├── .gitignore
├── LICENSE
├── README.md
├── conda
├── README
└── ldbp_env.yml
└── ldbp
├── .gitignore
├── config
├── essfm.ini
├── isit.ini
└── isit_pruning.ini
├── jobscript_essfm
├── jobscript_isit
├── kill_last_pid
├── ldbp.py
└── lib
└── fir.py
/.gitignore:
--------------------------------------------------------------------------------
1 | *.DS_Store
2 |
--------------------------------------------------------------------------------
/LICENSE:
--------------------------------------------------------------------------------
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674 | .
675 |
--------------------------------------------------------------------------------
/README.md:
--------------------------------------------------------------------------------
1 | # LDBP: Learned Digital Backpropagation
2 |
3 | ## Getting Started
4 |
5 | The code is based on [TensorFlow](https://www.tensorflow.org/) 1.13.1 and may
6 | not work properly with other (older or newer) versions. It is recommended to create a
7 | dedicated conda environment using the YAML file in the folder `conda` as
8 | follows:
9 |
10 | ```console
11 | (base)~$ conda env create -f ldbp_env.yml
12 | (base)~$ conda activate ldbp_env
13 | ```
14 |
15 | Afterwards, it should be possible to run the provided jobscripts in the folder `ldbp`. For example:
16 |
17 | ```console
18 | (ldbp_env)~$ ./jobscript_isit
19 | ```
20 |
21 | To train for different scenarios, most of the parameters and training options are set in a configuration file located in the folder `config`.
22 |
23 |
40 |
41 |
45 |
46 | ## Additional Information
47 |
48 | This repository is based on joint work with [Henry D.
49 | Pfister](http://pfister.ee.duke.edu).
50 | If you decide to use the source code for your research, please make sure
51 | to cite our paper(s):
52 |
53 | * C. Häger and H. D. Pfister, "[Physics-Based Deep Learning for Fiber-Optic Communication Systems](https://arxiv.org/abs/2010.14258)", in *IEEE J. Sel. Areas Commun.* (to appear), 2020
54 |
55 | * C. Häger and H. D. Pfister, "[Nonlinear Interference Mitigation via Deep Neural Networks](https://arxiv.org/abs/1710.06234)", in Proc. *Optical Fiber Communication Conf. (OFC)*, San Diego, CA, March 2018
56 |
57 | * C. Häger and H. D. Pfister, "[Deep Learning of the Nonlinear Schrödinger Equation in Fiber-Optic Communication](https://arxiv.org/abs/1804.02799)", In Proc. *IEEE Int. Symp. on Information Theory (ISIT)*, Vail, CO, June 2018
58 |
59 |
--------------------------------------------------------------------------------
/conda/README:
--------------------------------------------------------------------------------
1 | # to create environment:
2 | conda env create -f ldbp_env.yml
3 |
4 | # to remove
5 | conda env remove -n ldbp_env
6 |
--------------------------------------------------------------------------------
/conda/ldbp_env.yml:
--------------------------------------------------------------------------------
1 | name: ldbp_env
2 | channels:
3 | - conda-forge
4 | dependencies:
5 | - python==3.7.3
6 | - pip
7 | - numpy==1.16.4
8 | - scipy==1.2.1
9 | - tensorflow==1.13.1
10 | - pip:
11 | - tqdm
12 | - configargparse
13 |
--------------------------------------------------------------------------------
/ldbp/.gitignore:
--------------------------------------------------------------------------------
1 | *.DS_Store
2 | log
3 | last_pid
4 |
--------------------------------------------------------------------------------
/ldbp/config/essfm.ini:
--------------------------------------------------------------------------------
1 | [system parameters]
2 | span length [km] = 80
3 | alpha [dB/km] = 0.2
4 | D [ps/nm/km] = 17
5 | gamma [1/W/km] = 1.3
6 | amplifier noise figure [dB] = 5.0
7 | sigma scaling = 2
8 | number of spans = 25
9 | symbol rate [Gbaud] = 10.7
10 | modulation = Gaussian
11 | RRC roll-off = 0.1
12 | RRC delay = 10
13 | data symbols per block = 256
14 | low-pass filter bandwidth [GHz] = 21.4
15 | analog oversampling = 6
16 | digital oversampling = 2
17 |
18 | [LDBP parameters]
19 | step size method = linear
20 | split step method = asymmetric
21 | less steps than spans = yes
22 | total steps = 4
23 | cd filter method = LS-CO
24 | cd filter bandwidth = 0.6
25 | cd filter max out-of-band gain = 0.8
26 | optimize cd filters = no
27 | optimize Kerr parameters = yes
28 | tied Kerr parameters = yes
29 | nl filter length = 41
30 |
31 | [training]
32 | minibatch size = 100
33 | optimizer = adam
34 | summary writing interval = 100
35 | save results to file = yes
36 |
37 | [data generation]
38 | forward steps per span = 50
39 | number of queue elements = 50000
40 | generation batch size = 10
41 | number of parallel processors = 10
42 | data replication factor = 150
43 | minimum elements after dequeue = 2000
44 |
--------------------------------------------------------------------------------
/ldbp/config/isit.ini:
--------------------------------------------------------------------------------
1 | [system parameters]
2 | span length [km] = 80
3 | alpha [dB/km] = 0.2
4 | D [ps/nm/km] = 17
5 | gamma [1/W/km] = 1.3
6 | amplifier noise figure [dB] = 5.0
7 | sigma scaling = 2
8 | number of spans = 25
9 | symbol rate [Gbaud] = 10.7
10 | modulation = Gaussian
11 | RRC roll-off = 0.1
12 | RRC delay = 10
13 | data symbols per block = 256
14 | low-pass filter bandwidth [GHz] = 21.4
15 | analog oversampling = 6
16 | digital oversampling = 2
17 |
18 | [LDBP parameters]
19 | step size method = linear
20 | split step method = asymmetric
21 | steps per span = 1
22 | cd filter method = LS-CO
23 | cd filter length = 9
24 | cd filter bandwidth = 0.6
25 | cd filter max out-of-band gain = 1.05
26 | optimize cd filters = yes
27 | #pruning = yes
28 | #target cd filter length = -4,3
29 |
30 | [training]
31 | minibatch size = 100
32 | optimizer = adam
33 | summary writing interval = 100
34 | save results to file = yes
35 |
36 | [data generation]
37 | forward steps per span = 50
38 | number of queue elements = 50000
39 | generation batch size = 10
40 | number of parallel processors = 10
41 | data replication factor = 150
42 | minimum elements after dequeue = 2000
43 |
--------------------------------------------------------------------------------
/ldbp/config/isit_pruning.ini:
--------------------------------------------------------------------------------
1 | [system parameters]
2 | span length [km] = 80
3 | alpha [dB/km] = 0.2
4 | D [ps/nm/km] = 17
5 | gamma [1/W/km] = 1.3
6 | amplifier noise figure [dB] = 5.0
7 | sigma scaling = 2
8 | number of spans = 25
9 | symbol rate [Gbaud] = 10.7
10 | modulation = Gaussian
11 | RRC roll-off = 0.1
12 | RRC delay = 10
13 | data symbols per block = 256
14 | low-pass filter bandwidth [GHz] = 21.4
15 | analog oversampling = 6
16 | digital oversampling = 2
17 |
18 | [LDBP parameters]
19 | step size method = linear
20 | split step method = asymmetric
21 | steps per span = 1
22 | cd filter method = LS-CO
23 | cd filter length = 9
24 | cd filter bandwidth = 0.6
25 | cd filter max out-of-band gain = 1.05
26 | optimize cd filters = yes
27 | pruning = yes
28 | target cd filter length = 5,3
29 |
30 | [training]
31 | minibatch size = 100
32 | optimizer = adam
33 | summary writing interval = 100
34 | save results to file = yes
35 |
36 | [data generation]
37 | forward steps per span = 50
38 | number of queue elements = 50000
39 | generation batch size = 10
40 | number of parallel processors = 10
41 | data replication factor = 150
42 | minimum elements after dequeue = 2000
43 |
--------------------------------------------------------------------------------
/ldbp/jobscript_essfm:
--------------------------------------------------------------------------------
1 | #!/bin/bash
2 | echo process ID: $$
3 | echo $$ > last_pid
4 |
5 | # starts at SNR = 5.2 dB
6 | # ends at SNR = 18.2 dB
7 | python3 ldbp.py [-5,-4,-3,-2] 0.001 5000 --config_path=config/essfm.ini
8 |
--------------------------------------------------------------------------------
/ldbp/jobscript_isit:
--------------------------------------------------------------------------------
1 | #!/bin/bash
2 | echo process ID: $$
3 | echo $$ > last_pid
4 |
5 | # starts at SNR = 20.9 dB
6 | # converges to 22.5 dB (maximum)
7 | python3 ldbp.py [0] 0.001 1500 --config_path=config/isit.ini
8 |
9 | # 150,000 iterations = approx. 2 hours
10 | #python3 ldbp.py [-2,-1,0,1] 0.001 150000 --config_path=config/isit_pruning.ini
11 |
--------------------------------------------------------------------------------
/ldbp/kill_last_pid:
--------------------------------------------------------------------------------
1 | #!/bin/bash
2 | kill -9 -`cat last_pid`
3 |
--------------------------------------------------------------------------------
/ldbp/ldbp.py:
--------------------------------------------------------------------------------
1 | #========================================================#
2 | # Learned Digital Backpropagation (LDBP)
3 | # Author: Christian Haeger (christian.haeger@chalmers.se)
4 | # Last modified: December, 2018
5 | #========================================================#
6 | # imports and constants {{{
7 | #========================================================#
8 | import tensorflow as tf
9 | import sys # sys.exit()
10 | import warnings
11 | import os # os.path.exists(), os.environ['v'], os.makedirs()
12 | import numpy as np
13 | import scipy as sp # sp.fft(), sp.linalg.solve(), sp.optimize.fsolve(), sp.special.erf()
14 | import time # time.gmtime(), time.strftime()
15 | import math # math.isnan()
16 | import random # random.shuffle()
17 | import threading # threading.Thread()
18 | import multiprocessing
19 | import argparse as ap
20 | import configparser
21 | import shutil # shutil.copyfile(src, dst)
22 | from lib import fir # fir.cd_fir_filter()
23 |
24 | os.environ['TF_CPP_MIN_LOG_LEVEL'] = '3' # avoid TF logging output for GPU devices etc.
25 | sp.set_printoptions(precision = 4, suppress = True)
26 | np.set_printoptions(precision = 4)
27 | #np.seterr(divide='ignore', invalid='ignore') # ignore "divide by 0" warning
28 |
29 | # constants
30 | co_h = 6.6260657e-34
31 | co_c0 = 299792458
32 | co_lambda = 1550.0e-9
33 | co_dB = 10.0*np.log10(np.exp(1.0))
34 | nu = co_c0/co_lambda
35 | dB_conv = 4.342944819032518
36 |
37 | # }}}
38 | #========================================================#
39 | # functions {{{
40 | #========================================================#
41 | def rrcosine(rolloff, delay, OS):
42 | """ Root-raised cosine filter for pulse shaping
43 | Args:
44 | rolloff: between 0 and 1
45 | delay: in symbols
46 | OS: oversampling factor (samples per symbol)
47 |
48 | Returns:
49 | A vector of length 2*(OS*delay)+1
50 | """
51 | rrcos = np.zeros(2*delay*OS+1)
52 | rrcos[delay*OS] = 1 + rolloff*(4/np.pi-1)
53 | for i in range(1,delay*OS+1):
54 | t = i/OS
55 | if(t == 1/4/rolloff):
56 | val = rolloff/np.sqrt(2)*((1+2/np.pi)*np.sin(np.pi/(4*rolloff)) + (1-2/np.pi)*np.cos(np.pi/(4*rolloff)))
57 | else:
58 | val = (np.sin(np.pi*t*(1-rolloff)) + 4*rolloff*t*np.cos(np.pi*t*(1+rolloff))) / (np.pi*t*(1-(4*rolloff*t)**2))
59 | rrcos[delay*OS+i] = val
60 | rrcos[delay*OS-i] = val
61 | return rrcos / np.sqrt(np.sum(rrcos**2))
62 |
63 | def get_fvec(N,fs):
64 | return np.concatenate((np.linspace(0,N//2-1,N//2), np.linspace(-N//2,-1,N//2))) * fs/N
65 |
66 | def tf_print(tmp_var):
67 | init = tf.global_variables_initializer()
68 | sess = tf.Session()
69 | sess.run(init)
70 | print(sess.run(tmp_var))
71 |
72 | def get_optimizer():
73 | if optimizer == "adam":
74 | opt = tf.train.AdamOptimizer(learning_rate, float(conf_train['adam_A']), float(conf_train['adam_B']))
75 | elif optimizer == "rmsprop":
76 | opt = tf.train.RMSPropOptimizer(learning_rate, float(conf_train['rmsprop_A']), float(conf_train['rmsprop_B']))
77 | elif optimizer == "adadelta":
78 | opt = tf.train.AdadeltaOptimizer(learning_rate, float(conf_train['adadelta_A']))
79 | elif optimizer == "adagrad":
80 | opt = tf.train.AdagradOptimizer(learning_rate, float(conf_train['adagrad_A']))
81 | else:
82 | raise ValueError("wrong optimizer string: optimizer = '"+optimizer+"'")
83 | return opt
84 |
85 | def complex_multiply(x,y):
86 | """
87 | Args:
88 | x: Tensor of shape = [batch_size, N, 2]
89 | y: Tensor of shape = [batch_size, N, 2]
90 |
91 | Returns:
92 | A Tensor of shape = [batch_size, N, 2]
93 | """
94 | xr = x[:,:,0]
95 | xi = x[:,:,1]
96 | yr = y[:,:,0]
97 | yi = y[:,:,1]
98 | return tf.stack([xr*yr-xi*yi, xr*yi+xi*yr], axis=2)
99 |
100 | def tf_real_filter(init_coeffs, opt=False):
101 | """ Create arbitrary FIR filter with real coefficients
102 |
103 | Args:
104 | init_coeffs: real numpy array of shape [filter_length,] with initial filter coefficients
105 | opt: (Optional) True for variable, False for constant, default=False
106 |
107 | Returns:
108 | A Tensor with shape = [filter_length]
109 | """
110 |
111 | if opt == True:
112 | h = tf.Variable(init_coeffs, dtype=tf.float32)
113 | else:
114 | h = tf.constant(init_coeffs, tf.float32)
115 |
116 | return h
117 |
118 | def tf_real_symmetric_filter(init_coeffs, opt=False, mask=1):
119 | """ Create odd-length symmetric FIR filter with real coefficients
120 |
121 | For symmetric filters of length 2*L+1, there are (L+1) tunable parameters:
122 | coeffs: h_L, ..., h_1, [h_0, h_1, ..., h_L]
123 |
124 | Args:
125 | init_coeffs: real numpy array of shape [filter_length,] with initial filter coefficients,
126 | filter_length should be odd
127 | coefficients should be symmetric
128 | opt: (Optional) True for variable, False for constant, default=False
129 | mask: (Optional) binary mask for pruning, default=1
130 |
131 | Returns:
132 | A Tensor with shape = [filter_length]
133 | """
134 |
135 | filter_length = len(init_coeffs)
136 | if filter_length%2 is 0:
137 | raise ValueError("filter length has to be odd: filter_length = {}".format(filter_length))
138 | filter_delay = (filter_length-1)//2
139 | right_half = init_coeffs[filter_delay::]
140 |
141 | for i in range(filter_delay): # check if symmetric
142 | absdiff = abs(init_coeffs[i] - right_half[filter_delay-i])
143 | if absdiff > 1e-2:
144 | warnings.warn("inital filter coefficients are not symmetric: absolute difference = {}".format(absdiff))
145 |
146 | if opt == True:
147 | h_vars = tf.Variable(right_half, dtype=tf.float32)
148 | else:
149 | h_vars = tf.constant(right_half, tf.float32)
150 |
151 | hmasked = h_vars*mask # apply binary mask for pruning
152 | return tf.concat([tf.reverse(hmasked[1:], axis=[0]), hmasked], axis=0)
153 |
154 | def tf_complex_symmetric_filter(init_coeffs, opt=False, mask=1):
155 | """ Create odd-length symmetric FIR filter with complex coefficients
156 |
157 | For complex-valued symmetric filters of length 2*L+1, there are 2*(L+1) tunable parameters:
158 | real coeffs: h_L, ..., h_1, [h_0, h_1, ..., h_L]
159 | imag coeffs: g_L, ..., g_1, [g_0, g_1, ..., g_L]
160 |
161 | Args:
162 | init_coeffs: complex numpy array of shape [filter_length,] with initial filter coefficients,
163 | filter_length should be odd
164 | coefficients should be symmetric
165 | opt: (Optional) True for variable, False for constant, default=False
166 | mask: (Optional) binary mask for pruning, default=1
167 |
168 | Returns:
169 | A Tensor with shape = [filter_length, 2]
170 | column 1: real coefficients
171 | column 2: imaginary coefficients
172 | """
173 |
174 | h_real = tf_real_symmetric_filter(np.real(init_coeffs), opt, mask)
175 | h_imag = tf_real_symmetric_filter(np.imag(init_coeffs), opt, mask)
176 | return tf.stack([h_real, h_imag], axis=1)
177 |
178 | def cconv(x, h):
179 | """ y = cconv(x, h) uses tf.nn.conv1d to perform circular convolution of signal x with filter h
180 |
181 | Notes:
182 | - This function also circularly shifts y to remove the filter delay caused by h
183 | - The delay is (filter_length-1)/2 for odd-length filters and filter_length/2-1 for even-length filters
184 | - TensorFlow does not do convolution but correlation, so the filter "flipping"
185 | is performed manually in this function.
186 |
187 | Args:
188 | x: signal Tensor
189 | shape(x) = [batch_size, N] real signal
190 | shape(x) = [batch_size, N, 2] complex signal
191 | h: filter Tensor
192 | shape(h) = [filter_length] real filter
193 | shape(h) = [filter_length, 2] complex filter
194 |
195 | Returns:
196 | A Tensor with shape
197 | shape(y) = [batch_size, N] if both x and h are real
198 | shape(y) = [batch_size, N, 2] all other cases
199 | """
200 |
201 | filter_length = int(h.shape[0])
202 | batch_size = int(x.shape[0])
203 | N = int(x.shape[1])
204 |
205 | # expand dimensions in case of real signal and/or filter
206 | if len(x.shape) == 2:
207 | x = tf.expand_dims(x, axis=2)
208 |
209 | if len(h.shape) == 1:
210 | h = tf.expand_dims(h, axis=1)
211 |
212 | # extend x to achieve circular convolution and remove the filter delay
213 | if(filter_length%2==0): # even-length filters
214 | filter_delay = filter_length//2-1
215 | x = tf.concat([x[:, N-filter_delay-1:, :], x, x[:, :filter_delay, :]], axis=1) # [x_end, x, x_begin]
216 | else: # odd-length filters
217 | filter_delay = (filter_length-1)//2
218 | x = tf.concat([x[:, N-filter_delay:, :], x, x[:, :filter_delay, :]], axis=1) # [x_end, x, x_begin]
219 |
220 | # reshape filter
221 | if(x.shape[2] == 1 and h.shape[1] == 1): # real signal, real filter
222 | h = tf.reshape(h, [filter_length, 1, 1])
223 | conv1d_filter = tf.reverse(h, axis=[0]) # flip
224 | elif(x.shape[2] == 1 and h.shape[1] == 2): # real signal, complex filter
225 | hr = tf.reshape(h[:,0], [filter_length, 1, 1])
226 | hr = tf.reverse(hr, axis=[0]) # flip
227 | hi = tf.reshape(h[:,1], [filter_length, 1, 1])
228 | hi = tf.reverse(hi, axis=[0]) # flip
229 | conv1d_filter = tf.concat([hr, hi], axis=2)
230 | elif(x.shape[2] == 2 and h.shape[1] == 1): # complex signal, real filter
231 | hr = tf.reshape(h[:,0], [filter_length, 1, 1])
232 | hr = tf.reverse(hr, axis=[0]) # flip
233 | z = tf.zeros(shape=[filter_length, 1, 1]) # dummy
234 | filter_1 = tf.concat([hr, z], axis=1)
235 | filter_2 = tf.concat([z , hr], axis=1)
236 | conv1d_filter = tf.concat([filter_1, filter_2], axis=2)
237 | elif(x.shape[2] == 2 and h.shape[1] == 2): # complex signal, complex filter
238 | hr = tf.reshape(h[:,0], [filter_length, 1, 1])
239 | hr = tf.reverse(hr, axis=[0]) # flip
240 | hi = tf.reshape(h[:,1], [filter_length, 1, 1])
241 | hi = tf.reverse(hi, axis=[0]) # flip
242 | filter_1 = tf.concat([hr, -hi], axis=1)
243 | filter_2 = tf.concat([hi, hr], axis=1)
244 | conv1d_filter = tf.concat([filter_1, filter_2], axis=2)
245 | else:
246 | raise ValueError("signal or filter has wrong shape")
247 |
248 | # call conv1d
249 | # input has shape = [batch_size, N, in_channels]
250 | # filter has shape = [filter_length, in_channels, out_channels]
251 | # output has shape = [batch_size, N, out_channels]
252 | y = tf.nn.conv1d(x, conv1d_filter, stride=1, padding="VALID", name='conv1d')
253 |
254 | if y.shape[2] == 1: # real signal and filter
255 | return y[:,:,0]
256 | else:
257 | return y
258 |
259 | def periodically_extend(x, M):
260 | """ Extends a numpy vector of length N to length M>N by periodically copying the elements """
261 | N = x.shape[0]
262 | y = np.zeros(M, dtype=x.dtype);
263 | for i in range(M):
264 | y[i] = x[i%N]
265 | return y
266 |
267 | def line2array(line):
268 | ''' converts a string of comma-separated numbers to numpy array '''
269 | return np.array([float(v) for v in line.strip().split(",")])
270 |
271 | def effective_length(length, alpha_lin):
272 | if alpha_lin == 0:
273 | return length
274 | else:
275 | return (1-np.exp(-alpha_lin*length))/alpha_lin
276 |
277 | class ssfm_parameters:
278 | """ handles parameters related to the split-step Fourier method (SSFM)
279 |
280 | Initialization is performed with a dictionary that should have the following keys:
281 | step_size_method
282 | logarithmic
283 | linear
284 | step_size
285 | predefined
286 | StPS: steps per span (only for logarithmic and linear)
287 | adjusting_factor: recommended is 0.4 (only for logarithmic)
288 | ssfm_method
289 | symmetric: linear->nonlinear->linear
290 | asymmetric: linear->nonlinear
291 | combine_half_steps: wether to combine half-steps of adjacent spans (only for symmetric)
292 | alpha: attenuation parameter; should be 0 for less steps than spans
293 | beta2: dispersion parameter
294 | gamma: nonlinear parameter
295 | Nsp: number of spans
296 | Lsp: span length [m]
297 | fsamp: sampling frequency
298 | Nsamp: length of the assumed FFT
299 | direction: +1 for forward, -1 for backpropagation
300 |
301 | computed attributes:
302 | model_steps
303 | cd_length
304 | nl_param
305 | nl_length (not used)
306 |
307 | Usage example:
308 |
309 | bw = ssfm_parameters(parameter_dict)
310 | for NN in range(bw.model_steps):
311 | u = sp.ifft(bw.get_cd_filter_freq(NN)*sp.fft(u))
312 | u = u*np.exp(1J*bw.nl_param[NN]*np.abs(u)**2)
313 | """
314 |
315 | def __init__(self, opts):
316 | self.__dict__.update(opts) # converts all dictionary entries to attributes
317 |
318 | alpha_lin = self.alpha/(10*np.log10(np.exp(1)))
319 | Nsp = self.Nsp
320 | Lsp = self.Lsp
321 | direction = self.direction
322 |
323 | if direction == +1 and self.Nsp > 1:
324 | raise ValueError("forward propagation valid only for 1 span")
325 |
326 | if self.step_size_method == 'logarithmic':
327 | if 'adjusting_factor' not in opts:
328 | self.adjusting_factor = 0.4 # 0: linear, 1: very logarithmic
329 |
330 | if 'combine_half_steps' not in opts:
331 | self.combine_half_steps = True
332 |
333 | if self.step_size_method == 'step_size': # used only for subband processing
334 | step_size = self.step_size
335 | Ltot = Lsp*Nsp
336 | model_steps = int(np.floor(Ltot/step_size)+1)
337 | last_step_size = Ltot - (model_steps-1)*step_size
338 |
339 | cd_length = step_size*np.ones(model_steps)
340 | cd_length[model_steps-1] = last_step_size
341 |
342 | tmp = np.mod(np.cumsum(cd_length), Lsp)
343 | len_before = np.zeros(model_steps)
344 | len_after = np.zeros(model_steps)
345 | amplifier_location = np.zeros(model_steps)
346 | for NN in range(1, model_steps):
347 | if(tmp[NN-1] > tmp[NN]):
348 | amplifier_location[NN] = 1;
349 | len_after[NN] = tmp[NN]
350 | len_before[NN] = cd_length[NN] - len_after[NN]
351 | amplifier_location[0] = 1
352 | amplifier_location[-1] = 0
353 |
354 | nl_length = np.zeros(model_steps)
355 | eff_len_before = np.zeros(model_steps)
356 | for NN in range(model_steps):
357 | if (amplifier_location[NN] == 1) and (NN != 0):
358 | h = len_after[NN]
359 | eff_len_before[NN] = effective_length(len_before[NN],np.abs(alpha_lin))
360 | else:
361 | h = cd_length[NN]
362 | nl_length[NN] = effective_length(h,np.abs(alpha_lin))
363 | else:
364 | StPS = self.StPS
365 | # ====================================================== #
366 | # compute step sizes for one span
367 | # ====================================================== #
368 | if self.step_size_method == 'logarithmic':
369 | alpha_adj = self.adjusting_factor*alpha_lin
370 | delta = (1-np.exp(-alpha_adj*Lsp))/StPS
371 | if(direction == -1):
372 | nn = np.arange(StPS)+1 # 1,2,...,StPS
373 | else:
374 | nn = StPS-np.arange(StPS) # StPS,...,2,1
375 | step_size = -1/(alpha_adj) * np.log((1-(StPS-nn+1)*delta)/(1-(StPS-nn)*delta))
376 | elif self.step_size_method == "linear":
377 | step_size = Lsp/StPS*np.ones(StPS)
378 | else:
379 | raise ValueError("wrong step_size_method given (should be 'linear' or 'logarithmic'): "+self.step_size_method)
380 | # ====================================================== #
381 | # compute cd_length, nl_length, amplifier_location
382 | # ====================================================== #
383 | if self.ssfm_method == "symmetric":
384 | if self.combine_half_steps == True:
385 | model_steps = Nsp*StPS+1
386 | cd_length = np.zeros(model_steps)
387 | nl_length = np.zeros(model_steps)
388 | for NN in range(Nsp):
389 | for MM in range(StPS):
390 | cd_length[NN*StPS+MM] = step_size[MM]/2 + step_size[(MM+StPS-1)%StPS]/2
391 | nl_length[NN*StPS+MM] = step_size[MM]
392 | cd_length[0] = step_size[0]/2
393 | cd_length[model_steps-1] = step_size[StPS-1]/2
394 |
395 | amplifier_location = np.zeros(model_steps)
396 | amplifier_location[:-1:StPS] = 1
397 | else:
398 | model_steps = Nsp*(StPS+1)
399 | cd_length = np.concatenate([[step_size[0]/2], (step_size[0:-1]+step_size[1:])/2, [step_size[-1]/2]])
400 | cd_length = np.tile(cd_length, Nsp)
401 | nl_length = np.concatenate([step_size, [0]])
402 | nl_length = np.tile(nl_length, Nsp)
403 |
404 | amplifier_location = np.zeros(model_steps)
405 | amplifier_location[::StPS+1] = 1
406 | elif self.ssfm_method == "asymmetric":
407 | model_steps = Nsp*StPS
408 | cd_length = np.zeros(model_steps)
409 | nl_length = np.zeros(model_steps)
410 | for NN in range(Nsp):
411 | for MM in range(StPS):
412 | cd_length[NN*StPS+MM] = step_size[MM]
413 | nl_length[NN*StPS+MM] = effective_length(step_size[MM], np.abs(alpha_lin))
414 |
415 | amplifier_location = np.zeros(model_steps)
416 | amplifier_location[::StPS] = 1
417 | else:
418 | raise ValueError("wrong split step method given (should be 'symmetric' or 'asymmetric'): "+self.ssfm_method)
419 | # ====================================================== #
420 | # compute attenuation and nl_param
421 | # ====================================================== #
422 | nl_param = direction*self.gamma*nl_length
423 |
424 | attenuation = np.exp(-direction*alpha_lin*cd_length/2)
425 | for NN in range(model_steps):
426 | if direction == -1 and amplifier_location[NN] == 1:
427 | attenuation[NN] = attenuation[NN] * np.exp(direction*alpha_lin*Lsp/2)
428 |
429 | # re-normalize nl_param
430 | for NN in range(model_steps):
431 | nl_param[NN] = nl_param[NN]*np.prod(attenuation[0:NN+1:])**2
432 |
433 | if self.step_size_method == "step_size":
434 | for NN in range(model_steps):
435 | if amplifier_location[NN] == 1:
436 | nl_param[NN] = nl_param[NN] + direction*self.gamma*eff_len_before[NN]
437 |
438 | self.model_steps = model_steps
439 | self.cd_length = cd_length
440 | self.nl_length = nl_length
441 | self.nl_param = nl_param
442 |
443 | N = self.Nsamp
444 | self.fvec = np.concatenate((np.linspace(0,N//2-1,N//2), np.linspace(-N//2,-1,N//2))) * self.fsamp/N
445 |
446 | def get_cd_filter_freq(self, NN):
447 | return np.exp(1j*(self.beta2/2)*(2*np.pi*self.fvec)**2*(self.direction*self.cd_length[NN]))
448 |
449 | def ordered_direct_product(A,B):
450 | p = A.shape[0]
451 | q = B.shape[0]
452 | n = A.shape[1]
453 | m = B.shape[1]
454 |
455 | C = np.zeros([p*q,n+m])
456 | for i in range(q):
457 | C[i*q:(i+1)*q:, :n:] = A[i,:]
458 | for i in range(p):
459 | C[i*q:(i+1)*q:, n::] = B
460 | return C
461 |
462 | def QAM(M):
463 | Msqrt = (np.sqrt(M)).astype(np.int)
464 | if Msqrt**2 != M:
465 | raise ValueError("M has to be of the form M=4^m where m>0")
466 | x_pam = np.expand_dims(-(Msqrt-2*np.arange(start=1, stop=Msqrt+1)+1), axis=1)
467 | x_qam = ordered_direct_product(x_pam, x_pam)
468 | const = x_qam[:,0] + 1j * x_qam[:,1]
469 | return const/np.sqrt(np.mean(np.abs(const)**2))
470 |
471 | # }}}
472 | #========================================================#
473 | # parse function arguments {{{
474 | #========================================================#
475 | parser = ap.ArgumentParser("python3 ldbp.py")
476 | parser.description = "Learned Digital Backpropagation (LDBP)"
477 | parser.add_argument("P", help="set of training powers in dB, e.g., [5] or [5,6,7]")
478 | parser.add_argument("Lr", help="learning rate, e.g., 0.01")
479 | parser.add_argument("iter", help="gradient descent iterations, e.g., 1000")
480 | parser.add_argument("-c", "--config_path", help="path to configuration file (default is ldbp_config.ini)", default="ldbp_config.ini")
481 | parser.add_argument("-l", "--logdir", help="directory for log files (default is log)", default="log")
482 | parser.add_argument("-t", "--timing", help="time the forward propagation", action="store_true")
483 |
484 | args = parser.parse_args()
485 | args_dict = vars(args) # converts to a dictionary
486 |
487 | opt_list="P,Lr,iter".split(",")
488 | arg_str = ""
489 | for i in range(len(opt_list)):
490 | arg_str += opt_list[i]
491 | arg_str += args_dict[opt_list[i]]
492 | if(i != len(opt_list)-1):
493 | arg_str += "_"
494 |
495 | config_path = args.config_path
496 | P_dB_r = np.asarray(eval(args.P))
497 | P_W_r = pow(10, P_dB_r/10)*1e-3
498 | iterations = int(args.iter)
499 | learning_rate = float(args.Lr)
500 |
501 | # }}}
502 | #========================================================#
503 | # read config file {{{
504 | #========================================================#
505 | defaults = {
506 | # system
507 | "sigma scaling" : "1",
508 | "modulation" : "16-QAM",
509 | # LDBP
510 | "combine half-steps" : "yes",
511 | "load cd filter" : "no",
512 | "load cd filter filename" : "parameters.csv",
513 | "optimize cd filters" : "yes",
514 | "optimize Kerr parameters" : "no",
515 | "complex Kerr parameters" : "no",
516 | "tied Kerr parameters" : "no",
517 | "pruning" : "no",
518 | "less steps than spans" : "no",
519 | "cd alpha" : "1",
520 | "cd filter length margin" : "2.0",
521 | "cd filter length minimum" : "13",
522 | "nl alpha" : "1",
523 | "nl filter length" : "1",
524 | # training
525 | "adam_A" : "0.9", # decay for running average of the gradient
526 | "adam_B" : "0.999", # decay for running average of the square of the gradient
527 | "rmsprop_A" : "0.9",
528 | "rmsprop_B" : "0.1",
529 | "adadelta_A" : "0.1",
530 | "adagrad_A" : "0.1",
531 | # data
532 | 'forward step size method' : 'logarithmic',
533 | 'forward split step method' : 'symmetric'
534 | }
535 |
536 | config = configparser.ConfigParser(defaults)
537 |
538 | config_folder, config_file = os.path.split(config_path)
539 | print("configuration file name: '"+config_file+"'")
540 |
541 | if not os.path.exists(config_path):
542 | raise RuntimeError("config file in '"+config_file+"' does not exist")
543 | config.read(config_path)
544 |
545 | # system parameters
546 | conf_sys = config['system parameters']
547 | Lsp = conf_sys.getfloat('span length [km]')*1.0e3
548 | alpha = conf_sys.getfloat('alpha [dB/km]')*1.0e-3
549 | gamma = conf_sys.getfloat('gamma [1/W/km]')*1.0e-3
550 | noise_figure = conf_sys.getfloat('amplifier noise figure [dB]')
551 | sigma_scaling = conf_sys.getfloat('sigma scaling')
552 | Nsp = conf_sys.getint('number of spans')
553 | fsym = conf_sys.getfloat('symbol rate [Gbaud]')*1.0e9
554 | modulation = conf_sys['modulation']
555 | rolloff = conf_sys.getfloat('RRC roll-off')
556 | delay = conf_sys.getint('RRC delay')
557 | lp_bandwidth = conf_sys.getfloat('low-pass filter bandwidth [GHz]')*1.0e9
558 | Nsym = conf_sys.getint('data symbols per block')
559 | OS_a = conf_sys.getint('analog oversampling')
560 | OS_d = conf_sys.getint('digital oversampling')
561 | if config.has_option('system parameters', 'D [ps/nm/km]'):
562 | D = conf_sys.getfloat('D [ps/nm/km]')*1.0e-6
563 | beta2 = -D*co_lambda**2/(2*np.pi*co_c0)
564 | else:
565 | beta2 = conf_sys.getfloat('beta2 [ps^2/km]')*1.0e-27
566 |
567 | # LDBP parameters
568 | conf_ldbp = config['LDBP parameters']
569 | step_size_method_bw = conf_ldbp['step size method']
570 | ssfm_method_bw = conf_ldbp['split step method']
571 | combine_half_steps = conf_ldbp['combine half-steps']
572 | cd_opt = conf_ldbp.getboolean('optimize cd filters')
573 | cd_alpha = conf_ldbp.getfloat('cd alpha')
574 | load_cd_filter = conf_ldbp.getboolean('load cd filter')
575 | if load_cd_filter == True:
576 | cd_filter_filename = conf_ldbp['load cd filter filename']
577 | else:
578 | cd_filter_method = conf_ldbp['cd filter method']
579 | cd_filter_bandwidth = conf_ldbp.getfloat('cd filter bandwidth')
580 | cd_filter_oob_gain = conf_ldbp.getfloat('cd filter max out-of-band gain') # 0.58 for 17-taps 20 Gbaud
581 | nl_opt = conf_ldbp.getboolean('optimize Kerr parameters')
582 | if nl_opt == True:
583 | tied_Kerr = conf_ldbp.getboolean('tied Kerr parameters')
584 | nl_alpha = conf_ldbp.getfloat('nl alpha')
585 | nl_filter_length = conf_ldbp.getint('nl filter length')
586 | less_steps_than_spans = conf_ldbp.getboolean('less steps than spans')
587 |
588 | # training parameters
589 | conf_train = config['training']
590 | minibatch_size = conf_train.getint('minibatch size')
591 | optimizer = conf_train['optimizer']
592 | summary_interval = conf_train.getint('summary writing interval')
593 | SAVE_FILE = conf_train.getboolean('save results to file')
594 |
595 | # data generation
596 | conf_data = config['data generation']
597 | StPS_fw = conf_data.getint('forward steps per span')
598 | step_size_method_fw = conf_data['forward step size method']
599 | ssfm_method_fw = conf_data['forward split step method']
600 | QMAX = conf_data.getint('number of queue elements') # number of queue elements
601 | QBSIZE = conf_data.getint('generation batch size') # batch size to pupulate the queue
602 | NPROC = conf_data.getint('number of parallel processors') # number of processors used to populate the queue
603 | REPF = conf_data.getint('data replication factor') # replication factor for data
604 |
605 | if OS_a%OS_d != 0:
606 | raise ValueError('oversampling factors have to be divisible: OS_a={}, OS_d={}'.format(OS_a, OS_d))
607 |
608 | if nl_filter_length%2 == 0:
609 | raise ValueError('nl_filter_length has to be odd: nl_filter_length = {}'.format(nl_filter_length))
610 | nl_filter_delay = (nl_filter_length-1)//2
611 |
612 | # derived parameters
613 | L = Lsp*Nsp
614 | Gain = 10.0**(alpha*Lsp/10.0)
615 | sef = 10.0**(noise_figure/10.0)/2.0/(1.0-1.0/Gain)
616 | alpha_lin = alpha / dB_conv
617 | N0 = sigma_scaling*Nsp*(np.exp(alpha_lin*Lsp)-1.0)*co_h*nu*sef
618 | sigma2 = N0 * fsym * OS_a
619 | Nsamp_a = Nsym*OS_a
620 | Nsamp_d = Nsym*OS_d
621 | fsamp_a = fsym*OS_a
622 | fsamp_d = fsym*OS_d
623 | f_a = get_fvec(Nsamp_a, fsamp_a)
624 | f_d = get_fvec(Nsamp_d, fsamp_d)
625 |
626 | if "QAM" in modulation:
627 | splitstr = modulation.split("-")
628 | modulation_order = int(splitstr[0])
629 | modulation = "QAM"
630 |
631 | print("total memory of the data queue: {} MB".format(QMAX*64*(Nsamp_d+Nsym)/8/1e6))
632 |
633 | # }}}
634 | #========================================================#
635 | # forward propagation generative model {{{
636 | #========================================================#
637 | ps_filter_tx_coeffs = rrcosine(rolloff, delay, OS_a) # pulse shaping filter
638 | ps_filter_tx_length = 2*(OS_a*delay)+1
639 | ps_filter_tx_delay = OS_a*delay # delay in samples
640 |
641 | # pre-compute frequency responses
642 | ps_tmp = np.concatenate((ps_filter_tx_coeffs, np.zeros(Nsamp_a-ps_filter_tx_length)))
643 | ps_tmp = np.roll(ps_tmp, -ps_filter_tx_delay)
644 | ps_filter_tx_freq = sp.fft(ps_tmp, n=Nsamp_a)
645 | lp_filter_freq = (abs(f_a) <= lp_bandwidth/2).astype(float)
646 |
647 | if modulation == "QAM":
648 | const = QAM(modulation_order)
649 |
650 | ssfm_opts = {
651 | "alpha": alpha,
652 | "beta2": beta2,
653 | "gamma": gamma,
654 | "Nsp": 1,
655 | "Lsp": Lsp,
656 | "fsamp": fsamp_a,
657 | "Nsamp": Nsamp_a,
658 | "step_size_method": step_size_method_fw,
659 | "ssfm_method": ssfm_method_fw,
660 | "StPS": StPS_fw,
661 | "direction": 1
662 | }
663 |
664 | fw = ssfm_parameters(ssfm_opts)
665 |
666 | def forward_propagation():
667 | """
668 | Returns:
669 | y: received signal (shape = [Nsamp_d, 2], separate real and imaginary part)
670 | x: symbol vector (shape = [Nsym], complex)
671 | P: launch power (in W)
672 | """
673 | np.random.seed() # new seed is necessary for multiprocessor
674 | P = P_W_r[np.random.randint(P_W_r.shape[0])] # get random launch power
675 | # [SOURCE] random points from the signal constellation
676 | if modulation == "QAM":
677 | x = const[np.random.randint(const.shape[0], size=[1, Nsym])]
678 | elif modulation == "Gaussian":
679 | x = (np.random.normal(0,1,size=[1, Nsym]) + 1j*np.random.normal(0,1,size=[1, Nsym]))/np.sqrt(2)
680 | else:
681 | raise ValueError("wrong modulation format: " + modulation)
682 | # [MODULATION] upsample + pulse shaping
683 | x_up = np.zeros([1, Nsamp_a], dtype=np.complex64)
684 | x_up[:, ::OS_a] = x*np.sqrt(OS_a)
685 | u = sp.ifft(sp.fft(x_up)*ps_filter_tx_freq)*np.sqrt(P)
686 | # [CHANNEL] simulate forward propagation
687 | for NN in range(Nsp): # enter a span
688 | for MM in range(fw.model_steps): # enter a segment
689 | u = sp.ifft(fw.get_cd_filter_freq(MM)*sp.fft(u))
690 | u = u*np.exp(1j*fw.nl_param[MM]*np.abs(u)**2)
691 | #u = u*np.exp(1j*(8/9)*fw.nl_param[MM]*(np.abs(u[0,:])**2+np.abs(u[1,:])**2))
692 | # add noise, NOTE: amplifier gain (u = u*np.exp(alpha_lin*Lsp/2.0)) is absorbed in nl_param
693 | u = u + np.sqrt(sigma2/2/Nsp) * (np.random.randn(1,Nsamp_a) + 1j*np.random.randn(1,Nsamp_a))
694 | # [RECEIVER] low-pass filter + downsample
695 | u = sp.ifft(sp.fft(u)*lp_filter_freq)
696 | y = u[0, ::OS_a//OS_d]
697 | y = np.stack([np.real(y), np.imag(y)], axis=1)
698 | return y, x[0,:], P
699 |
700 | if args.timing == True:
701 | print("")
702 | print("timing the forward propation ...")
703 | t = time.time()
704 | _,_,_ = forward_propagation()
705 | elapsed = time.time()-t
706 | print("{0:.2f} seconds to generate 1 input/output data pair".format(elapsed))
707 | print("Generating approx. {0:.0f} input/output data pairs per seconds".format(NPROC*REPF/elapsed))
708 | sys.exit("")
709 |
710 | # }}}
711 | #========================================================#
712 | # compute step sizes for DBP {{{
713 | #========================================================#
714 | ssfm_opts = {}
715 | ssfm_opts['beta2'] = beta2
716 | ssfm_opts['gamma'] = gamma
717 | ssfm_opts['fsamp'] = fsamp_d
718 | ssfm_opts['Nsamp'] = Nsamp_d
719 | ssfm_opts['step_size_method'] = step_size_method_bw
720 | ssfm_opts['ssfm_method'] = ssfm_method_bw
721 | ssfm_opts['combine_half_steps'] = combine_half_steps
722 | ssfm_opts['direction'] = -1
723 |
724 | if less_steps_than_spans == False:
725 | ssfm_opts['alpha'] = alpha
726 | ssfm_opts['Nsp'] = Nsp
727 | ssfm_opts['Lsp'] = Lsp
728 | ssfm_opts['StPS'] = int(conf_ldbp['steps per span'])
729 | else:
730 | ssfm_opts['alpha'] = 0
731 | ssfm_opts['Nsp'] = 1
732 | ssfm_opts['Lsp'] = Lsp*Nsp
733 | ssfm_opts['StPS'] = int(conf_ldbp['total steps'])
734 |
735 | bw = ssfm_parameters(ssfm_opts)
736 |
737 | #}}}
738 | #========================================================#
739 | # compute or load initial cd filter coefficients {{{
740 | #========================================================#
741 | cd_filter_coeffs = {}
742 |
743 | if load_cd_filter == False:
744 | # create object for cd filter design
745 | fopt = {}
746 | fopt['beta2'] = beta2
747 | fopt['fsamp'] = fsamp_d
748 | fopt['Nsamp'] = Nsamp_d
749 | fopt['method'] = cd_filter_method
750 | fopt['bandwidth'] = cd_filter_bandwidth
751 | fopt['max_out_of_band_gain'] = cd_filter_oob_gain # 0.58 for 17-taps 20 Gbaud
752 | fir_obj = fir.cd_fir_filter(fopt)
753 |
754 | # determine length of cd filters
755 | if config.has_option('LDBP parameters', 'cd filter length'):
756 | tmp = (line2array(conf_ldbp['cd filter length'])).astype(np.int32)
757 | cd_filter_length = periodically_extend(tmp, bw.model_steps) # tile
758 | else:
759 | cd_filter_length_margin = float(conf_ldbp['cd filter length margin'])
760 | cd_filter_length_min = int(conf_ldbp['cd filter length minimum'])
761 | print("No cd filter length provided. Computing automatically with margin {} and minimum {}:".format(cd_filter_length_margin,cd_filter_length_min))
762 |
763 | req_len = fir_obj.get_required_filter_length(bw.cd_length)
764 | cd_filter_length = (2*np.ceil(req_len/2*(1+cd_filter_length_margin))+1).astype(np.int32)
765 | for NN in range(bw.model_steps):
766 | if cd_filter_length[NN] < cd_filter_length_min:
767 | cd_filter_length[NN] = cd_filter_length_min
768 | print(cd_filter_length)
769 |
770 | # compute filter taps
771 | for NN in range(bw.model_steps):
772 | cd_filter_coeffs[NN] = fir_obj.get_filter(bw.cd_length[NN], cd_filter_length[NN])
773 | else: # or load from file
774 | f = open(cd_filter_filename)
775 | lines = f.readlines()
776 | f.close()
777 |
778 | if len(lines) != 3*bw.model_steps:
779 | raise RuntimeError("File '"+cd_filter_filename+"' should have {} lines but has {}".format(3*bw.model_steps, len(lines)))
780 |
781 | cd_filter_length = np.zeros(bw.model_steps, dtype=np.int64)
782 | for NN in range(bw.model_steps):
783 | h_r = line2array(lines[NN*3+0])
784 | h_i = line2array(lines[NN*3+1])
785 | if np.size(h_r) != np.size(h_i):
786 | raise ValueError('real and imaginary part of loaded cd filters should be the same')
787 | cd_filter_length[NN] = np.size(h_r)
788 | if cd_filter_length[NN]%2 == 0:
789 | raise ValueError('loaded cd filter should have odd length: cd_filter_length[{}]={}'.format(NN,cd_filter_length[NN]))
790 | cd_filter_coeffs[NN] = h_r+1j*h_i
791 | print("loaded cd filters have lengths:")
792 | print(cd_filter_length)
793 |
794 | cd_filter_delay = (cd_filter_length-1)//2
795 |
796 | #}}}
797 | #========================================================#
798 | # define pruning parameters {{{
799 | #========================================================#
800 | pruning = config.getboolean('LDBP parameters', 'pruning')
801 |
802 | def get_prune_op(mask, mask_len):
803 | mask_len_descreased = tf.assign(mask_len, mask_len-1)
804 | pos = tf.constant(np.arange(0, int(mask.get_shape()[0]), 1, np.int32), tf.int32)
805 | new_mask = tf.cast(tf.less(pos, mask_len_descreased), tf.float32)
806 | return tf.assign(mask, new_mask)
807 |
808 | cd_mask = {}
809 |
810 | if pruning == True:
811 | # get target lengths and memory
812 | tmp = (line2array(conf_ldbp['target cd filter length'])).astype(np.int32)
813 | target_length = periodically_extend(tmp, bw.model_steps) # tile
814 | for NN in range(bw.model_steps):
815 | if target_length[NN] < 0:
816 | target_length[NN] = cd_filter_length[NN] + target_length[NN]
817 | if target_length[NN]%2 == 0:
818 | raise ValueError("target filter lengths have to be odd")
819 | print("pruned filters will have lengths:")
820 | print(target_length)
821 | target_delay = (target_length-1)//2
822 | # determine the pruning order
823 | prune_order = []
824 | max_len = np.max(cd_filter_delay)
825 | min_len = np.min(target_delay)
826 | for i in range(max_len-min_len+1):
827 | for NN in range(bw.model_steps):
828 | if cd_filter_delay[NN] >= max_len-i and target_delay[NN] < max_len-i:
829 | prune_order.append(NN)
830 | # shuffle the order
831 | random.shuffle(prune_order)
832 | # determine pruning schedule: train-prune-train-prune-train
833 | pruning_steps = len(prune_order)
834 | #pruning_interval = np.ceil(iterations/(pruning_steps+1))
835 | print("total pruning steps: {}".format(pruning_steps))
836 | pruning_schedule = (np.ceil(np.ceil(2.0**(-np.arange(pruning_steps,0,-1))*iterations)))
837 | pruning_schedule = np.ceil(pruning_schedule + np.arange(pruning_steps)*iterations/8/pruning_steps)
838 |
839 | cd_mask_len = {}
840 | prune_op = {} # each mask has a pruning op associated with it
841 |
842 | for NN in range(bw.model_steps):
843 | cd_mask[NN] = tf.Variable(np.ones([cd_filter_delay[NN]+1]), dtype=tf.float32, trainable=False)
844 | cd_mask_len[NN] = tf.Variable(cd_filter_delay[NN]+1, dtype=tf.int32, trainable=False)
845 | prune_op[NN] = get_prune_op(cd_mask[NN], cd_mask_len[NN])
846 | else:
847 | print("no pruning")
848 | for NN in range(bw.model_steps):
849 | cd_mask[NN] = 1
850 |
851 | # }}}
852 | #========================================================#
853 | # define tunable parameters {{{
854 | #========================================================#
855 | no_filter = np.zeros(nl_filter_length, dtype=np.float32)
856 | no_filter[nl_filter_delay] = 1.0
857 |
858 | if nl_opt == True and tied_Kerr == True:
859 | nl_filter_all = tf_real_symmetric_filter(no_filter*nl_alpha, nl_opt)
860 |
861 | cd_filter = {}
862 | nl_filter = {}
863 |
864 | for NN in range(bw.model_steps):
865 | # linear parameters
866 | cd_filter[NN] = tf_complex_symmetric_filter(cd_filter_coeffs[NN]*cd_alpha, cd_opt, mask=cd_mask[NN])
867 | # nonlinear parameters
868 | if nl_opt == True:
869 | if tied_Kerr == True:
870 | nl_filter[NN] = nl_filter_all
871 | else:
872 | nl_filter[NN] = tf_real_symmetric_filter(no_filter*nl_alpha, nl_opt)
873 | else:
874 | nl_filter[NN] = tf_real_symmetric_filter(no_filter*nl_alpha, nl_opt)
875 |
876 | # matched filter
877 | ps_filter = tf_real_symmetric_filter(rrcosine(rolloff, delay, OS_d))
878 |
879 | # }}}
880 | #========================================================#
881 | # build the computation graph in TensorFlow {{{
882 | #========================================================#
883 | print("building the TensorFlow graph ", end='', flush=True)
884 |
885 | y_enq = tf.placeholder(tf.float32, shape=[None, Nsamp_d, 2])
886 | x_enq = tf.placeholder(tf.complex64, shape=[None, Nsym])
887 | P_enq = tf.placeholder(tf.float32, shape=[None, 1])
888 |
889 | min_after_dequeue = int(conf_data["minimum elements after dequeue"]) # at least this many elements must remain after dequeue
890 |
891 | myq = tf.RandomShuffleQueue(QMAX, min_after_dequeue, dtypes=[tf.float32, tf.complex64, tf.float32], shapes=[[Nsamp_d, 2], [Nsym], [1]])
892 | enqueue_op = myq.enqueue_many([y_enq, x_enq, P_enq])
893 | dummy_dequeue = myq.dequeue_many(QBSIZE*NPROC*REPF)
894 | y,x,P_W = myq.dequeue_many(minibatch_size)
895 |
896 | # [LDBP], signals have shape = [batch_size, N, 2] (if complex) or [batch_size, N] (if real)
897 | for NN in range(bw.model_steps):
898 | print('.', end='', flush=True)
899 | # linear step
900 | y = cconv(y, cd_filter[NN]/cd_alpha) # complex(y) = complex(x) * complex(h)
901 | # nonlinear step, includes possible filtering of {|y_i|^2}
902 | #ysq = bw.nl_param[NN]*tf.reduce_sum(tf.square(y), axis=2)
903 | ysq = bw.nl_param[NN]*tf.reduce_sum(tf.square(y), axis=2)
904 | ysq_filtered = cconv(ysq, nl_filter[NN]/nl_alpha) # real(y) = real(x) * real(h)
905 | y = complex_multiply(y, tf.stack([tf.cos(ysq_filtered), tf.sin(ysq_filtered)], axis=2))
906 |
907 | # matched filter
908 | y = cconv(y, ps_filter) # complex(y) = complex(x) * real(h)
909 | y = tf.complex(y[:,:,0],y[:,:,1])
910 | # downsample
911 | y = y[:,::OS_d] / tf.complex(tf.sqrt(P_W), 0.0) / np.sqrt(OS_d)
912 | # constant phase-offset rotation
913 | tmp = tf.reduce_sum(tf.conj(x)*y, 1, keepdims=True)
914 | phi_cpe = -tf.atan2(tf.imag(tmp),tf.real(tmp))
915 | x_hat = y * tf.exp(tf.complex(0.0, phi_cpe))
916 |
917 | mean_squared_error = tf.reduce_mean(tf.square(tf.abs(x-x_hat)))
918 | effective_snr = -10.0*tf.log(mean_squared_error+1e-12)/tf.log(10.0)
919 |
920 | print("")
921 | print("calling optimizer ... ", end="", flush=True)
922 | optimizer = get_optimizer()
923 | train = optimizer.minimize(mean_squared_error)
924 |
925 | # compute total number of tunable parameters
926 | total_parameters = 0
927 | for variable in tf.trainable_variables():
928 | shape = variable.get_shape() # shape is an array of tf.Dimension
929 | variable_parameters = 1
930 | for dim in shape:
931 | variable_parameters *= dim.value
932 | total_parameters += variable_parameters
933 |
934 | print("done, total tunable parameters: {}".format(total_parameters))
935 |
936 | # }}}
937 | #========================================================#
938 | # start session {{{
939 | #========================================================#
940 | tf.summary.scalar("effective_snr", effective_snr)
941 | tf.summary.scalar("data_queue_size", myq.size())
942 | summary = tf.summary.merge_all()
943 |
944 | init_op = tf.global_variables_initializer()
945 | sess = tf.Session()
946 |
947 | # create log dir
948 | logdir = args.logdir+"/"+arg_str
949 | logdir += "/" + time.strftime("%Y-%m-%d_%H.%M.%S", time.gmtime())
950 |
951 | if not os.path.exists(logdir):
952 | os.makedirs(logdir)
953 | else:
954 | raise RuntimeError("log directory \'" + logdir + "\' already exists")
955 |
956 | print("name of the log directory: " + logdir)
957 |
958 | # copy the .ini file to log folder
959 | shutil.copyfile(config_path, logdir+"/"+config_file)
960 | summary_writer = tf.summary.FileWriter(logdir, sess.graph)
961 | sess.run(init_op) # run the OP that initializes global variables
962 |
963 | # }}}
964 | #========================================================#
965 | # populate the data queue {{{
966 | #========================================================#
967 | def forward_propagation_batch(ignore_arg):
968 | y_read = np.zeros([QBSIZE, Nsamp_d, 2], np.float32)
969 | x_read = np.zeros([QBSIZE, Nsym], np.complex64)
970 | P_read = np.zeros([QBSIZE, 1], np.float32)
971 | for i in range(QBSIZE):
972 | y_read[i,:,:], x_read[i,:], P_read[i,:] = forward_propagation()
973 | return y_read, x_read, P_read
974 |
975 | def populate_queue(sess, enqueue_op, coord):
976 | m = multiprocessing.cpu_count()
977 | pool = multiprocessing.Pool(m)
978 | while not coord.should_stop():
979 | results = pool.map(forward_propagation_batch, [0]*NPROC)
980 | y_batch = np.zeros([QBSIZE*NPROC*REPF, Nsamp_d, 2], np.float32)
981 | x_batch = np.zeros([QBSIZE*NPROC*REPF, Nsym], np.complex64)
982 | P_batch = np.zeros([QBSIZE*NPROC*REPF, 1], np.float32)
983 | for j in range(REPF):
984 | for i in range(NPROC):
985 | off = j*QBSIZE*NPROC
986 | y_batch[i*QBSIZE+off:(i+1)*QBSIZE+off,:,:] = results[i][0]
987 | x_batch[i*QBSIZE+off:(i+1)*QBSIZE+off,:] = results[i][1]
988 | P_batch[i*QBSIZE+off:(i+1)*QBSIZE+off,:] = results[i][2]
989 | sess.run(enqueue_op, feed_dict={y_enq: y_batch, x_enq: x_batch, P_enq: P_batch})
990 |
991 | coord = tf.train.Coordinator()
992 | t = threading.Thread(target=populate_queue, args=(sess, enqueue_op, coord))
993 | t.start()
994 |
995 | # }}}
996 | #========================================================#
997 | # optimization routine {{{
998 | #========================================================#
999 | # inital values
1000 | mse_tmp, snr_tmp = sess.run([mean_squared_error, effective_snr])
1001 | print("---------------------------------------------")
1002 | print("initial: MSE = {0:.6f}, effective SNR = {1:.3f} dB".format(mse_tmp, snr_tmp))
1003 | print("elements in the data queue: {}".format(sess.run(myq.size())))
1004 |
1005 | # write initial summary
1006 | sstr = sess.run(summary)
1007 | summary_writer.add_summary(sstr, 0)
1008 | summary_writer.flush()
1009 |
1010 | # gradient descent
1011 | start = time.time()
1012 |
1013 | pruned = 0
1014 | for i in range(1,iterations+1):
1015 | _, mse_tmp, snr_tmp, sstr = sess.run([train, mean_squared_error, effective_snr, summary]) # 1 step in gradient descent
1016 | if(math.isnan(mse_tmp)):
1017 | print("nan detected, exiting optimization loop")
1018 | break
1019 | # summary
1020 | if i%summary_interval == 0 or i==iterations:
1021 | summary_writer.add_summary(sstr, i)
1022 | summary_writer.flush()
1023 | print("iter {0}: MSE = {1:.6f}, effective SNR = {2:.3f} dB, summary written".format(i, mse_tmp, snr_tmp))
1024 | # pruning
1025 | if pruning == True:
1026 | pr_cnt = (pruning_schedule == i).sum()
1027 | for II in range(pr_cnt):
1028 | print("pruning (iter: {}, filter: {}, progress: {}/{})".format(i,prune_order[pruned],pruned+1,pruning_steps))
1029 | sess.run(prune_op[prune_order[pruned]])
1030 | pruned = pruned + 1
1031 |
1032 | end = time.time()
1033 |
1034 | print("requesting stop")
1035 | coord.request_stop()
1036 |
1037 | queue_size = sess.run(myq.size())
1038 | if(QMAX - queue_size < QBSIZE*NPROC*REPF):
1039 | print("dummy dequeue")
1040 | sess.run(dummy_dequeue) # otherwise the threads hang at enqueue_op
1041 |
1042 | print("joining threads")
1043 | coord.join([t]) # wait for threads to terminate
1044 |
1045 | opt_time = end-start
1046 | print("total optimization time: {0:.1f}s".format(opt_time))
1047 | print("processing approx. {0:.0f} input/output data pairs per second".format(iterations*minibatch_size/opt_time))
1048 |
1049 | # }}}
1050 | #========================================================#
1051 | # save results to csv file {{{
1052 | #========================================================#
1053 | if SAVE_FILE == True:
1054 | print("saving optimized parameters ... ", end="", flush=True)
1055 |
1056 | f=open(logdir+'/parameters.csv', 'ab') # a: append, b: binary mode
1057 | f.truncate(0)
1058 |
1059 | cd_filter_print = sess.run(cd_filter)
1060 | nl_filter_print = sess.run(nl_filter)
1061 |
1062 | for NN in range(bw.model_steps):
1063 | tmp = np.transpose(cd_filter_print[NN] / cd_alpha)
1064 | if pruning == True: # only store the pruned filter
1065 | delay_diff = cd_filter_delay[NN] - target_delay[NN]
1066 | tmp = tmp[:,delay_diff:delay_diff+target_length[NN]:]
1067 | np.savetxt(f, tmp, delimiter=',')
1068 | np.savetxt(f, np.transpose(nl_filter_print[NN]*bw.nl_param[NN] / nl_alpha), delimiter=',')
1069 | f.close()
1070 | print("done")
1071 | else:
1072 | print("nothing is saved ...")
1073 |
1074 | # }}}
1075 | #========================================================#
1076 |
--------------------------------------------------------------------------------
/ldbp/lib/fir.py:
--------------------------------------------------------------------------------
1 | import numpy as np
2 | from numpy import pi, cos, sin, exp, sqrt
3 | from scipy import special, linalg, optimize, ifft
4 | import warnings
5 | #import sympy as sym
6 |
7 | class cd_fir_filter:
8 | """ finite impulse response (FIR) filters for compensating chromatic dispersion (CD)
9 |
10 | Second-order dispersion is modeled in the (forward) split-step Fourier method as
11 |
12 | u = -j beta2/2 d^2u/dt^2
13 |
14 | which has the frequency-domain solution
15 |
16 | U(w,z) = exp(j beta/2 z w^2) U(w,0)
17 |
18 | In order to compensate, the ideal filter response is given by
19 |
20 | EDC(w) = exp(-j beta/2 z w^2)
21 |
22 | Args (provided as a dictionary):
23 | beta2: dispersion parameter
24 | fsamp: sampling frequency in Hz
25 | Nsamp: number of samples (for FFT)
26 | method: employed filter-design method
27 | 'truncate IDFT'
28 | 'direct sampling'
29 | 'least squares'
30 | 'LS-CO': least squares with constrained out-of-band gain
31 | bandwidth: percentage of compensated bandwidth, between 0 and 1, defaults to 1
32 | only used for 'least squares' and 'LS-CO'
33 | eps: regularization parameter for 'least squares', defaults to 1e-12
34 | max_out_of_band_gain: for 'LS-CO'
35 | """
36 |
37 | def __init__(self, opts):
38 | self.__dict__.update(opts) # converts all dictionary entries to attributes
39 |
40 | if 'bandwidth' not in opts:
41 | self.bandwidth = 1.0
42 | if opts['method'] == 'least squares' and 'eps' not in opts:
43 | self.eps = 1e-12
44 | if self.bandwidth < 0.0 or self.bandwidth > 1.0:
45 | raise ValueError("bandwidth parameter has to be between 0 and 1: bandwidth = {}".format(self.bandwidth))
46 |
47 | def get_required_filter_length(self, L):
48 | L = np.array(L)
49 | Df = self.bandwidth*self.fsamp
50 | return (2*np.floor(2*pi*np.abs(self.beta2)*L*Df*self.fsamp/2)+1).astype(np.int32)
51 |
52 | def get_filter(self, L, cd_filter_length):
53 | """ approximates exp(j*KK*w^2), where w=-pi..pi
54 |
55 | Args:
56 | L: fiber length [m]
57 | cd_filter_length: length of the FIR filter, has to be odd
58 |
59 | Returns:
60 | Filter coefficients as numpy array
61 | """
62 |
63 | if cd_filter_length%2 == 0:
64 | raise ValueError("cd_filter_length has to be odd: cd_filter_length={}".format(cd_filter_length))
65 |
66 | KK = -(self.beta2)/2*L*(self.fsamp**2)
67 | delay = (cd_filter_length-1)//2
68 | N = self.Nsamp
69 | xi = self.bandwidth
70 | Omega1 = -pi*xi
71 | Omega2 = pi*xi
72 | K = int(np.floor(N/2*self.bandwidth))
73 |
74 | if xi < 1:
75 | i = np.reshape(np.arange(K+1,(N-K-1)+1), [N-2*K-1, 1])
76 | k = np.reshape(np.arange(-delay, delay+1), [1, cd_filter_length])
77 | B = exp(-1j*i*k*2*pi/N) * sqrt((2*pi/N)/(2*pi+Omega1-Omega2))
78 | else:
79 | B = np.zeros([1, cd_filter_length])
80 |
81 | out_of_band_gain = lambda h: np.sum(np.abs(np.matmul(B,h))**2)
82 |
83 | i = np.reshape(np.arange(-K,K+1), [2*K+1, 1])
84 | k = np.reshape(np.arange(-delay, delay+1), [1, cd_filter_length])
85 | A = exp(-1j*i*k*2*pi/N) #* sqrt((2*pi/N)/(Omega2-Omega1))
86 | des = exp(1j*KK*(2*pi*i/N)**2) #* sqrt((2*pi/N)/(Omega2-Omega1))
87 |
88 | inband_error = lambda h: np.sum(np.abs(np.matmul(A,h)-des)**2)#/(2*xi*pi)/N
89 |
90 | if self.method == 'truncate IDFT':
91 | fvec = np.fft.fftshift(np.arange(-N//2, N//2)*self.fsamp/N)
92 | htmp = ifft(exp(-1j*self.beta2/2*L*(2*pi*fvec)**2))
93 | cd_filter_coeffs = np.concatenate([np.flipud(htmp[1:delay+1:]), htmp[0:delay+1:]])
94 | elif self.method == 'direct sampling': # Savory (2008)
95 | cd_filter_coeffs = np.zeros([cd_filter_length], dtype=np.complex64)
96 | for n in range(-delay, delay+1):
97 | cd_filter_coeffs[n+delay] = sqrt(1j/(4*KK*pi))*exp(-1j*n**2/(4*KK))
98 | elif self.method == 'least squares2':
99 | Q = xi*np.ones([delay+1, delay+1]) # Q[0,0] = xi
100 | for i in range(1,delay+1):
101 | Q[0,i] = Q[i,0] = 2*sin(i*pi*xi)/(i*pi)
102 | for i in range(1,delay+1):
103 | for j in range(1,delay+1):
104 | if i != j:
105 | AA = i*cos(j*pi*xi)*sin(i*pi*xi)
106 | BB = j*cos(i*pi*xi)*sin(j*pi*xi)
107 | Q[i,j] = 4*(AA-BB)/(i**2-j**2)/pi
108 | else:
109 | Q[i,i] = (2*pi*xi+sin(2*i*pi*xi)/i)/pi
110 |
111 | nn = np.arange(delay+1)
112 | D = exp(-1j*(nn**2/(4*KK) + 3*pi/4))/(2*sqrt(pi*KK+0j)) \
113 | *(special.erf(exp(1j*3*pi/4)*(2*Omega2*KK-nn)/(2*sqrt(KK+0j))) \
114 | + special.erf(exp(1j*3*pi/4)*(2*Omega2*KK+nn)/(2*sqrt(KK+0j))))
115 | D[0] = D[0]/2
116 |
117 | I = 2*np.eye(delay+1)
118 | I[0,0] = 1
119 |
120 | tmp = linalg.solve(Q+self.eps*I, D)
121 | cd_filter_coeffs = np.concatenate([np.flipud(tmp[1:]),tmp])
122 | elif self.method == 'least squares': # Eghbali et al. (2014)
123 | Q = np.ones([cd_filter_length, cd_filter_length])
124 | for i in range(cd_filter_length):
125 | for j in range(cd_filter_length):
126 | if i != j: # diagonal entries are 1
127 | Q[i,j] = sin(pi*(i-j)*xi)/(pi*(i-j)*xi)
128 | Q = xi*Q
129 |
130 | nn = np.arange(-delay, delay+1)
131 | v = xi*self.int_aux(nn, KK, xi)
132 |
133 | cd_filter_coeffs = linalg.solve(Q+self.eps*np.eye(cd_filter_length), v)
134 | elif self.method == 'LS-CO': # Sheikh et al. (2016)
135 | Q1 = np.ones([cd_filter_length, cd_filter_length])
136 | Q2 = np.ones([cd_filter_length, cd_filter_length])
137 | for i in range(cd_filter_length):
138 | for j in range(cd_filter_length):
139 | if i != j: # diagonal entries are 1
140 | Q1[i,j] = sin(pi*(i-j)*xi)/(pi*(i-j)*xi)
141 | if xi < 1:
142 | Q2[i,j] = sin(pi*(i-j)*xi)/(pi*(i-j)*(xi-1))
143 | else:
144 | Q2[i,j] = 0.0
145 |
146 | nn = np.arange(-delay, delay+1)[np.newaxis].T
147 | v = self.int_aux(nn, KK, xi)
148 |
149 | hopt = lambda l: linalg.solve(Q1+l*Q2, v)
150 | fun2 = lambda l: out_of_band_gain(hopt(np.abs(l)))-self.max_out_of_band_gain
151 |
152 | lambda_opt = np.abs(optimize.fsolve(fun2, 1e-10))
153 | #if fun2(0.0) > 0:
154 | # lambda_opt = np.abs(optimize.fsolve(fun2, 0.0))
155 | #else:
156 | # lambda_opt = 0.0
157 | #print(lambda_opt)
158 |
159 | cd_filter_coeffs = hopt(lambda_opt)
160 | elif self.method == 'maximally flat': # experimental
161 | Q = np.zeros([delay+1, delay+1], dtype=np.float64)
162 | Q[0,0] = 1
163 | for n in range(1,delay+1):
164 | Q[0,n] = 2
165 | for k in range(1,delay+1):
166 | for n in range(delay+1):
167 | Q[k,n] = 2*n**(2*k)
168 | if k%2 != 0: # odd rows
169 | Q[k,n] = -Q[k,n]
170 |
171 | w = sym.symbols('w')
172 |
173 | v = np.zeros([delay+1], dtype=np.complex128)
174 | for k in range(delay+1):
175 | v[k] = (sym.diff(sym.exp(sym.I*KK*w**2), w, 2*k)).subs(w,0)
176 |
177 | cd_filter_coeffs = linalg.solve(Q, v)
178 | cd_filter_coeffs = np.concatenate([np.flipud(cd_filter_coeffs[1::]), cd_filter_coeffs])
179 | else:
180 | raise ValueError("wrong cd filter method")
181 |
182 | eps_o = out_of_band_gain(cd_filter_coeffs)
183 | E = inband_error(cd_filter_coeffs)
184 | #print(E)
185 | h = cd_filter_coeffs
186 | #(np.abs(np.matmul(A,h)-des)**2))
187 | #np.set_printoptions(threshold=np.inf)
188 | tmp = (np.abs(np.matmul(A,h)-des)**2)
189 | #print(A.shape)
190 | #print(h.shape)
191 | #print(des.shape)
192 | #print((np.matmul(A,h)-des).shape)
193 |
194 | for i in range(delay):
195 | absdiff = abs(cd_filter_coeffs[i] - cd_filter_coeffs[cd_filter_length-i-1])
196 | if(absdiff > 1e-2):
197 | warnings.warn("filter coefficients are not symmetric: absolute difference = {}".format(absdiff))
198 |
199 | return cd_filter_coeffs.reshape([cd_filter_length])
200 |
201 | def int_aux(self, n, KK, x):
202 | # ( integrate exp(j*KK*w^2)exp(j*n*w) dw=-x*pi...x*pi ) / (2*pi*x)
203 | #
204 | # eq. (13) in Eghbali et al. (2014), with fixed typo
205 | # +0j to avoid NANs with sqrt(negative number)
206 | # D = exp(-1j*(nn**2/(4*KK) + 3*pi/4))/(4*sqrt(pi*KK+0j)) \
207 | # *(special.erf(exp(1j*3*pi/4)*(2*(Omega2/pi)*KK*pi-nn)/(2*sqrt(KK+0j))) \
208 | # + special.erf(exp(1j*3*pi/4)*(2*(Omega2/pi)*KK*pi+nn)/(2*sqrt(KK+0j))))
209 | #
210 | Omega1 = -pi*x
211 | Omega2 = pi*x
212 | y = exp(-1j*(n**2/(4*KK)+3*pi/4))/(2*(Omega2-Omega1))*sqrt(pi/KK+0j) \
213 | *(special.erf(exp(-1j*pi/4)*(2*Omega1*KK+n)/(2*sqrt(KK+0j))) \
214 | - special.erf(exp(-1j*pi/4)*(2*Omega2*KK+n)/(2*sqrt(KK+0j))))
215 | return y
216 |
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