27-EFT.WP.Packets.Light v1.0 | Chapter 5 — Wavelength / Subcarriers & Labels (WDM / SDM / Subcarrier Aggregation)

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Chapter 5 — Wavelength / Subcarriers & Labels (WDM / SDM / Subcarrier Aggregation)

One-sentence goal: Standardize the notation and assignment conventions for WDM / SDM / subcarrier aggregation, and provide minimal equations and interfaces for configure → measure → verify so that each optical packet’s label lambda / k_sub / space is traceable and auditable across routing and dashboards.

I. Scope & Objects

1. Inputs
   • Spectral / spatial resources: wavelength grid Λ = { lambda_c } (DWDM / flex-grid), subcarrier set K = { k_sub } (OFDM / SCM), spatial channels S = { s } (cores / modes / bundles).
   • Devices & constraints: WSS / ROADM / EDFA / Raman / filters with passbands, orders, isolation, gain tilt; fiber/device crosstalk and loss; guard band GB.
   • Service request: req = { rate, R_c, mod, OSNR_min, span, hold_time }; routing policy and RefCond.
2. Outputs
   • Resources & labels: label = ( lambda, k_sub_set, s_set ); allocated bandwidth / space alloc = { B_eff, S_eff }; power/OSNR equalization plan.
   • Spectral / spatial compliance metrics: ACLR / OBB / isolation / XT_pwr / SE; two-form gap delta_form_wdm/sdm (configured vs measured).
3. Boundary
   Physical propagation and compensation are covered in Chapters 2 and 6; this chapter focuses on resource labeling, allocation, compliance verification, and manifest persistence.

II. Terms & Variables

• Spectrum & grid: center frequency f_c = c_ref / λ_c; flex-grid slot Δf_slot (typ. 12.5 GHz); occupied bandwidth B_occ; guard band GB.
• Subcarrier aggregation: subcarrier spacing Δf_sc, selection set K_sel ⊂ K; in-band power P_inband = ∑_{k∈K_sel} P_k.
• Spatial dimension: spatial set S (MCF / MMF / bundled); coupling coefficient κ_{i→j}; crosstalk power XT_{i→j}.
• Device parameters: filter amplitude response H_m(f), WSS insertion loss IL(f), isolation Iso(f), amplifier gain G(f) and tilt Tilt.
• Metrics: ACLR = 10 log10( P_adj / P_main ); OBB (out-of-band power ratio); spectral efficiency SE = R_net / B_eff; spatial crosstalk power XT_pwr; channel isolation Iso_ch.
• Two forms: configured (grid/model–based allocations and metrics) vs measured (sweep/OTDR/OSA/ADC estimates); gaps delta_form_wdm/sdm.
• Dimensions: unit(B_eff) = "Hz", unit(ACLR) = "dB", unit(XT_pwr) = "dB", unit(SE) = "bit/s/Hz".

III. Postulates P605-*

• P605-1 (Traceable labels): Every allocation is persisted as label = ( lambda, k_sub_set, s_set ) with hashes of the device chain and RefCond.
• P605-2 (Two forms in parallel): For each label, publish configured and measured metrics and record the gap delta_form_wdm/sdm.
• P605-3 (Explicit measures): Spectral integrals ( ∫_{f∈B} |X(f)|^2 df ), subcarrier sums ( ∑_{k∈K_sel} • ), and spatial aggregations ( ∑_{s∈S_sel} • ) must declare domains and measures.
• P605-4 (Dimensional compliance): Power, bandwidth, isolation/crosstalk, and efficiency fields declare unit / dim and pass check_dim.
• P605-5 (Protection & isolation): GB ≥ GB_min, and adjacent-channel isolation Iso_ch ≥ Iso_min; violations require recompute or down-selection.
• P605-6 (Power equalization): Link-level power/OSNR equalization—including tilt compensation—must be persisted; port-total power alone is insufficient.

IV. Minimal Equations S605-*

1. Spectral occupancy & protection
   • Effective bandwidth: B_eff = B_occ + 2*GB, with B_occ = ∫_{f∈passband} df (per modulation/filter design).
   • Spectral isolation: Iso_ch = 10 log10( P_main / P_leak_to_adj ), ACLR = 10 log10( P_adj / P_main ).
   • Out-of-band ratio: OBB = ( ∫_{f∉B_eff} |X(f)|^2 df ) / ( ∫_{f∈B_eff} |X(f)|^2 df ).
2. Subcarrier aggregation (OFDM / SCM)
   • Aggregated power: P_inband = ∑_{k∈K_sel} P_k; occupied bandwidth B_occ ≈ |K_sel| * Δf_sc (neglecting roll-off).
   • Per-subcarrier OSNR: OSNR_k ≈ SNR_k * ( RBW / Δf_sc ); aggregation threshold: min_k OSNR_k ≥ OSNR_min.
3. Spatial dimension (SDM)
   • Crosstalk power (linear approx.): XT_{i→j} ≈ 10 log10( ∫ | κ_{i→j}(z) |^2 dz );
   • Effective spatial degree: S_eff = | S_sel |; spatial efficiency SE_space = R_net / ( B_eff * S_eff ).
4. Link-level device response
   • Cascaded transfer: H_link(f) = ( ∏_m H_m(f) ) * ( ∏_a G_a(f) ) * exp( − ∫ alpha(f, z) dz );
   • Tilt-compensation target: | H_link(f) | ≈ const over B_eff, with error
     ε_tilt = max_f | | H_link(f) | − \bar H | / \bar H |.
5. Spectral efficiency & channel capacity (engineering)
   SE = R_net / B_eff; capacity lower bound (AWGN approximation) C ≈ B_eff * log2( 1 + SNR_eff ), with SNR_eff from OSNR/equalization estimates.
6. Two-form gaps
   • Spectral: delta_form_wdm = | ACLR_config − ACLR_meas | + w_obb * | OBB_config − OBB_meas |;
   • Spatial: delta_form_sdm = | XT_config − XT_meas |;
     Composite: delta_form_label = w1 * delta_form_wdm + w2 * delta_form_sdm.

V. Metrology Pipeline M60-5 (Ready → Assign → Verify → Persist)

1. Ready: load grids and device chains (WSS / ROADM / EDFA), fix RefCond and mask/guard policies; unify units (Hz, dB, W).
2. Assignment: for request req, perform routing and spectrum/space assignment:
   • WDM: choose lambda_c and B_eff;
   • Subcarriers: select K_sel and Δf_sc;
   • SDM: select S_sel and evaluate crosstalk tolerance; emit label.
3. Power/OSNR equalization: compute H_link(f) and tilt; set amplifier and tunable-filter targets.
4. Verification: compute ACLR / OBB / Iso_ch / XT_pwr / SE (configured), and corroborate with OSA/ADC/OTDR (measured); produce delta_form_label. Lock only if assertions pass.
5. Persistence:
   manifest.packet.label.* = { label, B_eff, S_eff, Iso_ch, ACLR/OBB, XT_pwr, SE, power_plan, delta_form_label, RefCond, contracts.*, signature }.

VI. Contracts & Assertions C60-5x (Suggested Thresholds)

• C60-501 (Protection & isolation): GB ≥ GB_min, Iso_ch ≥ Iso_min_dB.
• C60-502 (Spectral compliance): ACLR ≥ ACLR_min_dB, OBB ≤ OBB_max, ε_tilt ≤ tilt_max.
• C60-503 (Spatial crosstalk): XT_pwr ≤ XT_max_dB (or XT_margin ≥ 0).
• C60-504 (Two-form gap): delta_form_label ≤ tol_label (tuned per service / device accuracy).
• C60-505 (Dimensional compliance): check_dim(B_eff) = "Hz", check_dim(SE) = "bit/s/Hz", ACLR / XT_pwr persisted in dB with conversion records.
• C60-506 (Power / OSNR): min_k OSNR_k ≥ OSNR_min; equalization plan persisted and replayable.

VII. Implementation Bindings I60-5* (interfaces, I/O, invariants)

• I60-51 grid_define(kind, Δf_slot|grid_spec) -> Λ where kind ∈ { DWDM, FlexGrid }
• I60-52 rsa_assign(req, net, Λ, K, S, policy) -> { label, alloc, path } (Routing & Spectrum/Space Assignment)
• I60-53 power_equalize(path, H_link, targets) -> plan (tilt compensation & OSNR balancing)
• I60-54 spectral_metrics(trace, B_eff, RBW) -> { ACLR, OBB, Iso_ch }
• I60-55 sdm_metrics(probe, S_sel) -> { XT_pwr, κ_est }
• I60-56 spectral_efficiency(R_net, B_eff, S_eff) -> SE
• I60-57 compare_config_vs_meas(cfg_metrics, meas_metrics) -> delta_form_label
• I60-58 emit_label_manifest(results, policy) -> manifest.packet.label
  Invariants: two_forms_present = true; check_dim(*) passes; label and device/path hashes are traceable; guard / isolation thresholds satisfied.

VIII. Cross-References

• Physical baselines & transport compensation: Chs. 2 / 6.
• Framing & timebase: Ch. 3 (R_net and T_guard).
• Arrival-time harmonization & path correction: Ch. 8.
• Queuing & scheduling: Ch. 10 (conflicts vs guard bands).
• Metrology & dashboards: Ch. 11 (spectral / crosstalk and OSNR panel fields).

IX. Quality & Risk Control

• SLI / SLO: Iso_ch_min, ACLR_min_dB, OBB, XT_pwr, SE_stability, delta_form_label_p95.
• Fallback strategies: insufficient isolation → enlarge GB / higher-order filtering; excessive crosstalk → change spatial channel / enable MIMO; excessive tilt → re-equalize; large two-form gap → default to measurements, back-write thresholds, and deploy via canary.
• Audit: persist assignment decisions, device/link hashes, spectral & crosstalk snapshots, compliance reports, and the manifest signature chain.

Summary

• This chapter unifies WDM / SDM / subcarrier aggregation within a label–resource–compliance framework: label = ( lambda, k_sub, s ), alloc = { B_eff, S_eff }.
• Through P605 / S605 / M60-5 / C60-5x / I60-5* it closes the loop from allocation to verification and manifest-based release.
• The two-form gap (configured vs measured) delta_form_label serves as the go-live gate and drives automated governance for dashboards and rollback.