simulations/models/end_to_end.py

import math

import tensorflow as tf
import numpy as np
import matplotlib.pyplot as plt
from sklearn.preprocessing import OneHotEncoder
from tensorflow.keras import layers, losses


class ExtractCentralMessage(layers.Layer):
    def __init__(self, messages_per_block, samples_per_symbol):
        """
        A keras layer that extracts the central message(symbol) in a block.

        :param messages_per_block: Total number of messages in transmission block
        :param samples_per_symbol: Number of samples per transmitted symbol
        """
        super(ExtractCentralMessage, self).__init__()

        temp_w = np.zeros((messages_per_block * samples_per_symbol, samples_per_symbol))
        i = np.identity(samples_per_symbol)
        begin = int(samples_per_symbol * ((messages_per_block - 1) / 2))
        end = int(samples_per_symbol * ((messages_per_block + 1) / 2))
        temp_w[begin:end, :] = i

        self.w = tf.convert_to_tensor(temp_w, dtype=tf.float32)

    def call(self, inputs, **kwargs):
        return tf.matmul(inputs, self.w)


class AwgnChannel(layers.Layer):
    def __init__(self, rx_stddev=0.1):
        """
        A additive white gaussian noise channel model. The GaussianNoise class is utilized to prevent identical noise
        being applied every time the call function is called.

        :param rx_stddev: Standard deviation of receiver noise (due to e.g. TIA circuit)
        """
        super(AwgnChannel, self).__init__()
        self.noise_layer = layers.GaussianNoise(rx_stddev)

    def call(self, inputs, **kwargs):
        return self.noise_layer.call(inputs, training=True)


class DigitizationLayer(layers.Layer):
    def __init__(self,
                 fs,
                 num_of_samples,
                 lpf_cutoff=32e9,
                 q_stddev=0.1):
        """
        This layer simulated the finite bandwidth of the hardware by means of a low pass filter. In addition to this,
        artefacts casued by quantization is modelled by the addition of white gaussian noise of a given stddev.

        :param fs: Sampling frequency of the simulation in Hz
        :param num_of_samples: Total number of samples in the input
        :param lpf_cutoff: Cutoff frequency of LPF modelling finite bandwidth in ADC/DAC
        :param q_stddev: Standard deviation of quantization noise at ADC/DAC
        """
        super(DigitizationLayer, self).__init__()

        self.noise_layer = layers.GaussianNoise(q_stddev)
        freq = np.fft.fftfreq(num_of_samples, d=1/fs)
        temp = np.ones(freq.shape)

        for idx, val in np.ndenumerate(freq):
            if np.abs(val) > lpf_cutoff:
                temp[idx] = 0

        self.lpf_multiplier = tf.convert_to_tensor(temp, dtype=tf.complex64)

    def call(self, inputs, **kwargs):
        complex_in = tf.cast(inputs, dtype=tf.complex64)
        val_f = tf.signal.fft(complex_in)
        filtered_f = tf.math.multiply(self.lpf_multiplier, val_f)
        filtered_t = tf.signal.ifft(filtered_f)
        real_t = tf.cast(filtered_t, dtype=tf.float32)
        noisy = self.noise_layer.call(real_t, training=True)
        return noisy


class OpticalChannel(layers.Layer):
    def __init__(self,
                 fs,
                 num_of_samples,
                 dispersion_factor,
                 fiber_length,
                 lpf_cutoff=32e9,
                 rx_stddev=0.01,
                 q_stddev=0.01):
        """
        A channel model that simulates chromatic dispersion, non-linear photodiode detection, finite bandwidth of
        ADC/DAC as well as additive white gaussian noise in optical communication channels.

        :param fs: Sampling frequency of the simulation in Hz
        :param num_of_samples: Total number of samples in the input
        :param dispersion_factor: Dispersion factor in s^2/km
        :param fiber_length: Length of fiber to model in km
        :param lpf_cutoff: Cutoff frequency of LPF modelling finite bandwidth in ADC/DAC
        :param rx_stddev: Standard deviation of receiver noise (due to e.g. TIA circuit)
        :param q_stddev: Standard deviation of quantization noise at ADC/DAC
        """
        super(OpticalChannel, self).__init__()

        self.noise_layer = layers.GaussianNoise(rx_stddev)
        self.digitization_layer = DigitizationLayer(fs=fs,
                                                    num_of_samples=num_of_samples,
                                                    lpf_cutoff=lpf_cutoff,
                                                    q_stddev=q_stddev)
        self.flatten_layer = layers.Flatten()

        self.fs = fs
        self.freq = tf.convert_to_tensor(np.fft.fftfreq(num_of_samples, d=1/fs), dtype=tf.complex128)
        self.multiplier = tf.math.exp(0.5j*dispersion_factor*fiber_length*tf.math.square(2*math.pi*self.freq))

    def call(self, inputs, **kwargs):
        # DAC LPF and noise
        dac_out = self.digitization_layer(inputs)

        # Chromatic Dispersion
        complex_val = tf.cast(dac_out, dtype=tf.complex128)
        val_f = tf.signal.fft(complex_val)
        disp_f = tf.math.multiply(val_f, self.multiplier)
        disp_t = tf.signal.ifft(disp_f)

        # Squared-Law Detection
        pd_out = tf.square(tf.abs(disp_t))

        # Casting back to floatx
        real_val = tf.cast(pd_out, dtype=tf.float32)

        # Adding photo-diode receiver noise
        rx_signal = self.noise_layer.call(real_val, training=True)

        # ADC LPF and noise
        adc_out = self.digitization_layer(rx_signal)

        return adc_out


class EndToEndAutoencoder(tf.keras.Model):
    def __init__(self,
                 cardinality,
                 samples_per_symbol,
                 messages_per_block,
                 channel):
        """
        The autoencoder that aims to find a encoding of the input messages. It should be noted that a "block" consists
        of multiple "messages" to introduce memory into the simulation as this is essential for modelling inter-symbol
        interference. The autoencoder architecture was heavily influenced by IEEE 8433895.

        :param cardinality: Number of different messages. Chosen such that each message encodes log_2(cardinality) bits
        :param samples_per_symbol: Number of samples per transmitted symbol
        :param messages_per_block: Total number of messages in transmission block
        :param channel: Channel Layer object. Must be a subclass of keras.layers.Layer with an implemented forward pass
        """
        super(EndToEndAutoencoder, self).__init__()

        # Labelled M in paper
        self.cardinality = cardinality
        # Labelled n in paper
        self.samples_per_symbol = samples_per_symbol
        # Labelled N in paper
        if messages_per_block % 2 == 0:
            messages_per_block += 1
        self.messages_per_block = messages_per_block
        # Channel Model Layer
        if isinstance(channel, layers.Layer):
            self.channel = tf.keras.Sequential([
                layers.Flatten(),
                channel,
                ExtractCentralMessage(self.messages_per_block, self.samples_per_symbol)
            ])
        else:
            raise TypeError("Channel must be a subclass of keras.layers.layer!")

        # Encoding Neural Network
        self.encoder = tf.keras.Sequential([
            layers.Input(shape=(self.messages_per_block, self.cardinality)),
            layers.Dense(2 * self.cardinality, activation='relu'),
            layers.Dense(2 * self.cardinality, activation='relu'),
            layers.Dense(self.samples_per_symbol),
            layers.ReLU(max_value=1.0)
        ])

        # Decoding Neural Network
        self.decoder = tf.keras.Sequential([
            layers.Dense(self.samples_per_symbol, activation='relu'),
            layers.Dense(2 * self.cardinality, activation='relu'),
            layers.Dense(2 * self.cardinality, activation='relu'),
            layers.Dense(self.cardinality, activation='softmax')
        ])

    def generate_random_inputs(self, num_of_blocks, return_vals=False):
        """
        A method that generates a list of one-hot encoded messages. This is utilized for generating the test/train data.

        :param num_of_blocks: Number of blocks to generate. A block contains multiple messages to be transmitted in
        consecutively to model ISI. The central message in a block is returned as the label for training.
        :param return_vals: If true, the raw decimal values of the input sequence will be returned
        """
        rand_int = np.random.randint(self.cardinality, size=(num_of_blocks * self.messages_per_block, 1))

        cat = [np.arange(self.cardinality)]
        enc = OneHotEncoder(handle_unknown='ignore', sparse=False, categories=cat)

        out = enc.fit_transform(rand_int)
        out_arr = np.reshape(out, (num_of_blocks, self.messages_per_block, self.cardinality))

        mid_idx = int((self.messages_per_block-1)/2)

        if return_vals:
            out_val = np.reshape(rand_int, (num_of_blocks, self.messages_per_block, 1))
            return out_val, out_arr, out_arr[:, mid_idx, :]

        return out_arr, out_arr[:, mid_idx, :]

    def train(self, num_of_blocks=1e6, batch_size=None, train_size=0.8, lr=1e-3):
        """
        Method to train the autoencoder. Further configuration to the loss function, optimizer etc. can be made in here.

        :param num_of_blocks: Number of blocks to generate for training. Analogous to the dataset size.
        :param batch_size: Number of samples to consider on each update iteration of the optimization algorithm
        :param train_size: Float less than 1 representing the proportion of the dataset to use for training
        :param lr: The learning rate of the optimizer. Defines how quickly the algorithm converges
        """
        X_train, y_train = self.generate_random_inputs(int(num_of_blocks*train_size))
        X_test, y_test = self.generate_random_inputs(int(num_of_blocks*(1-train_size)))

        opt = tf.keras.optimizers.Adam(learning_rate=lr)

        self.compile(optimizer=opt,
                     loss=losses.BinaryCrossentropy(),
                     metrics=['accuracy'],
                     loss_weights=None,
                     weighted_metrics=None,
                     run_eagerly=False
                     )

        self.fit(x=X_train,
                 y=y_train,
                 batch_size=batch_size,
                 epochs=1,
                 shuffle=True,
                 validation_data=(X_test, y_test)
                 )

    def view_encoder(self):
        '''
        A method that views the learnt encoder for each distint message. This is displayed as a plot with  asubplot for
        each image.
        '''
        # Generate inputs for encoder
        messages = np.zeros((self.cardinality, self.messages_per_block, self.cardinality))

        mid_idx = int((self.messages_per_block-1)/2)

        idx = 0
        for msg in messages:
            msg[mid_idx, idx] = 1
            idx += 1

        # Pass input through encoder and select middle messages
        encoded = self.encoder(messages)
        enc_messages = encoded[:, mid_idx, :]

        # Compute subplot grid layout
        i = 0
        while 2**i < self.cardinality**0.5:
            i += 1

        num_x = int(2**i)
        num_y = int(self.cardinality / num_x)

        # Plot all symbols
        fig, axs = plt.subplots(num_y, num_x, figsize=(2.5*num_x, 2*num_y))

        t = np.arange(self.samples_per_symbol)
        if isinstance(self.channel.layers[1], OpticalChannel):
            t = t/self.channel.layers[1].fs

        sym_idx = 0
        for y in range(num_y):
            for x in range(num_x):
                axs[y, x].plot(t, enc_messages[sym_idx], 'x')
                axs[y, x].set_title('Symbol {}'.format(str(sym_idx)))
                sym_idx += 1

        for ax in axs.flat:
            ax.set(xlabel='Time', ylabel='Amplitude', ylim=(0, 1))

        for ax in axs.flat:
            ax.label_outer()

        plt.show()
        pass

    def view_sample_block(self):
        '''
        Generates a random string of input message and encodes them. In addition to this, the output is passed through
        digitization layer without any quantization noise for the low pass filtering.
        '''
        # Generate a random block of messages
        val, inp, _ = self.generate_random_inputs(num_of_blocks=1, return_vals=True)

        # Encode and flatten the messages
        enc = self.encoder(inp)
        flat_enc = layers.Flatten()(enc)

        # Instantiate LPF layer
        lpf = DigitizationLayer(fs=self.channel.layers[1].fs,
                                num_of_samples=self.messages_per_block*self.samples_per_symbol,
                                q_stddev=0)

        # Apply LPF
        lpf_out = lpf(flat_enc)

        # Time axis
        t = np.arange(self.messages_per_block*self.samples_per_symbol)
        if isinstance(self.channel.layers[1], OpticalChannel):
            t = t / self.channel.layers[1].fs

        # Plot the concatenated symbols before and after LPF
        plt.figure(figsize=(2*self.messages_per_block, 6))

        for i in range(1, self.messages_per_block):
            plt.axvline(x=t[i*self.samples_per_symbol], color='black')

        plt.plot(t, flat_enc.numpy().T, 'x')
        plt.plot(t, lpf_out.numpy().T)
        plt.ylim((0, 1))
        plt.xlim((t.min(), t.max()))
        plt.title(str(val[0, :, 0]))
        plt.show()
        pass

    def call(self, inputs, training=None, mask=None):
        tx = self.encoder(inputs)
        rx = self.channel(tx)
        outputs = self.decoder(rx)
        return outputs


if __name__ == '__main__':

    SAMPLING_FREQUENCY = 336e9
    CARDINALITY = 32
    SAMPLES_PER_SYMBOL = 24
    MESSAGES_PER_BLOCK = 9
    DISPERSION_FACTOR = -21.7 * 1e-24
    FIBER_LENGTH = 50

    optical_channel = OpticalChannel(fs=SAMPLING_FREQUENCY,
                                     num_of_samples=MESSAGES_PER_BLOCK*SAMPLES_PER_SYMBOL,
                                     dispersion_factor=DISPERSION_FACTOR,
                                     fiber_length=FIBER_LENGTH)

    ae_model = EndToEndAutoencoder(cardinality=CARDINALITY,
                                   samples_per_symbol=SAMPLES_PER_SYMBOL,
                                   messages_per_block=MESSAGES_PER_BLOCK,
                                   channel=optical_channel)

    ae_model.train(num_of_blocks=1e6, batch_size=100)
    ae_model.view_encoder()
    ae_model.view_sample_block()

    pass