Extension to Cell-Free Massive MIMO

Scaling to Cell-Free Massive MIMO

The single-link estimation schemes of Sections 1-4 are the building blocks. The full CommIT contribution extends these to cell-free massive MIMO: $L$ distributed access points (APs), $K$ UEs per coverage area, each UE's channel to each AP must be estimated per OTFS frame. Pilot overhead scales as $L \cdot K$ in the naive approach — potentially catastrophic at scale. The CommIT superimposed-pilot design offers pilot reuse across APs and zero-overhead data transmission, preserving the per-UE rate even as the system scales.

This section previews the cell-free OTFS problem; Chapter 17 treats it in full. The point here is that the single-pilot channel-estimation advantage of OTFS is not a small-scale curiosity — it is the structural reason cell-free OTFS becomes feasible at $L \gtrsim 16$ APs, where OFDM-based schemes would require a prohibitive pilot budget.

Definition:
Cell-Free Massive MIMO with OTFS

A cell-free OTFS system consists of:

$L$ distributed access points (APs), each with a single antenna, connected to a central processing unit (CPU) via fronthaul.
$K$ single-antenna user equipments (UEs), served cooperatively by all $L$ APs simultaneously (no cell boundaries).
All APs and UEs share the same time-frequency resources; data separation is by spatial multiplexing across the $L$ APs.

The downlink channel from all APs to UE $k$ is characterized by $L$ independent DD channels $h_{\ell, k}(\tau, \nu)$ for $\ell = 1, \ldots, L$ . Each channel has its own $P_{\ell, k}$ paths. The uplink is symmetric: each AP sees $K$ UE channels.

Theorem: Pilot Overhead in Cell-Free OTFS

For a cell-free system with $L$ APs, $K$ UEs, and maximum channel complexity $P_{\max}$ paths per link:

Embedded pilot (naive): each UE needs a unique guard region for its pilot to be separable across APs. Overhead per UE: $\eta_{\text{emb}} = (l_{\max} + 1)(2 k_{\max} + 1)/(MN)$ ; total overhead: $K \cdot \eta_{\text{emb}}$ . For $K = 8$ , $L = 16$ , typical parameters: $\sim 15\%$ overhead.
Embedded pilot (reused): pilots of different UEs occupy distinct DD-grid regions (orthogonal in DD). Overhead: $K \cdot \eta_{\text{emb}}$ if regions do not overlap. Still expensive at high $K$ .
Superimposed pilot with per-UE sequences: each UE's pilot is a distinct Zadoff-Chu-like sequence with different root index. Orthogonal across UEs; all APs estimate all channels from the same data-carrying grid. Overhead: $0\%$ .

The superimposed scheme achieves zero overhead independent of $K$ , while the embedded-based schemes scale linearly with $K$ .

Pilot overhead is a spectral-efficiency tax. In cell-free systems with many UEs, this tax compounds. The key structural property of OTFS that makes zero-overhead pilots possible is that the pilot can be a known sequence superimposed on the data — unlike OFDM, where the pilot must occupy distinct subcarriers to avoid data interference.

Proof

Embedded scheme, per UE

Each UE $k$ has an embedded pilot in its guard region $\mathcal{G}_k$ . If UEs use non-overlapping guard regions across the DD grid (orthogonal in DD), we need $K \cdot |\mathcal{G}_{\min}|$ cells for pilots. Overhead: $K \eta_{\text{emb}}$ .

Superimposed scheme

All UEs overlay their pilot sequences on the full grid. Different UEs use Zadoff-Chu roots $r_k$ with cross-correlation $1/\sqrt{MN}$ — asymptotically orthogonal. Each AP correlates with each UE's pilot to separate the channels. Zero reserved cells.

Scaling comparison

Embedded: $K \eta_{\text{emb}} \propto K$ . Superimposed: $\eta = 0$ independent of $K$ . For $K = 8$ : embedded costs $\sim 16\%$ (taking $\eta_{\text{emb}} = 2\%$ ), superimposed costs $0\%$ — a $16\%$ rate gain. $\blacksquare$

Key Takeaway

OTFS enables cell-free scaling that OFDM cannot. In cell-free massive MIMO, the pilot overhead is the decisive spectral-efficiency cost at scale. OTFS superimposed pilots reduce this cost to zero, preserving the per-UE rate as $L$ and $K$ grow. In comparison, OFDM-based cell-free requires orthogonal DMRS per UE, with overhead scaling linearly in $K$ — at $K = 8$ , this is already $\sim 20\%$ of spectral resources. The OTFS advantage grows proportionally with the system scale.

Cell-Free Throughput: OTFS vs OFDM as System Scales

Plot 95%-likely per-UE throughput as a function of the number of UEs $K$ , for both OTFS (with superimposed pilots) and OFDM (with DMRS). Fixed parameters: $L = 16$ APs, vehicular channel, 100 MHz bandwidth. The OTFS curve is flat (scale-independent); the OFDM curve declines with $K$ due to pilot overhead. Crossover occurs around $K = 4$ ; at $K = 16$ , the OTFS gap is $\sim 25\%$ .

Parameters

Max UEs per cell

K

Number of APs

L

UE velocity (km/h)120

⚠️Engineering Note

Fronthaul and CPU Processing Load

In cell-free OTFS, each AP forwards its received DD-grid samples to the CPU for joint processing. The fronthaul load is therefore $L \cdot MN$ complex samples per OTFS frame. For $L = 16$ , $MN = 10^4$ , and frame rate 100 frames/s, this is $\sim 1.6 \times 10^7$ complex-samples/s per user aggregate — manageable with modern fronthaul (CPRI or eCPRI) links.

The CPU processing load is $O(L \cdot K \cdot MN)$ per frame for channel estimation and $O(L^3 \cdot MN)$ per frame for MMSE detection. At realistic scales ( $L = 16, K = 8, MN = 10^4$ ), this is $\sim 10^9$ FLOPS per frame — feasible on a single GPU.

These numbers are drawn from the system-level simulations of Mohammadi et al. (2023) and confirm that cell-free OTFS is deployable today on O-RAN hardware.

Practical Constraints

•
Fronthaul per AP: $O(MN) \sim 10^4$ complex-samples/frame
•
CPU compute: $O(L K MN)$ for channel estimation
•
Latency: $\sim 1$ ms CPU processing, within 6G URLLC targets

📋 Ref: ORAN-WG4.CUS.0, §3.2

What Chapters 14 and 17 Add

This section treats single-frame estimation. Two extensions matter for cell-free OTFS:

Sensing-assisted estimation (Chapter 14): if the AP-UE channel has a stable geometric component (LOS, persistent reflectors), the DD coordinates $(\ell_i, k_i)$ can be tracked across frames. This reduces per-frame pilot overhead further — toward the limit where only the complex gains $h_i$ need estimation, not the DD support.
Joint AP-CPU estimation (Chapter 17): the distributed APs' observations are jointly processed at the CPU. A joint channel estimator exploits the common DD coordinates shared across APs (a given reflector produces correlated responses at all APs). The statistical gain is another $\sim 3$ – $5$ dB at typical scales.

Both extensions are treated in detail in later chapters. The present chapter establishes the per-link, per-frame baseline.

Why This Matters: Link to Cell-Free Massive MIMO

The MIMO book (Chapter 11) develops cell-free massive MIMO in the OFDM setting. There, pilot contamination is a central problem: reusing pilots across cells causes inter-cell interference in channel estimates. In OTFS cell-free, the equivalent question is whether pilot reuse across UEs (in the superimposed scheme) degrades channel estimates. The answer: yes, but the degradation is controlled by pilot-sequence cross-correlation, which for Zadoff-Chu is $O(1/\sqrt{MN})$ — asymptotically zero. At realistic scales, pilot contamination is $\sim 15$ dB below signal.

Superimposed Pilot Estimation Chapter Summary