Dynamic Metasurface Array 用于近场重新总结

Main Point

加密和交织可以混合在一起吗？

\subsection{System Model}
Single User, One DMA as a transmitter. Alice, Bob, Willie. Covert, Artificial Noise, Sparse, Angle domain.

论文1 Beam Focusing for Near-Field Multiuser MIMO Communications

\subsection{Near Field channel model}

To evaluate the ability to exploit near-field operation in MIMO communications, we focus on downlink multi-user systems. In particular, we consider a downlink multi-user MIMO system where the BS employs a uniform planar array (UPA), i.e., a two-dimensional antenna surface, with $N_e$ uniformly spaced radiating elements in the horizontal direction and $N_d$ elements in the vertical direction. The total number of antenna elements is thus $N=N_d\times N_e$ . We denote the Cartesian coordinate of the $l$ th element of the $i$ th row as ${\mathbf{p}}_{i,l}=\left(x_l,y_i,0\right),l=1,2,\dots N_e,i=1,2,\dots N_d$ . The BS communicates with $M$ single-antenna receivers, as illustrated in Fig. 2. We consider that the receivers’ positioning information is known at the BS via high-accuracy wireless positioning techniques [3]. We focus on communications in the near-field, i.e., where the distance between the BS and the users is not larger than the Fraunhofer distance $d_{\mathrm{F}}$ and not smaller than the Fresnel limit $d_{\mathrm{N}}$ . The properties of near-field spherical waves allow for the generation of focused beams to facilitate communications.

To start, we model the near-field wireless channels following
existing modelling techniques for EM propagation in the radiating near-field, e.g., [30]. The signal received in free-space conditions by the legitimate user Bob, located at ${\mathbf{p}}_b=\left(x_b,y_b,z_b\right)$ is given by

$$\begin{array}{c}r\left({\mathbf{p}}_b\right)=\sum _{i=1}^{N_d}\sum _{l=1}^{N_e}{A}_{i,l}\left({\mathbf{p}}_b\right)e^{-ȷk|{\mathbf{p}}_b-{\mathbf{p}}_{i,l}|}{s}_{i,l}+n_b\end{array}$$

where $s_{i,l}$ denotes the signal emitted by the antenna at position ${\mathbf{p}}_{i,l}$ ; the term $e^{-ȷk|{\mathbf{p}}_m-{\mathbf{p}}_{i,l}|}$ contains the phase due to the distance travelled by the wave from ${\mathbf{p}}_{i,l}$ to ${\mathbf{p}}_m$ ; $k=2\pi /\lambda$ is the wave number; $A_{i,l}\left({\mathbf{p}}_m\right)$ denotes the channel gain coefficient; and $n_m\sim \mathcal{C}\mathcal{N}\left(0,{\sigma }^2\right)$ is the additive white Gaussian noise (AWGN) at user $m$ . Following [30], we write

$$\begin{array}{c}{A}_{i,l}\left({\mathbf{p}}_m\right)=\sqrt{F\left({\Theta }_{i,l,m}\right)}\frac{\lambda }{4\pi \left|{\mathbf{p}}_m-{\mathbf{p}}_{i,l}\right|}\end{array}$$

where ${\Theta }_{i,l,m}=\left({\theta }_{i,l,m},{\varphi }_{i,l,m}\right)$ is the elevation-azimuth pair from the $l$ th element of the $i$ th row to the $m$ th user, while $F\left({\Theta }_{i,l,m}\right)$ is the radiation profile of each element, modeled as

$$\begin{array}{c}F\left({\Theta }_{i,l,m}\right)=\{\begin{array}{ll}2(b+1){\cos }^b\left({\theta }_{i,l,m}\right)& {\theta }_{i,l,m}\in [0,\pi /2]\\ 0& \text{ otherwise }\end{array}\end{array}$$

In (3), the parameter $b$ determines the Boresight gain, whose value depends on the specific technology adopted [30]. As an example, for the dipole case we have $b=2$ , which yields $F\left({\Theta }_{i,l,m}\right)=6{\cos }^2{\theta }_{i,l,m}$ . Here, the model accounts for the fact that the transmitted power is doubled by the reflective ground behind the antenna.

To obtain a more compact formulation of the received signal in (1), we define the vector

$$\begin{array}{rl}{\mathbf{a}}_m=& [A_{1,1}\left({\mathbf{p}}_m\right)e^{-ȷk|{\mathbf{p}}_m-{\mathbf{p}}_{1,1}|},A_{1,2}\left({\mathbf{p}}_m\right)e^{-ȷk|{\mathbf{p}}_m-{\mathbf{p}}_{1,2}|}\\ & {\cdots ,A_{N_d,N_e}\left({\mathbf{p}}_m\right)e^{-ȷk|{\mathbf{p}}_m-{\mathbf{p}}_{N_d,N_e}|}]}^H\end{array}$$

For convenience, we omit the location index ${\mathbf{p}}_m$ in ${\mathbf{a}}_m\left({\mathbf{p}}_m\right)$ for the rest of this paper. Using (4), we can then write the received signal at the $m$ th user as

$$\begin{array}{r}r\left({\mathbf{p}}_m\right)={\mathbf{a}}_m^H\mathbf{s}+n_m,m\in \mathcal{M},\end{array}$$

where $\mathbf{s}=\left[s_{1,1},s_{1,2}\cdots ,s_{N_d,N_e}\right]$ collects the transmitted signals of all antennas.

Assume the eavesdropper Willie’s location is at ${\mathbf{p}}_w=\left(x_w,y_w,z_w\right)$. The signal received by Willie is given by:

$$\begin{array}{c}r\left({\mathbf{p}}_w\right)=\sum _{i=1}^{N_d}\sum _{l=1}^{N_e}{A}_{i,l}\left({\mathbf{p}}_w\right)e^{-ȷk|{\mathbf{p}}_w-{\mathbf{p}}_{i,l}|}{s}_{i,l}+n_w\end{array}$$

$$\begin{array}{r}r\left({\mathbf{p}}_w\right)={\mathbf{a}}_w^H\mathbf{s}+n_w,m\in \mathcal{M},\end{array}$$

${\mathbf{a}}_b\in {\mathbb{C}}^{N_d{N}_e\times 1}$

${\mathbf{a}}_w\in {\mathbb{C}}^{N_d{N}_e\times 1}$

$\mathbf{s}\in {\mathbb{C}}^{N_d{N}_e\times 1}$

\subsection{DMA}

DMAs utilize radiating metamaterial elements
embedded onto the surface of a waveguide to realize recon-
figurable antennas of low cost and power consumption [24].
The typical DMA architecture is comprised of multiple
waveguides, e.g. microstrips, and each microstrip contains
multiple metamaterial elements. The elements are typically
sub-wavelength spaced, implying that one can pack a larger
number of elements in a given aperture compared to conven-
tional architectures based on, e.g., patch arrays [24]. The fre-
quency response of each individual element can be externally
adjusted by varying its local electrical properties [33].

For DMA-based transmitting architectures, each microstrip is fed by one RF-chain, and the input signal is radiated by all the elements located on the microstrip, as shown in Fig. 3©. Fig. 4 shows an example of transmitting a signal using a single microstrip with multiple elements. To formulate its input-output relationship, consider a DMA consisting of $N=N_d\cdot N_e$ metamaterial elements, where here $N_d$ and $N_e$ are the numbers of microstrips and elements in each microstrip, respectively. The equivalent baseband signal radiated from the $l$ th element of the $i$ th microstrip is $s_{i,l}=$