Capacity-Optimized Antenna Selection (COAS)

• Capacity-Optimized Antenna Selection (COAS) is a technique that selects the optimal antenna subset to maximize system capacity using instantaneous or statistical CSI.
• It leverages greedy, submodular, and learning-based algorithms to balance performance gains with the inherent complexity of combinatorial subset selection.
• COAS extends to joint designs with RIS, fluid-MIMO, and hardware-aware methods, enhancing capacity in diverse large-scale MIMO applications.

Capacity-Optimized Antenna Selection (COAS) denotes antenna-subset selection that maximizes a capacity metric under a cardinality or structural constraint. In the classical sense, COAS typically means choosing the antenna subset that maximizes capacity or sum-rate based on instantaneous channel state information (CSI); in broader formulations, the same capacity-maximization principle is extended to ergodic throughput, statistical-CSI-based selection, joint transmit-and-receive port selection, and antenna selection coupled with precoding or reconfigurable intelligent surface (RIS) phase design (Ouyang et al., 2022, Ouyang et al., 2022, Efrem et al., 2024).

1. Canonical optimization problem

In its canonical receive-selection form, COAS appears as the problem of selecting $L$ antennas from $N$ candidates so as to maximize the uplink sum-rate. For a multiuser massive MIMO uplink with full-array switching (FAS), the exact optimization is

$$\overline{\mathbf G}_{\rm opt} =\arg\max_{\overline{\mathbf G}\in\mathcal S} \log_2\det\!\left(\mathbf I_L+\rho_u\overline{\mathbf G}\,\overline{\mathbf G}^{\mathsf H}\right),$$

where $\mathcal S$ is the set of all $\binom{N}{L}$ possible antenna subsets. This optimization is NP-hard, and exhaustive search has complexity $\mathcal O(N^L)$ (Ouyang et al., 2022).

The same capacity-maximizing logic recurs in broader architectures. In RIS-assisted massive MIMO, the active BS antenna subset $\mathcal S$ is selected jointly with the RIS reflection matrix $\bm\Theta$ through

$$\max_{\mathcal S\subseteq \mathcal L,\ \bm\Theta}\ C_{\bm H(\mathcal S,\bm\Theta)} \quad \text{s.t.}\quad |\mathcal S|=N_S,\ \ |\beta_n|=1,$$

with effective channel

$$\bm{H}(\mathcal S,\bm{\Theta})=\hat{\bm H}(\mathcal S)+\bm R\bm\Theta \bm T(\mathcal S).$$

In fluid-MIMO, COAS becomes a joint transmit-and-receive port-selection problem in which exactly one port per fluid antenna is chosen on each side and the exact objective is

$N$0

These formulations preserve the defining feature of COAS: the decision variable is a combinatorial subset or binary selection structure, and the objective is a log-determinant capacity expression (He et al., 2020, Efrem et al., 2024).

Setting	Selection variables	Capacity objective
Massive MIMO uplink receive selection	choose $N$1 of $N$2 BS antennas	$N$3 (Ouyang et al., 2022)
RIS-assisted massive MIMO	choose $N$4 and $N$5 jointly	$N$6 (He et al., 2020)
Fluid-MIMO port selection	binary $N$7, one port per fluid antenna	$N$8 (Efrem et al., 2024)

These formulations also make clear why COAS is computationally demanding: the feasible set grows combinatorially, while the objective is non-separable and depends on the selected subchannel or effective channel matrix.

2. Greedy capacity maximization and approximation structure

A central algorithmic theme in COAS is greedy incremental capacity maximization. In the conventional fast capacity-maximization setting, the selected antenna is the one that yields the largest incremental capacity gain. For large-scale MIMO receivers with low-resolution ADCs, this structure is generalized by the quantization-aware rule

$N$9

where

$$\overline{\mathbf G}_{\rm opt} =\arg\max_{\overline{\mathbf G}\in\mathcal S} \log_2\det\!\left(\mathbf I_L+\rho_u\overline{\mathbf G}\,\overline{\mathbf G}^{\mathsf H}\right),$$0

Here $$\overline{\mathbf G}_{\rm opt} =\arg\max_{\overline{\mathbf G}\in\mathcal S} \log_2\det\!\left(\mathbf I_L+\rho_u\overline{\mathbf G}\,\overline{\mathbf G}^{\mathsf H}\right),$$1 captures incremental channel gain and $$\overline{\mathbf G}_{\rm opt} =\arg\max_{\overline{\mathbf G}\in\mathcal S} \log_2\det\!\left(\mathbf I_L+\rho_u\overline{\mathbf G}\,\overline{\mathbf G}^{\mathsf H}\right),$$2 is a quantization penalty. In the high-resolution limit, $$\overline{\mathbf G}_{\rm opt} =\arg\max_{\overline{\mathbf G}\in\mathcal S} \log_2\det\!\left(\mathbf I_L+\rho_u\overline{\mathbf G}\,\overline{\mathbf G}^{\mathsf H}\right),$$3, $$\overline{\mathbf G}_{\rm opt} =\arg\max_{\overline{\mathbf G}\in\mathcal S} \log_2\det\!\left(\mathbf I_L+\rho_u\overline{\mathbf G}\,\overline{\mathbf G}^{\mathsf H}\right),$$4, and the rule reduces to the standard fast COAS-style criterion. The resulting Quantization-Aware Fast Antenna Selection (QAFAS) algorithm preserves the greedy COAS structure and has overall complexity $$\overline{\mathbf G}_{\rm opt} =\arg\max_{\overline{\mathbf G}\in\mathcal S} \log_2\det\!\left(\mathbf I_L+\rho_u\overline{\mathbf G}\,\overline{\mathbf G}^{\mathsf H}\right),$$5, with no increase in overall complexity relative to the conventional fast antenna selection algorithm (Choi et al., 2018).

A second major line of work establishes submodularity. For RIS-assisted massive MIMO with fixed $$\overline{\mathbf G}_{\rm opt} =\arg\max_{\overline{\mathbf G}\in\mathcal S} \log_2\det\!\left(\mathbf I_L+\rho_u\overline{\mathbf G}\,\overline{\mathbf G}^{\mathsf H}\right),$$6, the antenna-selection subproblem

$$\overline{\mathbf G}_{\rm opt} =\arg\max_{\overline{\mathbf G}\in\mathcal S} \log_2\det\!\left(\mathbf I_L+\rho_u\overline{\mathbf G}\,\overline{\mathbf G}^{\mathsf H}\right),$$7

is monotone and submodular with respect to $$\overline{\mathbf G}_{\rm opt} =\arg\max_{\overline{\mathbf G}\in\mathcal S} \log_2\det\!\left(\mathbf I_L+\rho_u\overline{\mathbf G}\,\overline{\mathbf G}^{\mathsf H}\right),$$8. This yields the greedy update

$$\overline{\mathbf G}_{\rm opt} =\arg\max_{\overline{\mathbf G}\in\mathcal S} \log_2\det\!\left(\mathbf I_L+\rho_u\overline{\mathbf G}\,\overline{\mathbf G}^{\mathsf H}\right),$$9

together with a $\mathcal S$0 approximation ratio. The greedy method requires $\mathcal S$1 objective evaluations, whereas exhaustive search is described as often infeasible within 120 hours; the reported runtime advantage is at least four orders of magnitude (He et al., 2020).

The common structure is therefore not a specific heuristic but a family of capacity-driven approximations: incremental gain rules, submodular greedy selection, matrix-inverse updates, and complexity reductions that preserve the underlying log-det objective.

3. CSI-aware and hardware-aware generalizations

Classical COAS typically assumes instantaneous CSI. Several later formulations replace this assumption with long-term or partial statistical knowledge while keeping throughput maximization as the design goal. In uplink multiuser MIMO with only statistical CSI at the base station, the joint receive antenna selection and precoding problem is

$\mathcal S$2

subject to a binary antenna-selection vector $\mathcal S$3 with $\mathcal S$4 and per-user covariance constraints $\mathcal S$5, $\mathcal S$6. For joint decoding,

$\mathcal S$7

Random matrix theory yields deterministic equivalents, the optimal eigenvectors satisfy $\mathcal S$8, power allocation becomes water-filling, and the receive-antenna subproblem is handled by greedy selection on the deterministic-equivalent objective. The resulting alternating optimization and majorization-maximization framework converges in about 3–4 AO iterations in the reported simulations (Ouyang et al., 2022).

A different generalization is driven by CSI-acquisition overhead in large cloud radio access networks. There, the downlink scheme selects $\mathcal S$9 active antennas from $\binom{N}{L}$0 based only on large-scale fading $\binom{N}{L}$1, while acquiring instantaneous CSI only for the selected antennas. The long-term control policy jointly maps the large-scale fading matrix $\binom{N}{L}$2 to the active antenna set $\binom{N}{L}$3, the regularization factor $\binom{N}{L}$4, and the power vector $\binom{N}{L}$5, maximizing the conditional average weighted sum-rate under per-antenna average power constraints. Random matrix theory provides asymptotically accurate deterministic equivalents for both SINR and per-antenna transmit power; the resulting decomposition uses a WMMSE-based power optimizer, a bisection search over $\binom{N}{L}$6, and a greedy large-scale-fading-based antenna selection algorithm (Liu et al., 2013).

Hardware constraints can also alter the objective itself. In low-resolution ADC receivers, the achievable capacity under the additive quantization noise model is

$\binom{N}{L}$7

with

$\binom{N}{L}$8

The capacity metric thus depends not only on selected channel strength but also on a quantization-noise penalty (Choi et al., 2018).

4. Joint design with RIS, fluid antennas, and learning-based selection

In RIS-assisted massive MIMO, COAS is no longer an isolated antenna-selection rule. The active antenna subset and RIS phase configuration are coupled through the effective channel

$\binom{N}{L}$9

and the paper’s stated purpose is to compensate the performance loss due to antenna selection by reconfiguring the propagation environment with RIS passive beamforming. Alternating optimization separates antenna selection from passive beamforming, while block coordinate descent updates the RIS phases in closed form under perfect CSI (He et al., 2020).

Fluid-MIMO extends the selection space further. The exact problem selects one port per fluid antenna on both the transmit and receive sides. Because the joint log-det capacity is hard to optimize directly, the paper upper-bounds $\mathcal O(N^L)$0 by $\mathcal O(N^L)$1, obtains the surrogate

$\mathcal O(N^L)$2

and exploits the binary relation $\mathcal O(N^L)$3 to construct the jointly concave relaxation

$\mathcal O(N^L)$4

This joint convex relaxation (JCR) supports two COAS solvers with different performance-complexity tradeoffs: JCR&RES, which uses reduced exhaustive search, and JCR&AO, which refines a feasible binary initialization through alternating one-port-at-a-time exact-capacity maximization (Efrem et al., 2024).

A learning-based extension appears in RIS-empowered receive quadrature spatial modulation (RIS-RQSM). There, COAS is explicitly the classical baseline rule that selects the $\mathcal O(N^L)$5 receive antennas with the largest channel norms: $\mathcal O(N^L)$6 with selected channel matrix

$\mathcal O(N^L)$7

The same COAS labels supervise a DNN whose output is one of $\mathcal O(N^L)$8 possible antenna subsets. For $\mathcal O(N^L)$9, $\mathcal S$0, $\mathcal S$1, the reported BER gains of DNN-COAS-RIS-RQSM over COAS-RIS-RQSM at $\mathcal S$2 BER are $\mathcal S$3 dB for $\mathcal S$4, $\mathcal S$5 dB for $\mathcal S$6, and $\mathcal S$7 dB for $\mathcal S$8. The same paper states that COAS complexity is

$\mathcal S$9

while the DNN complexity is substantially larger; the tabulated examples are $\bm\Theta$0 versus $\bm\Theta$1, $\bm\Theta$2 versus $\bm\Theta$3, and $\bm\Theta$4 versus $\bm\Theta$5 (Ozden et al., 7 Jul 2025).

5. Asymptotic laws and performance metrics

The cited literature gives model-specific capacity laws for COAS benchmarks. In a multiuser massive MIMO uplink with Nakagami-$\bm\Theta$6 fading, perfect CSI at the base station, fixed selected-antenna count $\bm\Theta$7, and exact capacity-based receive selection, the paper derives the deterministic equivalent

$\bm\Theta$8

which implies

$\bm\Theta$9

The same analysis shows

$$\max_{\mathcal S\subseteq \mathcal L,\ \bm\Theta}\ C_{\bm H(\mathcal S,\bm\Theta)} \quad \text{s.t.}\quad |\mathcal S|=N_S,\ \ |\beta_n|=1,$$0

so the sum-rate becomes increasingly deterministic as $$\max_{\mathcal S\subseteq \mathcal L,\ \bm\Theta}\ C_{\bm H(\mathcal S,\bm\Theta)} \quad \text{s.t.}\quad |\mathcal S|=N_S,\ \ |\beta_n|=1,$$1 grows (Ouyang et al., 2022).

In very large distributed MIMO or cloud-RAN downlinks, the asymptotic law differs. With $$\max_{\mathcal S\subseteq \mathcal L,\ \bm\Theta}\ C_{\bm H(\mathcal S,\bm\Theta)} \quad \text{s.t.}\quad |\mathcal S|=N_S,\ \ |\beta_n|=1,$$2 fixed and $$\max_{\mathcal S\subseteq \mathcal L,\ \bm\Theta}\ C_{\bm H(\mathcal S,\bm\Theta)} \quad \text{s.t.}\quad |\mathcal S|=N_S,\ \ |\beta_n|=1,$$3, the maximum achievable sum-rate $$\max_{\mathcal S\subseteq \mathcal L,\ \bm\Theta}\ C_{\bm H(\mathcal S,\bm\Theta)} \quad \text{s.t.}\quad |\mathcal S|=N_S,\ \ |\beta_n|=1,$$4 satisfies

$$\max_{\mathcal S\subseteq \mathcal L,\ \bm\Theta}\ C_{\bm H(\mathcal S,\bm\Theta)} \quad \text{s.t.}\quad |\mathcal S|=N_S,\ \ |\beta_n|=1,$$5

and the paper states that the proposed large-scale-fading-based antenna selection algorithm is asymptotically optimal in this regime (Liu et al., 2013). A plausible implication is that COAS scaling depends strongly on architecture, geometry, and the selection constraint, rather than on the capacity objective alone.

Capacity-oriented antenna selection also appears in delay-sensitive analysis. For a downlink MIMO-OSTBC system under co-channel interference, receive antenna selection chooses the antenna with the largest instantaneous SINR, and the performance metric is effective capacity,

$$\max_{\mathcal S\subseteq \mathcal L,\ \bm\Theta}\ C_{\bm H(\mathcal S,\bm\Theta)} \quad \text{s.t.}\quad |\mathcal S|=N_S,\ \ |\beta_n|=1,$$6

With single receive antenna selection,

$$\max_{\mathcal S\subseteq \mathcal L,\ \bm\Theta}\ C_{\bm H(\mathcal S,\bm\Theta)} \quad \text{s.t.}\quad |\mathcal S|=N_S,\ \ |\beta_n|=1,$$7

where $$\max_{\mathcal S\subseteq \mathcal L,\ \bm\Theta}\ C_{\bm H(\mathcal S,\bm\Theta)} \quad \text{s.t.}\quad |\mathcal S|=N_S,\ \ |\beta_n|=1,$$8 is the maximum of the branch-quality variables. The paper reports a closed-form effective-capacity expression and numerical gains over a $$\max_{\mathcal S\subseteq \mathcal L,\ \bm\Theta}\ C_{\bm H(\mathcal S,\bm\Theta)} \quad \text{s.t.}\quad |\mathcal S|=N_S,\ \ |\beta_n|=1,$$9 MISO-OSTBC system; at $$\bm{H}(\mathcal S,\bm{\Theta})=\hat{\bm H}(\mathcal S)+\bm R\bm\Theta \bm T(\mathcal S).$$0 dB the gains are $$\bm{H}(\mathcal S,\bm{\Theta})=\hat{\bm H}(\mathcal S)+\bm R\bm\Theta \bm T(\mathcal S).$$1, $$\bm{H}(\mathcal S,\bm{\Theta})=\hat{\bm H}(\mathcal S)+\bm R\bm\Theta \bm T(\mathcal S).$$2, and $$\bm{H}(\mathcal S,\bm{\Theta})=\hat{\bm H}(\mathcal S)+\bm R\bm\Theta \bm T(\mathcal S).$$3 bits/s/Hz for $$\bm{H}(\mathcal S,\bm{\Theta})=\hat{\bm H}(\mathcal S)+\bm R\bm\Theta \bm T(\mathcal S).$$4, $$\bm{H}(\mathcal S,\bm{\Theta})=\hat{\bm H}(\mathcal S)+\bm R\bm\Theta \bm T(\mathcal S).$$5, and $$\bm{H}(\mathcal S,\bm{\Theta})=\hat{\bm H}(\mathcal S)+\bm R\bm\Theta \bm T(\mathcal S).$$6, respectively (Lari, 2016).

6. Terminological scope, misconceptions, and documentation gaps

The literature does not use the acronym “COAS” in a completely uniform way. Some papers describe their methods as COAS directly, while others are described as “COAS-like,” “capacity-oriented,” or “in spirit and function” because the antenna or port subset is still chosen to maximize a capacity-type objective, but the setting departs from classical instantaneous-CSI subset selection (Ouyang et al., 2022, Efrem et al., 2024).

A recurrent misconception is that COAS is always equivalent to sorting antennas by channel norm. The cited papers do not support that interpretation. Norm-based ranking is explicit in the RIS-RQSM baseline, where the top $$\bm{H}(\mathcal S,\bm{\Theta})=\hat{\bm H}(\mathcal S)+\bm R\bm\Theta \bm T(\mathcal S).$$7 channel norms are selected (Ozden et al., 7 Jul 2025); by contrast, low-resolution ADC receivers use the generalized greedy ratio $$\bm{H}(\mathcal S,\bm{\Theta})=\hat{\bm H}(\mathcal S)+\bm R\bm\Theta \bm T(\mathcal S).$$8, which balances channel gain and quantization penalty (Choi et al., 2018). In interference-limited MIMO-OSTBC, the selected receive antenna is the one with the largest instantaneous SINR rather than the one with the largest desired-signal norm (Lari, 2016). In statistical-CSI uplink MIMO, the objective is long-term expected throughput with joint covariance design, not instantaneous capacity evaluated on the full instantaneous channel (Ouyang et al., 2022). This suggests that “capacity-optimized” is objective-driven rather than metric-fixed.

A second misconception is that COAS is necessarily an antenna-only problem. The cited formulations include joint antenna selection and passive beamforming, joint receive antenna selection and precoding, joint power and antenna selection, and joint transmit-and-receive port selection (Efrem et al., 2024, Ouyang et al., 2022). In such cases, the selected subset is only one part of a larger coupled optimization.

The supplied RIS-receive-spatial-modulation entry titled "Antenna Selection For Receive Spatial Modulation System Empowered By Reconfigurable Intelligent Surface" contains no equations, system models, antenna-selection rules, detector descriptions, performance results, or comparisons in the available excerpt; it consists only of a minimal LaTeX skeleton with an empty introduction. COAS-specific details therefore cannot be extracted from that excerpt, despite the title and abstract metadata (Ozden et al., 2023).