simulations/models/OFDM.py

import numpy as np
import matplotlib.pyplot as plt
import scipy
from scipy import interpolate
import tensorflow as tf
from tensorflow.keras import layers, losses
import math

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=0.03,
                 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

SAMPLING_FREQUENCY = 336e9
CARDINALITY = 4
SAMPLES_PER_SYMBOL = 128
MESSAGES_PER_BLOCK = 9
DISPERSION_FACTOR = -21.7 * 1e-24
FIBER_LENGTH = 50

optical_channel = OpticalChannel(fs=SAMPLING_FREQUENCY,
                                     num_of_samples=80,
                                     dispersion_factor=DISPERSION_FACTOR,
                                     fiber_length=FIBER_LENGTH)
K = 64 # number of OFDM subcarriers
CP = K//4  # length of the cyclic prefix: 25% of the block
P = 8 # number of pilot carriers per OFDM block
pilotValue = 3+3j # The known value each pilot transmits

allCarriers = np.arange(K)  # indices of all subcarriers ([0, 1, ... K-1])

pilotCarriers = allCarriers[::K//P] # Pilots is every (K/P)th carrier.

# For convenience of channel estimation, let's make the last carriers also be a pilot
pilotCarriers = np.hstack([pilotCarriers, np.array([allCarriers[-1]])])
P = P+1

# data carriers are all remaining carriers
dataCarriers = np.delete(allCarriers, pilotCarriers)

print ("allCarriers:   %s" % allCarriers)
print ("pilotCarriers: %s" % pilotCarriers)
print ("dataCarriers:  %s" % dataCarriers)
plt.plot(pilotCarriers, np.zeros_like(pilotCarriers), 'bo', label='pilot')
plt.plot(dataCarriers, np.zeros_like(dataCarriers), 'ro', label='data')

mu = 4 # bits per symbol (i.e. 16QAM)
payloadBits_per_OFDM = len(dataCarriers)*mu  # number of payload bits per OFDM symbol

mapping_table = {
    (0,0,0,0) : -3-3j,
    (0,0,0,1) : -3-1j,
    (0,0,1,0) : -3+3j,
    (0,0,1,1) : -3+1j,
    (0,1,0,0) : -1-3j,
    (0,1,0,1) : -1-1j,
    (0,1,1,0) : -1+3j,
    (0,1,1,1) : -1+1j,
    (1,0,0,0) :  3-3j,
    (1,0,0,1) :  3-1j,
    (1,0,1,0) :  3+3j,
    (1,0,1,1) :  3+1j,
    (1,1,0,0) :  1-3j,
    (1,1,0,1) :  1-1j,
    (1,1,1,0) :  1+3j,
    (1,1,1,1) :  1+1j
}

mapping_table_dec = {
    (0) : -3-3j,
    (1) : -3-1j,
    (2) : -3+3j,
    (3) : -3+1j,
    (4) : -1-3j,
    (5) : -1-1j,
    (6) : -1+3j,
    (7) : -1+1j,
    (8) :  3-3j,
    (9) :  3-1j,
    (10) :  3+3j,
    (11) :  3+1j,
    (12) :  1-3j,
    (13) :  1-1j,
    (14) :  1+3j,
    (15) :  1+1j
}
for b3 in [0, 1]:
    for b2 in [0, 1]:
        for b1 in [0, 1]:
            for b0 in [0, 1]:
                B = (b3, b2, b1, b0)
                Q = mapping_table[B]
                plt.plot(Q.real, Q.imag, 'bo')
                plt.text(Q.real, Q.imag+0.2, "".join(str(x) for x in B), ha='center')

demapping_table = {v: k for k, v in mapping_table.items()}

# Replace with our channel
channelResponse = np.array([1, 0, 0.3+0.3j])  # the impulse response of the wireless channel
H_exact = np.fft.fft(channelResponse, K)
plt.plot(allCarriers, abs(H_exact))

SNRdb = 25  # signal to noise-ratio in dB at the receiver

# Here

#water filling, gradient decent methods for optimising the symbol mapping, instead of 16 QAM

bits = np.random.binomial(n=1, p=0.5, size=(payloadBits_per_OFDM, ))
print ("Bits count: ", len(bits))
print ("First 20 bits: ", bits[:20])
print ("Mean of bits (should be around 0.5): ", np.mean(bits))

def SP(bits):
    return bits.reshape((len(dataCarriers), mu))
bits_SP = SP(bits)
print ("First 5 bit groups")
print (bits_SP[:5,:])


def generate_random_inputs(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(16, size=(num_of_blocks, 1))

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

    # out = enc.fit_transform(rand_int)
    # for symbol in rand_int:

    #out_arr = np.reshape(rand_int, (num_of_blocks, self.messages_per_block))
    #t_out_arr = np.repeat(out_arr, self.samples_per_symbol, axis=1)

    #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 rand_int

bits_SP1 = generate_random_inputs(num_of_blocks=1000).astype('uint8')
#bits_SP11 = np.unpackbits(bits_SP1, axis=1)

def Mapping(bits):
    return np.array([mapping_table[tuple(b)] for b in bits])

def Mapping_dec(bits):
    return np.array([mapping_table_dec[tuple(b)] for b in bits])
QAM = Mapping(bits_SP)
QAM1 = Mapping_dec(bits_SP1)
print("First 5 QAM symbols and bits:")
print(bits_SP[:5,:])
print(QAM[:5])

def OFDM_symbol(QAM_payload):
    symbol = np.zeros(K, dtype=complex) # the overall K subcarriers
    symbol[pilotCarriers] = pilotValue  # allocate the pilot subcarriers
    symbol[dataCarriers] = QAM_payload  # allocate the pilot subcarriers
    return symbol
OFDM_data = OFDM_symbol(QAM)
print("Number of OFDM carriers in frequency domain: ", len(OFDM_data))

def IDFT(OFDM_data):
    return np.fft.ifft(OFDM_data)
OFDM_time = IDFT(OFDM_data)
print("Number of OFDM samples in time-domain before CP: ", len(OFDM_time))

def addCP(OFDM_time):
    cp = OFDM_time[-CP:]               # take the last CP samples ...
    return np.hstack([cp, OFDM_time])  # ... and add them to the beginning
OFDM_withCP = addCP(OFDM_time)
print("Number of OFDM samples in time domain with CP: ", len(OFDM_withCP))


def channel(signal):
    convolved = np.convolve(signal, channelResponse)
    signal_power = np.mean(abs(convolved ** 2))
    sigma2 = signal_power * 10 ** (-SNRdb / 10)  # calculate noise power based on signal power and SNR

    print("RX Signal power: %.4f. Noise power: %.4f" % (signal_power, sigma2))

    # Generate complex noise with given variance
    noise = np.sqrt(sigma2 / 2) * (np.random.randn(*convolved.shape) + 1j * np.random.randn(*convolved.shape))
    return convolved + noise


OFDM_TX = OFDM_withCP
OFDM_RX = channel(OFDM_TX)
#OFDM_RX1 = optical_channel(OFDM_TX).numpy
plt.figure(figsize=(8, 2))
plt.plot(abs(OFDM_TX), label='TX signal')
plt.plot(abs(OFDM_RX), label='RX signal')
plt.legend(fontsize=10)
plt.xlabel('Time')
plt.ylabel('$|x(t)|$')
plt.grid(True)

def removeCP(signal):
    return signal[CP:(CP+K)]
OFDM_RX_noCP = removeCP(OFDM_RX)

def DFT(OFDM_RX):
    return np.fft.fft(OFDM_RX)
OFDM_demod = DFT(OFDM_RX_noCP)


def channelEstimate(OFDM_demod):
    pilots = OFDM_demod[pilotCarriers]  # extract the pilot values from the RX signal
    Hest_at_pilots = pilots / pilotValue  # divide by the transmitted pilot values

    # Perform interpolation between the pilot carriers to get an estimate
    # of the channel in the data carriers. Here, we interpolate absolute value and phase
    # separately
    Hest_abs = interpolate.interp1d(pilotCarriers, abs(Hest_at_pilots), kind='linear')(allCarriers)
    Hest_phase = interpolate.interp1d(pilotCarriers, np.angle(Hest_at_pilots), kind='linear')(allCarriers)
    Hest = Hest_abs * np.exp(1j * Hest_phase)

    plt.plot(allCarriers, abs(H_exact), label='Correct Channel')
    plt.stem(pilotCarriers, abs(Hest_at_pilots), label='Pilot estimates')
    plt.plot(allCarriers, abs(Hest), label='Estimated channel via interpolation')
    plt.grid(True)
    plt.xlabel('Carrier index')
    plt.ylabel('$|H(f)|$')
    plt.legend(fontsize=10)
    plt.ylim(0, 2)

    return Hest


Hest = channelEstimate(OFDM_demod)
def equalize(OFDM_demod, Hest):
    return OFDM_demod / Hest
equalized_Hest = equalize(OFDM_demod, Hest)

def get_payload(equalized):
    return equalized[dataCarriers]
QAM_est = get_payload(equalized_Hest)
plt.plot(QAM_est.real, QAM_est.imag, 'bo');


def Demapping(QAM):
    # array of possible constellation points
    constellation = np.array([x for x in demapping_table.keys()])

    # calculate distance of each RX point to each possible point
    dists = abs(QAM.reshape((-1, 1)) - constellation.reshape((1, -1)))

    # for each element in QAM, choose the index in constellation
    # that belongs to the nearest constellation point
    const_index = dists.argmin(axis=1)

    # get back the real constellation point
    hardDecision = constellation[const_index]

    # transform the constellation point into the bit groups
    return np.vstack([demapping_table[C] for C in hardDecision]), hardDecision


PS_est, hardDecision = Demapping(QAM_est)
for qam, hard in zip(QAM_est, hardDecision):
    plt.plot([qam.real, hard.real], [qam.imag, hard.imag], 'b-o');
    plt.plot(hardDecision.real, hardDecision.imag, 'ro')


def PS(bits):
    return bits.reshape((-1,))


bits_est = PS(PS_est)

print("Obtained Bit error rate: ", np.sum(abs(bits-bits_est))/len(bits))