CUMA: Compact Ultra-Massive Antenna Array

• CUMA is defined as a reconfigurable fluid antenna array that activates selected ports to coherently amplify desired signals while minimizing interference through non-coherent aggregation.
• It employs adaptive port-selection methods, including exact optimal half-space (EOHS) and PCA-based rules, to maximize instantaneous signal gain with low computational complexity.
• Analytical models for CUMA cover wireless, cellular, satellite, and secure communications, offering closed-form SIR analyses, outage approximations, and scalable multiuser performance insights.

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 (Rao et al., 24 Sep 2025). 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 (Vega-Sánchez et al., 2024).

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 (Rao et al., 24 Sep 2025).

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 (Han et al., 26 Apr 2026).

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 (Vega-Sánchez et al., 2024). 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=N_1\times N_2$0 fixed antennas. Let $N=N_1\times N_2$1 be the BS–FAS channel matrix, $N=N_1\times N_2$2 the beamforming vector for user $N=N_1\times N_2$3, and $N=N_1\times N_2$4 the port-activation matrix selecting $N=N_1\times N_2$5 active ports out of $N=N_1\times N_2$6. The post-combiner received signal is given as

$N=N_1\times N_2$7

With per-port channel vectors $N=N_1\times N_2$8, the single-RF-chain CUMA output simplifies to

$N=N_1\times N_2$9

Original CUMA defines

$N$0

and selects the sign-group with larger aggregate real gain. If $N$1 and $N$2, then the desired-signal power is

$N$3

while the interference power $N$4 grows only linearly with $N$5, giving instantaneous SIR $N$6 (Rao et al., 24 Sep 2025).

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 $N$7 and $N$8 candidate ports, with at most $N$9 activated ports. For a desired UE $N$0, the BS forms

$N$1

and selects the group with larger total in-phase amplitude $N$2; all its ports are then activated, and no knowledge of inter-cell interference is required (Rao et al., 22 May 2026).

In the satellite uplink LoS scenario, the same principle is expressed through

$N$3

where each desired-user channel follows a known phase progression across the 1-D fluid-antenna line. The normalized desired and interference powers are

$N$4

with $N$5 and

$N$6

Across these settings, the common structural idea is coherent superposition of a desired-signal-selected subset, using only desired-link information (Han et al., 26 Apr 2026).

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

$N$7

and projected onto a unit vector $N$8. The resulting half-space partition is

$N$9

The exact optimal half-space (EOHS) rule chooses the projection direction that maximizes the instantaneous signal build-up: $\mathcal K$0 In polar form, with $\mathcal K$1, this becomes

$\mathcal K$2

where $\mathcal K$3 and $\mathcal K$4. The function $\mathcal K$5 is piecewise unimodal between the $\mathcal K$6 boundary angles $\mathcal K$7, and the global maximizer lies among those boundaries or at a unique interior peak per segment. Enumerating these $\mathcal K$8 candidate $\mathcal K$9 yields an exact solution with complexity $N_t$0 per block (Rao et al., 24 Sep 2025).

A lower-complexity alternative is based on principal component analysis. With

$N_t$1

the $N_t$2 covariance matrix $N_t$3 is formed, and $N_t$4 is chosen as the eigenvector of $N_t$5 associated with its largest eigenvalue. Ports are then partitioned by the sign of $N_t$6, and the half-space with larger aggregate projected magnitude is selected. Forming $N_t$7 costs $N_t$8, while the $N_t$9 eigendecomposition is constant-cost. The resulting method is therefore an $U$0 approximation to EOHS with near-optimal performance (Rao et al., 24 Sep 2025).

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 $U$1, define

$U$2

Then

$U$3

where $U$4 is the random sign-selection indicator. For large $U$5 and $U$6, a central-limit argument gives $U$7, with

$U$8

while $U$9 is chi-square with $u$0 degrees of freedom and scale $u$1. The normalized SIR $u$2 then admits a closed-form PDF involving Whittaker’s $u$3-function and hypergeometric functions, with normalization constant

$u$4

This tractable form permits fast numerical integration of ergodic rate, BER, and outage (Rao et al., 24 Sep 2025).

A different asymptotic strategy is used for reliable and secure communications analysis. There, exact SIR expressions involve Whittaker-$u$5 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 $u$6, and because the in-phase and quadrature SIRs are i.i.d. Gamma$u$7, their sum is Gamma$u$8. Hence

$u$9

This directly yields closed-form approximations for ergodic rate and outage probability (Vega-Sánchez et al., 2024).

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 $W_1\lambda\times W_2\lambda$0 and $W_1\lambda\times W_2\lambda$1, and under nearest-BS association the serving distance has PDF

$W_1\lambda\times W_2\lambda$2

Conditioned on $W_1\lambda\times W_2\lambda$3, the desired signal $W_1\lambda\times W_2\lambda$4 is approximated as Gamma$W_1\lambda\times W_2\lambda$5, with moment-matched

$W_1\lambda\times W_2\lambda$6

The aggregate interference Laplace transform is

$W_1\lambda\times W_2\lambda$7

and a tight approximation to the coverage probability follows via Alzer’s inequality (Rao et al., 22 May 2026).

In the satellite setting, closed-form distributions are derived directly under LoS. Let $W_1\lambda\times W_2\lambda$8. Then

$W_1\lambda\times W_2\lambda$9

with a corresponding PDF on

$N$0

Each interferer’s normalized power $N$1 has the same form with $N$2, and for large $N$3, $N$4 concentrates into a truncated Gaussian by CLT (Han et al., 26 Apr 2026).

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 $N$5 is

$N$6

with $N$7 and spatial correlation

$N$8

The post-combining SIR is

$N$9

The analysis emphasizes how $N=N_1\times N_2$00, $N=N_1\times N_2$01, the Bessel-type correlation in $N=N_1\times N_2$02, and network densification shape coverage probability, average user rate, and cell sum-rate. Increasing $N=N_1\times N_2$03 improves selection gain, but correlation causes non-monotonic fluctuations in $N=N_1\times N_2$04 for large apertures; larger $N=N_1\times N_2$05 yields higher coherent gain but also mild interference growth; and in dense deployments, smaller $N=N_1\times N_2$06 is favored to limit intra-cell interference (Rao et al., 22 May 2026).

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 $N=N_1\times N_2$07 containing $N=N_1\times N_2$08 electrically movable ports, port density $N=N_1\times N_2$09, and LoS channels

$N=N_1\times N_2$10

with $N=N_1\times N_2$11. The analysis identifies a deterministic-signal regime: for very compact array ($N=N_1\times N_2$12), $N=N_1\times N_2$13 and $N=N_1\times N_2$14, so $N=N_1\times N_2$15 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: $N=N_1\times N_2$16 The same study compares orthogonal and non-orthogonal multiple access variants, stating that under wideband conditions the non-orthogonal form achieves superior performance (Han et al., 26 Apr 2026).

In physical-layer security analysis, CUMA is shown to have a structural limitation when eavesdroppers are equipped with the same type of CUMA. With $N=N_1\times N_2$17 eavesdroppers and main/eavesdropper SIRs $N=N_1\times N_2$18, the secrecy outage probability for target secrecy rate $N=N_1\times N_2$19 is

$N=N_1\times N_2$20

with $N=N_1\times N_2$21. Under the Gamma approximations, a lower bound becomes

$N=N_1\times N_2$22

When Bob and Eve have identical CUMA parameters, $N=N_1\times N_2$23, producing a non-vanishing secrecy outage floor. The proposed remedy is imperfect interference cancellation at the legitimate receiver, modeled by $N=N_1\times N_2$24, which reduces Bob’s effective $N=N_1\times N_2$25 relative to Eve’s (Vega-Sánchez et al., 2024).

6. Performance, complexity, and implementation-oriented design considerations

The performance-complexity trade-off is a recurring theme in the CUMA literature. For geometric port selection, EOHS requires enumerating up to $N=N_1\times N_2$26 candidate angles, each costing $N=N_1\times N_2$27 to evaluate, for overall $N=N_1\times N_2$28. The PCA scheme requires one $N=N_1\times N_2$29 matrix multiply, $N=N_1\times N_2$30, plus a constant-cost $N=N_1\times N_2$31 eigendecomposition. Across user densities $N=N_1\times N_2$32, port counts $N=N_1\times N_2$33, and aperture sizes $N=N_1\times N_2$34, both EOHS and PCA yield 20–40% higher per-user rates, 2–10 dB lower BER, and orders-of-magnitude lower outage than conventional CUMA; PCA tracks EOHS within 1–2% of rate while incurring only a small fraction of the computational cost. Even against a two-RF-chain CUMA benchmark, PCA closes over 70% of the gap (Rao et al., 24 Sep 2025).

For network-level cellular design, practical guidance is explicit. One recommendation is to choose $N=N_1\times N_2$35 large enough, specifically $N=N_1\times N_2$36, to justify Gaussian approximations, while performing coarse sweeps over aperture $N=N_1\times N_2$37 to locate favorable apertures because of correlation-induced oscillations. Suggested operating points are $N=N_1\times N_2$38 for typical $N=N_1\times N_2$39, with smaller $N=N_1\times N_2$40 preferred when $N=N_1\times N_2$41 or when $N=N_1\times N_2$42. Simulations at carrier $N=N_1\times N_2$43 GHz, $N=N_1\times N_2$44, $N=N_1\times N_2$45, $N=N_1\times N_2$46, and $N=N_1\times N_2$47 show that CUMA outperforms SISO and fixed-antenna MRC/ZF under limited CSI, reaches within 10% of idealized full-CSI MMSE for $N=N_1\times N_2$48, and is only slightly below a locally optimized movable-antenna-plus-beamforming baseline that requires vastly greater computational and CSI overhead (Rao et al., 22 May 2026).

In the secure-communications study, numerical settings include UE aperture $N=N_1\times N_2$49, port spacings $N=N_1\times N_2$50, $N=N_1\times N_2$51, and $N=N_1\times N_2$52, and frequencies $N=N_1\times N_2$53, $N=N_1\times N_2$54, and $N=N_1\times N_2$55 GHz. Very-compact FAS spacing is identified as key to maximizing CUMA’s multiuser gains. Ergodic rate grows nearly linearly with $N=N_1\times N_2$56, outage probability degrades with increasing $N=N_1\times N_2$57 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 (Vega-Sánchez et al., 2024).

For satellite CUMA, the numerical findings emphasize port density rather than physical size: at fixed $N=N_1\times N_2$58, increasing array length $N=N_1\times N_2$59 and thereby lowering $N=N_1\times N_2$60 worsens performance; steep reductions in outage occur as $N=N_1\times N_2$61 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 (Han et al., 26 Apr 2026).

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

$N=N_1\times N_2$62

while the HSPM keeps inter-subarray propagation spherical and approximates intra-subarray phase by a planar-wave steering vector. The Rayleigh distance is

$N=N_1\times N_2$63

and the approximation error

$N=N_1\times N_2$64

tends to zero as $N=N_1\times N_2$65. For channel estimation, vectorization yields

$N=N_1\times N_2$66

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

$N=N_1\times N_2$67

and a widely spaced multi-subarray system can achieve $N=N_1\times N_2$68 at $N=N_1\times N_2$69, $N=N_1\times N_2$70, and $N=N_1\times N_2$71 dBm (Han et al., 2023).

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 $N=N_1\times N_2$72-factor of the array, and in the asymptotic colinear ULA limit the purely resistive condition yields

$N=N_1\times N_2$73

The achievable spectral efficiency is written as

$N=N_1\times N_2$74

with water-filling

$N=N_1\times N_2$75

Numerically, colinear tight coupling is reported to widen the SNR curve and boost capacity by 20–50% over 100 MHz–30 GHz (Akrout et al., 2022).

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.