Contents Introduction
Massive multiple-input–multiple-output (MIMO), also named as large-scale MIMO, has been a successful enabler to boost the data transmission rate in mobile communication systems in the fifth-generation (5G) era [1], and will keep serving as an important physical layer technology in future mobile communication systems. By employing tens or hundreds of antennas at the base station (BS), massive MIMO produces high spatial resolution and supports multiuser transmission on the same time–frequency resources. As the number of BS antennas grows unconventionally large, the multiuser interference and the uncorrelated noise diminish [2], providing preferable conditions for multiuser transmission. In order to further harness the gain caused by using more antennas, the concept of extra large-scale MIMO has been proposed for the sixth-generation mobile communications [3], [4], [5]. Extra large-scale MIMO employs hundreds or even thousands of antennas at the BS to simultaneously provide service to a certain set of users, and is an augmented version of massive MIMO.
In practical implementations, there are two deployment types of an extra large number of antennas, including the centralized type and the distributed type. The centralized type is a direct extension of 5G large-aperture arrays, where all the antennas are uniformly deployed in a co-located fashion, while we can sustain the half-wavelength distance between two adjacent antennas, forming an extra-large aperture array [6]. Alternatively, the antennas can be confined within a predetermined area, resulting in the concept of holographic MIMO [7]. If the practical environment does not allow the deployment of such a large array, then we can distribute the antennas across multiple sites, corresponding to the distributed type [8]. Each site is equipped with a small amount of antennas. These sites jointly serve a same set of users. A typical example is cell-free massive MIMO [9]. In this article, we focus on the centralized type with an extra large-aperture array.
Compared with distributed systems, synchronization among antennas is much easier in centralized extra large-scale MIMO systems. Moreover, extra large-aperture arrays can cover the external walls of buildings in populated city centres or be employed at stadiums/airports to provide wireless communication services to a plethora of users. Therefore, in a centralized extra large-scale MIMO system, high beamforming gains can be harvested. Narrow beams with very low sidelobes can be generated by the extra large-aperture array and flexibly steered towards desired direction. Several orthogonal beams can be generated simultaneously, yielding an increase of the spatial–division multiplexing gain. Apart from satisfying the traditional requirements of high data rates, employing an extra large-aperture array enables new emerging applications. For instance, in indoor environments, such as in a factory, the autonomous driving of an electric car can be achieved by leveraging the high spatial resolution provided by such an array. There have been studies on extra large-aperture array-enabled new applications, including sensing and localization [10], [11], physical-layer security [12], [13], wireless energy transfer [14], [15], etc., as illustrated in Fig. 1.
Extra large-aperture arrays provide opportunities for high-rate data transmission, wireless energy transfer, physical-layer security, sensing, and localization.
Historically, the study of an emerging wireless architecture begins with the investigation of the propagation channel. Channel modeling of an extra large-aperture array system does not simply mean to expand the array size in a traditional MIMO channel model. With the increase of the array aperture, new channel properties kick in. First, the lower bound of the far field, known as the Rayleigh distance, is proportional to the array aperture. Considering that extra large-aperture arrays will generally be deployed in crowded urban or indoor factory environments, users will be close to the array. Different from traditional MIMO systems, where users are in the far field and signals experience plane wave propagation, in an extra large-aperture array system, there is a high probability that spherical waves will be created. Second, for users who are very close to the array, the pathloss between them fluctuates significantly across the array. If obstacles exist in the channel, then the channel power will be concentrated in a proportion of the array elements, known as the visibility region (VR). The spherical wave propagation and the existence of VR reflect the spatial nonstationarity of the channel. On the one hand, the new channel properties require new channel models for extra large-aperture array systems. On the other hand, these properties facilitate the above-mentioned new applications. Therefore, a deep and comprehensive study of the new channel properties is indispensable.
When translating a theoretical architecture into a commercial technology, the implementation and deployment costs are of pivotal importance. The employment of an extra large-aperture array entails the challenges of high hardware cost, high processing and computational complexity, and high training overhead. Regarding the hardware cost, a fully digital structure, where each active antenna is connected with a unique radio frequency (RF) chain, is unacceptably expensive when the number of active antennas grows large. Inspired by the low-cost designs in 5G millimeter wave systems, active antenna arrays with less RF chains can be adopted. Moreover, with the development of materials, extra large-aperture arrays can take the form of reconfigurable intelligent surfaces (RISs), which have the advantages of low cost and low power consumption. Therefore, the problem of high hardware cost can be tackled via different approaches.
In traditional MIMO systems with a limited number of antennas, signal processing, and computations are centralized at a common module, and the complexity is moderate. However, in an extra large-aperture array system, completely centralized processing and computations result in high complexity and are time consuming. In order to reduce the complexity and the processing latency, two approaches can be followed. One is to directly reduce the complexity of an algorithm in the centralized module. The other is to distribute the processing and computations to multiple local modules, thereby easing the burden in the centralized module. The distributed approach is more attractive, but the information exchange among the centralized module and the local modules affects the overall complexity and needs to be carefully assessed.
In a mobile communication system, an efficient transceiver design heavily depends on the precise knowledge of the wireless channel. The training overhead required to acquire the channel state information (CSI) usually increases with the number of antennas. Then, when an extra large-aperture array is deployed, the training overhead becomes substantial, which is evidently prohibitive for practical systems. Fortunately, the extra-large–dimensional channel shows directionality and sparsity in multiple domains. Traditional sparse channel estimation methods, such as compressed sensing, can be applied to reduce the training overhead. The directionality of a spherical wave channel further supports localization and sensing. Further, the existence of the VR enables overhead reduction among multiple users. The feasibility of low-overhead communication and sensing, together with low-cost architectures and low-complexity processing and computations, guarantee the practical implementation of an extra large-aperture array.
This article makes a comprehensive survey on the new channel properties and the low-cost designs of extra large-scale MIMO systems. Section II investigates the spherical wave propagation by analyzing the channel responses on a point, an antenna, and an array step by step, and provides guidance to the selection of channel models in different fields/regions. With the analytical results on spherical waves, Section III explains why the VR appears and investigates the existing categories of VR and their definitions and models. The spatial nonstationarity is verified theoretically and further taken into account in the subsequent low-cost designs in Sections IV–VI. The low-cost architectures with active antenna arrays and RISs are illustrated in Section IV. A comparison of the hardware cost, implementation and synchronization difficulties, and scalability of different architectures is provided. Then, the low-complexity processing and computation designs are introduced in Section V. Existing methods to reduce the complexity in centralized and distributed processing structures are summarized. Finally, the low-overhead communication and sensing based on the directionality and channel sparsity in the transformation domains are studied in Section VI.
Notations: We use letters in normal fonts, lowercase, and uppercase letters in boldface for scalars, vectors, and matrices, respectively. The transpose, conjugate-transpose, and pseudo-inverse are indicated by the superscripts
Spherical Wave
In a traditional MIMO system, the aperture of the BS antenna array is usually negligible when compared with the distance between it and a user served by the BS. The entire array can be regarded as one point. Thus, a signal sent from the user experiences an equal path loss and has a common angle-of-arrival (AoA) when arriving at different antennas of the BS array. Experiencing equal path loss and having a common AoA are two key features of a plane wave, which is typically modeled in the far-field region. However, when the aperture of the BS array grows large, the array cannot be regarded as one point any more. Then, spherical waves kick in and the plane wave model becomes irrelevant. In this section, we will make a comprehensive study on spherical waves.
A. Channel Response on Point
We start from the modeling of channel response. In a three-dimensional (3-D) free space, an isotropic point source
(a) Isotropic point source radiates EM waves in all directions. (b) Receiver covers a continuous surface
1) Channel Response Model 1:
The distance between the receiving point 
\begin{equation*} \gamma \left ({{\textbf {p}},{\textbf {s}}}\right) = \frac {1}{4\pi \|{\textbf {p}}-{\textbf {s}}\|^{2}}.\tag{1}\end{equation*}
\begin{align*} h_{\textrm {CR1}}\left ({{\textbf {p}},{\textbf {s}}}\right)=&\sqrt {\gamma \left ({{\textbf {p}},{\textbf {s}}}\right)} e^{-j \frac {2\pi }{\lambda }\|{\textbf {p}}-{\textbf {s}}\|} \\=&\frac {1}{\sqrt {4\pi } \|{\textbf {p}}-{\textbf {s}}\|} e^{-j \frac {2\pi }{\lambda }\|{\textbf {p}}-{\textbf {s}}\|}\tag{2}\end{align*}
Model 1 describes an ideal case where the power on point
2) Channel Response Model 2:
In practice, patch antennas are widely utilized in mobile communication systems. Under this condition, the surface \begin{equation*} F\left ({{\textbf {p}},{\textbf {s}}}\right) = \cos < {\textbf {p}}-{\textbf {s}},{\textbf {v}}_{\mathcal A}\left ({{\textbf {p}}}\right)> = \frac {|\left ({{\textbf {p}}-{\textbf {s}}}\right)^{H}{\textbf {v}}_{\mathcal A}\left ({{\textbf {p}}}\right)|}{\|{\textbf {p}}-{\textbf {s}}\|}\tag{3}\end{equation*}
The channel response on point \begin{align*} h_{\textrm {CR2}}\left ({{\textbf {p}},{\textbf {s}}}\right)=&\sqrt {F\left ({{\textbf {p}},{\textbf {s}}}\right)} h_{\textrm {CR1}}\left ({{\textbf {p}},{\textbf {s}}}\right) \\=&\sqrt {\frac {|\left ({{\textbf {p}}-{\textbf {s}}}\right)^{H}{\textbf {v}}_{\mathcal A}\left ({{\textbf {p}}}\right)|}{4\pi \|{\textbf {p}}-{\textbf {s}}\|^{3}}} e^{-j \frac {2\pi }{\lambda }\|{\textbf {p}}-{\textbf {s}}\|}\tag{4}\end{align*}
3) Channel Response Model 3:
Papers [17], [21] considered the current density of the radiative EM waves from the source \begin{equation*} {\textbf {J}}\left ({{\textbf {s}}}\right) = J_{x}\left ({{\textbf {s}}}\right) {\textbf {u}}_{x} + J_{y}\left ({{\textbf {s}}}\right) {\textbf {u}}_{y} + J_{z}\left ({{\textbf {s}}}\right) {\textbf {u}}_{z}\tag{5}\end{equation*}
\begin{equation*} \|{\textbf {J}}\left ({{\textbf {s}}}\right)\|^{2} = |J_{x}\left ({{\textbf {s}}}\right)|^{2} + |J_{y}\left ({{\textbf {s}}}\right)|^{2} + |J_{z}\left ({{\textbf {s}}}\right)|^{2} = 1.\tag{6}\end{equation*}
\begin{equation*} \eta \left ({{\textbf {p}},{\textbf {s}}}\right) = \left \|{\left ({{\textbf {I}}-\frac {\left ({{\textbf {p}}-{\textbf {s}}}\right)\left ({{\textbf {p}}-{\textbf {s}}}\right)^{H}}{\|{\textbf {p}}-{\textbf {s}}\|^{2}} }\right){\textbf {J}}\left ({{\textbf {s}}}\right) }\right \|^{2}.\tag{7}\end{equation*}
\begin{equation*} \eta \left ({{\textbf {p}},{\textbf {s}}}\right) = 1 - \frac {\left [{{\textbf {p}}-{\textbf {s}}}\right]_{2}^{2}}{\|{\textbf {p}}-{\textbf {s}}\|^{2}}.\tag{8}\end{equation*}
With \begin{align*} h_{\textrm {CR3}}\left ({{\textbf {p}},{\textbf {s}}}\right)=&\sqrt {\eta \left ({{\textbf {p}},{\textbf {s}}}\right)} h_{\textrm {CR2}}\left ({{\textbf {p}},{\textbf {s}}}\right) \\=&\left \|{\left ({{\textbf {I}}-\frac {\left ({{\textbf {p}}-{\textbf {s}}}\right)\left ({{\textbf {p}}-{\textbf {s}}}\right)^{H}}{\|{\textbf {p}}-{\textbf {s}}\|^{2}} }\right){\textbf {J}}\left ({{\textbf {s}}}\right) }\right \| \\&\times \sqrt {\frac {|\left ({{\textbf {p}}-{\textbf {s}}}\right)^{H}{\textbf {v}}_{\mathcal A}\left ({{\textbf {p}}}\right)|}{4\pi \|{\textbf {p}}-{\textbf {s}}\|^{3}}} e^{-j \frac {2\pi }{\lambda }\|{\textbf {p}}-{\textbf {s}}\|}\tag{9}\end{align*}
B. Channel of Antenna
By integrating the response across the entire surface \begin{equation*} h_{\mathcal {A}} = \frac {1}{\sqrt {A}}\int _{{\textbf {p}}\in {\mathcal {A}}} h\left ({{\textbf {p}},{\textbf {s}}}\right) d{\textbf {p}}.\tag{10}\end{equation*}
1) Case 1:
In this case, the receiver antenna is isotropic and located at \begin{equation*} A_{\textrm {iso}} = \frac {\lambda ^{2}}{4\pi }.\tag{11}\end{equation*}
\begin{equation*} h_{\mathcal {A},{\textrm {case 1}}} = \sqrt {A_{\textrm {iso}}} h_{\textrm {CR1}}\left ({{\textbf {p}},{\textbf {s}}}\right) = \frac {\lambda }{4\pi |z_{p}|} e^{-j \frac {2\pi }{\lambda }|z_{p}|}.\tag{12}\end{equation*}
\begin{equation*} {\textrm {PL}}_{fs} = |h_{\mathcal {A},{\textrm {case 1}}}|^{2} = \frac {\lambda ^{2}}{16\pi ^{2} z_{p}^{2}}\tag{13}\end{equation*}
2) Case 2:
Case 2 illustrates a patch antenna whose surface \begin{equation*} A_{\textrm {pat}} \le \frac {\lambda ^{2}}{4}\tag{14}\end{equation*}
In [20], the channel on the patch antenna under channel response model 2 was studied. By applying (10), the channel can be approximated by \begin{equation*} h_{\mathcal {A},{\textrm {case 2}}} \approx \sqrt {eA_{\textrm {pat}}} h_{\textrm {CR2}}\left ({{\textbf {p}}_{c},{\textbf {s}}}\right)\tag{15}\end{equation*}
\begin{equation*} h_{\textrm {CR2}}\left ({{\textbf {p}}_{c},{\textbf {s}}}\right) = \frac {|z_{p}|^{\frac {1}{2}}}{\sqrt {4\pi } \left ({x_{c}^{2} + y_{c}^{2} + z_{p}^{2}}\right)^{\frac {3}{4}}} e^{-j \frac {2\pi }{\lambda }\sqrt {x_{c}^{2} + y_{c}^{2} + z_{p}^{2}}}.\tag{16}\end{equation*}
\begin{equation*} h_{\mathcal {A},{\textrm {case 2}}} \approx \frac {\sqrt {eA_{\textrm {pat}}}|z_{p}|^{\frac {1}{2}}}{\sqrt {4\pi } \left ({x_{c}^{2} + y_{c}^{2} + z_{p}^{2}}\right)^{\frac {3}{4}}} e^{-j \frac {2\pi }{\lambda }\sqrt {x_{c}^{2} + y_{c}^{2} + z_{p}^{2}}}.\tag{17}\end{equation*}
\begin{equation*} h_{\textrm {CR2}}\left ({{\textbf {p}}_{c},{\textbf {s}}}\right) = \frac {1}{\sqrt {4\pi } |z_{p}|} e^{-j \frac {2\pi }{\lambda } |z_{p}|}\tag{18}\end{equation*}
\begin{equation*} |h_{\mathcal {A},{\textrm {case 2}}}|^{2} < e A_{\textrm {pat}} |h_{\textrm {CR2}}\left ({{\textbf {p}}_{c},{\textbf {s}}}\right)|^{2} = \frac {\lambda ^{2}}{16\pi ^{2} z_{p}^{2}}\tag{19}\end{equation*}
3) Case 3:
Case 3 studies a more complicated modeling of the channel on a patch antenna under channel response model 3, which was considered in [17] and [21]. The patch antenna with area \begin{equation*} -\frac {\sqrt {A_{\textrm {pat}}}}{2}\le x_{p}, y_{p} \le \frac {\sqrt {A_{\textrm {pat}}}}{2}.\tag{20}\end{equation*}
\begin{equation*} \eta \left ({{\textbf {p}},{\textbf {s}}}\right) = \frac {x_{p}^{2}+z_{p}^{2}}{x_{p}^{2}+y_{p}^{2}+z_{p}^{2}}.\tag{21}\end{equation*}
\begin{align*} h_{\textrm {CR3}}\left ({{\textbf {p}},{\textbf {s}}}\right)=&\sqrt {\eta \left ({{\textbf {p}},{\textbf {s}}}\right)}h_{\textrm {CR2}}\left ({{\textbf {p}},{\textbf {s}}}\right) \\=&\frac {|z_{p}|^{\frac {1}{2}}\left ({x_{p}^{2}+z_{p}^{2}}\right)^{\frac {1}{2}}} {\sqrt {4\pi } \left ({x_{p}^{2}+y_{p}^{2}+z_{p}^{2}}\right)^{\frac {5}{4}}} e^{-j \frac {2\pi }{\lambda } \left ({x_{p}^{2}+y_{p}^{2}+z_{p}^{2}}\right)^{\frac {1}{2}}}.\tag{22}\end{align*}
Given (20) and (22), according to (10), the channel between source \begin{equation*} |h_{\mathcal {A},{\textrm {case 3}}}|^{2} = \left |{ \int _{\mathcal A} h_{\textrm {CR3}}\left ({{\textbf {p}},{\textbf {s}}}\right) \, d{\textbf {p}} }\right |^{2} \le \frac {1}{\pi } \left ({\frac {1}{3}\alpha + \frac {2}{3}\beta }\right)\tag{23}\end{equation*}
\begin{equation*} \alpha =\frac {\frac {A_{\textrm {pat}}}{4}|z_{p}|} {\left ({\frac {A_{\textrm {pat}}}{4}+z_{p}^{2}}\right) \left ({\frac {A_{\textrm {pat}}}{2}+z_{p}^{2}}\right)^{\frac {1}{2}}}\tag{24}\end{equation*}
\begin{equation*} \beta =\arctan \left ({\frac {\frac {A_{\textrm {pat}}}{4}} {|z_{p}| \left ({\frac {A_{\textrm {pat}}}{2}+z_{p}^{2}}\right)^{\frac {1}{2}}} }\right).\tag{25}\end{equation*}
\begin{align*} \alpha=&\frac {\frac {\lambda ^{2}}{16}|z_{p}|} {\left ({\frac {\lambda ^{2}}{16}+z_{p}^{2}}\right) \left ({\frac {\lambda ^{2}}{8}+z_{p}^{2}}\right)^{\frac {1}{2}}} < \frac {\lambda ^{2}}{16 z_{p}^{2}} \\ \beta=&\arctan \left ({\frac {\frac {\lambda ^{2}}{16}} {|z_{p}| \left ({\frac {\lambda ^{2}}{8}+z_{p}^{2}}\right)^{\frac {1}{2}}} }\right) < \frac {\lambda ^{2}}{16 z_{p}^{2}}.\tag{26}\end{align*}
\begin{equation*} |h_{\mathcal {A},{\textrm {case 3}}}|^{2} \le \frac {\lambda ^{2}}{16\pi z_{p}^{2}}\tag{27}\end{equation*}
C. Field Partition of Antenna
According to (2), (4), and (9), the channel response varies at different points on the surface spanned by an antenna. The variance of the channel response across the surface differs when the antenna is at different locations with respect to the source point
Near field, in which both the amplitude and the phase variations of the channel response are nonnegligible across the surface.
Fresnel region, in which the amplitude variance of the channel response is negligible but the phase variance of the channel response is nonnegligible across the surface.
Fraunhofer region, also known as far field, in which both the amplitude and the phase variations of the channel response are negligible across the surface.
Some research works have considered the two-region partition by focusing only on the phase variance. In [24] and [25], the two regions are the Fresnel and the Fraunhofer regions, where the phase of channel response is dependent on and independent from the distance between transmitter and receiver, respectively. Another two-region partition can be found in [26], [27], [28], and [29], where the two regions were named as near and far fields, respectively. In the near field, a plane wavefront is created, whilst in the far field, a spherical wavefront is created.
1) Rayleigh/Fraunhofer Distance:
The Rayleigh or Fraunhofer distance is the boundary between the Fresnel and the Fraunhofer regions or that between the near and the far field [21], [26], [27]. It is defined by the maximum phase variance of the channel response. The maximum phase variance cannot exceed \begin{equation*} \angle h_{\textrm {CR}}\left ({{\textbf {p}},{\textbf {s}}}\right)= -\frac {2\pi }{\lambda }\|{\textbf {p}}-{\textbf {s}}\|.\tag{28}\end{equation*}
\begin{equation*} |\angle h_{\textrm {CR}}\left ({{\textbf {p}}_{c},{\textbf {s}}}\right) - \angle h_{\textrm {CR}}\left ({{\textbf {p}}_{v},{\textbf {s}}}\right)| = \frac {\pi }{8}\tag{29}\end{equation*}
\begin{align*} \|{\textbf {p}}_{v}-{\textbf {s}}\| -\|{\textbf {p}}_{c}-{\textbf {s}}\|=\sqrt {\frac {A_{\textrm {pat}}}{2}+z_{p}^{2}} - |z_{p}| = \frac {\lambda }{2\pi }\cdot \frac {\pi }{8} = \frac {\lambda }{16}. \tag{30}\end{align*}
\begin{equation*} \sqrt {1+x} \approx 1+\frac {x}{2}\tag{31}\end{equation*}
\begin{equation*} \sqrt {\frac {A_{\textrm {pat}}}{2}+z_{p}^{2}} - |z_{p}| \approx \frac {A_{\textrm {pat}}}{4 |z_{p}|}.\tag{32}\end{equation*}
\begin{equation*} |z_{p}| = \frac {4 A_{\textrm {pat}}}{\lambda }.\tag{33}\end{equation*}
\begin{equation*} |z_{p}| = \frac {2 D_{\textrm {pat}}^{2}}{\lambda }.\tag{34}\end{equation*}
\begin{equation*} d_{\textrm {Rayleigh}} = \frac {4 A_{\textrm {pat}}}{\lambda } = \frac {2 D_{\textrm {pat}}^{2}}{\lambda }.\tag{35}\end{equation*}
2) Lower Bound of Fresnel Region:
Papers [20], [21], and [23] introduced a lower bound of the Fresnel region, which is defined by the maximum amplitude variance of the channel response across the surface. Unlike the variance of the phase, which is captured by the difference, the variance of the amplitude is described by the ratio \begin{equation*} \Gamma =\frac {\min _{{\textbf {p}}\in \mathcal {A}}|h_{\textrm {CR}}\left ({{\textbf {p}},{\textbf {s}}}\right)|} {\max _{{\textbf {p}}\in \mathcal {A}}|h_{\textrm {CR}}\left ({{\textbf {p}},{\textbf {s}}}\right)|}.\tag{36}\end{equation*}
We still consider the patch antenna above. The amplitude of the channel response has different expressions when different models are applied. According to (2), (4), and (9)\begin{align*}&\min _{{\textbf {p}}\in \mathcal {A}}|h_{\textrm {CR}}\left ({{\textbf {p}},{\textbf {s}}}\right)|=\left |{h_{\textrm {CR}}\left ({{\textbf {p}}_{v},{\textbf {s}}}\right)}\right | \\&\max _{{\textbf {p}}\in \mathcal {A}}|h_{\textrm {CR}}\left ({{\textbf {p}},{\textbf {s}}}\right)|=\left |{h_{\textrm {CR}}\left ({{\textbf {p}}_{c},{\textbf {s}}}\right)}\right |.\tag{37}\end{align*}
\begin{equation*} |h_{\textrm {CR1}}\left ({{\textbf {p}},{\textbf {s}}}\right)| = \frac {1}{\sqrt {4\pi } \|{\textbf {p}}-{\textbf {s}}\|}\tag{38}\end{equation*}
\begin{equation*} \frac {\|{\textbf {p}}_{c}-{\textbf {s}}\|}{\|{\textbf {p}}_{v}-{\textbf {s}}\|} =\frac {|z_{p}|}{\sqrt {\frac {A_{\textrm {pat}}}{2}+z_{p}^{2}}}=\Gamma _{\textrm {th}}.\tag{39}\end{equation*}
\begin{align*} d_{\textrm {Fresnel, CR1}}=|z_{p}|=\sqrt {\frac {A_{\textrm {pat}}\Gamma _{\textrm {th}}^{2}}{2\left ({1- \Gamma _{\textrm {th}}^{2}}\right)}}=\frac {D_{\textrm {pat}}}{2}\sqrt {\frac {\Gamma _{\textrm {th}}^{2}}{1-\Gamma _{\textrm {th}}^{2}}}. \tag{40}\end{align*}
\begin{equation*} h_{\textrm {CR2}}\left ({{\textbf {p}},{\textbf {s}}}\right) = \sqrt {\frac {|\left ({{\textbf {p}}-{\textbf {s}}}\right)^{H}{\textbf {v}}_{\mathcal A}\left ({{\textbf {p}}}\right)|}{4\pi \|{\textbf {p}}-{\textbf {s}}\|^{3}}}.\tag{41}\end{equation*}
\begin{equation*} \frac {\|{\textbf {p}}_{c}-{\textbf {s}}\|^{\frac {3}{2}}}{\|{\textbf {p}}_{v} -{\textbf {s}}\|^{\frac {3}{2}}}=\Gamma _{\textrm {th}}.\tag{42}\end{equation*}
\begin{equation*} d_{\textrm {Fresnel, CR2}}=\sqrt {\frac {A_{\textrm {pat}}\Gamma _{\textrm {th}}^{\frac {4}{3}}}{2\left ({1-\Gamma _{\textrm {th}}^{\frac {4}{3}}}\right)}}=\frac {D_{\textrm {pat}}}{2}\sqrt {\frac {\Gamma _{\textrm {th}}^{\frac {4}{3}}}{1-\Gamma _{\textrm {th}}^{\frac {4}{3}}}}\tag{43}\end{equation*}
\begin{equation*} \frac {d_{\textrm {Fresnel, CR3}}^{\frac {3}{2}}\left ({\frac {A_{\textrm {pat}}}{4}+d_{\textrm {Fresnel, CR3}}^{2}}\right)^{\frac {1}{2}}} {\left ({\frac {A_{\textrm {pat}}}{2}+d_{\textrm {Fresnel, CR3}}^{2}}\right)^{\frac {5}{4}}}=\Gamma _{\textrm {th}}.\tag{44}\end{equation*}
\begin{equation*} d_{\textrm {Fresnel, CR3}} > d_{\textrm {Fresnel, CR2}} > d_{\textrm {Fresnel, CR1}}.\tag{45}\end{equation*}
The lower bound of the Fresnel region can be alternatively calculated since the concept of near field is not unique. A Fresnel distance which equals
D. Field Partition of Array
The field partition of a single antenna can be extended to that of a multiantenna array [20], [21]. Consider a widely applied uniform plane array (UPA) at the receiver. The UPA is composed of \begin{equation*} {\textbf {p}}_{v}=\left [{\frac {N_{h} \lambda }{4},\frac {N_{v} \lambda }{4},d }\right]^{T}.\tag{46}\end{equation*}
\begin{equation*} D_{\textrm {UPA}} = \frac {\sqrt {N_{h}^{2}+N_{v}^{2} }\lambda }{2}.\tag{47}\end{equation*}
1) Rayleigh/Fraunhofer Distance:
The Rayleigh or Fraunhofer distance of the UPA is still defined by the maximum phase variance across the array, which equals \begin{align*} \|{\textbf {p}}_{v}-{\textbf {s}}\| -\|{\textbf {p}}_{c}-{\textbf {s}}\|=\sqrt {\left ({N_{h}^{2}+N_{v}^{2} }\right) \frac {\lambda ^{2}}{16} + d^{2}} - d = \frac {\lambda }{2\pi }\cdot \frac {\pi }{8}. \!\!\tag{48}\end{align*}
\begin{equation*} d_{\textrm {Rayleigh}} = \frac {\left ({N_{h}^{2}+N_{v}^{2} }\right) \lambda }{2} = \frac {2 D_{\textrm {UPA}}^{2}}{\lambda }\tag{49}\end{equation*}
2) Lower Bound of Fresnel Region:
Following a similar approach as in the single-antenna case, we further study the lower bound of the Fresnel region of the UPA. Under channel response model 1, by applying (39), we get that \begin{equation*} \frac {\|{\textbf {p}}_{c}-{\textbf {s}}\|}{\|{\textbf {p}}_{v}-{\textbf {s}}\|}=\frac {d}{\sqrt {\left ({N_{h}^{2}+N_{v}^{2} }\right)\frac {\lambda ^{2}}{16}+d^{2}}}=\Gamma _{\textrm {th}}.\tag{50}\end{equation*}
\begin{align*} d_{\textrm {Fresnel, CR1}}=&\frac {\lambda }{4}\sqrt {\frac {\Gamma _{\textrm {th}}^{2}\left ({N_{h}^{2}+N_{v}^{2} }\right)}{\left ({1-\Gamma _{\textrm {th}}^{2}}\right)}} \\=&\frac {D_{\textrm {UPA}}}{2}\sqrt {\frac {\Gamma _{\textrm {th}}^{2}}{1-\Gamma _{\textrm {th}}^{2}}}.\tag{51}\end{align*}
\begin{equation*} d_{\textrm {Fresnel, CR2}}=\frac {D_{\textrm {UPA}}}{2}\sqrt {\frac {\Gamma _{\textrm {th}}^{\frac {4}{3}}}{1- \Gamma _{\textrm {th}}^{\frac {4}{3}}}}.\tag{52}\end{equation*}
Both
For Example 1, the aperture of a small-scale array is limited. Then, the values of
E. Modeling of Channel Between Source and Array
Now, we study the channel model between the point source and the UPA. Denote by \begin{align*} {\textbf {H}} = \left [{ \begin{matrix} h\left ({-\frac {N_{h}}{2}, -\frac {N_{v}}{2}}\right) & \cdots & h\left ({\frac {N_{h}}{2}-1,-\frac {N_{v}}{2}}\right) \\ \vdots & \ddots & \vdots \\ h\left ({-\frac {N_{h}}{2}, \frac {N_{v}}{2}-1}\right) & \cdots & h\left ({\frac {N_{h}}{2}-1, \frac {N_{v}}{2}-1}\right) \\ \end{matrix} }\right].\tag{53}\end{align*}
1) Channel Model 1:
This model is for the region \begin{equation*} h_{\textrm {CM1}}\left ({n_{h}, n_{v}}\right) = |h\left ({n_{h}, n_{v}}\right)| e^{j \angle h\left ({n_{h}, n_{v}}\right)}\tag{54}\end{equation*}
2) Channel Model 2:
This model is for the region of \begin{equation*} h_{\textrm {CM2}}\left ({n_{h}, n_{v}}\right) = |h| e^{j \angle h\left ({n_{h}, n_{v}}\right)}.\tag{55}\end{equation*}
3) Channel Model 3:
This model is for the region of \begin{equation*} h_{\textrm {CM3}}\left ({n_{h}, n_{v}}\right) = |h| e^{j \angle h}.\tag{56}\end{equation*}
Plane wave arrives at an array. (a) No phase difference exists across the array. (b) Phase difference is introduced across the array.
The model in (56) also means that the incident wave seen by each antenna comes from the same direction. That is, a plane wave instead of a spherical wave is experienced at the UPA. Hence, channel model 3 is referred to as the plane wave channel model. Consider a more general case that the UPA is parallel with the \begin{equation*} \theta = \arccos \frac {y_{c}}{\sqrt {x_{c}^{2}+ y_{c}^{2}+ z_{c}^{2}}}.\tag{57}\end{equation*}
\begin{equation*} \phi = \arccos \frac {x_{c}}{\sqrt {x_{c}^{2}+ y_{c}^{2}}}.\tag{58}\end{equation*}
\begin{align*} {\textbf {p}}_{n_{h},n_{v}}=&\left [{ x_{c}+\frac {2n_{h}+1}{4}\lambda, y_{c}+\frac {2n_{v}+1}{4}\lambda, z_{c}}\right]^{T} \\ n_{h}=&-\frac {N_{h}}{2},\ldots,\frac {N_{h}}{2}-1, n_{v} = -\frac {N_{v}}{2},\ldots,\frac {N_{v}}{2}-1.\tag{59}\end{align*}
\begin{equation*} h_{\textrm {CM3}}\left ({n_{h}, n_{v}}\right) = |h| e^{j \left ({\angle h+\Delta \phi \left ({n_{h}, n_{v}}\right) }\right)}\tag{60}\end{equation*}
\begin{equation*} \Delta \phi \left ({n_{h}, n_{v}}\right)=\pi \left ({n_{h} \cos \theta + n_{v} \sin \theta \cos \phi }\right)\tag{61}\end{equation*}
Channel model 3 has been widely applied in the fourth-generation and 5G systems, since the aperture of antenna arrays is not large and users are in the far-field region of the array [31], [32], [33]. However, in 6G systems, extra large-aperture arrays, such as example 2 in Table I, will be employed. Then, users probably fall in the near-field region or the Fresnel region, and channel models 1 and 2 should be utilized. The presence of spherical waves instead of plane waves is one of the major unique characteristics of extra large-scale MIMO systems. Thus, far-field channel models will become inaccurate in the practical near or Fresnel field [11].
Visibility Region
When a user is very close to an extra large-aperture array, most of the channel power can be captured by only a part of the array. This part of the array is referred to as the VR of the user w.r.t. the array. The VR is another key characteristic in extra large-scale MIMO systems [3], [6], [34], [35]. In this section, we will make a comprehensive study on the origins, definition, and modeling of the VR.
A. Origins of the VR
The VR reflects the uneven distribution of the channel power over the array. There are two major manifestations behind the creation of the VR [6]. One is the unequal path loss across different antennas of the array. The other is the blockage stemming from the obstacles between the user and the array.
1) Unequal Path Loss:
When the distance between a user and the array is below \begin{equation*} |h_{\textrm {case 1}}\left ({n_{h}, n_{v}}\right)| \propto \frac {1}{\|{\textbf {p}}_{n_{h},n_{v}}-{\textbf {s}}\|}.\tag{62}\end{equation*}
\begin{equation*} \frac {\min |h_{\textrm {case 1}}\left ({n_{h}, n_{v}}\right)|}{\max |h_{\textrm {case 1}}\left ({n_{h}, n_{v}}\right)|} = \frac {\|{\textbf {p}}_{c}-{\textbf {s}}\|}{\|{\textbf {p}}_{v}-{\textbf {s}}\|} = \frac {d}{\sqrt {d^{2}+\frac {D_{\textrm {UPA}}^{2}}{4}}}.\tag{63}\end{equation*}
A similar phenomenon can be observed when the UPA is customized as described in cases 2 and 3. Considering that \begin{align*}&0< F\left ({{\textbf {p}}_{v},{\textbf {s}}}\right)< F\left ({{\textbf {p}}_{c},{\textbf {s}}}\right)\le 1\tag{64}\\&0< \eta \left ({{\textbf {p}}_{c},{\textbf {s}}}\right)< \eta \left ({{\textbf {p}}_{c},{\textbf {s}}}\right)\le 1\tag{65}\end{align*}
\begin{align*} \frac {\min |h_{\textrm {case 3}}\left ({n_{h}, n_{v}}\right)|}{\max |h_{\textrm {case 3}}\left ({n_{h}, n_{v}}\right)|}\le&\frac {\min |h_{\textrm {case 2}}\left ({n_{h}, n_{v}}\right)|}{\max |h_{\textrm {case 2}}\left ({n_{h}, n_{v}}\right)|} \\\le&\frac {\min |h_{\textrm {case 1}}\left ({n_{h}, n_{v}}\right)|}{\max |h_{\textrm {case 1}}\left ({n_{h}, n_{v}}\right)|}.\tag{66}\end{align*}
![Fig. 5. - Comparison of
$({|h(n_{h}, n_{v})|}/[{\max |h(n_{h}, n_{v})|}])$
in antenna cases 1, 2, and 3 when
$N_{h}=512$
,
$N_{v}=64$
, and
$d=100\lambda $
.](/mediastore/IEEE/content/media/6488907/10210448/10117500/han5-3273328-large.gif)
Comparison of
2) Blockage Due to Obstacles:
An extra large-aperture array can be widely spread on the wall of a building in an urban city. Then,
Unlike in the far field, where the entire channel is blocked, in the near field or the Fresnel region, only a part of the array may be blocked. The blocked part of the array is determined by the geometry of the array, user, and obstacle, as shown in Fig. 6. Assume that only a line-of-sight (LoS) path exists. For antenna
Blockage of the channels on part of the array caused by obstacles, such as trees and cars. Red and gray squares represent the antennas whose channels are connected and blocked, respectively.
B. Definition of the VR
Uneven power distribution across the array is a new channel feature that appears when extra large-aperture arrays are employed in wireless systems. Then, the VR of a user w.r.t. the array is introduced to model the uneven channel power distribution [34], [35], [36], [37], [38], [39], [40], [41], [42], [43], [44], [45]. Actually, the VR is not a novel concept. In this section, we introduce different VR categories.
1) VR of User w.r.t. the Array:
In the literature, the VR of a user w.r.t. the array is defined as the part of the array that captures the biggest proportion of the channel power over the entire array [6], [34], [35], [36]. It reflects the sparsity of a user channel in the antenna domain. Denote the VR of a user w.r.t. the array as \begin{equation*} \frac {\sum _{\left ({n_{h}, n_{v}}\right)\in \Phi _{\textrm {UA}}} |h\left ({n_{h}, n_{v}}\right)|^{2}}{\|{\textbf {H}}\|^{2}_{F}} \ge \zeta\tag{67}\end{equation*}
We first consider the channel under unequal path loss but without blockage. The VR caused simply by a spherical wavefront covers a continuous part of the array. Recall the example in Fig. 5, where
The VR can be obvious if a blockage occurs. At the first antenna in the blocked subarray, a sharp decrease of the channel power can be observed. Consider now the LoS channel case without any non-LoS (NLoS) paths. Then, the channel power on each antenna in the blocked subarray is zero. In (67),
2) Two-Tier VRs:
In the previous context, we focused on the case that only the LoS path exists in the channel. In practice, the wireless propagation environment is composed of various scatterers. Signals can be scattered and then arrive at the array along NLoS paths as well. Unlike the obstacles that block the signal propagation, scatterers provide new propagation paths and act as intermediate nodes. Then, the one-tier user–array channel becomes a two-tier user–scatterer and scatterer–array channel. Accordingly, the VR of a user w.r.t. the array is further partitioned by the VR of a scatterer w.r.t. the array and the VR of a user w.r.t. the scatterers [6], [39], [46], [47], [48], [49].
The scatterers are usually grouped into multiple clusters. Each cluster includes one or multiple neighboring scatterers. Scatterers in a cluster see the same antennas in the array and can be simultaneously observed by a user. The VR of a cluster w.r.t. the array, denoted by
The VR of a user w.r.t. the clusters, denoted by
By cascading the two-tier VRs, the VR of a user w.r.t. the array can be obtained. For user \begin{equation*} \Phi _{{\textrm {UA}},k} = \bigcup _{c\in \Phi _{{\textrm {UC}},k}} \Phi _{{\textrm {CA}},c}\tag{68}\end{equation*}
Example of the two-tier VRs. A circular subarray in a particular color represents the VR of the cluster in the same color.
C. Channel Modeling With VR
Now, we investigate the modeling of a channel with VR. According to (67), the VR almost harvests the total power of channel. To simplify the expression, only the channel in VR is modeled to be nonzero, and the channel out of the VR is assumed to be zero. There have been channel models that capture the new feature of VR [34], [35], [36], [37], [38], [39], [40], [41], [42], [43], [44], [45], [46], [47], [49], where the VR is described in different ways.
1) Channel Covariance Matrix With VR:
A channel covariance matrix reflects the statistical covariance of channels across different antennas. It has been widely applied in the modeling of multiantenna channels. When the channel experiences correlated Rayleigh fading, the channel between the single-antenna user \begin{equation*} {\textbf {h}}_{k} \sim \mathcal {CN}\left ({{\textbf {0}}, {\textbf {R}}_{k}}\right)\tag{69}\end{equation*}
\begin{equation*} {\textbf {R}}_{k} = \mathbb {E}\left \{{{\textbf {h}}_{k} {\textbf {h}}_{k}^{H}}\right \}.\tag{70}\end{equation*}
\begin{equation*} {\textbf {h}}_{k} = {\textbf {R}}_{k}^{\frac {1}{2}}{\textbf {h}}_{w,k}\tag{71}\end{equation*}
\begin{align*} {\textbf {R}}_{k} = \begin{bmatrix} {\textbf {0}} & & \\ & {\textbf {R}}_{{\textrm {UA}},k} & \\ & & {\textbf {0}} \\ \end{bmatrix}\tag{72}\end{align*}
\begin{equation*} {\textbf {h}} = {\textbf {D}}_{{\textrm {UA}},k}{\textbf {R}}_{{\textrm {UA}},k}^{\frac {1}{2}} {\textbf {h}}_{{\textrm {UA}},w,k}\tag{73}\end{equation*}
When scatterer clusters are further considered, the scatterers can be regarded as a virtual antenna array [46]. In traditional multiantenna systems, the covariance matrix-based scattering channel model is [52] \begin{equation*} {\textbf {h}}_{k} = {\textbf {R}}_{A}^{\frac {1}{2}} {\textbf {H}}_{w} {\textbf {R}}_{\textrm {S}}^{\frac {1}{2}} {\textbf {h}}_{w,k}\tag{74}\end{equation*}
\begin{equation*} {\textbf {h}} = \left [{ {\textbf {G}}_{1},\ldots,{\textbf {G}}_{C} }\right] {\textbf {R}}_{\textrm {S}}^{\frac {1}{2}} {\textbf {D}}_{{\textrm {UC}},k} {\textbf {h}}_{w,k}\tag{75}\end{equation*}
\begin{equation*} {\textbf {G}}_{c} = {\textbf {D}}_{{\textrm {CA}},c}{\textbf {R}}_{{\textrm {CA}},c}^{\frac {1}{2}} {\textbf {H}}_{w,c} \in \mathbb {C}^{N\times S_{c}}\tag{76}\end{equation*}
Channel covariance matrix-based channel models pave the way for the analysis of key performance indicators, such as the signal-to-interference and noise (SINR) [35] and the ergodic capacity [46], which further helps the design of transceivers.
2) Steering Vectors With VR:
The discrete physical model is another widely used multiantenna channel model [54], [55]. It focuses on the distinguished paths in the environment. The discrete physical channel model is expressed as follows:\begin{equation*} {\textbf {h}}_{k} = \sum _{c\in \Phi _{{\textrm {UC}},k}} \sum _{s=1}^{S_{c}} \beta _{c,s} {\textbf {a}}_{c,s}\tag{77}\end{equation*}
In extra large-aperture array systems, when introducing the concept of VR, the limited dimensional channel model becomes [39], [49] \begin{equation*} {\textbf {h}}_{k} = \sum _{c\in \Phi _{{\textrm {UC}},k}} \sum _{s=1}^{S_{c}} \beta _{c,s} {\textbf {a}}_{c,s} \odot {\textbf {p}}_{c}\tag{78}\end{equation*}
\begin{align*} \left [{{\textbf {p}}_{c}}\right]_{n} = \begin{cases} 1, & {\mathrm {if} n \in \Phi _{{\textrm {CA}},c}} \\ 0, & \text {else.} \end{cases}\tag{79}\end{align*}
Depending on whether blockage happens or not, the VR mask
D. Spatial Nonstationarity
The spherical wave propagation as well as the VR caused by blockages contribute to spatial nonstationarity, which is the new channel property that appears in extra large-aperture array systems. The concept of spatial stationarity of a multiantenna channel is derived from the wide sense stationarity of a stochastic process [56], where the stochastic process becomes the multiantenna channel \begin{equation*} \mathbb {E}\left \{{ \left [{{\textbf {h}}}\right]_{l+m}^{\ast} \left [{{\textbf {h}}}\right]_{l+n}}\right \} = \mathbb {E}\left \{{ \left [{{\textbf {h}}}\right]_{m}^{\ast} \left [{{\textbf {h}}}\right]_{n}}\right \}\tag{80}\end{equation*}
If the VR of the user w.r.t. the array does not cover the entire array, then the channel is definitely spatially nonstationary. This is because \begin{align*} \mathbb {E}\left \{{ \left [{{\textbf {h}}}\right]_{n} }\right \} \begin{cases} >0, & {\mathrm {if} n \in \Phi _{{\textrm {UA}}}} \\ =0, & \text {else} \end{cases}\tag{81}\end{align*}
\begin{align*} \mathbb {E}\left \{{ \left [{{\textbf {h}}}\right]_{m}^{\ast} \left [{{\textbf {h}}}\right]_{n}}\right \} \begin{cases} >0, & {\mathrm {if} m,n \in \Phi _{{\textrm {UA}}}} \\ =0, & \text {else.} \end{cases}\tag{82}\end{align*}
If the VR of the user w.r.t. the array covers the entire array, but the user is in the near field or Fresnel region of the array, then the multiantenna channel
Low-Cost Extra Large-Aperture Array Architectures
The new channel properties brought by an extra large-aperture array will inform the hardware and transceiver design. The multiantenna arrays used in traditional systems do not have a large size, and a fully digital architecture is widely employed to connect each active antenna with a unique RF chain. However, with the increase of the antenna array size, the fully digital architecture with high resolution will be expensive and not suitable for practical applications. Low-cost architecture designs are of great importance for the commercial deployment of extra large-aperture arrays. Moreover, for an active antenna array, each antenna is driven by a power amplifier (PA) or a low noice amplifier (LNA) and has the ability to transmit and receive wireless signals. Thereafter, the power consumption of an active antenna array is usually large as well. Fortunately, the new channel features provide room for cost reduction. By jointly considering the hardware and power cost as well as the new channel properties, in this section, we will introduce the potential low-cost extra large-aperture array architectures.
A. Active Arrays With Less RF Chains
Research in this type of architectures originates in the beginning of the 5G era [62], [63], [64], [65], [66], [67], [68], [69], [70], [71]. A large array with massive active antennas is controlled by a small amount of RF chains. The numbers of active antennas and RF chains are denoted as \begin{equation*} {\textbf {r}} = {\textbf {F}}_{\textrm {BB}}{\textbf {F}}_{\textrm {RF}} {\textbf {y}}\tag{83}\end{equation*}
1) Connection Type:
The connection type directly determines the hardware cost, transceiver design, transmission performance, as well as the scalability of the architecture. Generally, there are two main types. One is the single-RF chain single-antenna type, and the other is the single-RF chain multiple-antenna type [69], [70].
Single-RF Chain Single Antenna: When this connection type is adopted, a single RF chain can be only connected to a single antenna. A switch is required at each RF chain to enable antenna selection, that is, to determine whether this RF chain is activated and which antenna it is connected with. If the RF chain is activated, then only one antenna will be connected with it. A total of
N_{\textrm {RF}} Antenna selection can be further categorized into two types, including full array selection and partial array selection. Full array selection enables an RF chain to connect with any antenna in the array. Partial array selection means that each RF chain can select from a subarray which is physically closest to it. For a certain RF chain, the partial array for antenna selection is usually fixed, and the size of the partial array is determined by the sweeping space of the switch at the RF chain side. Partial arrays corresponding to different RF chains can be disjoint or overlapped. If two RF chains select antennas from a same partial array, then their selection strategy needs to be different.
Single-RF Chain Multiple Antennas: When applying this connection type, a single RF chain can be connected with multiple antennas. Signal combination or beamforming is achieved at the RF module, and then the array gain can be harvested. Most studies focus on this connection type.
Similar to antenna selection, one RF chain can be connected with the full array or a partial array close to it, corresponding to the full array connection structure and the partial array connection structure, respectively. In the full array connection structure, each antenna can be connected with all the RF chains and vice versa. A unique physical link is established between each RF chain and each antenna. In each link, a PS can be deployed at the antenna side to enable analog beamforming, or an ON/OFF switch can be deployed at the antenna side to reduce the cost and achieve a simple signal combination. A total of
In the partial array connection structure, one RF chain can be connected with a proportion of antennas, but one antenna can be connected with only one RF chain. For a certain RF chain, the partial array that can be connected with is fixed or dynamic. In the former case, a physical link exists between the RF chain and each antenna in the partial array. In each link, a PS or an ON/OFF switch can be deployed at the antenna side as well. The size of each partial array or subarray is fixed, and a total of
2) Component Type:
Now, we turn our attention on the three component mentioned above, including the PS, the ON/OFF switch, and the switch for selection.
PS: A PS can adjust the phase of an RF signal. It is a key enabler of analog beamforming in multiantenna systems. When PSs are deployed, the RF matrix
{\textbf {F}}_{\textrm {RF}} ON/OFF Switch: An ON/OFF switch can be turned ON or OFF to determine whether the signal can pass through the connection. When a switch is in the physical link between one RF chain and one antenna, this connection can be activated or inactivated by choosing the ON and OFF status, respectively. The cost of an ON/OFF switch is significantly lower than that of a PS, but the insertion loss is a major problem.
Switch for selection: A switch for selection has a sweeping space and can be connected to one of the physical links in this sweeping space. It can be deployed at the RF chain side to achieve antenna selection, or be deployed at the antenna side to make RF chain selection. A switch for selection is more expansive than an ON/OFF switch.
3) State-of-the-Art Architectures:
The various connection types and device types can jointly form many different combinations, each corresponding to a particular architecture. Here, we introduce the architectures that have appeared in existing studies, which are listed in Table II, and make an analysis on their signal model, advantages, and drawbacks.
a) Single-RF chain single antenna in full array selection:
This is the traditional antenna selection architecture as shown in Fig. 9 (i). In this architecture, we have \begin{align*}&0\le \sum _{j=1}^{N}\left [{{\textbf {F}}_{\textrm {RF}}}\right]_{i,j}\le 1 \forall i \\&0\le \sum _{i=1}^{N_{\textrm {RF}}}\left [{{\textbf {F}}_{\textrm {RF}}}\right]_{i,j}\le 1 \forall j.\tag{84}\end{align*}
Architectures of active arrays with less RF chains that have appeared in existing studies (i)–(vii) versus the proposed double layer architecture (viii).
b) Single-RF chain single antenna in partial array selection:
This architecture is more easily implemented in an extra large-aperture array system. Considering the scalability issue as well, a subarray-based antenna selection architecture is naturally considered. As shown in Fig. 9 (ii), the entire array is composed of multiple subarrays. Each subarray has completely the same topology, including the number of antennas and the number of RF chains. Denote the number of subarrays as \begin{align*} {\textbf {F}}_{\textrm {RF}} = \begin{bmatrix} {\textbf {F}}_{{\textrm {RF}},1} & & \\ & \ddots & \\ & & {\textbf {F}}_{{\textrm {RF}},B} \\ \end{bmatrix}\tag{85}\end{align*}
\begin{align*} 0\le&\sum _{j=1}^{\frac {N}{B}}\left [{{\textbf {F}}_{{\textrm {RF}},b}}\right]_{i,j}\le 1 \forall i \\ 0\le&\sum _{i=1}^{\frac {N_{\textrm {RF}}}{B}}\left [{{\textbf {F}}_{{\textrm {RF}},b}}\right]_{i,j}\le 1 \forall j.\tag{86}\end{align*}
c) Single-RF chain multiple antennas in full array connection with PSs:
This is the widely studied full-connection hybrid beamforming architecture in 5G millimeter wave systems [65], [66], [67], [68], [69], [70] and has been considered in the extra large-aperture array system as in [29]. As shown in Fig. 9 (iii), each RF chain is connected with all antennas through PSs. The RF matrix \begin{align*} {\textbf {F}}_{\textrm {RF}} = \begin{bmatrix} {\textbf {f}}_{{\textrm {RF}},1}^{T} \\ \vdots \\ {\textbf {f}}_{{\textrm {RF}},N_{\textrm {RF}}}^{T} \\ \end{bmatrix}\tag{87}\end{align*}
d) Single-RF chain multiple- antennas in full array connection with ON/OFF switches:
This architecture is a reduced version of architecture iii by replacing the expensive PSs with low-cost ON/OFF switches as illustrated in Fig. 9 (iv). The RF matrix
e) Single-RF chain multiple antennas in fixed partial array connection with PSs:
This is the well known subarray hybrid beamforming architecture [63], [64], [68], [69], [70]. In Fig. 9 (v), each subarray has equal size with only one RF chain and \begin{align*} {\textbf {F}}_{\textrm {RF}} = \begin{bmatrix} {\textbf {f}}_{{\textrm {RF}},1}^{T} & & \\ & \ddots & \\ & & {\textbf {f}}_{{\textrm {RF}},N_{\textrm {RF}}}^{T} \\ \end{bmatrix}\tag{88}\end{align*}
f) Single-RF chain multiple antennas in fixed partial array connection with ON/OFF switches:
This architecture is deduced from architecture
g) Single-RF chain multiple antennas in dynamic partial array connection with PSs:
The concept of a dynamic partial array or dynamic subarray appeared in [71]. It is an improved version of architecture
However, this architecture has the following drawbacks. First, it is hard to implement. There are two solutions denoted as architectures vii -1 and vii -2, respectively. The first solution is to deploy a switch for selection at each antenna to select one of the
4) Proposed Double-Layer Architecture:
Considering the advantage of dynamic subarrays as well as the practical implementation and scalability, in this article, we integrate the full-connection and subarray structures and propose a double-layer architecture, which is refered to as architecture viii. As shown in Fig. 9 (viii), the outer layer follows the fixed subarray structure, and the inner layer follows the dynamic subarray structure. The extra large-aperture array is composed of
Architecture vii is adopted in each physical subarray. For convenient implementation, a physical link is established between each RF chain and each antenna in the common physical subarray. An ON/OFF switch is deployed in each physical link. For a certain antenna, only one RF chain can be selected, and thus no more than one physical link connected with this antenna is finally turned ON. To enable analog beamforming, each antenna is further equipped with a PS. A total of
In the proposed double-layer architecture, the RF matrix \begin{equation*} {\textbf {F}}_{{\textrm {RF}},b} = {\textbf {S}}_{b} \odot \left ({{\textbf {1}}_{\frac {N_{\textrm {RF}}}{B}}\otimes {\textbf {f}}_{b}^{T} }\right)\tag{89}\end{equation*}
\begin{equation*} 0\le \sum _{i=1}^{\frac {N_{\textrm {RF}}}{B}}\left [{{\textbf {S}}_{b}}\right]_{i,j}\le 1 \forall j.\tag{90}\end{equation*}
The proposed double-layer architecture sustains the advantage of easy synchronization and scalability of the subarray structure. Equally importantly, the hardware cost is greatly reduced compared with architecture vii. The insertion loss is substantially mitigated by using much less switches. This architecture also can harvest the full array gain by activating all antennas in a subarray simultaneously. Alternatively, in spatial nonstationary channel conditions, we can only activate the antennas where the biggest proportion of channel power is concentrated in. For the above-mentioned reasons, this is a potential architecture for extra large-aperture arrays.
Table III summarizes the hardware cost, advantages, and disadvantages of the nine architectures, including the two solutions of architecture vii and the proposed architecture viii. Considering the scalability, architectures ii,
B. Reconfigurable Intelligent Surfaces
Another low-cost extra large-aperture array is the RIS [73], [74], [75], [76], [77], which is also known as metasurface [75], [78], [79], or intelligent reflecting surface (IRS) [80]. An RIS is composed of low-cost near passive unit cells, each with independently tunable EM responses controlled by external signals. An incident EM wave can be reflected or refracted by the RIS, or the reflection and the refraction happen simultaneously [81], [82], [83]. An RIS flexibly adjusts the amplitude, phase, or polarization of the incident EM wave in real time. Then, a preferable EM propagation environment can be customized by properly controlling the RIS.
The widely studied category of RISs reflect the EM waves toward the desired directions by adjusting their phases. An RIS works as a controllable reflector in the wireless environment, providing an additional controllable link between the transmitter and the receiver to assist the wireless communication. Suppose the transmitter and the receiver are equipped with a single antenna, respectively. The number of unit cells in the RIS is \begin{equation*} r = gs + {\textbf {h}}_{2}^{T} {\boldsymbol{\Lambda }} {\textbf {h}}_{1} s + z\tag{91}\end{equation*}
\begin{equation*} {\boldsymbol{\Lambda }} = {\textrm {diag}}\left \{{ {\textbf {v}} }\right \},\quad {\textbf {v}} = \left [{e^{j\phi _{1}},\ldots,e^{j\phi _{N}}}\right]^{T}\tag{92}\end{equation*}
\begin{equation*} g_{\textrm {eff}} = g + {\textbf {h}}_{2}^{T} {\mathbf {\boldsymbol \Lambda }} {\textbf {h}}_{1}.\tag{93}\end{equation*}
1) Fully Passive RIS:
Most existing RISs that work in the reflection mode are fully passive regardless of the low external control voltage. No signal processing module exists at the RIS, and, thus, the RIS is not able to transmit or receive wireless signals. Since the individual channels \begin{equation*} {\textbf {h}}_{2}^{T} {\mathbf {\boldsymbol \Lambda }} {\textbf {h}}_{1} = {\textbf {h}}_{2}^{T} {\textrm {diag}}\left \{{ {\textbf {v}} }\right \} {\textbf {h}}_{1} = {\textbf {h}}_{2}^{T} {\textrm {diag}}\left \{{ {\textbf {h}}_{1} }\right \} {\textbf {v}}\end{equation*}
2) Semi-Passive RISs:
To tackle the channel estimation problem, semi-passive RISs were proposed in [84], [85], [86], and [87]. As shown in Fig. 10, a semi-passive RIS introduces a few active sensors that can receive signals to enable channel estimation at the RIS. These active sensors are connected with RF chains and have two modes. One is the reflection mode, same as a common RIS unit cell. The other is the reception mode, in which the incident signals are received and conveyed to the signal processing module through RF chains. Suppose
Semi-passive RIS. Unit cells in blue are passive and only have the reflection mode with phase shift capability. Unit cells in red are active and have the reflection and receiving modes.
The above low-cost architectures enable the deployment of extra large-aperture arrays. Active antenna arrays and RISs can be jointly applied to satisfy specific service requirements in different application scenarios.
Low-Complexity Processing and Computation
Apart from the problem of high cost, the implementation of an extra large-aperture array also requires high-complexity processing and computations. In multiantenna systems, the computational complexity of the widely used linear signal processing algorithms usually has an order of
Extra large-scale array is controlled by (a) single CPU, (b) multiple LPUs, or (c) CPU and multiple LPUs.
A. Complexity Reduction at CPU
One method is to directly reduce the complexity of some high-complexity algorithms for their simplified or scalable implementation in the CPU. Complexity reduction in massive MIMO systems is not a novel concept [88], [89], [90], [91], [92]. Some of these methods can be extended to fit in extra large-aperture array systems.
There have been studies focusing on the complexity reduction in the CPU of extra large-aperture array systems [36], [40], [93], [94], [95]. Most of these studies focus on zero-forcing (ZF), which is a widely used linear signal processing method in multiuser multiantenna systems. The ZF precoder and combiner can be applied at the transmitter and the receiver, respectively, to cancel out the interuser interference. For example, let us denote the downlink channel between the extra large-aperture array at the BS and the single-antenna user \begin{equation*} {\textbf {W}}_{\textrm {ZF}} = {\textbf {H}} \left ({{\textbf {H}}^{H}{\textbf {H}}}\right)^{-1} \in \mathbb {C}^{N\times K}.\tag{94}\end{equation*}
In addition to the ZF receiver, variational message passing (VMP) is another widely used multiuser MIMO detector, which has lower complexity than ZF because no matrix inversion is involved. In this context, Amiri et al. [36] applied VMP in the extra large-aperture array system under spatial nonstationary channel conditions, and further utilized a maximal ratio combiner (MRC) for initialization. The complexity of VMP and MRC is linear with
Some other works focused on the complexity reduction of antenna selection [94] and user scheduling [95] in extra large-aperture array systems. Given the number of antennas
B. Distributed Processing and Computation
Assigning all the processing and computation tasks to a single CPU is not a reasonable choice in the extra large-aperture array system. An alternative is to partition the entire array into multiple subarrays and distribute the tasks to the subarrays [6], [34], [37], [38], [39], [41], [42], [43], [96]. This is a logical concept of subarray different from the physical subarray above. A logical subarray may have a fully digital physical architecture, but it has its own local processing unit (LPU) as shown in Fig. 11 (b) and (c). Some processing and computation tasks of an individual logical subarray, such as channel estimation, antenna selection, etc., can be handled by its own LPU. When LPUs exist, there can be arranged via two logical architectures.
1) Single Layer With LPUs:
This logical architecture is illustrated in Fig. 11 (b) and solely composed of LPUs. That is to say, all the processing and computation tasks are distributed and performed at the LPUs, without a centralized control over the LPUs. Since no CPU exists, this architecture can be easily scaled up.
Notably, some tasks are local tasks and can be handled by a single LPU. A typical example of a local task is channel estimation. The channel across the entire array can be uniformly partitioned into
Most of the tasks are global tasks that require the cooperation among LPUs. A typical example is signal detection. We write the uplink signal model in a time-division duplexing system as follows:\begin{equation*} {\textbf {y}} = \sum _{k=1}^{K} {\textbf {h}}_{k} s_{k} + {\textbf {n}}\tag{95}\end{equation*}
2) Double Layers With CPU and LPUs:
A more reasonable and widely studied logical architecture is the double-layer architecture with LPUs in the lower layer and CPU in the upper layer as shown in Fig. 11 (c). When spatial nonstationarity holds, different users have different VRs w.r.t. the array. If subarray
In this architecture, each LPU is connected with the CPU. Having completed the distributed processing and calculation, each LPU feeds its local result back to the CPU. Then, the CPU integrates the local results from all the LPUs and obtains the final global result by means of hard decision or data fusion [6]. At the receiver, [37] decentralizes the RK-ZF algorithm and applies it in multiuser signal detection in extra large-scale MIMO systems. LPU \begin{equation*} \hat {\textbf {s}}_{b} = {\textbf {V}}_{b}{\textbf {y}}_{b}.\tag{96}\end{equation*}
The concept of LPUs of subarrays can be extended to LPUs of users. In [38], transmit antenna selection and user mapping were studied. Considering that different users have unequal VRs, parallel user mapping convolutional neural networks (CNNs) were proposed to learn the selected antennas for each user independently. The
Some recent works proposed the information exchange among LPUs or iterations between CPU and LPUs to gradually improve the performance. Information exchange between two distinct LPUs can be achieved with the assistance of CPU, or, a direct connection can be further established between the two LPUs. At the receiver, the LPUs in [34] performed ZF-based signal detection on a per user basis, while the detection results of a certain user were shared by the LPUs for the detection of signal from the next user. This serial interference cancelation method was also applied in [47], where VMP is employed in each LPU. Notably, given the VR of each user, the operation order of LPUs as well as the detection order of user signals can be initially determined by CPU [34], which further improves the detection performance.
Apart from ZF and VMP, expectation propagation (EP) is another effective algorithm that has been utilized at the receiver for multiuser signal detection in extra large-aperture array systems [97], [98]. EP in a centralized processing strategy that has excellent performance and moderate complexity. In this context, [97] initially implemented EP in a decentralized manner and made efforts on the reduction of computational complexity and information exchange amount, while [98] further refined the decentralized EP by approximating the matrix inversion at the CPU, whose complexity is
In [96], antenna selection and resource allocation were considered at the downlink transmitter. Even though in this work the LPUs operate in parallel, back-and-force information exchange between CPU and LPUs occurs since a genetic algorithm was adopted. Successive operation of LPUs and iterative optimization between two layers inevitably increase the latency.
Multilayer processing can be further applied in extra large-aperture RIS-assisted mobile communication systems [43]. The RIS can be uniformly partitioned into
Low-Overhead Communication and Sensing
In this section, we focus on low-overhead design in extra large-aperture array systems. Training is an effective and reliable approach to acquire CSI. With the increase of user equipments and the diversification of device types that are connected to the extra large-aperture array system, the amount of pilots required will grow prohibitively high if independent training is performed across them. Furthermore, for an extra large-aperture array with massive active antennas but less RF chains, estimation of the huge dimensional channel on each antenna inevitably involves a beam sweeping or antenna switching process, which will be time consuming if the number of RF chains is much smaller than the number of active antennas.
Fortunately, the directionality and sparsity of propagation channels create room for overhead reduction, which will be explained in detail in the following part of this section. Furthermore, the extra large-aperture array has an extremely high spatial resolution, and the high-dimensional channel contains the environment information, such as knowledge about the user location and surrounding obstacles. Therefore, sensing can be achieved together with communication during the training process [99]. In this section, we study the low-overhead communication and sensing paradigm.
A. Directionality and Channel Sparsity
In a traditional multiantenna system, the serving area of a BS is large, and users are in the far-field region of the array. The plane wave channel model (60) is then applied, and the plane wave is expressed by its AoA/AoD as shown in (61). Due to the high spatial resolution of the large-aperture array, and the much smaller number of propagation paths than the number of antennas, the channel shows significant sparsity and directionality in the angular domain. In an extra large-aperture array system, there is a high probability that the distance between a user and the BS is smaller than the Rayleigh distance. Under these conditions, the spherical wave channel model (54) should be introduced, and the spherical wave is expressed by the position of the source (28). Moreover, the VR kicks in when blockage exists, which means that the effective array size is reduced. Then, whether the channel sparsity and directionality hold becomes a question.
Assume the BS is equipped with an extra large-aperture uniform linear array (ULA) with \begin{equation*} {\textbf {h}}_{k} = \beta _{k} {\textbf {a}}\left ({{\textbf {s}}_{k}}\right) \odot {\textbf {p}}\left ({\Phi _{k}}\right)\tag{97}\end{equation*}
\begin{equation*} \left [{{\textbf {a}}\left ({{\textbf {s}}}\right)}\right]_{n} = \frac {\lambda }{4\pi d_{k,n} } e^{-j \frac {2\pi }{\lambda } d_{k,n} }.\tag{98}\end{equation*}
\begin{equation*} d_{k,n}=\sqrt {\left ({x_{k}+\frac {2n+1}{2}d}\right)^{2}+z_{k}^{2}}\tag{99}\end{equation*}
1) Angular Domain:
We start by investigating whether the directionality and sparsity hold for
Directionality and sparsity of channels in (a) angular, (b) Cartersian, and (c) polar domains, respectively, when
2) Cartesian Domain:
From (98), we see that
Let \begin{align*}&\left \{{ \bar {x} = x_{{\mathrm {min}}}, x_{{\mathrm {min}}}+\Delta x,\ldots,x_{{\mathrm {max}}} }\right. \\&\quad \left.{ \bar {z} = z_{{\mathrm {min}}}, z_{{\mathrm {min}}}+\Delta z,\ldots,z_{{\mathrm {max}}} }\right \}\tag{100}\end{align*}
3) Polar Domain:
The spherical wave channel is more frequently expressed by the polar coordinates \begin{align*} D_{k}=&\sqrt {x_{k}^{2}+z_{k}^{2}},\quad \theta _{k} = \arcsin {\frac {x_{k}}{D_{k}}} \\ x_{k}=&D_{k}\sin \theta _{k},\quad z_{k} = D_{k}\cos \theta _{k}.\tag{101}\end{align*}
\begin{equation*} d_{k,n}=\sqrt {D_{k}^{2}+\frac {(2n+1)^{2}}{4}d^{2}+(2n+1)dD_{k}\sin \theta _{k}}.\tag{102}\end{equation*}
Similar to the Cartesian domain samples, we can let \begin{align*}&\left \{{ \lg \bar {D} = \lg D_{{\mathrm {min}}}, \lg D_{{\mathrm {min}}}+\Delta D,\ldots,\lg D_{{\mathrm {max}}} }\right. \\&\quad \left.{ \bar {\theta } = \theta _{{\mathrm {min}}}, \theta _{{\mathrm {min}}}+\Delta \theta,\ldots,\theta _{{\mathrm {max}}} }\right \}\tag{103}\end{align*}
To decrease the correlation among rows of
4) Antenna Domain:
When the user is very close to the array as the example in Fig. 5, or severe blockage happens as illustrated in Fig. 6, the VR of the user w.r.t. the array is a small-scale subset of antennas in the array. Then, the channel shows sparsity in the antenna domain. In the simplest case that the VR of user \begin{align*} {\textbf {h}}_{k} \approx \left [{ \begin{matrix} {\textbf {0}}\\ {\textbf {h}}_{k,VR}\\ {\textbf {0}} \end{matrix} }\right]\tag{104}\end{align*}
B. Low-Overhead Design
Channel directionality and sparsity in the transformation domains provide room for overhead reduction. More particularly, channel directionality guarantees the accuracy of user localization, which further supports channel reconstruction and sensing. Channel sparsity enables the application of compressed sensing techniques in the estimation of channels and the orthogonal transceiver design among multiple users. Details are given as follows.
Consider an extra large-aperture array system with less RF chains than active antennas at the BS. The spatially nonstationary channel \begin{equation*} {\textbf {h}}_{k} = \sum _{l=1}^{L_{k}} \beta _{k,l} {\textbf {a}}\left ({{\textbf {s}}_{k,l}}\right) \odot {\textbf {p}}\left ({\Phi _{k,l}}\right)\tag{105}\end{equation*}
\begin{equation*} {\textbf {Y}}_{t} = \sqrt {P} {\textbf {F}}_{{\textrm {RF}},t}\sum _{k=1}^{K} {\textbf {h}}_{k} {\textbf {x}}_{k}^{H} + {\textbf {F}}_{{\textrm {RF}},t}{\textbf {N}}_{t}\tag{106}\end{equation*}
\begin{equation*} {\textbf {y}}_{k} = \sqrt {P} {\textbf {F}} {\textbf {h}}_{k} + {\textbf {n}}_{k}\tag{107}\end{equation*}
1) Localization Based on Directionality:
When an LoS path exists between user \begin{equation*} {\textbf {y}}_{k} = \sum _{l=1}^{L_{k}} \sqrt {P}\beta _{k,l} {\textbf {F}}\left ({{\textbf {a}}\left ({{\textbf {s}}_{k,l}}\right) \odot {\textbf {p}}\left ({\Phi _{k,l}}\right)}\right) + {\textbf {n}}_{k}.\tag{108}\end{equation*}
\begin{equation*} \left ({\hat {x}_{k,1},\hat {z}_{k,1}}\right) = \arg \max _{\left ({\bar {x},\bar {z}}\right)\in (100) } \frac {\bar {\textbf {c}}\left ({\bar {x},\bar {z}}\right)^{H} {\textbf {y}}_{k}}{\|\bar {\textbf {c}}\left ({\bar {x},\bar {z}}\right)\|}\tag{109}\end{equation*}
\begin{equation*} \left ({\hat {D}_{k,1},\hat {\theta }_{k,1}}\right) = \arg \max _{\left ({\bar {D},\bar {\theta }}\right)\in (103) } \frac {\bar {\textbf {c}}\left ({\left ({\bar {D},\bar {\theta }}\right)^{H} }\right) {\textbf {y}}_{k}}{\|\bar {\textbf {c}}\left ({\bar {D},\bar {\theta }}\right)\|}\tag{110}\end{equation*}
For sensing, given the estimates of position and VR, we can generally decide where the obstacle is. With more paths interacting with a common obstacle, the localization, size, and even shape of the obstacle can be more accurately determined from the positions and VRs of these paths. Then, the environment can be identified.
2) Channel Estimation Based on Sparsity:
In practical environments, when the system works in higher frequency bands, the NLoS paths becomes fewer due to the severe pathloss and blockage. In an extra large-aperture array system, we usually have
Compressed sensing aims to estimate the reduced dimensional sparse channel in a transformation domain. The precondition is that the row vectors of the transformation matrix maintain the orthogonality between them, which can be achieved by the polar domain transformation in [29]. For \begin{equation*} {\textbf {y}}_{k} = \sqrt {P} {\textbf {F}} {\textbf {U}}_{P}^{\dagger } \tilde {\textbf {h}}_{P,k} + {\textbf {n}}_{k}\approx \sqrt {P} {\textbf {F}} \left [{{\textbf {U}}_{P}}\right]_{\Upsilon _{k},:}^{\dagger } \left [{\tilde {\textbf {h}}_{P,k}}\right]_{\Upsilon _{k}} + {\textbf {n}}_{k}.\tag{111}\end{equation*}
\begin{equation*} \hat {\textbf {h}}_{k} = \left [{{\textbf {U}}_{P}}\right]_{\hat \Upsilon _{k},:} \left [{\hat {\tilde {\textbf {h}}}_{P,k}}\right]_{\hat \Upsilon _{k}}.\tag{112}\end{equation*}
3) Multiuser Pilot Transmission Based on Sparsity:
The nonoverlapping sparsity of different users’ antenna-domain channels enables the simultaneous transmission of pilots from or to these users. A common pilot sequence can be shared among users that have nonoverlapping VRs, and the orthogonal pilot sequences are assigned to users with overlapping VRs. Due to the limited amount of orthogonal pilot sequences, the nonoverlapping sparsity among users creates potential for the reduction of the overall training time. By knowing the VR of user \begin{equation*} {\textbf {Y}} = \sqrt {P}{\textbf {F}}_{{\textrm {RF}}}\left ({\sum _{b=1}^{B} {\textbf {h}}_{b} {\textbf {x}}_{1}^{H} + {\textbf {h}}_{B+1} {\textbf {x}}_{2}^{H}}\right) + {\textbf {F}}_{{\textrm {RF}}}{\textbf {N}}.\tag{113}\end{equation*}
\begin{equation*} {\textbf {y}} = \sqrt {P} {\textbf {F}}_{{\textrm {RF}}} \sum _{b=1}^{B} {\textbf {h}}_{b} + {\textbf {n}}\tag{114}\end{equation*}
\begin{equation*} y_{b} = \sqrt {P}{\textbf {f}}_{{\textrm {RF}},b}^{T} {\textbf {h}}_{b,VR} + n_{b}\tag{115}\end{equation*}
In extra large-aperture RIS-assisted systems, directionality, and channel sparsity still hold in the angular, Cartesian, polar, and RIS unit domains at the RIS side. Therefore, the low-cost designs are also applicable in RIS-assisted systems. Notably, when applying the multiuser pilot transmission scheme, the RIS should be equipped with signal reception capabilities.
Conclusion
We investigated the new channel properties of spatial nonstationarity, including the spherical wave propagation and the VR, and made a survey about existing works in the context of hardware cost, processing and computation complexity, and training overhead for extra large-scale MIMO systems. We also studied the origins of spatial nonstationarity and illustrated the modifications of channel modeling when spatial nonstationarity was considered. This new property paves the way for low-cost hardware architectures. Through a detailed comparison, we proposed a double-layer architecture and the RIS as the most promising implementation architecture of an extra large-aperture array. Then, the complexity reduction problem was investigated and the distributed solution with one CPU and multiple LPUs demonstrated the most promising potential. Finally, the low-overhead communication and sensing strategies were investigated, which can be realized given the directionality and sparsity of the channel in the Cartesian, polar, and antenna domains. Summarizing, this article reviewed the early stage research efforts of extra large-scale MIMO, and highlighted the importance of low-cost designs in future practical implementations.