---
title: Decremental Port Selection (DPS)
url: https://www.emergentmind.com/topics/decremental-port-selection-dps
type: topic
---

# Decremental Port Selection (DPS)

Decremental Port Selection (DPS) is a port selection methodology designed for multi-active-port systems, such as fluid antenna multiple access (FAMA) networks, which require the selection of a subset of ports from a large candidate pool to optimize communication performance subject to RF-chain constraints. In contrast to incremental (greedy-additive) strategies, DPS employs a subtractive (pruning) approach: beginning with the full set of available ports, the algorithm sequentially eliminates one port at each step until only the target number of active ports remains. DPS is particularly relevant in scenarios where the number of active ports $N^*$ to be selected approaches the total number of available ports $N$, and where optimal selection via exhaustive search is computationally infeasible due to the combinatorial explosion in possibilities. The algorithm, along with performance and complexity analyses, has been recently formalized in the context of FAMA systems [2511.17897].

## 1. System Context and Problem Definition

DPS arises in the context of interference-limited wireless networks with multi-user FAMA. In these systems, each user terminal (UT) is equipped with a fluid antenna system (FAS) comprising $N$ spatially distributed radiating ports, of which $N^*$ must be allocated to $N_{\mathrm{RF}}$ RF chains. The downlink received signal at UT $u$ is
$$
r_u = g_{(u,u)} s_u + \sum_{ \tilde{u} \neq u } g_{(\tilde{u},u)} s_{ \tilde{u} } + \eta_u,
$$
where $g_{(u,u)} \in \mathbb{C}^N$ is the port-indexed channel vector, $s_u$ is the transmitted symbol, and $\eta_u$ is complex Gaussian noise plus unmodeled interference. Given a subset of port indices $\kappa \subset \{1, ..., N\}$ with $|\kappa| = N^*$, the post-combining SINR at UT $u$ with interference rejection combining (IRC) is
$$
\gamma(\kappa) = h^H \Phi_\kappa^{-1} h,
$$
where $h$ comprises the selected channel coefficients and $\Phi_\kappa$ is the interference-plus-noise covariance across the chosen ports. The combinatorial port-selection problem is thus
$$
\kappa^* = \arg \max_{\kappa \subset \{1, ..., N\},\, |\kappa| = N^*} \gamma(\kappa).
$$

## 2. Decremental Port Selection Algorithm

DPS begins with the full port set $\kappa_0 = \{1,...,N\}$. At each iteration, the algorithm identifies and removes the port whose exclusion results in the maximum improvement (or minimal degradation) in the system utility, typically the SINR. The process continues until only $N^*$ ports remain. At each decrement step $i$, for the current port set $\kappa_{i-1}$, every candidate port $k$ is temporarily removed to form the reduced set $\kappa_{i,k} = \kappa_{i-1} \setminus \{ k \}$, and the SINR $\gamma_{i,k}$ is recomputed:
$$
k_i^* = \arg\max_{k \in \kappa_{i-1}} \gamma( \kappa_{i-1} \setminus \{ k \} ),
$$
then update $\kappa_i = \kappa_{i-1} \setminus \{ k_i^* \}$. This iterative pruning continues until $|\kappa_i| = N^*$.

The computation of the SINR for reduced port sets at each step requires updating or inverting the corresponding interference-plus-noise covariance matrices. The matrix-inverse lemma (Woodbury identity) enables efficient recursive updates to reduce computational burden per step.

## 3. Complexity Analysis and Comparison

The computational complexity of DPS for selecting $N^*$ active ports from $N$ candidates is
$$
O( (N-N^*) \cdot N \cdot \min\{ (N-i)^3, U^2 \} ),
$$
where $U$ is the number of users and $i$ steps through the decremental process. DPS is efficient when $N^* \approx N$ but becomes increasingly less favorable as $N^*$ decreases relative to $N$, since the initial iterations must consider a large candidate pool. For comparison:
- Exhaustive port selection (EPS) requires $O\left( \binom{N}{N^*} \cdot \min\{ (N^*)^3, U^2 \} \right)$ operations—prohibitive for moderate $N$.
- Incremental port selection (IPS) executes $O\left( N^* \cdot N \cdot \min\{ (N^*)^3, U^2 \} \right)$ operations—quadratic in $N$ and $N^*$, and preferable when $N^* \ll N$.
The following table summarizes the computational regimes:

| Method      | Complexity (Big-O)                                        | Best Use Case           |
|-------------|-----------------------------------------------------------|-------------------------|
| EPS         | $\sim \binom{N}{N^*}$                                     | Tiny $N$, $N^*$         |
| DPS         | $(N-N^*) N \min\{ (N-i)^3,U^2 \}$                         | $N^* \approx N$         |
| IPS         | $N^* N \min\{ (N^*)^3,U^2 \}$                             | $N^* \ll N$             |

## 4. Performance Characteristics

DPS achieves performance close to EPS when the number of retained ports $N^*$ is near $N$. It is less effective for small $N^*$, where the pruned subset is far from optimal. Simulation results confirm that:
- For large $N^*$, DPS achieves sum-rate, symbol-error probability, and reliability metrics approaching those of EPS.
- For small $N^*$, DPS lags behind IPS in both SINR and overall throughput.
- In FAMA settings, DPS supports nearly optimal SINR and multiplexing gain when the number of eliminated ports is small [2511.17897].

## 5. Comparative Evaluation with Incremental Port Selection

In the regime where $N^* \ll N$, incremental port selection (IPS) consistently outperforms DPS in both computational efficiency and post-selection SINR. IPS also allows for recursive matrix updates similar to DPS but on a much smaller search tree, leading to practical scalability for typical FAS dimensions (e.g., $N \simeq 150$ and $N^* \leq 8$). By contrast, as $N^*$ increases and approaches $N$, DPS achieves slightly better performance since pruning weak ports may correct residual suboptimality inherent in constructive (greedy) selection.

## 6. Practical Implications and Design Guidance

The selection of DPS versus IPS should be based on system size and target active port count:
- DPS is well suited when the active-port count is large relative to the total ports available, such as when minimal pruning is required to achieve feasible implementation on $N_{\mathrm{RF}}$ chains.
- For scenarios requiring aggressive reduction to a small subset, IPS yields superior performance and substantially lower runtime.
DPS, in providing a constructive lower-complexity alternative to brute-force optimization, expands the toolkit for practical multi-port FAMA deployments by offering a scalable compromise between selection optimality and implementation cost [2511.17897].

## 7. References

- Multi-Port Selection for FAMA: Massive Connectivity with Fewer RF Chains than Users [2511.17897]

Source: https://www.emergentmind.com/topics/decremental-port-selection-dps