and 𝜏. 6
40
As expected, for 𝜏 = 0 the EVM is at its lowest, independently 10
of the linewidth, as phase noise cancellation is ideal. Assuming 2 4 8
20 6
that the FSOLO is delayed on purpose by 𝜏/2, the maximum 4
2 2
absolute delay between the FSOLO and any delayed optical 0
0 2 4 6 8 10 12
signal is of 𝜏/2, instead of 𝜏. This means that, in practice, the /TRF
degradation quantified in Fig. 5 can be achieved for a value of Fig. 7. EVM (%) as a function of the maximum time delay of the
𝜏 that is twice as indicated. As an example, let us consider a TODL, 𝜏, and the phase shift 𝜙, responsible for tuning the time
realistic linewidth of 1 MHz. For such a value, the EVM delay between 0 (0º) and 𝜏 (180º), for a system comprising a single
estimated for an indicated time delay of 𝜏 = 6TRF is twice the AE. The dots represent the angles 𝜙 which result in the highest
minimum EVM. Given the considered maximum value of EVM for the corresponding values of τ.
𝛿max = 14.17 ps, the maximum number of AEs supported by
such value is of (𝑁 − 1)𝛿max = 2𝜏, which yields 𝑁 = 29 AEs. 18
RRC=0
B. Intermodulation distortion 16
RRC=0.25
In order to quantify the impact of modulation-imposed 14 RRC=0.5
distortion, the IMD3 was characterized. Without loss of
generality, a system with a single AE was once again 12 RRC=0.75
considered. The MZM was modulated by two purely sinusoidal RRC=1
EVM [%]

10
signals with frequencies of 30 and 30.05 GHz. Different
modulation indexes were applied to the IQM. In order to avoid 8
overdrive, the maximum modulation index was of 50%.
The input third-order intercept point (IIP3), was measured at 6
43.7 dBm, regardless of the modulation index of the IQM. As 4
discussed in section II, the non-ideal generation of the OLO
only produces undesired tones in the output electrical signal, 2
which can be filtered out after bandpass filtering. Hence, the
0
generation of the OLO does not impact the IMD3 of the system. 0 2 4 6 8 10 12
The measured output third-order intercept points (OIP3) are /TRF
shown in Fig. 6. Increasing the modulation index of the IQM Fig. 8. EVM as a function of 𝜏 for a system comprising a single AE
from 10% to 50% results in an increase of the OIP3 of 12 dB. and 𝜙 = 90o. Different roll-off factors of the pulse-shaping filter
are considered. The insets correspond to the constellation diagrams
C. Performance assessment for a single antenna element obtained for 𝜏 = 1.5 ∙ TRF and 𝜏 = 10 ∙ TRF , for 𝛽RRC = 0.5.
The TODL has an ideal behavior only when configured for

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6 1

9
3
14

22 20 18 16

11
5
6

8
12
5

10
0.8

7
4
2
10

6
4

12
4 9

8
0.6

11
[%]

max

8
12 10
6
3

/
RF

10
2

7
/T

4
0.4 6

2
4
8 9
2
3 5 8
6
0.2 4 67
1 2 4 5
2 3 4
2 3
2 2
0
0 10 15 20 25 30
0 20 40 60 80
Number of AEs
|| [degrees]
Fig. 9. EVM (%) as a function of the detuning between the frequency
Fig. 10. EVM (%) as a function of the number of AEs and of the
response of the TODL and the input optical signal, ∆𝛾, and τ, for a
normalized time interval between the radio signals received by
system comprising a single AE and a for 𝜙 = 90o.
two adjacent AEs , 𝛿/𝛿max .

zero or maximum delay. For any other configuration, the

degradation imposed to the input optical signal depends on 𝜏, 𝜙 18 EVM variation
and 𝛾. In order to quantify the degradation imposed by 𝜏 and 𝜙, Mean EVM
16
in a first stage 𝛾 was fixed at an ideal value. As shown in Fig. 7 Worst case performance
the EVM increases with 𝜏, and the worst-case value of 𝜙 tends 14
to 𝜋⁄2 as 𝜏 increases. Such angle corresponds to having the
lowest bandwidth in the amplitude response of the MZDI, 12
EVM (%)

however with an ideally flat group delay response. This means 10

that degradation stems mainly from narrowband filtering, and
not from group delay distortion. 8
The spectral width of the signal is defined by the symbol rate
6
and by the roll-off factor of the RRC filter. Since the symbol
rate is fixed to 1 GBd, it is important to quantify the impact of 4
the roll-off factor in the degradation caused by the TODL
narrowband filtering. Fig. 8 shows that for low values of 𝜏 a 2
higher roll-off factor enables a lower degradation. This is due
0
to the fact that signals with a larger spectral width have better 10 20 15 25 30
performance when narrowband filtering is negligible. However, Number of AEs
for higher values of 𝜏, narrowband filtering becomes dominant. Fig. 11. Variation and mean value of the EVM as function of the
Hence, lower roll-off factors, which result in a signal with lower number of AEs. Insets: worst-case constellation diagrams for 16
and 32 AEs, respectively.
spectral width, offer better robustness against narrowband
filtering.
Having quantified the impact of 𝜙 and 𝜏 for an ideal 𝛾, it is
important also evaluating the degradation imposed from having D. Performance assessment for multiple antenna elements
the MZDI decentered from the input optical signal, i.e., having The performance of the system comprising multiple AEs and
a deviation of 𝛾 from the correct value. The results are shown experiencing a time interval between the radio signals received
in Fig. 9. As increasing values of 𝜏 decrease the bandwidth of by two adjacent AEs between 0 and 𝛿max is assessed in this
the MZDI the tolerance to a deviation of 𝛾 decreases with 𝜏 section. For each set of parameters 100 realizations were run,
These results show that the performance of the TODL leading to a final accurate averaged EVM. The attenuation
degrades both with an increase of the spectral width of the input imposed by each TODL to its input optical signal, 𝛼(𝜙), was
signal, and with an increase of 𝜏. As defined in (39), 𝜏 increases compensated in order to obtain the same power for all delayed
with the number of AEs, and therefore it is important optical signals. Further simulations without such compensation
quantifying the performance degradation of the system for were also performed, resulting in identical EVMs. This means
multiple AEs. that the optical amplifiers of the system may have a constant

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gain without affecting the performance of the system. QPSK input signal centered at 30 GHz, and a unidimensional
Fig. 10 shows that the EVM increases with 𝛿 and with the PAA with a steering range of |Θ| ≤ 30o and with a distance
number of AEs. For 𝛿 = 0 all MZDIs have 𝜙 = 0. Hence, the between adjacent AEs of 0.85𝜆. It was confirmed that the
delayed optical signals are not impaired by the TODLs, and degradation imposed by non-ideal phase noise cancelation is
consequently the output optical signal has the lowest EVM. negligible for realistic laser linewidths. Concerning the
However, as 𝛿 increases, so does the delay added by each distortion introduced by the non-ideal frequency response of
consecutive TODL, given by each TODL, it was observed that it is caused by narrowband
filtering and not by group delay distortion. For multiple AEs the
𝜏𝑛 = 𝛿 ∙ (𝑛 − 1), (40) distortion induced by narrowband filtering increases with the
number of AEs, as so does the value of 𝜏. The distortion
where 𝑛 = 1, … , 𝑁. The bandwidth of the amplitude response observed in the output signal is the average of the distortion
of the 𝑛th MZDI depends on 𝜏𝑛 , reaching a minimum for 𝜏𝑛 = imposed by all TODLs. This means that the worst-case
𝜏/2. Consequently, the delayed optical signals are subject to performance of the system can be conservatively estimated by
narrowband filtering whose bandwidth depends on 𝜏𝑛 . The considering a system with a single AE, the same value of 𝜏, and
𝜋
output optical signal is the addition of delayed optical signals the worst case value of 𝜙 = . Reduced distortion was observed
2
with different levels of distortion. Hence, the distortion for a system comprising up to 32 AEs, which means that for the
observed in the output optical signal is the average of the considered simulation scenario, the system is suitable for a
distortions observed in the 𝑁 delayed optical signals. The bidimensional PAA with 16 × 16 AEs.
strongest distortion is observed when the average value of 𝜏𝑛 is Within the scope of project BEACON [18], future work will
closest to its worst-case value of 𝜏/2. This is generally the case take two directions. On a theoretical side, as the presented work
when 𝛿 = 𝛿max , as in this case 𝜏𝑛 varies from 0 up to 𝜏. Fig. 11 only addresses the impact of signal distortion, it is important to
shows the variation of the EVM as a function of the number of assess the relevance of noise and beam squinting, also in a
AEs. The dashed line corresponds to the worst performance scenario based on [16]. On a practical side, the beamformer will
obtained in a system comprising a single AE with 𝜙 = 90o and be demonstrated resorting to silicon photonic integrated
with a value of 𝜏 given by (39). Such performance is circuits.
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