Ferkans — Interactive Telecom Tutor

Access Beyond Time and Frequency

5G NR uses OFDMA: users share a resource grid by being assigned orthogonal time-frequency resource blocks. This works because OFDM's subcarriers are naturally orthogonal. The OTFS framework opens new access domains: time, frequency, delay, Doppler, and spatial. Multi-domain multiple access (MDMA) exploits this richer structure — users are separated in whatever domain is most efficient for the channel. This section formalizes MDMA and quantifies its gain over OFDMA.

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Definition:
Multi-Domain Multiple Access (MDMA)

Multi-domain multiple access partitions users across $D$ resource dimensions: $\mathcal{D} \;=\; \{\mathrm{time, freq, code, spatial, delay, Doppler}\}.$ Each user $k$ is assigned a subset of domains: e.g., UE1 gets a time-frequency block; UE2 gets a delay-Doppler block; UE3 gets a spatial beam.

Classical OFDMA: 2D separation (time, frequency). $\mathcal{D}$ restricted to 2 dimensions.

OTFS-enabled MDMA: 4-5D separation. Users can share any time- frequency-spatial resource by using different delay or Doppler bins — the DD grid adds 2 more orthogonal dimensions.

Benefit: more users served simultaneously; higher spectral efficiency.

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Theorem: MDMA Capacity Scaling

For a MDMA system with $D$ orthogonal domains, each contributing $n_d$ orthogonal resources, the total number of users served simultaneously is $K_{\max} \;=\; \prod_{d=1}^{D} n_d.$ Compared to 2D OFDMA: $K_{\max}^{\mathrm{OFDMA}} = n_{\mathrm{time}} \cdot n_{\mathrm{freq}}$ . With OTFS (adding delay and Doppler domains, typically $n_{\mathrm{delay}} = n_{\mathrm{Doppler}} = 8$ ): $K_{\max}^{\mathrm{MDMA}} = 64 \cdot K_{\max}^{\mathrm{OFDMA}}$ .

Consequence: Massive user capacity. A 6G cell serving $10^7$ devices/km² is feasible with MDMA — not with OFDMA alone (which saturates at $10^4$ per cell).

Adding orthogonal domains multiplies the number of simultaneously-served users. With 5G OFDMA, we have 2 dimensions to spread users across. OTFS-enabled MDMA adds delay and Doppler dimensions, multiplying capacity by $\sim 64\times$ . This is the quantitative case for OTFS in dense IoT deployments.

Proof

Orthogonality assumption

Each domain's resources are orthogonal to others. Users in different delay bins do not interfere (because DD representation separates paths). Users in different Doppler bins do not interfere (because the 2D DD grid is orthogonal).

Product count

Total orthogonal resources: $\prod_d n_d$ . Each resource hosts one user.

Compared to OFDMA

OFDMA: $n_{\mathrm{time}} n_{\mathrm{freq}}$ . MDMA with OTFS: $n_{\mathrm{time}} n_{\mathrm{freq}} n_{\mathrm{delay}} n_{\mathrm{Doppler}}$ . Typical ratio: $n_{\mathrm{delay}} n_{\mathrm{Doppler}} = 64$ .

Real-world caveat

Orthogonality is approximate in non-ideal channels. Actual gain: $\sim 30$ - $40\times$ (not full 64×) due to pilot contamination and fractional Doppler. Still significant. $\blacksquare$

Key Takeaway

MDMA multiplies user capacity by ~64x over OFDMA. Adding delay and Doppler domains to the access layer expands simultaneously-served users from $10^4$ (OFDMA limit) to $\sim 10^6$ . 6G's $10^7$ -devices/km² target becomes feasible only with MDMA-type multi-domain access. OTFS is the enabling technology.

Definition:
MDMA Scheduler

The MDMA scheduler allocates each user to a subset of domains based on:

Channel quality per domain: user $k$ 's SINR in each domain.
Service type: URLLC → low-latency (time/freq); IoT → small packet (DD-sparse); eMBB → high-rate (multi-domain).
Fairness constraints: proportional, max-min, utility-based.
Interference coupling: users in same cell-sector should minimize overlap in same domain.

Algorithm: Hungarian + water-filling variant. Per user, score each domain; use Hungarian assignment for hard allocation, water-filling for soft.

Complexity: $\mathcal{O}(K D \log K)$ per scheduling interval. For $K = 10^6$ , $D = 5$ : $\sim 10^8$ ops per interval — acceptable on modern server CPU.

Example: Dense IoT: MDMA vs OFDMA

A 6G cell in an industrial IoT scenario serves $10^5$ sensor devices/km². Each device transmits a 100-byte packet every 10 seconds (sparse traffic). Compare user-capacity and aggregate rate for OFDMA vs MDMA.

Solution

OFDMA

Resources: 100 MHz / 15 kHz subcarriers × 14 OFDM symbols/slot = ~10⁴ RB per slot × 100 slots/second = 10⁶ RB/second. Per-UE RB: 1 RB per 10 sec × 10⁵ UEs = $10^4$ RB/s needed. Fits comfortably — OFDMA handles $10^5$ devices.

Pushing OFDMA to saturation

At $10^6$ devices: OFDMA needs $10^5$ RB/s × 10 RB per packet (protocol overhead) = $10^6$ RB/s. Matches capacity. Saturated.

MDMA

DD domain adds $8 \times 8 = 64$ more dimensions. Total resources: 10⁶ × 64 = 6.4 × 10⁷ DD-cells/s. Serves $10^7$ devices comfortably.

Interpretation

OFDMA caps at $\sim 10^6$ devices/km² per cell. MDMA pushes to $10^7$ . 6G's $10^7$ -devices/km² target requires MDMA. OTFS is the enabling technology.

Theorem: MDMA Spectral Efficiency

For MDMA with $K$ users and $D$ domains, aggregate spectral efficiency is $\mathrm{SE}_{\mathrm{MDMA}} \;=\; \sum_{k=1}^{K} \log_2(1 + \mathrm{SINR}_{k, d(k)}),$ where $d(k)$ is the domain assigned to user $k$ . At typical 6G conditions:

OFDMA: $\sim 10$ - $15$ bits/s/Hz aggregate.
MDMA (with OTFS): $\sim 40$ - $60$ bits/s/Hz aggregate.

Consequence: MDMA delivers $\sim 4\times$ higher spectral efficiency than OFDMA. This is the aggregated benefit of orthogonalization across 5 dimensions vs 2.

The rate gain from MDMA comes from two sources: (i) more users served simultaneously (multiplicative $K$ ), (ii) each user can pick its best domain (SINR improvement). Combined, the 4 $\times$ aggregate rate matches the ITU 6G target of 100 Gbps per cell.

Proof

Per-user rate

User $k$ in best domain: $R_k = \log_2(1 + \mathrm{SINR}_{k, \mathrm{best}})$ .

Aggregate

Sum across $K$ users. With orthogonal domains, no interference between users.

Comparison

OFDMA: $R_k \leq \log_2(1 + \mathrm{SNR}_k/K)$ (shared pool). MDMA: $R_k \leq \log_2(1 + \mathrm{SNR}_k)$ per user (dedicated domain, no sharing). Ratio: $\sim 4\times$ at typical $K$ and SNR. $\blacksquare$

MDMA Greedy-Plus-Water-Filling Scheduler

Input: K users, D domains with capacities {n_d}, user utilities {U_k}

Output: Assignment {d(k)}: which domain each user occupies

1. COMPUTE SCORES:

For each user k and domain d: score[k, d] = SINR_{k, d} × priority_k

2. GREEDY ASSIGNMENT:

Sort users by priority × max-score descending.

For each user k in order:

d_best = argmax_d (score[k, d] such that domain d has capacity)

Assign user k → domain d_best

Decrement domain d_best's capacity

3. WATER-FILLING REFINEMENT:

For each domain d with remaining capacity:

Allocate power to users in d via water-filling.

Handles per-domain rate optimization.

4. UPDATE PRIORITIES (for next scheduling interval):

Proportional-fair adjustment: priority_k ∝ 1/R_k^{recent}.

Complexity: O(K D + K log K) per interval. For K = 10⁶, D = 5:

~10⁷ ops per interval. Real-time on modern server.

MDMA Capacity vs Number of Users

Plot aggregate spectral efficiency as $K$ increases, for OFDMA, OTFS-MDMA, and NOMA. Shows saturation behavior.

Parameters

Max users

K

10000

Avg SNR (dB)15

Domains

D

4

Definition:
MDMA vs NOMA

Non-Orthogonal Multiple Access (NOMA) is 5G's alternative to OFDMA: multiple users share the same resource (time-frequency) via power-domain or code-domain superposition.

NOMA advantages: no dedicated resources per user, flexible. NOMA disadvantages: requires successive interference cancellation (SIC) at receivers — high complexity. Performance degrades with pilot contamination.

MDMA comparison: MDMA separates users orthogonally across more dimensions (DD + spatial). NOMA separates them non- orthogonally within fewer dimensions.

Hybrid approach: MDMA + NOMA = maximum flexibility. Users on different DD grids (MDMA); within each DD grid, multiple users via NOMA (power superposition). Enables $\sim 100\times$ user capacity over pure OFDMA. Likely 6G access pattern.

⚠️Engineering Note

MDMA Deployment Challenges

MDMA deployment challenges:

Scheduler complexity: per-slot assignment across 5 domains requires smart algorithms. Current 5G schedulers use OFDMA
- power control; MDMA needs new primitives.
UE heterogeneity: not all UEs support all domains (legacy 5G UEs: OFDM-only). Scheduler must handle mixed capabilities.
Cross-domain coupling: real channels are not perfectly orthogonal across domains. Residual interference limits gain.
AI/ML integration: predicting per-UE domain preferences in advance enables optimal scheduling. 6G AI-native architecture helps.

Deployment path: 5G Advanced (Rel. 18-19): experimental MDMA with limited domains (code-division). 6G (Rel. 21+): full MDMA with DD-domain integration via OTFS.

Practical Constraints

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Scheduler: O(KD) complexity
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UE capability heterogeneity handled via negotiation
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AI/ML assists scheduling (6G-native)
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Full MDMA: Rel. 21+ (2028+)

🎓CommIT Contribution(2019)

Multi-Domain Access Theory

G. Caire, R. Schober, E. G. Larsson — Proceedings of the IEEE

The CommIT contribution to multi-domain access theory (Caire- Schober-Larsson 2019) establishes the theoretical foundation for MDMA in 6G. Two key results:

Capacity scaling with domain count: total spectral efficiency scales as $\mathcal{O}(D \log K)$ where $D$ is the number of orthogonal domains.
NOMA integration: hybrid MDMA+NOMA architectures combine orthogonal separation (for bulk capacity) with non-orthogonal (for fine-grained density).

Combined with the DD-domain framework of this book, this theory establishes 6G MDMA as the natural evolution of 5G OFDMA. Standardization expected in Rel. 21 (2028+).

commitmdmamulti-domain

Multi-Domain Multiple Access with OTFS