Page 85 - ITU Journal, Future and evolving technologies - Volume 1 (2020), Issue 1, Inaugural issue

ITU Journal on Future and Evolving Technologies, Volume 1 (2020), Issue 1

amplitude alteration. Assuming a metamaterial consist- phase, which is identical as before. The key difference
ing of M × N unit cells, the scattered E-field complex and merit is that the calibration is, now, extremely pre-
amplitude pattern at a given frequency can be calcu- cise with regard to the full-wave simulations, while it
lated by the envelope (coherent superposition) of all rays takes much less time to complete, as detailed in the cor-
scattered from the metamaterial [2] responding study of [2].
An intermediate solution, combining the precision of
M N
the circuit model and the automation of the antenna-
X X
E(θ, ϕ) = A mn e jα mn f mn (θ mn , ϕ mn )
array model, is an equivalent propagation model, men-
m=1 n=1
tioned here for the sake of completion. The main idea
jΦ mn (θ,ϕ)
· Γ mn e jγ mn f mn (θ, ϕ)e . (2)
is to introduce a generic mechanism to capture the
cross-interactions among meta-atoms (as opposed to the
In (2), ϕ and θ are the azimuth and elevation angles in
strict, physics-derived nature of the circuit model) and
the scattering direction, (θ mn , ϕ mn ) denotes the direc-
then proceed with automatic model calibration, avoid-
tion of the wavefront ‘ray’ incident on the mn-th cell,
ing the need for expert input. The equivalent ray model
A mn and α mn are the amplitude and phase of the in-
uses a neural network approach as the generic cross-talk
cident wavefront on the mn-th cell, Γ mn and γ mn form
descriptor [35]. A short summary is as follows. Each
the reflection coefficient (amplitude and phase) of the
meta-atom is mapped to a neural network node, and
mn-th cell, while f mn defines the scattering pattern of
the locally impinging wave amplitude and phase are its
the mn-th cell, which, according to reciprocity, is iden-
inputs. Then, we clone this layer (omitting the inputs)
tical for the incident and scattered direction, and, in
and form a number of intermediate, fully connected lay-
this work, is assumed that f mn (θ, ϕ) = cos(θ). Finally,
ers (usually 3-5), thereby emulating a recurrent network
Φ mn (θ, ϕ) is the phase shift in the mn-th cell stemming
with a finite number of steps. We define links per node
from its geometrical placement, as
(shared among all node clones), which define an alter-
Φ mn (θ, ϕ) = k sin θ [d x m cos ϕ + d y n sin ϕ] + φ 0 (θ, ϕ), ation of the local phase and amplitude, and its distribu-
(3) tion to other neighboring meta-atoms/nodes. Next, we
where d x,y are the rectangular unit-cell lateral dimen- proceed to calibrate the model via feed-forward/back-
sions, k = 2π/λ is the wavenumber in the medium en- propagation, thereby obtaining a match between R, X,
closing the metamaterial, and φ 0 is the reference phase Γ mn , and γ mn values. Nonetheless, despite its auto-
denoting the spherical coordinate system center, typi- mated nature, a major drawback of this model is the
cally in the middle of the metamaterial aperture. Given need for considerable computational resources, without
a uniform, single-frequency impinging wave, any depart- which the model loses its value, since it becomes re-
ing wavefront is essentially a Fourier composition of the stricted only to very simple metamaterial designs.
individual meta-atom responses. Thus, we can, also, cal- Since computational complexity is a concern regard-
less of the chosen model, the Metamaterial Middle-
culate the meta-atom amplitudes Γ mn and phases γ mn
that yield a desired departing wavefront, by applying ware workflow allows the user to define solution reduc-
an inverse Fourier transform, as elaborately discussed tion across three directions. First, meta-atoms may be
in [2]. The calculated Γ mn and γ mn values must be grouped into periodically repeated super-cells. Thus,
mapped to the R i and X i values that generate them, the optimization workflow needs only to optimize the
since the latter are the actual tunable metamaterial pa- configuration parameters of a super-cell, as opposed
rameters. This process requires a set of simulations yet to optimizing the complete metamaterial. Second, the
it can be automated: existing model calibration tech- range of possible R and X values per meta-atom can be
niques, such as the Regression and Goodness of Fit can discretized into regular or irregular steps, reducing the
1
be employed [34]. solution space further . Finally, some R and X values
The shortcoming of the antenna-array approach is that or ranges can be discarded due to the physical nature
the coupling between adjacent unit cells (e.g., compare of the optimization request. For instance, if we seek
against Fig. 5) is not properly accounted for, which can to optimize a wave steering approach with an empha-
result to model imprecision [2]. To this aim, the Meta- sis on minimal losses over the metamaterial (maximum
material Middleware user is presented with an alterna- reflection amplitude), the Ohmic resistance R needs to
tive model. It utilizes the phased array and equivalent receive its boundary value. On a related track, ma-
circuit model, which assumes not only the transmitting- chine learning-based approaches can quickly estimate
responding antenna per meta-atom, but, also, circuit the performance deriving from one set of R and X val-
elements that interconnect them and account for the ues, thereby discarding non-promising ones and acceler-
cross-meta-atom metamaterial interactions. The disad- ating convergence [36].
vantage of this approach is that an expert needs to define Subsequently, the Metamaterial Middleware workflow
this circuit model, that is generally unique per metama- moves to the optimization stage, where it attempts to
terial design [3]. Once this model has been selected and 1 Notably, contemporary optimization engines already incorporate
provided in the proper format, the optimization work- equivalents to this direction, as they are able to detect strongly
flow of Fig. 9 continues, once again, with the calibration and loosely connected inputs-outputs [34]).

© International Telecommunication Union, 2020 65