Comparison with optical-networking-gym OSNR Model

This page compares XLRON's GN model with the OSNR computation in optical-networking-gym (optical_networking_gym.core.osnr and optical_networking_gym.envs.qrmsa), highlighting the key differences in physics, implementation, and scope.

Model Formulation

Both implementations compute GSNR (generalised signal-to-noise ratio) as the ratio of signal power to the sum of ASE noise and nonlinear interference, accumulated across spans on the path:

1/GSNR_path = sum over spans of (P_ASE + P_NLI) / P_signal

The NLI in both cases is based on the GN model closed-form approximation, but they differ in the level of detail:

Aspect	optical-networking-gym	XLRON
NLI formula	Single arcsinh-based expression combining SPM and XPM into one sum_phi accumulator	Separate SPM (eta_spm) and XPM (eta_xpm) efficiency coefficients with distinct formulas
SPM term	arcsinh(pi^2 * \|beta_2\| * B^2 / (4*alpha)) -- standard GN model form	arcsinh-based but includes ISRS Raman tilt correction term T, dispersion slope beta_3, and optionally beta_4
XPM term	arcsinh(upper) - arcsinh(lower) using channel frequency separation and bandwidth, minus a modulation-format-dependent correction	arctan-based XPM formula with full ISRS Raman tilt, inter-channel dispersion walk-off (phi_ik depends on beta_2, beta_3, beta_4), and optional modulation format excess kurtosis correction
ISRS (Raman tilt)	Not modelled	Full ISRS correction: Raman gain slope C_r modifies effective attenuation per channel, with tilt term T in both SPM and XPM
Dispersion model	Single coefficient beta_2 only	Three coefficients: beta_2, beta_3 (dispersion slope), beta_4 (curvature)

ASE Noise

Aspect	optical-networking-gym	XLRON
Formula	P_ASE = B * h * f * (exp(2*alpha*L) - 1) * NF_linear	P_ASE = 2 * N_sp * (G-1) * h * f * B where N_sp is derived from NF and gain
Gain model	Implicit: G = exp(2*alpha*L) (pure loss compensation, no ISRS)	ISRS-aware gain: G = exp(alpha*L) / g_SRS where g_SRS corrects for Raman tilt
Per-band NF	Single scalar NF per span (or single default for all spans)	Per-frequency-slot NF loaded from CSV, supporting multi-band scenarios (S/C/L)
ROADM ASE	Not modelled	Full ROADM model with configurable express and add/drop losses, booster amplifier NF
DRA support	Not available	Optional Friis cascade model for hybrid Raman+EDFA with per-channel Raman gain from ODE solution

NLI Computation Details

The optical-networking-gym NLI uses a simplified formula derived from the incoherent GN model (Poggiolini 2014):

# SPM contribution (self-channel)
sum_phi = arcsinh(pi^2 * |beta_2| * B_ch^2 / (4*alpha))

# XPM contribution (each interfering channel k)
phi_k = arcsinh(pi^2 * |beta_2| * L_eff_a * B_k * (delta_f + B_k/2))
      - arcsinh(pi^2 * |beta_2| * L_eff_a * B_k * (delta_f - B_k/2))
      - phi_mod_k * (B_k / |delta_f|) * (5/3) * (L_eff / L)

P_NLI = (P_ch / B_ch)^3 * (8 / (27*pi*|beta_2|)) * gamma^2 * L_eff * sum_phi * B_ch

XLRON computes SPM and XPM separately with higher-order dispersion and ISRS:

# SPM efficiency (per channel i)
eta_spm = (4/9) * (gamma^2/B^2) * pi / (phi_i * a_bar * (2a + a_bar))
          * [(T - a^2)/a * arcsinh(phi_i*B^2/(a*pi))
             + ((a+a_bar)^2 - T)/(a+a_bar) * arcsinh(phi_i*B^2/((a+a_bar)*pi))]

# XPM efficiency (channel i due to channel k)
eta_xpm_ik = (32/27) * (P_k/P_i)^2 * (gamma^2/denom)
              * [(T_k - a_k^2)/a_k * arctan(phi_ik*B_i/a_k)
                 + ((a_k+a_bar_k)^2 - T_k)/(a_k+a_bar_k) * arctan(phi_ik*B_i/(a_k+a_bar_k))]

Key physics differences:

• ISRS tilt term T: XLRON includes T = (a + a_bar - f*P_total*Cr)^2 which captures the frequency-dependent power transfer due to stimulated Raman scattering. This is absent in optical-networking-gym.
• arctan vs arcsinh for XPM: XLRON uses arctan for XPM (appropriate for inter-channel walk-off), while optical-networking-gym uses arcsinh (the same kernel as SPM). The arctan form is the standard closed-form GN model result for XPM.
• Modulation format correction: optical-networking-gym applies a phi_modulation_format correction per interfering channel based on spectral efficiency index. XLRON uses per-format excess_kurtosis values in an optional correction term.
• Coherent accumulation: XLRON supports both coherent and incoherent NLI accumulation across spans (controlled by --coherent flag). optical-networking-gym assumes incoherent accumulation (linear scaling with span count).

Fibre Parameters

Parameter	optical-networking-gym	XLRON	Notes
beta_2	-21.3e-27 s^2/m (hardcoded)	Derived from --dispersion_coeff (default 17e-6 s/m^2)	XLRON value gives beta_2 ~ -21.7e-27 at 1550 nm
gamma	1.3e-3 1/(W.m) (hardcoded)	--nonlinear_coefficient (default 1.2e-3)	Slightly different defaults
alpha	Per-span from topology, or single default	--attenuation (default 4.605e-5 Np/m = 0.2 dB/km)	XLRON also supports per-band values
NF	Per-span from topology, or single default	Per-frequency-slot from CSV, or --amplifier_noise_figure	Multi-band support in XLRON
Raman gain slope C_r	Not used	--raman_gain_slope (default 2.8e-17)	ISRS tilt correction
Dispersion slope	Not modelled	--dispersion_slope (default 60.7 s/m^3)	Higher-order dispersion

Environment Integration

Aspect	optical-networking-gym (QRMSAEnv)	XLRON (rmsa_gn_model / rsa_gn_model)
Language	Cython (.pyx) compiled to C for speed	JAX (Python), JIT-compiled to XLA for GPU/TPU
Execution	Sequential: Python loops over links, spans, and interfering services	Vectorised: jax.vmap over links and channels; broadcasting for XPM N x N matrix
When GSNR is computed	At action time: calculate_osnr() called once per candidate placement	At masking time (rmsa) or post-placement (rsa): full link SNR array recomputed
Disruption checking	After provisioning, recalculates OSNR for all co-link services to detect disruptions	Built into action check: all existing channels on affected links must still meet thresholds
Parallelism	Single environment, single service at a time	NUM_ENVS parallel environments via batched vectorisation
Topology	NetworkX graph with per-edge attributes	Static JAX arrays (link_slot_array, channel_power_array, etc.)
Action space	(path_index, modulation_index, initial_slot) tuple	Flat integer encoding path and slot (modulation selected automatically in rmsa_gn_model)
Reward	1 - log10(1 + OSNR - min_OSNR) / 1.6 (OSNR-margin-aware)	Binary: +1 for accepted, 0 for blocked (configurable via reward shaping)

Span Model

Aspect	optical-networking-gym	XLRON
Span definition	Explicit Span objects per link with individual length, attenuation_normalized, noise_figure_normalized	Computed from link length: num_spans = ceil(link_length / max_span_length), all spans equal length
Per-span parameters	Each span can have unique attenuation and NF	Uniform parameters per link (all spans share same fibre type)
Multi-span links	Explicit loop over topology-defined spans	Automatic subdivision of links into equal-length spans

Power Model

Aspect	optical-networking-gym	XLRON
Launch power	Per-service, set at provisioning time from launch_power_dbm	Per-channel, configurable via --power_per_channel or RL-controlled
Power budget	No explicit per-fibre power constraint	--max_power_per_fibre enforced during masking and action checking
Power spectral density	P_ch / B_ch used as PSD in NLI formula	Per-channel power with ISRS-aware tilt across spectrum

Scope and Capabilities Summary

Feature	optical-networking-gym	XLRON
GN model NLI (SPM + XPM)	Yes (simplified)	Yes (full ISRS GN model)
ISRS Raman tilt	No	Yes
Higher-order dispersion (beta_3, beta_4)	No	Yes
Coherent NLI accumulation	No	Optional
Modulation format NLI correction	Yes (phi array)	Optional (excess kurtosis)
Nyquist subchannel modelling	No	Yes (--num_subchannels)
ROADM noise model	No	Yes
Transceiver back-to-back noise	No	Yes
Per-band amplifier NF / TRX SNR	No	Yes (CSV data)
Distributed Raman Amplification	No	Yes (--use_raman_amp)
Multi-band (S+C+L)	No	Yes
Per-fibre power budget	No	Yes
GPU/TPU acceleration	No (CPU/Cython)	Yes (JAX JIT + vmap)
Parallel environments	No	Yes (--NUM_ENVS)
Differentiable through physics	No	Yes (--differentiable)
Service disruption tracking	Yes (recalculates OSNR for co-link services)	Yes (built into SNR validity check)