--- title: 'CUMA: Compact Ultra-Massive Antenna Array' url: https://www.emergentmind.com/topics/compact-ultra-massive-antenna-array-cuma type: topic --- # CUMA: Compact Ultra-Massive Antenna Array Searching arXiv for recent CUMA papers to ground the article. Compact ultra-massive antenna-array (CUMA) denotes a multiple access architecture built on the fluid antenna system (FAS) concept, in which a reconfigurable aperture with many candidate ports activates a selected subset of ports and superimposes their outputs with a single RF chain. In the formulations reported for wireless, cellular, and satellite settings, CUMA is positioned as an evolution of fluid antenna multiple access (FAMA), with the central mechanism being port selection based on the desired-link channel so that desired components combine coherently while interference aggregates largely non-coherently through random superposition [2509.20299]. Across the literature represented here, CUMA is studied as an open-loop or low-CSI multiple-access method, as an uplink combining architecture, and as a compact-array platform whose behavior is shaped by aperture geometry, port correlation, and, in some extensions, tightly coupled broadband array physics [2409.15164]. ## 1. Conceptual origin and defining architecture CUMA originates from the FAS paradigm, which treats the antenna as a reconfigurable physical resource. In the downlink multiuser setting, an FAS comprises a continuous aperture of size \(W_1\lambda\times W_2\lambda\) within which a small RF chain can switch to any of \(N=N_1\times N_2\) candidate ports. Each port samples the channel at a distinct spatial location, yielding \(N\) independent, albeit correlated, channel gains. In the original transition from FAMA to CUMA, the key change is that, instead of activating a single port per user, CUMA partitions all \(N\) ports into two complementary subsets and superimposes all ports in the better half-space [2509.20299]. This many-port activation rule is intended to amplify the desired signal linearly in the number of activated ports, while interfering users’ signals, being randomly signed across ports, aggregate only at their variance rate and thus partly self-cancel. The architecture is repeatedly characterized by low RF-chain count: in the baseline downlink description, CUMA requires one RF chain per user; in the satellite uplink formulation, each fluid antenna similarly uses only one RF chain while activating a subset \(\mathcal K\) of ports and summing their baseband signals [2604.23891]. The baseline multiuser interpretation is open-loop. A multi-antenna BS with \(N_t\) antennas serves \(U\) UEs in the same time-frequency resource, and no CSI is required at the BS; instead, the BS employs random unit-norm beamforming vectors and performs no per-user power control or precoding. At the UE, ports are grouped so that in-phase and quadrature components add coherently, and the resulting signal-to-interference ratio is analyzed in the interference-limited regime [2409.15164]. This suggests that CUMA occupies a design space distinct from conventional multiuser MIMO, where scaling to hundreds or thousands of users would otherwise demand many RF chains, complex precoding, or SIC. ## 2. System models and port-selection rules In the downlink system model, user \(u\) is equipped with an FAS of aperture \(W_1\lambda\times W_2\lambda\) and \(N\) discrete ports, while the BS has \(N_t\ge U\) fixed antennas. Let \(\mathbf{H}_u\in\mathbb C^{N\times N_t}\) be the BS–FAS channel matrix, \(\mathbf f_v\in\mathbb C^{N_t}\) the beamforming vector for user \(v\), and \(\mathbf A_u\in\{0,1\}^{N\times M}\) the port-activation matrix selecting \(M\) active ports out of \(N\). The post-combiner received signal is given as \[ y_u = \underbrace{\mathbf A_u^T\,\mathbf H_u\,\mathbf f_u\,s_u}_{\text{desired} \;+\;\underbrace{\sum_{v\neq u}\mathbf A_u^T\,\mathbf H_u\,\mathbf f_v\,s_v}_{\text{interference} \;+\;n_u. \] With per-port channel vectors \(\mathbf h_{v,u}=\mathbf H_u\,\mathbf f_v\in\mathbb C^N\), the single-RF-chain CUMA output simplifies to \[ y_u = \Bigl(\sum_{k\in\mathcal K_u}h^{(k)}_{u,u}\Bigr)s_u + \sum_{v\neq u}\Bigl(\sum_{k\in\mathcal K_u}h^{(k)}_{v,u}\Bigr)s_v + n_u. \] Original CUMA defines \[ \mathcal K_u^+ = \{\,k: \Re\{h^{(k)}_{u,u}\}\ge 0\},\quad \mathcal K_u^- = \{\,k: \Re\{h^{(k)}_{u,u}\}< 0\}, \] and selects the sign-group with larger aggregate real gain. If \(X_k=\Re\{h_{u,u}^{(k)}\}\) and \(X_k^+=\max\{X_k,0\}\), then the desired-signal power is \[ \alpha_u =\Bigl\lvert\sum_{k\in\mathcal K_u}h_{u,u}^{(k)}\Bigr\rvert^2 =\Bigl(\sum_{k=1}^N X_k^+\Bigr)^2, \] while the interference power \(\beta_u=\sum_{v\neq u}\lvert\sum_{k\in\mathcal K_u}h^{(k)}_{v,u}\rvert^2\) grows only linearly with \(|\mathcal K_u|\), giving instantaneous SIR \(z_u=\alpha_u/\beta_u\) [2509.20299]. A closely related sign-based rule appears in the uplink cellular formulation. There, each BS is equipped with a two-dimensional FAS of physical size \(W_1\times W_2\) and \(N=N_1\cdot N_2\) candidate ports, with at most \(M\le N\) activated ports. For a desired UE \(u\), the BS forms \[ K_u^+ = \{n: \Re\{h_u(n)\} \ge 0\}, \qquad K_u^- = \{n: \Re\{h_u(n)\} < 0\}, \] and selects the group with larger total in-phase amplitude \(\sum_{n\in K}|\Re\{h_u(n)}|\); all its ports are then activated, and no knowledge of inter-cell interference is required [2605.23366]. In the satellite uplink LoS scenario, the same principle is expressed through \[ \mathcal K_1=\{\,k: \Re\{h_{u,k}\}>0\}, \] where each desired-user channel follows a known phase progression across the 1-D fluid-antenna line. The normalized desired and interference powers are \[ \alpha_I=\Bigl[\sum_{k\in\mathcal K_1}\Re\{h_{u,k}\}\Bigr]^2, \qquad Y_{\tilde u}=\Bigl[\sum_{k\in\mathcal K_1}\Re\{h_{\tilde u,k}\}\Bigr]^2, \] with \(\beta_I=\sum_{\tilde u\ne u}Y_{\tilde u}\) and \[ \mathrm{SINR}_I=\frac{\alpha_I}{\beta_I+\frac{|\mathcal K_1|}{2\,\Gamma}}. \] Across these settings, the common structural idea is coherent superposition of a desired-signal-selected subset, using only desired-link information [2604.23891]. ## 3. Geometric and statistical refinements of port selection The principal refinement of original CUMA port selection is the replacement of the fixed real-axis partition by adaptive geometric partitioning. In the geometric formulation, each port is represented in two real dimensions by \[ \mathbf g_{u,u,k}=[\Re\{h_{u,u}^{(k)}\},\;\Im\{h_{u,u}^{(k)}\}]^T, \] and projected onto a unit vector \(\mathbf c\in\mathbb R^2\). The resulting half-space partition is \[ \mathcal K_{u,1}(\mathbf c)=\{k:\mathbf g_{u,u,k}^T\mathbf c\ge0\},\quad \mathcal K_{u,2}(\mathbf c)=\{k:\mathbf g_{u,u,k}^T\mathbf c<0\}. \] The exact optimal half-space (EOHS) rule chooses the projection direction that maximizes the instantaneous signal build-up: \[ \mathbf c^\star =\arg\max_{\|\mathbf c\|=1} \;\sum_{k=1}^N\bigl[\max\{0,\mathbf g_{u,u,k}^T\mathbf c\}\bigr]. \] In polar form, with \(\mathbf c=[\cos\theta,\sin\theta]^T\), this becomes \[ \max_{\theta\in[0,2\pi)} f(\theta) =\sum_{k=1}^N\max\{w_k\cos(\theta-\phi_k),\,0\}, \] where \(\phi_k=\arg(\mathbf g_{u,u,k})\) and \(w_k=\|\mathbf g_{u,u,k}\|\). The function \(f(\theta)\) is piecewise unimodal between the \(2N\) boundary angles \(\phi_k\pm\pi/2\), and the global maximizer lies among those boundaries or at a unique interior peak per segment. Enumerating these \(O(N)\) candidate \(\theta\) yields an exact solution with complexity \(O(N^2)\) per block [2509.20299]. A lower-complexity alternative is based on principal component analysis. With \[ V=[\mathbf g_{u,u,1},\dots,\mathbf g_{u,u,N}]^T, \] the \(2\times2\) covariance matrix \(R=V^TV\) is formed, and \(\mathbf c_{\rm PCA}\) is chosen as the eigenvector of \(R\) associated with its largest eigenvalue. Ports are then partitioned by the sign of \(\mathbf g_{u,u,k}^T\mathbf c_{\rm PCA}\), and the half-space with larger aggregate projected magnitude is selected. Forming \(R\) costs \(O(N)\), while the \(2\times2\) eigendecomposition is constant-cost. The resulting method is therefore an \(O(N)\) approximation to EOHS with near-optimal performance [2509.20299]. These refinements are significant because original CUMA fixes the partition at the real axis and therefore does not fully exploit instantaneous channel geometry. The geometric formulation shows that CUMA port selection can be interpreted as a half-space partitioning problem in the real-imaginary plane. A plausible implication is that the performance of CUMA depends not only on the number of ports and aperture size but also on the alignment between channel-vector geometry and the selected projection direction. ## 4. Statistical analysis, asymptotics, and closed-form performance characterizations CUMA has motivated several analytical frameworks because the exact distributions of the combined desired and interference terms are mathematically intricate. Under the PCA-based scheme, and analogously under any fixed \(\mathbf c\), define \[ X_k=\mathbf g_{u,u,k}^T\mathbf c,\quad X_k^+=\max\{X_k,0\},\quad Y_k^{(i)}=\mathbf g_{i,u,k}^T\mathbf c,\;i\ne u. \] Then \[ \alpha=\Bigl(\sum_{k=1}^NX_k^+\Bigr)^2,\qquad \beta=\sum_{i\neq u}\Bigl|\sum_{k=1}^Nt_kY_k^{(i)}\Bigr|^2, \] where \(t_k\in\{0,1\}\) is the random sign-selection indicator. For large \(N\) and \(U\), a central-limit argument gives \(\sqrt\alpha\sim\mathcal N(\mu_1,\sigma_1^2)\), with \[ \mu_1 =N\E[X_k^+] =N\sqrt{\frac{\delta\,\Omega}{2\pi},\quad \sigma_1^2 =\mathrm{Var}\!\Bigl(\sum_{k=1}^NX_k^+\Bigr), \] while \(\beta\) is chi-square with \(I=U-1\) degrees of freedom and scale \(\sigma_2^2\). The normalized SIR \(z=\alpha/\beta\) then admits a closed-form PDF involving Whittaker’s \(M\)-function and hypergeometric functions, with normalization constant \[ C_{\rm norm} =\Gamma\bigl(\tfrac I2\bigr)\big/\Bigl[\sqrt\pi\, e^{\mu_1^2/(2\sigma_1^2)}\sqrt{1-\mu_1^2/(2\sigma_1^2)}\Bigr]. \] This tractable form permits fast numerical integration of ergodic rate, BER, and outage [2509.20299]. A different asymptotic strategy is used for reliable and secure communications analysis. There, exact SIR expressions involve Whittaker-\(M\) functions and multi-fold sums over correlations, so an Asymptotic Matching (AoM) method is applied. The in-phase SIR PDF is approximated by a Gamma law with \(\alpha_I=\tfrac12\), and because the in-phase and quadrature SIRs are i.i.d. Gamma\((\tfrac12,\beta_I)\), their sum is Gamma\((1,\beta_I)\). Hence \[ f_Z(z)\approx\frac{1}{\beta_I}e^{-z/\beta_I},\quad F_Z(z)\approx1-\Gamma\bigl(1,z/\beta_I\bigr). \] This directly yields closed-form approximations for ergodic rate and outage probability [2409.15164]. In the uplink cellular network setting, the analysis is framed by stochastic geometry. BS and UE locations are modeled as independent homogeneous PPPs of densities \(\lambda_b\) and \(\lambda_u\), and under nearest-BS association the serving distance has PDF \[ f_{R_0}(r)=2\pi\lambda_b r \exp(-\pi\lambda_b r^2). \] Conditioned on \(R_0=r\), the desired signal \(S\) is approximated as Gamma\((m(r),\theta_s(r))\), with moment-matched \[ E\{S|r\}= \ell(r)\cdot(\bar\mu_1+\bar\sigma_1)\cdot M, \qquad \mathrm{Var}\{S|r\}=\ell(r)^2\cdot[2\bar\sigma_1^2+4\bar\mu_1\bar\sigma_1]\cdot M. \] The aggregate interference Laplace transform is \[ \mathcal L_I(s)=\exp\{-4\pi\lambda_u\cdot\Gamma(1-2/\eta)\Gamma(1+2/\eta)/(\eta)\cdot s^{2/\eta}\}, \] and a tight approximation to the coverage probability follows via Alzer’s inequality [2605.23366]. In the satellite setting, closed-form distributions are derived directly under LoS. Let \(V=\frac{\sin(\pi/\mu)}{W}\). Then \[ \alpha_I=\zeta_u V^2\cos^2(X),\quad X\sim\mathcal U\Bigl(-\tfrac\pi\mu,\tfrac\pi\mu\Bigr), \] with a corresponding PDF on \[ \alpha\in\Bigl[\zeta_u\,V^2\cos^2(\tfrac\pi\mu),\,\zeta_u\,V^2\Bigr]. \] Each interferer’s normalized power \(Y_{\tilde u}\) has the same form with \(\zeta_u\to\zeta_{\tilde u}\), and for large \(U\), \(\beta_I\) concentrates into a truncated Gaussian by CLT [2604.23891]. ## 5. Networked, satellite, and secure-communication regimes The network-level role of CUMA differs across terrestrial cellular, satellite, and physical-layer security formulations, but all retain the premise that only desired-link CSI is needed for port selection. In uplink cellular networks, CUMA is analyzed in an interference-dominated regime where interference CSI is rarely available at scale. The received-signal vector from UE \(u\) is \[ h_u = \sqrt{\beta_u}\,g_u,\qquad \beta_u=R_u^{-\eta}, \] with \(g_u\sim\mathbb C\mathcal N(0,J)\) and spatial correlation \[ [J]_{k,\ell} = J_0\bigl(2\pi\cdot|d_1(n_1-m_1)/N_1 + d_2(n_2-m_2)/N_2|/\lambda\bigr). \] The post-combining SIR is \[ \gamma = S/I,\qquad S=|w_0^H h_0|^2,\qquad I=\sum_{v\in\Phi_u\setminus\{0\}} |w_0^H h_v|^2. \] The analysis emphasizes how \(N\), \(M\), the Bessel-type correlation in \(J\), and network densification shape coverage probability, average user rate, and cell sum-rate. Increasing \(N\) improves selection gain, but correlation causes non-monotonic fluctuations in \(P_c(\theta)\) for large apertures; larger \(M\) yields higher coherent gain but also mild interference growth; and in dense deployments, smaller \(M\) is favored to limit intra-cell interference [2605.23366]. In satellite communications, CUMA is studied for uplink transmission where all ground users share the same satellite. The system is modeled with a 1-D line of length \(W\lambda\) containing \(K\) electrically movable ports, port density \(\mu=(K-1)/W\), and LoS channels \[ h_{\tilde u,k}\approx\sqrt{\zeta_{\tilde u}\;e^{j\bigl(\psi_{\tilde u}+2\pi\upsilon\,\mu(k-1)\bigr)}, \] with \(\psi_{\tilde u}\sim\mathcal U[0,2\pi)\). The analysis identifies a deterministic-signal regime: for very compact array (\(\mu\to\infty\)), \(V\to0\) and \(\cos^2(X)\approx1\), so \(\alpha_I\approx\zeta_uV^2\) becomes nearly constant. Increasing the number of ports yields a linear beamforming gain, and a criterion is given for when CUMA exceeds MRC in the noise-limited case: \[ 4\frac{K-1}{\pi^2}>M \quad\Longleftrightarrow\quad K>\frac{\pi^2}{4}\,M+1. \] The same study compares orthogonal and non-orthogonal multiple access variants, stating that under wideband conditions the non-orthogonal form achieves superior performance [2604.23891]. In physical-layer security analysis, CUMA is shown to have a structural limitation when eavesdroppers are equipped with the same type of CUMA. With \(U_E=U\) eavesdroppers and main/eavesdropper SIRs \(Z_B,Z_E\), the secrecy outage probability for target secrecy rate \(R_s\) is \[ \mathrm{SOP} =\Pr\{\log_2(1+Z_B)-\log_2(1+Z_E)10\) or when \(\eta>3\). Simulations at carrier \(f=4\) GHz, \(W_1=W_2=10\lambda\), \(\eta\in\{2.4,2.7\}\), \(N=144\), and \(M=\lceil1.5\Lambda\rceil\) show that CUMA outperforms SISO and fixed-antenna MRC/ZF under limited CSI, reaches within 10% of idealized full-CSI MMSE for \(\Lambda\le6\), and is only slightly below a locally optimized movable-antenna-plus-beamforming baseline that requires vastly greater computational and CSI overhead [2605.23366]. In the secure-communications study, numerical settings include UE aperture \(15\rm\,cm\times8\rm\,cm\), port spacings \(0.5\lambda\), \(0.1\lambda\), and \(0.05\lambda\), and frequencies \(6\), \(26\), and \(40\) GHz. Very-compact FAS spacing is identified as key to maximizing CUMA’s multiuser gains. Ergodic rate grows nearly linearly with \(U\), outage probability degrades with increasing \(U\) but is mitigated by denser ports, and higher frequencies further push down outage because they imply more ports for the fixed aperture. If secrecy is required, either Eve’s CUMA must be sparser than Bob’s or Bob must employ partial interference cancellation [2409.15164]. For satellite CUMA, the numerical findings emphasize port density rather than physical size: at fixed \(K\), increasing array length \(W\) and thereby lowering \(\mu\) worsens performance; steep reductions in outage occur as \(\mu\) grows; and in the wideband regime, non-orthogonal CUMA surpasses orthogonal CUMA in ergodic sum-rate. The same study states that with sufficiently compact fluid antenna configurations the received signal becomes deterministic, indicating that performance is dominated by interference statistics [2604.23891]. ## 7. Relation to ultra-large and super-wideband compact-array research CUMA is not identical to the terahertz ultra-large antenna array and tightly coupled massive MIMO frameworks, but the cited literature places it in close conceptual proximity to both. In THz ultra-large antenna arrays, cross far- and near-field operation is addressed by a hybrid spherical- and planar-wave model (HSPM), subarray-based sparse channel estimation, and widely-spaced multi-subarray hybrid beamforming. The exact spherical-wave model uses \[ h_{q,p}[m,n] = \alpha_\ell\cdot(\lambda/4\pi d_{mn,\ell})\cdot e^{-j k d_{mn,\ell}}, \] while the HSPM keeps inter-subarray propagation spherical and approximates intra-subarray phase by a planar-wave steering vector. The Rayleigh distance is \[ r_B = 2S^2/\lambda, \] and the approximation error \[ \epsilon(d) = \|H_{\rm PWM}(d)-H_{\rm SWM}(d)\|_F^2/\|H_{\rm SWM}(d)\|_F^2 \] tends to zero as \(d\gg r_B\). For channel estimation, vectorization yields \[ \mathrm{vec}(H)\approx (A_T^{\rm sub *}\otimes A_R^{\rm sub})x,\qquad \|x\|_0=L, \] and CS reconstruction can use OMP or LASSO, with separate-side estimation and dictionary-shrinkage estimation reducing complexity and overhead. For beamforming, the spectral-efficiency objective is \[ R = \log_2\det\!\Bigl(I + (1/\sigma_n^2)H F_{\rm RF}F_{\rm BB}F_{\rm BB}^H F_{\rm RF}^H H^H\Bigr), \] and a widely spaced multi-subarray system can achieve \(R_{\rm WSMS}/R_{\rm compact}\approx3.2\times\) at \(D=128\lambda\), \(P=4\), and \(15\) dBm [2301.03035]. This THz ULAA framework is presented in the source material as a basis for “cross-field CUMA systems.” A plausible implication is that future CUMA realizations in THz regimes may require subarray-aware channel models and estimation algorithms rather than solely the port-domain stochastic models used in sub-6-GHz and generic Rayleigh settings. A second neighboring line of work concerns super-wideband massive MIMO based on tightly coupled arrays. There, a physically consistent multi-port circuit-theoretic model is used to show that tight mutual coupling can widen operational bandwidth and produce a “bandwidth gain.” For canonical minimum-scattering Chu antennas, tight coupling can dramatically lower the effective \(Q\)-factor of the array, and in the asymptotic colinear ULA limit the purely resistive condition yields \[ \boxed{(\delta/a)^*=\sqrt[3]{6\,\zeta(3)}\approx1.932.} \] The achievable spectral efficiency is written as \[ C=\max_{\{P_r(f)\}} \sum_{r=1}^R \int \log_2\!\bigl(1+P_r(f)\lambda_r(f)\bigr)\,df, \] with water-filling \[ P_r^\star(f)=\Bigl[\tfrac1\nu-\tfrac1{\lambda_r(f)}\Bigr]^+. \] Numerically, colinear tight coupling is reported to widen the SNR curve and boost capacity by 20–50% over 100 MHz–30 GHz [2208.01556]. Although this work is not a CUMA paper in the narrow sense, the supplied technical summary explicitly frames it as guidance for super-wideband CUMA design. This suggests that compact ultra-massive arrays may eventually be analyzed not only through port-selection statistics but also through broadband multi-port network theory, especially when compactness pushes mutual coupling beyond the assumptions implicit in conventional FAS channel models. Source: https://www.emergentmind.com/topics/compact-ultra-massive-antenna-array-cuma