The signal-to-noise ratio (SNR) after coherent detection and digital dispersion compensation is given by SNR = P⁄(PASE+PNLI), where P is the launch power, PASE is the linear noise power and PNLI is the nonlinear interference power. All quantities are channel (frequency) dependent.
The ISRS GN model function returns the nonlinear interference (NLI) power PNLI = ηP3 [W] and the NLI coefficient η [1⁄W2] for every channel slot (Nch × 1). The function needs the following variables as input parameters:
| Input Parameter | Variable | Dimension | Format |
|---|---|---|---|
| Attenuation coefficient (α) | Att | Np⁄m | Nch × n |
| Attenuation coefficient (bar) (ᾱ) | Att_bar | Np⁄m | Nch × n |
| Linear regression of Raman gain function (Cr) | Cr | 1⁄(W·m·Hz) | Nch × n |
| Channel launch power (Pi) | Pch | W | Nch × n |
| Channel center frequency (fi) | fi | Hz | Nch × n |
| Channel bandwidth (Bi) | Bch | Hz | Nch × n |
| Number of spans (n) | n | scalar | |
| Fiber length (L) | L | m | 1 × n |
| Dispersion coefficient (D) | D | s⁄m2 | 1 × n |
| Dispersion slope (S) | S | s⁄m3 | 1 × n |
| Nonlinearity coefficient (γ) | γ | 1⁄(W·m) | 1 × n |
| Reference wavelength (λ) | λ | m | scalar |
| coherent NLI accumulation | coherent | boolean | scalar |
The format Nch × n is represented by a matrix, where Nch is the number of channel slots and n is the number of fiber spans. Essentially, this expressed the channel and span dependency on certain parameters. Generally, it holds that ᾱ=α. For more information and explanation, please see [1]. The input parameters are passed to the function as an object which handled slightly differently in Python and in Matlab.
In Python, the input parameters are passed as a dictionary with the input parameters as keys/values. An example is listed below
n = 1 # number of spans
Bch = 40.004e9 # WDM channel bandwidth
channels = 251 # number of channels
spacing = 40.005e9 # WDM channel spacing
P = {
'fi' : np.repeat(np.reshape(
(np.arange(channels) - (channels-1)/2)*spacing
,[-1,1]),n,axis=1), # center frequencies
'n' : n, # number of spans
'Bch' : np.tile(40.004e9,[channels,n]), # channel bandwith
'RefLambda': 1550e-9, # reference wavelength
'D' : 17 *1e-12/1e-9/1e3 * np.ones(n), # dispersion coefficient
'S' : 0.067 *1e-12/1e-9/1e3/1e-9 * np.ones(n), # dispersion slope
'Att' : 0.2 /4.343/1e3 * np.ones([channels, n]), # attenuation coefficient
'Cr' : 0.028 /1e3/1e12 * np.ones([channels, n]), # Raman gain spectrum slope
'gamma' : 1.2 /1e3 * np.ones(n), # nonlinearity coefficient
'Length' : 100 *1e3 * np.ones(n), # fiber length
'coherent' : 1 # coherent NLI accumulation
'Pch' : 10**(0/10)*0.001 * np.ones([channels, n]) # channel launch power
}
P['Att_bar'] = P['Att'] # attenuation (bar)
NLI_power, NLI_coefficient = ISRSGNmodel(**P) # ISRS GN model function callIn Matlab, the input parameters are passed as a struct with the input parameters as attributes. An example is listed below
P.n = 1; % number of spans
Bch = 40.004e9; % WDM channel bandwidth
channels = 251; % number of channels
spacing = 40.005e9; % WDM channel spacing
P.fi = -channels*spacing/2+0.5*spacing+(0:(channels-1))'*spacing; % center frequencies
P.fi = repmat(P.fi, 1, P.n); % center frequencies
P.Bch = Bch * ones(channels, P.n); % channel bandwidth
P.RefLambda = 1550e-9; % reference wavelength
P.D = 17 *1e-12/1e-9/1e3 * ones(1, P.n); % dispersion coefficient
P.S = 0.067 *1e-12/1e-9/1e3/1e-9 * ones(1, P.n); % dispersion slope
P.Att = 0.2 /4.343/1e3 * ones(channels, P.n); % attenuation coefficient
P.Att_bar = P.Att; % attenuation coefficient (bar)
P.Cr = 0.028 /1e3/1e12 * ones(channels, P.n); % Raman gain spectrum slope
P.Gamma = 1.2 /1e3 * ones(1, P.n); % nonlinearity coefficient
P.Length = 100 *1e3 * ones(1, P.n); % fiber length
P.coherent = 1; % coherent NLI accumulation
P.Pch = 10.^(0/10)*0.001 * ones(channels, P.n); % launch power per channel
[NLI_power, NLI_coeffcient] = ISRSGNmodel( P ); % ISRS GN model function call[1] D. Semrau, R. I. Killey, P. Bayvel, "A Closed-Form Approximation of the Gaussian Noise Model in the Presence of Inter-Channel Stimulated Raman Scattering, " J. Lighw. Technol., Early Access, DOI: 10.1109/JLT.2019.2895237, Jan. 2019.