Slow Fluid Antenna Multiple Access with Multiport Receivers

Abstract

We investigate whether equipping fluid-antenna (FA) receivers with multiple ($L>1$) radiofrequency (RF) chains can improve the performance of the slow fluid-antenna multiple access (FAMA) technique, which enables open-loop connectivity with channel state information (CSI) available only at the receiver side. We analyze the case of slow-FAMA users equipped with multiport receivers, so that $L$ ports of the FA are selected and combined to reduce interference. We show that a joint design of the port selection matrix and the combining vector at each receiver yields significant performance gains over reference schemes, demonstrating the potential of multiport reception in FA systems with a limited number of RF chains.

I Introduction

Fluid antenna systems (FASs) have gained considerable attention in recent years as a promising alternative to conventional MIMO (MIMO) systems that rely on fixed-position antennas [1]. FASs refer to any controllable structure —whether electronically, mechanically, or otherwise actuated— that can dynamically alter its fundamental radio-frequency (RF) characteristics, effectively emulating physical changes in shape or position to adapt to the wireless environment [2]. The fine-grained capability of FASs to sample spatial locations brings enhanced flexibility to exploit spatial diversity, by selecting the receive antenna port (akin to position) that is more beneficial for signal reception [3].

One of the key potential use cases of FASs is the provision of simplified open-loop multiple access, without the need for CSI (CSI) at the transmitter side or SIC (SIC) at the receiver side. This technique, referred to as FAMA (FAMA), allows serving multiple users in the same time/frequency resource with CSI required only at the receiver side. Specifically, the slow-FAMA paradigm introduced in [4] manages to relax the stringent port-switching requirements of the fast-FAMA counterpart [5], thus reducing complexity while still allowing for user multiplexing.

Since their inception, FASs have been envisioned as a low-complexity alternative to conventional MIMO architectures to improve system performance. For that reason, virtually all FAMA-based schemes consider a single RF (RF) chain at the receiver (user) ends, and the port selection mechanism aims to choose that with the best SINR (SINR). Indeed, there have been attempts to consider the case with a larger number of RF chains at the receiver ends in the context of FASs: for instance, the use of MRC (MRC) to combine the signals of the $L$ best ports was proposed in [6] for a point-to-point (single user) case. However, MRC offers limited benefits in the presence of interference, which is the operational regime in FAMA. In [7], the CUMA (CUMA) architecture was proposed, allowing to select a subset of ports for which the desired signal is phase-aligned. While CUMA manages to improve slow-FAMA multiplexing capabilities by using a limited number of RF chains (up to four [8]), it comes in hand with some practical challenges: (i) requires a pre-processing stage to configure the subset of active ports; (ii) assumes that an arbitrary number of ports are active at the same time; and (iii) requires precise knowledge of CSI at all ports.

In this work, we revisit the problem of slow-FAMA when FA users have multiport receivers, i.e., they can be equipped with more than one RF chain. Contrary to prior art, we propose a method to jointly select the active ports of the FA and the combining vector for the signals of the designated ports. One of the key novelties lies in the fact that the spatial features of the channel matrix for the FA array are considered in the procedure. This novel approach enhances the achievable gain and, more importantly, considerably reduces the inter-user interference. Results show that the use of only a few RF chains at the FA users can significantly boost the SINR compared to state-of-the-art alternatives.

Notation: $a$ is a scalar, $\mathbf{a}$ is a vector, and $\mathbf{A}$ is a matrix. Transpose and conjugate transpose of $\mathbf{A}$ are denoted by $\mathbf{A}^{\operatorname{T}}$ and $\mathbf{A}^{\operatorname{H}}$, respectively. Calligraphic letters, e.g., $\mathcal{A}$ denote sets and sequences. $\mid\mathcal{A}\mid$ represents the set cardinality. Finally, the expectation operator is $\mathbb{E}\left\{\cdot\right\}$ and $\parallel\cdot\parallel_{p}$ denotes the $p$-norm.

II System Model

Let us consider a general MIMO system with a BS (BS) deploying $M$ antennas that serves $K$ users, each equipped with a FA array of $N$ ports capable of selecting $L$ active FA ports based on channel conditions. In coherence with the original formulation of slow-FAMA [4], we assume that the number of antennas at the BS $M$ and the number of users $K$ are equal, i.e., $M=K$.

We denote the data symbol intended for user $k$ as $z_{k}\in\mathbb{C}$ with $\mathbb{E}\left\{|z_{k}|^{2}\right\}=\sigma_{S}^{2}$ , so that the received signal at the $k$-th user can be written as:

$$\mathbf{x}_{k}=\mathbf{H}_{k}\mathbf{p}_{k}z_{k}+\sum_{j\neq k}\mathbf{H}_{k}\mathbf{p}_{j}z_{j}+\mathbf{n}_{k},$$ (1)

where $\mathbf{H}_{k}\in\mathbb{C}^{N\times M}$ is the channel matrix between the base station and user $k$, and $\mathbf{x}_{k}\in\mathbb{C}^{N\times 1}$ denotes the received signal vector at the FA-user side. As one of the key features of slow-FAMA is its simplicity, each of the transmit antennas is dedicated to a different user, i.e., no channel knowledge is required at the BS [4]. Accordingly, the precoding vector at the BS is simply set as $\mathbf{p}_{k}=\mathbf{e}_{k}$, where $\mathbf{e}_{k}$ is the $M$-dimension canonical vector with zero entries except for the $k$-th position. We consider that such $\mathbf{p}_{k}$ is given and fixed. Finally, $\mathbf{n}_{k}\in\mathbb{C}^{N\times 1}$ represents the additive Gaussian white noise vector whose elements have $\sigma^{2}$ power.

At the receiver side, each FA-equipped user selects the appropriate $L$ ports based on the user channel gain and interference. We model this feature by introducing the port selection matrix $\mathbf{S}_{k}\in\mathcal{B}$, with the set of matrices $\mathcal{B}:=\left\{\mathbf{Z}\in\{0,1\}^{N\times L},\|\mathbf{Z}\|_{0,\infty}\leq 1\right\}$. Moreover, the resulting signals from the $L$ ports can be coherently received by using the combiner $\mathbf{w}_{k}\in\mathbb{C}^{L}$, with $\|\mathbf{w}_{k}\|_{2}=1$, $\forall k$. As such, the received symbol results in

$$\hat{z}_{k}=\mathbf{w}_{k}^{H}\mathbf{S}_{k}^{T}\mathbf{x}_{k}.$$ (2)

From a channel modeling perspective, the fluid antenna array resembles a collection of co-located radiating elements, representing the ports where the fluid antenna can switch into. Thus, when considering the case of spatially correlated Rayleigh fading, the $m$-th column of the channel matrix $\mathbf{H}_{k}$ can be expressed as

$$\mathbf{h}_{k,m}\sim\mathcal{N}_{\mathbb{C}}(\mathbf{0},\boldsymbol{\Sigma}_{k}),$$ (3)

where the dependence on the port positions appears in the channel spatial correlation matrix $\boldsymbol{\Sigma}_{k}\in\mathbb{C}^{N\times N}$. In general, the structure of $\boldsymbol{\Sigma}_{k}$ is determined by the fluid antenna topology, i.e., the relative positions of the antenna ports within the overall aperture. For a 1D fluid antenna, Jakes’ correlation model is widely adopted. However, this model does not generalize properly to planar (2D) arrays with $N_{1}\times N_{2}$ ports. For such systems, we will employ Clarke’s model to define $\boldsymbol{\Sigma}_{k}$, considering $N=N_{1}\times N_{2}$ [9]. In all instances, we assume that the ports in each dimension are equally spaced and denote by $W$, (or equivalently $W_{1}\times W_{2}$), the length of the fluid antenna normalized by the wavelength.

To evaluate the performance of the proposed setup, we consider the SINR of each user, as follows

$$\text{SINR}_{k}=\frac{|\mathbf{w}_{k}^{H}\mathbf{S}_{k}^{T}\mathbf{H}_{k}\mathbf{p}_{k}|^{2}}{\sum_{j\neq k}|\mathbf{w}_{k}^{H}\mathbf{S}_{k}^{T}\mathbf{H}_{k}\mathbf{p}_{j}|^{2}+\frac{1}{\mathrm{SNR}}},$$ (4)

as it is directly related to the achievable SE (SE) $R_{k}$, with $\mathrm{SNR}=\sigma_{S}^{2}/\sigma^{2}$ being the transmit SNR. Thus, we define the problem formulation as follows

$$\underset{\{\mathbf{S}_{k}\in\mathcal{B},\mathbf{w}_{k}\}_{k=1}^{K}}{\text{max}}\quad \sum\nolimits_{k=1}^{K}R_{k}\;=\;\sum\nolimits_{k=1}^{K}\log_{2}\big{(}1+\text{SINR}_{k}\big{)}.$$ (5)

Since FAMA operates in open-loop, each user can design their corresponding $\mathbf{S}_{k}$ and $\mathbf{w}_{k}$ independently. From the perspective of the $k$-th user, the problem formulation requires the joint design of the port selection matrix $\mathbf{S}_{k}$ and the combining vector $\mathbf{w}_{k}$. The FAMA-based literature has primarily focused in the baseline case where $L=1$; hence, the usual strategy is to select the port that maximizes the SINR, and a trivial scalar value of one is used as the combining vector.

For the cases of CUMA using more than one RF chain [7], $\mathbf{S}_{k}$ and $\mathbf{w}_{k}$ are designed sequentially: first, the selection matrix is configured following a sign-based criterion for selecting a subset of ports for which the desired signal adds up constructively. Then, direct detection or matrix inversion-based strategies are proposed to implement $\mathbf{w}_{k}$. Taking a look at the related literature regarding classical antenna selection schemes, algorithms that avoid an exhaustive search over all candidate antenna subsets to design $\mathbf{S}_{k}$ are described, e.g. [10, 11, 12, 13]. In general, these approaches rewrite the performance metric $R_{k}$ by isolating the contribution of a particular column of the channel matrix. However, such formulations are well-suited for a single-user scenario, but cannot be adapted to the multi-user case in FAMA due to the inter-user interference term.

III SINR-based port selection and combining

In this section, we focus on the design of the selection matrix and the combining vector for a FA-based multiport receiver equipped with $L>1$ RF chains.

III-A Digital Combining

We first aim to generalize the port selection criterion in slow-FAMA to the case with $L$ active ports. Similar to [11, 13], we solve the problem formulation in (5) in two stages. First, we start by designing the matrix $\mathbf{S}_{k}$ following the slow FAMA heuristic in [4] (i.e., selecting the $L$ ports with the best SINR). Then, after the active ports are decided, we determine $\mathbf{w}_{k}$ aiming to maximize the SINR after combination. This scheme will be referred to as DC (DC).

Let us denote as $\mathbf{h}_{k,r}^{T}$ the $r$-th row of $\mathbf{H}_{k}$. Then, for the canonical precoding vectors $\mathbf{p}_{k}$ described in Sect. II, we can formulate the slow FAMA port selection procedure with $L$ ports as follows

$$\underset{\mathcal{N}_{k}\subset\{1,2,\dots,N\},\,|\mathcal{N}_{k}|=L}{\operatorname{arg\,max}}\sum_{r\in\mathcal{N}_{k}}\frac{|\mathbf{h}_{k,r}^{T}\mathbf{p}_{k}|^{2}}{\|\mathbf{h}_{k,r}\|_{2}^{2}-|\mathbf{h}_{k,r}^{T}\mathbf{p}_{k}|^{2}+\frac{1}{\mathrm{SNR}}}.$$ (6)

By finding the solution to this formulation, we build the selection matrix with the canonical vectors corresponding to the rows in $\mathcal{N}_{k}$, i.e. $\mathbf{S}_{k}=[\mathbf{e}_{\mathcal{N}_{k}(1)},\mathbf{e}_{\mathcal{N}_{k}(2)},\ldots,\mathbf{e}_{\mathcal{N}_{k}(L)}]$. For the given selection matrix $\mathbf{S}_{k}$, we need to design an adequate combining vector $\mathbf{w}_{k}$. This vector should increase the signal strength and, at the same time, reduce the inter-user interference. In other words, we aim to solve

$$\underset{\mathbf{w}_{k}}{\text{max}}\frac{\mathbf{w}_{k}^{H}\tilde{\mathbf{A}}_{k}\mathbf{w}_{k}}{\mathbf{w}_{k}^{H}\tilde{\mathbf{B}}_{k}\mathbf{w}_{k}},$$ (7)

where we introduced $\tilde{\mathbf{A}}_{k}=\mathbf{S}_{k}^{T}\mathbf{A}_{k}\mathbf{S}_{k}$ as a submatrix of $\mathbf{A}_{k}=\mathbf{H}_{k}\mathbf{p}_{k}\mathbf{p}_{k}^{H}\mathbf{H}_{k}^{H}$, and $\tilde{\mathbf{B}}_{k}=\mathbf{S}_{k}^{T}\mathbf{B}_{k}\mathbf{S}_{k}$ as a positive definite submatrix of $\mathbf{B}_{k}=\sum_{j\neq k}\mathbf{H}_{k}\mathbf{p}_{j}\mathbf{p}_{j}^{H}\mathbf{H}_{k}^{H}+\mathbf{I}_{R}/\mathrm{SNR}$. Due to $\mathbf{S}_{k}$, the selected row and column indices are common for both $\tilde{\mathbf{A}}_{k}$ and $\tilde{\mathbf{B}}_{k}$. Hence, finding the optimal combining vector $\mathbf{w}_{k}$ can be recast as a generalized eigenvalue problem [14], and solved by the dominant generalized eigenvector of the matrix pair $(\tilde{\mathbf{A}}_{k},\tilde{\mathbf{B}}_{k})$ [15]. In particular, note that defining the vector $\mathbf{x}_{k}=\tilde{\mathbf{B}}_{k}^{-1/2}\mathbf{w}_{k}$ we can find a solution using that $\mathbf{x}_{k}$ is the dominant eigenvector of $\tilde{\mathbf{C}}_{k}=\tilde{\mathbf{B}}_{k}^{-H/2}\tilde{\mathbf{A}}_{k}\tilde{\mathbf{B}}_{k}^{-1/2}$, and the achievable SINR for the $k$-th user is the associated dominant eigenvalue.

III-B Generalized Eigenvector Port Selection

The extension of the slow-FAMA port selection scheme to the multiport case from in (6) aims to select the most promising $L$ ports from the SINR perspective. However, under this criterion the effect of spatial correlation among ports is neglected in the process. In other words, DC selects isolated entries from $\mathbf{A}$ and $\mathbf{B}$, but the structure of such matrices is ignored. Besides, the sequential design of the selection matrix and the combining vector may not yield optimal performance. Hence, it is legitimate to ask whether some improvement over the DC scheme can be attained when these aspects are taken into consideration. In the sequel, for the sake of notational simplicity, the dependence on the user index $k$ is dropped.

We propose an alternative strategy that jointly designs $\mathbf{S}$ and $\mathbf{w}$, and exploits the spatial information provided by $\mathbf{A}$ and $\mathbf{B}$. This scheme will be referred to as GEPort (GEPort). Let us take as starting assumption that we can afford to select all $N$ ports at the FA. Then, let us evaluate what is the SINR loss introduced by switching off one of the $N$ available ports. This measure will be obtained by considering the SINRs related to the matrix entries as well as the matrix structures, potentially achieving improved system performance. We define the proposed metric in the following lemma.

Lemma 1.

Let $\mathbf{v}_{1},\mathbf{v}_{2},\ldots,\mathbf{v}_{N}$ be the generalized eigenvectors of the matrix pair $(\mathbf{A},\mathbf{B})$, associated with the corresponding generalized eigenvalues $\lambda_{1}\leq\lambda_{2}\dots\leq\lambda_{N}$, and $v_{N,l}$ the $l$-th element of $\mathbf{v}_{N}$. In addition, let $\alpha_{l,1}\leq\alpha_{l,2}\dots\leq\alpha_{l,N-1}$ be generalized eigenvalues of the matrix pair $(\tilde{\mathbf{A}}_{l},\tilde{\mathbf{B}}_{l})$ obtained by disabling the $l$-th port (i.e. removing row $l$ and column $l$ from $\mathbf{A}$ and $\mathbf{B}$). Then, the SINR drop $\delta_{l}$ due to deactivating port $l$ is given by

$$\delta_{l}=|v_{N,l}|^{2}(\lambda_{N}-\lambda_{N-1})\prod_{t=1}^{N-2}\frac{(\lambda_{N}-\lambda_{t})}{(\lambda_{N}-\alpha_{l,t})}.$$ (8)

Proof.

See Appendix. ∎

The result in Lemma (1) is useful to the discard the port that presents the lowest performance reduction. As we will later discuss, this process can be iterated until we reach the subset of $L$ ports with the lowest aggregate SINR loss. After observing Lemma (1), some relevant remarks are in order: Note that the first and third factors in (8) depend on the candidate port $l$. Unfortunately, the third factor includes $\alpha_{l,n}$ in the denominator, which is unknown unless the generalized eigenvalues of the reduced matrix pair $(\tilde{\mathbf{A}},\tilde{\mathbf{B}})$ are computed. Obtaining $\alpha_{l,t}$ $\forall l,t$ can be impractical when the number of ports $N$ grows large. To avoid this and reduce complexity, we can exploit the Cauchy interlacing theorem, which states that the eigenvalues of a Hermitian matrix interlace with those of any of its principal submatrices. Specifically, the eigenvalues of a matrix and a submatrix satisfy [16]

$$\lambda_{i+1}\geq\alpha_{l,i}\geq\lambda_{i},\;\forall i\in\{1,\ldots,N-1\},\;\forall l\in\{1,\ldots,N\}.$$ (9)

As such, all the differences in the product of the third factor (8) are positive valued, and the quotients for such a factor are smaller than or equal to $1$. Consequently, we set a lower bound for the SINR drop as follows

$$\delta_{l}\geq|v_{N,l}|^{2}(\lambda_{N}-\lambda_{N-1}).$$ (10)

Note also that the first factor $|v_{N,l}|^{2}$, which is given by the entries of the dominant generalized eigenvector of the complete matrix pair $(\mathbf{A},\mathbf{B})$, depends on $l$, while the remaining factor in (10) is equal for different ports. Moreover, when $|v_{N,l}|^{2}\approx 0$, the SINR drop satisfies $\delta_{l}\approx 0$ and deactivating the port $l$ has a negligible impact on the performance. As a consequence, we are interested in the index $l$ attaining the smallest value of $|v_{N,l}|^{2}$, potentially leading to a small performance reduction when the port $l$ becomes inactive.

Algorithm 1 Generalized Eigenvector Port Selection (GEPort)

1:  Initialization: $n\leftarrow 0$, $\mathcal{N}\leftarrow\emptyset$, $\tilde{\mathbf{A}}\leftarrow\mathbf{A},\tilde{\mathbf{B}}\leftarrow\mathbf{B}$

2:  while $N-n>L$ do

3:     $\mathbf{v}_{N-n}\leftarrow$ Power method for $(\tilde{\mathbf{A}},\tilde{\mathbf{B}})$

4:     $\lambda_{N-n}\leftarrow$ Compute with (12)

5:     $l^{*}\leftarrow\arg\min_{l}|v_{N-n,l}|^{2}$

6:     $\mathcal{N}\leftarrow\mathcal{N}\cup\{l^{*}\}$ 

7:     $\tilde{\mathbf{A}}\leftarrow$ Remove row and column $l^{*}$ from $\tilde{\mathbf{A}}$

8:     $\tilde{\mathbf{B}}\leftarrow$ Remove row and column $l^{*}$ from $\tilde{\mathbf{B}}$

9:     $\delta\leftarrow\lambda_{N}-\lambda_{N-n}$. Accumulated performance loss

10:     $n\leftarrow n+1$

11:  end while

12:  Return: $\mathbf{S}=[\mathbf{e}_{\mathcal{N}(1)},\mathbf{e}_{\mathcal{N}(2)},\ldots,\mathbf{e}_{\mathcal{N}(L)}]$, $\mathbf{w}=\mathbf{v}_{L}$

Recall that Lemma 1 considers the effect of removing the first port. As previously mentioned, the same idea can be repeated until the desired number of ports $L$ is selected. Alternatively, ports can be deactivated to achieve a desired spectral efficiency value or until a predefined performance reduction is attained. In particular, we propose a criterion for building the matrix $\mathbf{S}$ based on the iterative application of the result in Lemma 1 for the determination of the set $\mathcal{N}$. Hence, for the $n$-th step in the iteration procedure, we have that

$$\mathcal{N}=\mathcal{N}\cup\{l^{*}\}\;\text{s.t.}\;l^{*}=\arg\min_{l}|v_{N-n,l}|^{2},$$ (11)

where $\mathbf{v}_{N-n}$ is the dominant generalized eigenvector for the matrix pair $(\tilde{\mathbf{A}},\tilde{\mathbf{B}})$, which are obtained by removing the $n-1$ rows and the columns with indices belonging to the set $\mathcal{N}$, and $v_{N-n,l}$ is the $l$-th entry of such a vector. The procedure proposed to find the dominant generalized eigenvector $\mathbf{v}_{N}$ is the so-called power method [16], which starts with an initial candidate for the eigenvector, $\mathbf{t}$, and refines the current approximation using $\mathbf{t}=\tilde{\mathbf{B}}^{-1}\tilde{\mathbf{A}}\mathbf{t}$. Once $\mathbf{t}$ converges, the corresponding eigenvalue $\lambda_{N-n}$ is calculated as follows

$$\lambda_{N-n}=\frac{\mathbf{t}^{H}\tilde{\mathbf{A}}\mathbf{t}}{\mathbf{t}^{H}\tilde{\mathbf{B}}\mathbf{t}}.$$ (12)

This method is far more efficient than computing the full decomposition. The complete procedure for the GEPort algorithm to jointly select the $L$ ports and design $\mathbf{w}$ is summarized in Alg. 1.

IV Numerical Results

In this section, we conduct some experiments to assess the performance of the proposed schemes for multiport FAMA. Baseline parameters for the comparison are: $\sigma_{S}^{2}=1$, $M=K=4$ users/antennas at the BS side, a $W=4$ normalized fluid antenna length (1D case) and $W_{1}\times W_{2}=4\times 1$ (2D case), $N=100$ FA ports, and $L=2$ active ports. Monte Carlo simulations based on the channel model in (3) are used. For benchmarking purposes, we use the cases of conventional slow-FAMA [9] (single RF chain) and CUMA (2 RF chains)[7], and compare them with the DC and GEPort strategies here proposed.

In Fig. 1 we evaluate the improvements in terms of the achievable average SE of user $k$ for the aforementioned schemes, as a function of the transmit SNR. Solid lines represent the case of users equipped with a 1D FA ($N=100$, $W=4$), while dotted lines correspond to a 2D FA ($N=60\times 15$, $W=4\times 1$). We see that GEPort achieves the highest SINR across all SNR levels. More importantly, the performance improvement grows when the system operates in the interference-limited regime (i.e., high transmit SNR). Also, we see that in such a regime, DC behaves similarly as CUMA (even better for the 2D case). Note that while CUMA only operates with 2 RF chains, it requires an arbitrary number of ports to be activated for signal combination.

Figure 1: Average spectral efficiency for user $k$ vs. transmit SNR for the different schemes. Solid and dotted lines represent $N=100$ with $W=4$, and $N_{1}\times N_{2}=60\times 15$, with $W_{1}\times W_{2}=4\times 1$, respectively.

Fig. 2 shows the relationship between the average SE and the number of active ports, $L$. The transmit SNR is fixed and set to $5$dB. As the number of active ports increases (number of RF chains in the proposed schemes), the performance of DC and GEPort substantially improves. The conventional slow FAMA scheme uses single port (i.e., $L=1$); CUMA implementation used 2 RF chains (i.e., $L=2$ in our comparison), although it effectively activates a much larger of FA ports as long as the SINR is improved under this combination scheme. Hence, the SE curves associated to these methods are constant. Interestingly, the simpler DC combining method performs better than CUMA beyond $L=5$. Finally, the performance gap of GEPort compared to the reference schemes grows with the number of active ports for the ranges evaluated in our experiment.

Figure 2: Average spectral efficiency for user $k$ vs. number of active ports $L$. The number of ports is $N=100$ for a size of $W=4$. The transmit SNR is set to $5$dB.

Figure 3: Average spectral efficiency vs. number of available ports $N$. Parameter values are $W=4$, $L=2$ and SNR=$15$dB.

In Fig. 3 we evaluate the effect of densification in the performance, i.e., increasing $N$ for $W=4$ fixed. The simplest case of $L=2$ has been considered for benchmarking, with a transmit SNR=$15$ dB. We see that the effect of densification (i.e., increasing spatial correlation for the desired and interfering signals) affects the performance of the DC scheme: this confirms the rationale that the sequential design of the selection matrix $\mathbf{S}$ and the combining filter $\mathbf{w}$ (i.e., the multiport extension of slow-FAMA) does not optimally exploit the dependence structures between the matrices $\mathbf{A}$ and $\mathbf{B}$. Conversely, GEPort scheme provides a substantial improvement over all competing schemes, although this effect tends to saturate under strong port densification.

V Conclusion

We showcased the potential of multiport reception in FA-assisted multiuser communications. The use of a reduced number of RF chains opens the potential to substantially improve performance under the open-loop slow-FAMA paradigm, as long as the design of the port selection matrix and combining vectors effectively incorporates the correlation structures of signals. This paves the way for the development of new signal processing schemes in FA-enabled multiport receivers.