import numpy as np import matplotlib.pyplot as plt from scipy import interpolate from models.custom_layers import OpticalChannel 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))