# Sum Spectral Efficiency

> Evaluates the sum spectral efficiency of a hybrid centralized-distributed precoding scheme in fronthaul-constrained cell-free massive MIMO networks, comparing it against fully centralized and fully distributed baselines under varying fronthaul capacities and antenna configurations. Use when the user has predictions and gold and needs to compute sum spectral efficiency (sum SE).

- Skill: `qhjqhj00/sum-spectral-efficiency` (Agent Skill)
- Install (CLI): `npx skillmds add qhjqhj00/sum-spectral-efficiency`
- Raw SKILL.md: https://api.skillmd.com/api/skills/qhjqhj00/sum-spectral-efficiency/raw
- Safety review: pending
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: Coding & Dev Tools
- Author: qhjqhj00 (https://skillmd.com/u/qhjqhj00)
- Updated: 2026-09-08
- Page: https://skillmd.com/skills/qhjqhj00/sum-spectral-efficiency

---


# sum-spectral-efficiency

> Hybrid centralized-distributed precoding in fronthaul-constrained CF-mMIMO systems — Mobini et al. (2025) (arXiv:2510.12406, 2025)

## What this evaluates

Evaluates the sum spectral efficiency of a hybrid centralized-distributed precoding scheme in fronthaul-constrained cell-free massive MIMO networks, comparing it against fully centralized and fully distributed baselines under varying fronthaul capacities and antenna configurations.

## Datasets

- (no dataset; pure metric skill)

## Metrics

- `sum spectral efficiency (sum SE)` **(primary)** — range: other
  - Total achievable data rate across all served users, measured in bit/s/Hz. Computed as the sum of individual user spectral efficiencies over 2000 random user distribution samples.

## Input / output format

**Input**: Network topology parameters (M APs, K users in 2x2 km²), fronthaul capacity limit (FH_max), antennas per AP (L), transmit power limits (500 mW pilot, 1 W data), noise power (-92 dBm), and channel models (path loss, large-scale fading).

**Output**: Average sum SE (bit/s/Hz) as a function of FH_max, L, or M, reported via simulation over 2000 samples.

## Scoring recipe

```python
def compute_sum_se(users, channels, precoding_scheme, fh_max):
    total_se = 0.0
    for _ in range(2000):  # τ samples
        # 1. Generate user locations & channel realizations
        # 2. Determine user grouping & power allocation per scheme
        # 3. Compute SINR per user based on precoding (ZF/Hybrid)
        se_per_user = [compute_se(sinr) for sinr in sinrs]
        total_se += sum(se_per_user)
    return total_se / 2000
```

## Common pitfalls

- Assuming increasing fronthaul capacity (FH_max) always improves distributed precoding performance; it is actually capped by the number of antennas per AP (L-1).
- Ignoring the trade-off where increasing antennas (L) improves macro-diversity but simultaneously increases fronthaul load, potentially reducing the number of centrally served users.
- Confusing the fronthaul capacity limit (FH_max) with the actual fronthaul usage metric (FH_m,pr) reported in complexity tables.

## Evidence (verbatim from paper)

> The proposed power allocation and user grouping solution, yields significant sum-SE performance gain against EPA and random user grouping. More specifically, the K-means-based user grouping provides a performance gain of 34%, while the K-means based user grouping together with the power allocation can provide a performance gain of 83% when FH_max=12 Gbps.

## Citation

```bibtex
@misc{mobini2025hybridprecoding,
  title={Hybrid centralized-distributed precoding in fronthaul-constrained CF-mMIMO systems},
  author={Mobini et al. (2025)},
  year={2025},
  note={arXiv:2510.12406}
}
```

- arXiv: 2510.12406