Joint Microstrip Selection and Beamforming Design for MmWave Systems with Dynamic Metasurface Antennas Wei Huang Haiyang Zhang Nir Shlezinger and Yonina C. Eldar

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Joint Microstrip Selection and Beamforming Design for

MmWave Systems with Dynamic Metasurface Antennas

Wei Huang, Haiyang Zhang, Nir Shlezinger, and Yonina C. Eldar

Abstract—Dynamic metasurface antennas (DMAs) provide a new

paradigm to realize large-scale antenna arrays for future wireless systems.

In this paper, we study the downlink millimeter wave (mmWave) DMA

systems with limited number of radio frequency (RF) chains. By using

a speciﬁc DMA structure, an equivalent mmWave channel model is ﬁrst

explicitly characterized. Based on that, we propose an effective joint

microstrip selection and beamforming scheme to accommodate for the

limited number of RF chains. A low-complexity digital beamforming

solution with channel gain-based microstrip selection is developed, while

the analog beamformer is obtained via a coordinate ascent method. The

proposed scheme is numerically shown to approach the performance of

DMAs without RF chain reduction, verifying the effectiveness of the

proposed schemes.

Index terms— Dynamic metasurface antennas, millimeter wave.

I. INTRODUCTION

In order to increase the capacity of wireless communication

systems, millimeter wave (mmWave) bands ranging from 30GHz

to 300GHz, are regarded as a promising candidate. The small

wavelength of mmWave signals allows a large number of antenna

elements to be be packed in a small area, facilitating multiple-input

multiple-output (MIMO) processing with very large arrays. However,

realizing large antenna arrays for mmWave communication systems

in practice can be challenging. A key difﬁculty stems from the fact

that radio frequency (RF) chains in mmWave are costly in terms of

hardware implementation, signal processing complexity, and energy

consumption. To overcome this issue, various cost-aware hybrid

architectures with limited number of RF chains have been proposed

[1]–[3]. However, typical hybrid architectures come at the cost of

additional analog circuitry, typically comprised of multiple phase

shifters, which can lead to relatively high energy consumption [4].

An alternative large-scale MIMO technology utilizes dynamic

metasurface antennas (DMAs) [5]. DMAs consist of multiple waveg-

uides (microstrips) and each embedded with many metamaterial

antenna elements, which inherently provides analog beamforming

capabilities with lower power consumption and cost compared with

typical phased array antennas [6]. Moreover, DMAs are typically

utilized with sub-wavelength element spacing, allowing to pack a

larger number of elements in a given antenna area compared to

conventional phased array antennas. This ability has been exploited

to improve communication capacity and energy efﬁciency [7], [8].

Over the last few years, several transmission schemes with DMAs

have been studied under various wireless scenarios, such as orthogo-

nal frequency multiplex systems [9], hybrid reconﬁgurable intelligent

surfaces and DMAs network [10], and wireless power transfer [11].

The wireless channels considered in the above works are based on

statistical models commonly employed in lower bands, i.e., Rayleigh

or Rician distributions. However, for the high-frequency mmWave

bandwidth, these models may be not applicable, and one should

account for the geometry of the physical channel [12]. In this case,

W. Huang is with the School of Computing Science and Informa-

tion Engineering, Hefei University of Technology, Hefei, China (e-mail:

huangwei@hfut.edu.cn). H. Zhang is with School of Communications and

Information Engineering, Nanjing University of Posts and Telecommuni-

cations, Nanjing, China (e-mail: 20220142@njupt.edu.cn). N. Shlezinger

is with the School of ECE, Ben-Gurion University of the Negev, Beer-

Sheva, Israel (e-mail: nirshl@bgu.ac.il). Y. C. Eldar is with the Faculty

of Math and CS, Weizmann Institute of Science, Rehovot, Israel (e-mail:

yonina.eldar@weizmann.ac.il).

the speciﬁc propagation characteristics of DMAs, where signals at

different elements propagate differently inside the waveguides [13]

is translated into an important consideration for transmission designs

in mmWave communication systems. In particular, the equivalent

physical channel depends on both the speciﬁc DMA structure and

mmWave wireless channel model. On the other hand, due to the

mmWave channel sparsity, only a small number of beams are needed.

Since each beam corresponds to a single RF chain [14], one can use

only part of the DMAs microstrips via a switching network, which

can further reduce cost and power.

Based on the above observations, in this paper we propose a joint

microstrip selection and beamforming design scheme for mmWave

signalling with DMAs. We ﬁrst explicitly characterize the equivalent

mmWave physical channel model with a DAM, accounting for the

propagation characteristics of mmWave signals and the DAM struc-

ture. Based on the obtained equivalent channel model, we then study

the hybrid beamforming design problem to maximize the single-noise

ratio (SNR), subject to a limit on the number of activated RF chains.

The formulated joint microstrip selection and beamforming design

problem is non-convex due to both the non-convex l0norm constraint

and the non-convex Lorentz constraint [15]. To overcome the issue,

we develop an iterative algorithm to set the digital beamforming

and conﬁgure the DMAs weights, alternately. Our optimizer uses

a channel-gain based microstrip selection and beamforming, while

conﬁguring the DMAs weights via the coordinate ascent method.

Simulations result indicate that the proposed scheme could reduce

the number of RF chains by 75%, while the spectral efﬁciency

approaches the case without the RF chain constraint.

Notations: In this paper, the upper and lower case bold symbols

denote matrices and vectors, respectively. We use (·)T,(·)∗,(·)H,|·|,

and k·kpto denote the transpose, conjugate, Hermitian transpose,

absolute value, and p-norm, respectively. CM×Nis the space of M×

Ncomplex-value matrices, symbol ∠(·)denotes the angle, while ⊗

and denote the Kronecker and Hadamard product, respectively.

II. SYSTEM MODEL AND PROBLEM FORMULATION

A. Dynamic Metasurface Antennas

Here, we give a brief review of DMAs. DMAs are metasurface-

based antennas comprised of multiple microstrips, which are one-

dimensional arrays of metamaterial elements placed on a waveguide

cavity [5]. In such architectures, each RF chain is connected with the

port located at the edge of the microstrip. Thus, during transmission,

the signals in the microstrip propagating from that port undergo a

different path for each element, which results in different propagation

delay depending on their location. Deﬁne αnas the wavenumber

along microstrip n, and ρn,m denotes the relative location of the

mth element of the nth microstrip, which is usually proportional to

the distance between the port of microstrip nand the mth element.

Thus, element-dependent propagation effect is formulated as

fn,m =e−ρn,m(βm+jαn),∀n, m , (1)

where βmis the waveguide attenuation coefﬁcient of element m.

Each metamaterial elements acts as a resonant circuit whose

frequency response for narrowband signaling is approximated as the

arXiv:2210.12390v1 [eess.SP] 22 Oct 2022

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JointMicrostripSelectionandBeamformingDesignforMmWaveSystemswithDynamicMetasurfaceAntennasWeiHuang,HaiyangZhang,NirShlezinger,andYoninaC.EldarAbstractDynamicmetasurfaceantennas(DMAs)provideanewparadigmtorealizelarge-scaleantennaarraysforfuturewirelesssystems.Inthispaper,westudythedownlinkmillimeter...

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Joint Microstrip Selection and Beamforming Design for MmWave Systems with Dynamic Metasurface Antennas Wei Huang Haiyang Zhang Nir Shlezinger and Yonina C. Eldar

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