Basic OFDM implementation with wireless channel

models/OFDM.py

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+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))