Constant–εr Lens Beamformer for Low–Complexity Millimeter–Wave
Hybrid MIMO
Abbasi, M. A. B., Fusco, V. F., Tataria, H., & Matthaiou, M. (2019). Constant–ε
r
Lens Beamformer for
Low–Complexity Millimeter–Wave Hybrid MIMO.
IEEE Transactions on Microwave Theory and Techniques
,
67
(7), 2894. https://doi.org/10.1109/TMTT.2019.2903790
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IEEE Transactions on Microwave Theory and Techniques
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1
Constant–
r
Lens Beamformer for Low–Complexity
Millimeter–Wave Hybrid MIMO
M. Ali Babar Abbasi, Member, IEEE, Vincent F. Fusco, Fellow, IEEE, Harsh Tataria, Member, IEEE, and
Michail Matthaiou, Senior Member, IEEE
Abstract—It is well established that the utilization of un-
used millimeter–wave (mmWave) spectrum is inevitable due to
unavailability of required bandwidth in the conventional RF
band to support the high data demands of 5G. Large antenna
arrays with beamforming capabilities are required to compensate
for the high path–loss at mmWave frequencies. We are at the
verge of a massive mmWave radio front-end deployment and
low–complexity low–cost hardware beamforming solutions are
required now at this stage than ever before. In this work, one
such solution is demonstrated and analyzed. A high performance
and low–complexity lens based beamformer consisting of constant
dielectric material (
r
) with antenna–feeds is presented for multi–
beams operation. A prototype is developed based on the classical
synthesis approach, and in line with the requirements of mmWave
hybrid multi–user multiple–input multiple–output (MU–MIMO)
systems. A characterization at 28 GHz is performed wherein
uplink signal–to–noise–ratio of user terminals is evaluated with
the zero–forcing (ZF) baseband signal processing. Radiation
performance of a single source beamformer is measured in
an anechoic environment and end–to–end ergodic sum spectral
efficiency performance is estimated based on the measured data.
It is shown that the constant–
r
based beamformer solution is
simple, yet significantly outperforms conventional antenna array
beamformers with analog phase shifter network, making it a
promising candidate for future hybrid massive MIMO systems.
Index Terms—Beam forming, lens, millimeter–waves, MIMO,
MU–MIMO, spectral efficiency, 5G
I. INTRODUCTION
D
URING the last decade, we have witnessed an enor-
mous evolution in commercial wireless communication
systems, from simple voice and messaging services to data
hungry mobile broadband. End user data rate is expected to
grow even further and current cellular infrastructure is in no
position to meet these formidable demands. Researchers are
putting together efforts in finding novel approaches to further
improve the overall throughput of the wireless systems. By the
end of 2020 we are expecting a data rate 10 times compared
to 2010. Multiple-input multiple-output (MIMO) are posed to
meet the expected spectral efficiency demands by providing
a higher capacity gains and a better link reliability. Lack of
wide spectrum at conventional cellular a.k.a. sub–6 GHz, fre-
quencies has compelled a migration towards millimeter–waves
This work was supported by the UK Engineering and Physical Science
Research Council (EPSRC) under Grant EP/P000673/1 and EP/N020391/1.
M. A. B. Abbasi, V. F. Fusco, and M. Matthaiou are with the Institute of
Electronics, Communications and Information Technology (ECIT), School of
Electronics, Queen’s University Belfast, Belfast BT3 9DT, United Kingdom.
H. Tataria is with the Department of Electrical Engineering, Lund Uni-
versity, Lund, Sweden. (emails: m.abbasi@qub.ac.uk, v.fusco@ecit.qub.ac.uk,
harsh.tataria@eit.lth.se, m.matthaiou@qub.ac.uk)
(mmWave); however, in order to reap the real potential of
mmWave MIMO systems, a number of fundamental challenges
are yet to be addressed. First and foremost, the propagation
characteristics of a mmWave radio channels relatively different
to the sub–6 GHz channels. The free space path–loss of a
radio wave at mmWave frequencies requires compensation
in terms of gain, and in order to do this, multiple–antenna
beamforming is a necessity. Many of the specialized telecom-
munication research groups and wireless equipment vendors
are putting together their efforts in an attempt to propose
the most suitable specialized hybrid transceiver architectures
[1]–[4]. The objective is the inclusion of mmWave to the
future cellular infrastructure enabling 5G, and beyond. Theo-
retically, mmWave massive MIMO is found to surpasses other
technologies in this respect [5], however, practical mmWave
radio–frequency (RF) front–end is complex and expensive. In
addition to reducing the this complexity, the throughput per
square meter needs to be increased to meet the unprecedented
projected increase in data rate demand. Shrinking the cell
size with the associated interference mitigation is considered
to be one possible approach. With this, the requirement
of hardware increases, so do the deployment cost. A low–
complexity and low–cost mmWave radio front–end hardware
with beamforming capabilities, supported by a hybrid MIMO
for small cell size can be the answer. In this paper we propose
one such solution. In particular, our focus is on synthesis and
characterization of a low–complexity constant–
r
lens based
beamformer. We evaluate the performance of the lens with
the help of theoretical principles, real-time measurements and
electromagnetic/numerical simulations. Unlike gradient refrac-
tive index material based, and metamaterials based lenses,
the implementation of the presented solution is simpler and
effective. Taking into account the overall framework for the
multiuser communication system, we then integrate the lens
with the hybrid architecture. We consider the RF switching,
finite numbers of RF chains, and zero–forcing (ZF) base–
band signal processing (SP) to predict the end–to–end uplink
performance. A detailed insight into the engineering trade–offs
of the proposed architecture is discussed.
II. LENS BASED BEAMFORMERS
Hybrid antenna array beamformers comprising of a phase
shifter network demonstrate high directivity and beam scan-
ning, however, their practical implementation at mmWave fre-
quencies is complex and expensive. Lens based beamforming
systems are found to be a lucrative alternative [6]. In spherical
2
or semi–spherical lenses, a beam traveling along the principle
axis of the lens is focused to a spot, known as the focal point.
Conversely, an electromagnetic radiation source placed at the
focal point can convert into a directional beam by the lens, so
an object at the focal point has an image at infinity, and vice
versa. There always exist anomalies in lenses such as coma,
chromatic, spherical aberration, astigmatism and so on, caused
because of lens imperfections. This limits the focusing abilities
of lenses. One of the most common type of lens used at the
radio frequencies is the Luneburg lens, originally proposed in
[7]. Variation of similar lens type are generally designed based
on transformation optics theory. By carefully grading the re-
fractive index of the lens material, different focusing properties
can be achieved. One of such gradient index principle is given
by n =
p
(2−(
r
0
r
)
2
) when n is the refractive index and r is the
radius of the sphere. For such spherical lenses, the diameter
is inversely proportional to the achievable half power beam
width (HPBW). Theoretical conversion of 3–dimensional (3–
D) lens action on 2–D surface has also been demonstrated
via focusing beam in a limited azimuthal or elevation planes
[8]. Lundberg lens principle can be re–created by varying the
parallel plate spacing along the radius of a circular lens in [9],
where a slot antenna is used to feed the lens and air is used as
dielectric. In a recent studies, a 2–D slab based lens with field
control capabilities to achieve similar graded index principle
is shown [10]. Beamforming has also been achieved using
3–D monolithic low–loss periodic structures with uniform
r
[11]. Another two–layered metamaterial planar lens is shown
in [12], that uses a linear substrate integrated waveguide
(SIW) antenna array for spatial beamforming. It is shown
that the wave impedance can be controlled in the structure by
geometrical adjustments on a periodic lattice. A special class
of metasurfaces composed of densely packed thin planar ar-
rays, utilizing the physics of subwavelength resonant material
elements, are found to focus the EM energy in a similar fashion
as a lens does [13]. Similar 3–D mertasurfaces based lens is
realized in [14] machined by drilling inhomogeneous holes
in multilayered dielectric plates. The design strategy shows a
successful reduction in the reflection and insertion losses of
the lens at mmWaves. The capabilities of lenses can further be
advanced by adding polarization manipulation, multi–band op-
eration, frequency agility, sometimes amplification [15] using
advanced and more sophisticated design approaches. Devising
of all the aforementioned lenses is a complex task and in
addition to fundamental design variations, they sometimes
require reconfigurability within the lens main structure to
realize the propagating wave manipulations and phase shifting.
A comparatively easier approach of realizing the lens operation
using transmission line theory, known as Rotman lens, is also
well known. The simplification of such lens type stems from
using standard photolithography method, widely used for rapid
circuit boards fabrication. A Rotman lens with a compact
antenna array and integrated amplifiers at 60 GHz is shown
to be capable of beam–steering and active beam–switching
at the same time [16]. Both these functions are essential
for hybrid MIMO operation [6]. Another similar SIW based
Rotman lens is presented in [17] capable of 7 beam selection
using SIW antenna array. A thorough investigation of Rotman
lens based MIMO system with beam selection and digital
beamforming is reported in [18]. Regardless of Rotman’s,
Fourier’s or Luneburg’s theoretical synthesis approaches, lens
arrays are generally found to be much effective in simplifying
the mmWave MIMO radio freuency (RF) front–end. Moreover,
it has also been shown that lens antenna arrays are effective
in simplify the signal processing required to achieve high data
rates with multiple antennas [19]. This is done by exploiting
the mmWave channel angular sparsity, even when channels are
frequency selective.
At sub–6 GHz frequencies, especially at below 1 GHz, the
size of a lens based beamformer becomes large and impractical
compared to other similar antenna types with same desirable
specifications. At mmWave frequencies, the only constraint
i.e. size, is no more a problem [20]. One can argue that
the size of a lens at mmWave frequencies is more practical
compared to lower frequencies since it offers a high directivity
as well as a fairly controllable integration with the mmWave
electronics. Beamformers for cellular application need an
outdoor deployment where weather conditions, material aging
and thermal expansion play a vital role. This makes the
gradient
r
lenses, like the Luneburg, not the best choice
since the maintenance of gradient
r
requiring layering of
varying refractive index material is problematical. A constant–
r
lens is capable of solving these issues. The synthesis
approach and electromagnetic analysis of such lens type is
available in classical literature [21]–[23]. Constant dielectric
lens operation at the mmWave spectrum is shown in a number
of studies [24]–[28]. Full spherical lens with a mmWave feed
is shown to be a reliable source of multibeam operation.
Hemispherical or grooved constant dielectric lenses are other
similar ways to enhance the feed antenna gain. However, to
analyze the rightfulness of such lens types for the high–data
rate communication is yet to be shown. Also, in addition
to the low–complexity prospective of such lens types, the
scalability factor of the RF front–end hardware is missing
from the literature to the best of author’s knowledge. In the
work, we fill this gap by showing the end–to–end sum spectral
efficiency performance of constant–
r
lens for the mmWave
hybrid multi–user MIMO (MU–MIMO) uplink. The constant–
r
lens is constructed from a single plastic billet and has
the property that the focal point can be made to lie just off
the surface of the lens. This latter aspect makes sampling of
the rays for further beamforming considerably simpler than
by other methods. Devising a lens with a single dielectric
material not only decreases the implementation complexity
and manufacturing cost, but also gives a full control on the
choice of the material. Modern plastics exhibit low mmWave
losses, are homogeneous, and do not readily age or absorb
moisture [29]. The radiation performance of the constant–
r
lens is comparable to planar array configurations like the
ones presented in [6], [30]–[31], with comparatively marginal
deployment complexity.
III. HYBRID MIMO ARCHITECTURE
A. System Model
The mmWave MIMO model considered in this study is a
typical uplink multiuser system in a single–cell with a radius
3
of K
sector
. A base station (BS) is located at the origin of the
cell. To perform a comprehensive comparison, we separately
considered the BS to be equipped with a M element ULA
beamformer, a URA beamformer and a constant–
r
based
beamformer. The beamforming mechanism in both ULA and
URA is governed by the Rotman lens based passive phase
shifters [18], [32]. Description on the URA and ULA are
discussed is detail in [33]–[35]. Although MIMO operation is
also expected at mmWave user equipment (UE), for the sake of
simplicity, in this study we assume single–antenna terminals.
UEs send L independent data streams within the same time–
frequency resource with a uniform uplink power. We assumed
a uniform distribution of UEs within a discrete sector of 100
◦
in azimuth for the case of ULA beamformer. In case of URA
and constant–
r
lens beamformer, we added an elevation sector
of 30
◦
in the simulations.
1
To keep our analysis simple, we
assume that the BS has perfect knowledge of the propagation
channels.
Remark 1. The assumption of perfect channel knowledge
may at first sight may seem rather naive. However, there are
several fundamental reasons for this: Firstly, unlike previous
studies, the central focus of our work is on aggressive RF
circuit reduction techniques to lower the implementation com-
plexity of mmWave hybrid beamforming, where we propose
a modification on the conventional architecture with a Rot-
man lens–based beamformer. Here, the assumption of perfect
channel knowledge is necessary in order not to obfuscate
the findings from the aforementioned study. Secondly, in line
with [36], this assumption is reasonable in scenarios with
low terminal mobility, where a large fraction of the channel
coherence time can be spent for accurate channel acquisition
at the BS. Thirdly, the results obtained from subsequent
evaluations can be treated as a useful upper bound on what
may be achieved in practice, with imperfect channel estimates
at the BS.
The method of receiving and processing the direction-of-
arrival (DOA) in all three considered beamformers is different.
For an ideal lens, the core objective is to simultaneously
provide power combining and phase shifting in order to focus
the incoming energy to a specific RF port. In the case of ULA,
the Rotman lens is responsible of this function as it delivers L
DOAs to the beam–port outputs. The only difference in URA
beamformer, compared to ULA, is that the output beam–ports
of the Rotman lens connected to URA includes both azimuth
and elevation coverage zone DOAs. On the other hand, the
beam forming mechanism is happening at the electromagnetic
domain in the case of constant–
r
lens, the DOAs are directly
delivered to the horn–feed output. The constant–
r
lens with
the horn–feed conforms to the simplest approach i.e. dou-
ble convex lens in [31]. Following the conventional hybrid
mmWave MIMO topologies, the output of all beamformers is
then connected to a L ×M network of RF switches. The main
purpose of the RF switch network is to ensure selection of L
non–overlapping and independent streams, out of M possible
outputs from the beamformer. After the RF switching, the
1
The 100
◦
azimuth and 30
◦
elevation sector is defined from [−50
◦
, +50
◦
]
and [−15
◦
, +15
◦
] from the reference axis at the array broadside direction
0
◦
, respectively.
remainder of the down conversion chains in this study is as-
sumed to be perfect, since after beam selection, L independent
data streams have to have a dedicated RF chain [33]. After
the down conversion, zero-forcing is employed to separate the
gain and phase of L data streams. Assume the beamformer to
be capable of creating M fixed analog beams along azimuth
and elevation sectors as (φ
1
, θ
1
), (φ
2
, θ
2
), . . . , (φ
M
, θ
M
). The
dimension–reduced L ×1 signals after the switching matrix is
given by
y = ρ
1
2
t
S
RF
F
RF
Hx + n. (1)
Boldface upper case symbols represents matrix while the
lower case symbols are vectors. The average transmit power
of each terminal is denoted by ρ
t
, when E[|x
`
|
2
] = 1 and
∀` = 1, 2, . . . , L, where statistical expectation and scalar
norm operations are denoted by E and |·|, respectively. Also,
ρ
1/2
t
x is the payload data in uplink, formulated as L × 1
vector. Here the additive Gaussian noise is modeled such
that each entry of n ∼ CN (0, 1). S
RF
is the switching
network represented by a binary matrix, when it only have
one non–zero entry in a row that corresponds to the selected
beam index. Also, G = S
RF
F
RF
H = [g
1
g
2
. . . g
L
] is an
L ×L matrix comprising of L vectors. Here g
`
= S
RF
F
RF
h
`
,
∀` = 1, 2, . . . , L [35]. We use a double–directional uplink
channel model `–th terminal described in [37], [38] with
finite multipath components (MPCs) at 28 GHz. The model
assuming N
P
MPCs is described by:
h
`
=
1
√
N
P
N
P
X
p=1
α
`,p
Λ (φ
`,p
, θ
`,p
) a
H
(φ
`,p
, θ
`,p
) , (2)
where α
`,p
defines the gain of the p-th MPC for the l- uplink
channel. For the case of URA and ULA, the per–antenna
element gain is represented by Λ (φ
`,p
, θ
`,p
), while the far–
field steering vector is denoted by a (φ
`,p
, θ
`,p
). Equation (2) is
used for the ULA case, where isotropic antenna elements were
assumed. On the other hand for the case of URA and constant–
r
based beamformer, instead of a classical description of an
array gain defined by the product of per–antenna element gain
and array factor, measured data is included discussed a the
later stage.
B. Constant–
r
Lens Beamformer
Due to large size compared to λ, collimated beam with ray
tracing approach can be implemented to define the controlling
parameters of a constant–
r
lens. In Fig. 1, we consider a
mmWave point source at location A. To create a constant phase
plane wavefront parallel to contour DE in a mmWave channel,
the path length along the diameter AE needs to be the same as
AC + CD. This can be possible when the overall path length
of the propagating wave along the AC + CD is greater than
the path length along AE such that
σ = AE
√
r
− (AC
√
r
+ CD), (3)
where σ defines the deviation. Normalizing (3) w.r.t to diam-
eter of the lens gives:
4
dcosθ
θ
2θ
rsin2θ
A
O
E
r-rcos2θ
C
D
θ
r = d/2
r'
A
B
1
A
n-1
A
n
A
n+1
A
2n
.
.
.
.
.
.
Fig. 1. Geometry of the constant–
r
Lens.
Fig. 2. Normalized deviation factor for a constant–
r
Lens.
σ
d
= 2
√
r
sin
2
θ
2
− sin
2
θ. (4)
All the sets of rays following a path AC and leaving the lens
surface thus defines the effective aperture area of the lens,
given by:
2 × DE = d × sin 2θ. (5)
It can be noticed from Fig. 2 that the normalized deviation
from a plane wavefront parallel to DE is higher with high θ.
As
r
increases from 1 to 5, the deviation decreases with the
lowest value when
r
≈ 3.5. Further increase in
r
will cause
the rays after a certain θ to exhibit total internal reflection
defined by:
θ >= sin
−1
1
√
r
. (6)
The effective aperture area of the lens is thus defined by the
largest value of θ before which the ray from the point source
A exhibits total internal reflection. The effective aperture
area can also be postulated to decrease with an increase
r
. Therefore, the lens’s material
r
is bounded by the two
choices. One is the maximum utilizable lens spherical area
when
r
≈ 2.0 and θ ≈ ±45
◦
. The second choice is to
use the
r
required for minimum deviation factor, creating
an efficient plane wavefront at the cost of limiting the usable
lens surface aperture bounded by θ ≈ ±32.5
◦
. Based on this,
it can be established that suitable lens operation is feasible for
2.0 <
r
< 3.5. Approximately similar conclusions hold if the
source is moved from point A to a point A
n
outside the lens
sphere provided that AA
n
<< AE.
(a)
0 40 80 120 160 200 240 280 312
Curve length (mm)
0
5
10
15
E-field (V/m)
xz
yz
126 141 156 171 186
0
5
10
A
n+1
A
n-1
A
n
(b)
Fig. 3. (a) Simulated instantaneous real E–field strength with the plane
wavefront excitation of constant–
r
lens in full–wave EM solver (color map
scale from 0 to 15 V/m). (b) Field strength along the curve.
Following this condition, A
n
outside the lens at the Petzval
curvature [39], offers constant–
r
lens another advantage over
Luneburg’s configuration with respect to the scalability of
MIMO. However, it should be noted that for d >> λ,
propagation loss within the lens increases. From Fig. 2, it
can be noticed that an incoming plane wavefront parallel to
DE cannot be focused at a single point. To further elaborate,
take for example lens with
r
= 3. Ideally, focusing on a
single point means σ/d = 0 throughout the usable range of θ
(i.e. from 0
◦
to 35
◦
). However, practically this is not the case
since the
r
= 3 contour is curved. Hence, the constant–
r
lens will face the fundamental defect of aberration. It will be
shown at a later stage that even when the focusing capability
of a constant–
r
lens is non–ideal, a large aperture area feed
located at point A can mitigate this defect. For example, a
horn antenna–feed can handle a larger d/λ ratio compared to
a wire antenna–feed. Also, the homogeneity of
r
is relative, so
an inhomogeneous material can be considered homogeneous
when the spatial variations occurring within the medium are,
at a scale, smaller than λ.
A proof–of–concept constant–
r
lens is realized using Rex-
olite [29] with
r
= 2.53. Other material properties like density
= 1.05 g/cm
3
, dispersion factor = 0.00066 and low coefficient
of linear thermal expansion = 3.8 × 10
−5
in./in./
◦
F make
Rexolite a very good choice for lens prototyping. Initially,