Ferkans — Interactive Telecom Tutor

The 35% Number

The headline result of the Mohammadi-Ngo-Matthaiou-Caire paper is a $\sim 35\%$ improvement in 95%-likely per-user throughput of cell-free OTFS over cell-free OFDM at high mobility. This section breaks down where the 35% comes from, quantifies the contributing factors (macro-diversity, DD-diversity, pilot efficiency), and discusses when the gain shrinks or grows. The 35% is an average across typical urban scenarios; the actual range is 20-50% depending on parameters.

Definition:
95%-Likely Per-User Throughput

The 95%-likely per-user throughput $R_k^{95\%}$ is the value such that $95\%$ of UEs achieve rate $\geq R_k^{95\%}$ . Formally: $R_k^{95\%} \;=\; \inf\{R : \mathbb{P}(R_k \geq R) \geq 0.95\}.$ This captures the bottleneck UE performance — the worst-served 5% of the user population. Operators typically engineer for this metric because it defines the service-level agreement (SLA).

Cellular baseline: Users near the cell edge drag the 95%- likely down. Typical $R_k^{95\%} \sim 0.1$ bits/s/Hz. Cell-free baseline: Uniform coverage. $R_k^{95\%} \sim 0.5$ - $1$ bits/s/Hz — $5$ - $10\times$ better. Cell-free OTFS (high mobility): Maintains the uniform coverage advantage under Doppler. $R_k^{95\%} \sim 0.5$ - $1.5$ bits/s/Hz.

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Theorem: Cell-Free OTFS: 35% Throughput Gain

For cell-free OTFS vs cell-free OFDM under typical urban mobility (60-150 km/h, $\text{SNR} = 15$ - $20$ dB), the 95%-likely per-user throughput ratio satisfies $\frac{R_k^{95\%}(\mathrm{OTFS})}{R_k^{95\%}(\mathrm{OFDM})} \;\geq\; 1.35,$ with the gap widening to $\sim 1.5$ at higher mobility (200-300 km/h).

Attribution:

Macro-diversity from $L$ APs: same contribution to both OFDM and OTFS. Does not affect the ratio.
DD-diversity $P$ (OTFS): $\sim 20\%$ of the ratio.
Pilot efficiency (OTFS superimposed vs OFDM DMRS): $\sim 5\%$ .
ICI robustness under mobility: $\sim 10\%$ .
Total: $\sim 35\%$ improvement.

Cell-free architecture helps both OFDM and OTFS equally — the macro-diversity is a physical effect. The 35% OTFS gain comes from the ways OTFS exploits the resulting rich channel better than OFDM: (i) DD-diversity compounds the macro-diversity, (ii) superimposed pilots save overhead, (iii) OTFS maintains performance under mobility where OFDM suffers ICI. The quantitative breakdown above is from the Mohammadi-Caire 2023 simulation — matching measurements on CommIT testbeds.

Proof

Cell-free OFDM 95%-throughput

Under mobility, OFDM ICI creates per-UE SINR ceiling: $\mathrm{SINR}_{\text{OFDM}} \leq 3/(\pi^2 (\nu/\Delta f)^2)$ . For $\nu/\Delta f = 0.1$ : ceiling 20 dB. 95%-tile: ~0.6 bits/s/Hz (cell-edge).

Cell-free OTFS 95%-throughput

OTFS does not hit the ICI ceiling. SINR determined by $L\bar\beta/K$ . Same cell-edge users: 0.8 bits/s/Hz.

Ratio

$0.8 / 0.6 = 1.33$ . Close to 1.35. (Other factors like superimposed pilots add a few percent.)

Operational

35% throughput gain at the 95%-tile is a substantial operational improvement — SLA violations drop significantly. $\blacksquare$

Key Takeaway

The 35% gain comes from compounding effects. DD-diversity (~20%)

pilot efficiency (~5%) + ICI robustness (~10%) multiplies to ~35% at typical mobility. At 300 km/h: closer to 50%. The baseline cell-free improvement over cellular is orthogonal to OTFS vs OFDM — roughly $5$ - $10\times$ at the 95%-tile regardless of modulation.

Example: Urban Deployment: Detailed Performance

Urban scenario: 1 km² area, $L = 64$ APs ( $N_a = 4$ each), $K = 100$ UEs at density 100/km², UE velocities uniform in [0, 150] km/h, 28 GHz, 100 MHz bandwidth, $\text{SNR} = 15$ dB reference.

Compute: (a) Cellular OFDM, cellular OTFS, cell-free OFDM, cell-free OTFS 95%-likely throughput. (b) Overall gain.

Solution

Cellular OFDM

1 BS (32 antennas). Per-UE SNR varies: cell-edge UEs at $\sim 5$ dB. ICI ceiling at $\nu_{\max}/\Delta f \approx 0.1$ : SINR $\leq 15$ dB. 95%-tile $\sim 0.4$ bits/s/Hz.

Cellular OTFS

Same BS, OTFS: no ICI ceiling. Full DD diversity $P = 6$ . 95%-tile $\sim 0.8$ bits/s/Hz (2× cellular OFDM).

Cell-free OFDM

64 APs: macro-diversity ~6 dB. 95%-tile: 0.9 bits/s/Hz. Same ICI ceiling as cellular.

Cell-free OTFS

Full compound gain: $L \cdot P$ diversity + superimposed pilots. 95%-tile: ~1.3 bits/s/Hz.

Gain table

Config	95%-tile	Cell-free gain	OTFS gain
Cellular OFDM	0.4	—	—
Cellular OTFS	0.8	—	2.0×
Cell-free OFDM	0.9	2.3× (vs cell)	—
Cell-free OTFS	1.3	3.3× (vs cell)	1.45× (vs CF OFDM)
Total cell-free OTFS vs cellular OFDM: 3.3× — massive operational improvement.

Per-User Throughput CDF: Cell-Free OTFS vs Others

Plot the cumulative distribution of per-user throughput for cellular OFDM, cellular OTFS, cell-free OFDM, cell-free OTFS. Sliders: UE density, mobility, $L$ .

Parameters

L

64

K

100

Avg velocity (km/h)80

Theorem: Cell-Free OTFS Scaling with $L$

The 95%-likely throughput gain of cell-free OTFS over cellular OFDM scales as $\frac{R_k^{95\%}(\mathrm{CF\text{-}OTFS})}{R_k^{95\%}(\mathrm{cellular\text{-}OFDM})} \;=\; \mathcal{O}(L^{0.7} \cdot P^{0.3})$ (empirically fit to simulation). The exponents are not integer: the combined effect of macro-diversity ( $L$ ) and DD-diversity ( $P$ ) is sublinear in each due to saturation as interference grows.

At $L = 64$ , $P = 6$ : gain $\approx 64^{0.7} \cdot 6^{0.3} \approx 27$ . The 95%-tile goes from 0.4 bits/s/Hz to ~10 bits/s/Hz — a dramatic operational uplift.

Doubling $L$ from 50 to 100: gain ratio grows by $2^{0.7} = 1.6$ . Quadrupling: by $2.3\times$ . Diminishing returns from pilot contamination and MU interference. Doubling $P$ (denser scattering): less dramatic ( $2^{0.3} = 1.23$ ), but compounds with $L$ . Combined: practical upper bound on gain is $\sim 30\times$ at $L = 100$ with rich scattering. Beyond this, interference saturates.

Proof

Signal power

Coherent beamforming: signal power $\propto L^{0.7}$ (sublinear due to UE-specific phase variations).

Interference

Multi-user interference grows as $K \cdot L^{0.3}$ (pilot contamination + spatial overlap).

SINR

Ratio signal/interference $\propto L^{0.4}$ . Rate $\propto \log L$ .

DD-diversity $P$

Additional $P$ -fold gain from OTFS's DD structure. Empirical exponent 0.3.

Combined

$L^{0.7} \cdot P^{0.3}$ empirical fit. $\blacksquare$

Definition:
Coverage Uniformity

Coverage uniformity measures how equally UEs are served: $\mathcal{U} \;=\; \frac{R_k^{95\%}}{R_k^{50\%}} \;\in\; [0, 1].$ $\mathcal{U} = 1$ means all users achieve the same rate; $\mathcal{U} \to 0$ means large rate disparity.

Cellular: $\mathcal{U} \sim 0.05$ - $0.1$ — cell-edge UEs get $\sim 10$ - $20\%$ of cell-center UEs' rate. Cell-free OFDM: $\mathcal{U} \sim 0.3$ - $0.5$ . Cell-free OTFS: $\mathcal{U} \sim 0.4$ - $0.6$ — most uniform.

High uniformity is a deployment advantage: operator can engineer for the median user without worrying about catastrophic cell-edge performance.

🔧Engineering Note

Key Deployment Metrics

Cell-free OTFS deployment KPIs:

95%-likely per-user throughput: primary SLA metric. Target $> 1$ bit/s/Hz at cell-edge in 2028+ deployments.
Coverage uniformity: $\geq 0.4$ (cell-free OTFS typically 0.5-0.6).
Maximum mobility: $\geq 200$ km/h without significant rate degradation.
Fronthaul utilization: $\leq 80\%$ of available eCPRI capacity under peak load.
Handover failure rate: $\leq 0.01\%$ (vs cellular 1-5%).
Energy efficiency: $\sim 5\times$ better than cellular at the 95%-tile (joint TX power lower for same rate).

Operational deployment maturity:

2024-2026: Lab and small-cell trials (academic, Ericsson-lab).
2026-2028: Urban pilot deployments, primarily sub-6 GHz.
2028+: Mass deployment alongside 6G standardization.

Practical Constraints

•
Primary KPI: 95%-tile throughput $\geq 1$ bit/s/Hz
•
Coverage uniformity $\geq 0.4$
•
Mobility: $\geq 200$ km/h
•
2028+ commercial deployments

🎓CommIT Contribution(2023)

Performance Evaluation of Cell-Free OTFS

M. Mohammadi, H. Q. Ngo, M. Matthaiou, G. Caire — IEEE Trans. Wireless Communications

The Mohammadi-Ngo-Matthaiou-Caire performance analysis establishes the quantitative case for cell-free OTFS deployments. Three key results:

35% 95%-likely throughput gain: cell-free OTFS beats cell-free OFDM by $\sim 35\%$ at the critical 95%-tile metric under typical urban mobility (60-150 km/h).
Scaling law: gain $\propto L^{0.7} \cdot P^{0.3}$ (empirical fit). At $L = 64$ : ~27× vs cellular OFDM.
Coverage uniformity: cell-free OTFS achieves 0.5-0.6 uniformity — smooth coverage without cell-edge penalty.

This paper is the operational anchor for cell-free OTFS research: it provides the numbers that operators and vendors use to justify investment in the architecture. The CommIT framework of DD-domain processing is the enabler — without it, the cell-free advantage is cut by half.

commitcell-freeperformance

Common Mistake: 35% Is a Scenario-Dependent Number

Mistake:

Quoting "35% gain" as universal. The actual gain depends on mobility, scattering richness, AP density, and UE density. At low mobility (pedestrian), the gain shrinks to ~10%. At very high mobility (LEO), it grows to ~50%.

Correction:

Present the 35% as a typical urban mobility number. For other scenarios, present the full gain formula: $\propto L^{0.7} \cdot P^{0.3}$ with context-dependent exponents. Engineering designs should re-compute based on actual deployment parameters using the Mohammadi-Caire model.

Performance: 35% Throughput Gain