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@turnersr
Last active March 22, 2017 03:09
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Estimating Pilots given CP and number of subcarriers
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import scipy.interpolate\n",
"from scipy.signal import argrelextrema\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"K = 64 # number of OFDM subcarriers\n",
"CP = K//4 # length of the cyclic prefix: 25% of the block\n",
"P = 20 # number of pilot carriers per OFDM block\n",
"pilotValue = 4+4j # The known value each pilot transmits"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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"text/plain": [
"<matplotlib.figure.Figure at 0x10fd38790>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"allCarriers = np.arange(K) # indices of all subcarriers ([0, 1, ... K-1])\n",
"\n",
"pilotCarriers = allCarriers[::K//P] # Pilots is every (K/P)th carrier.\n",
"\n",
"# For convenience of channel estimation, let's make the last carriers also be a pilot\n",
"pilotCarriers = np.hstack([pilotCarriers, np.array([allCarriers[-1]])])\n",
"P = P+1\n",
"\n",
"# data carriers are all remaining carriers\n",
"dataCarriers = np.delete(allCarriers, pilotCarriers)\n",
"\n",
"#print (\"allCarriers: %s\" % allCarriers)\n",
"#print (\"pilotCarriers: %s\" % pilotCarriers)\n",
"#print (\"dataCarriers: %s\" % dataCarriers)\n",
"plt.figure(figsize=(8,0.8))\n",
"plt.plot(pilotCarriers, np.zeros_like(pilotCarriers), 'bo', label='pilot')\n",
"plt.plot(dataCarriers, np.zeros_like(dataCarriers), 'ro', label='data')\n",
"plt.legend(fontsize=10, ncol=2)\n",
"plt.xlim((-1,K)); plt.ylim((-0.1, 0.3))\n",
"plt.xlabel('Carrier index')\n",
"plt.yticks([])\n",
"plt.grid(True);"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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EPKSqpZ4f7fR1fwBYoKrT3ekv4Hw2YXHScjZGYIwxneTn9xG8BmwEvqaq/5cw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\nzhoCY4zp4awhMMaYHs4aAmOM6eH+PxcrO7bWLq/9AAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10fd53610>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"mu = 4 # bits per symbol (i.e. 16QAM)\n",
"payloadBits_per_OFDM = len(dataCarriers)*mu # number of payload bits per OFDM symbol\n",
"\n",
"mapping_table = {\n",
" (0,0,0,0) : -3-3j,\n",
" (0,0,0,1) : -3-1j,\n",
" (0,0,1,0) : -3+3j,\n",
" (0,0,1,1) : -3+1j,\n",
" (0,1,0,0) : -1-3j,\n",
" (0,1,0,1) : -1-1j,\n",
" (0,1,1,0) : -1+3j,\n",
" (0,1,1,1) : -1+1j,\n",
" (1,0,0,0) : 3-3j,\n",
" (1,0,0,1) : 3-1j,\n",
" (1,0,1,0) : 3+3j,\n",
" (1,0,1,1) : 3+1j,\n",
" (1,1,0,0) : 1-3j,\n",
" (1,1,0,1) : 1-1j,\n",
" (1,1,1,0) : 1+3j,\n",
" (1,1,1,1) : 1+1j\n",
"}\n",
"for b3 in [0, 1]:\n",
" for b2 in [0, 1]:\n",
" for b1 in [0, 1]:\n",
" for b0 in [0, 1]:\n",
" B = (b3, b2, b1, b0)\n",
" Q = mapping_table[B]\n",
" plt.plot(Q.real, Q.imag, 'bo')\n",
" plt.text(Q.real, Q.imag+0.2, \"\".join(str(x) for x in B), ha='center')\n",
"plt.grid(True)\n",
"plt.xlim((-4, 4)); plt.ylim((-4,4)); plt.xlabel('Real part (I)'); plt.ylabel('Imaginary part (Q)')\n",
"plt.title('16 QAM Constellation with Gray-Mapping');"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"demapping_table = {v : k for k, v in mapping_table.items()}"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"channelResponse = np.array([1, 0, 0.3+0.3j]) # the impulse response of the wireless channel\n",
"H_exact = np.fft.fft(channelResponse, K)\n",
"SNRdb = 25 # signal to noise-ratio in dB at the receiver "
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"('Bits count: ', 168)\n",
"('First 20 bits: ', array([0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0]))\n",
"('Mean of bits (should be around 0.5): ', 0.48809523809523808)\n"
]
}
],
"source": [
"bits = np.random.binomial(n=1, p=0.5, size=(payloadBits_per_OFDM, ))\n",
"print (\"Bits count: \", len(bits))\n",
"print (\"First 20 bits: \", bits[:20])\n",
"print (\"Mean of bits (should be around 0.5): \", np.mean(bits))"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def SP(bits):\n",
" return bits.reshape((len(dataCarriers), mu))\n",
"\n",
"def Mapping(bits):\n",
" return np.array([mapping_table[tuple(b)] for b in bits])"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"bits_SP = SP(bits)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"QAM = Mapping(bits_SP)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"('Number of OFDM carriers in frequency domain: ', 64)\n"
]
}
],
"source": [
"def OFDM_symbol(QAM_payload):\n",
" symbol = np.zeros(K, dtype=complex) # the overall K subcarriers\n",
" symbol[pilotCarriers] = pilotValue # allocate the pilot subcarriers \n",
" symbol[dataCarriers] = QAM_payload # allocate the pilot subcarriers\n",
" return symbol\n",
"OFDM_data = OFDM_symbol(QAM)\n",
"print (\"Number of OFDM carriers in frequency domain: \", len(OFDM_data))"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"('Number of OFDM samples in time-domain before CP: ', 64)\n"
]
}
],
"source": [
"def IDFT(OFDM_data):\n",
" return np.fft.ifft(OFDM_data)\n",
"OFDM_time = IDFT(OFDM_data)\n",
"print (\"Number of OFDM samples in time-domain before CP: \", len(OFDM_time))"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"('Number of OFDM samples in time domain with CP: ', 80)\n"
]
}
],
"source": [
"def addCP(OFDM_time):\n",
" cp = OFDM_time[-CP:] # take the last CP samples ...\n",
" return np.hstack([cp, OFDM_time]) # ... and add them to the beginning\n",
"OFDM_withCP = addCP(OFDM_time)\n",
"print (\"Number of OFDM samples in time domain with CP: \", len(OFDM_withCP))"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"RX Signal power: 0.2944. Noise power: 0.0003\n"
]
},
{
"data": {
"image/png": 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OHZVNw9nrSkTdV2qlVzYd+iiLjqioKLO8Pr20T3BwsNltKOsnKirKKNfPLM5eCLFcCBEn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\nAcyYAXTqZJzy2vm0Q1ZuFla9tgpBPkEF6eXRMCR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"text/plain": [
"<matplotlib.figure.Figure at 0x10fd74e50>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def channel(signal):\n",
" convolved = np.convolve(signal, channelResponse)\n",
" signal_power = np.mean(abs(convolved**2))\n",
" sigma2 = signal_power * 10**(-SNRdb/10) # calculate noise power based on signal power and SNR\n",
" \n",
" print (\"RX Signal power: %.4f. Noise power: %.4f\" % (signal_power, sigma2))\n",
" \n",
" # Generate complex noise with given variance\n",
" noise = np.sqrt(sigma2/2) * (np.random.randn(*convolved.shape)+1j*np.random.randn(*convolved.shape))\n",
" return convolved + noise\n",
"\n",
"\n",
"OFDM_TX = OFDM_withCP\n",
"OFDM_RX = channel(OFDM_TX)\n",
"\n",
"\n",
"plt.figure(figsize=(8,2))\n",
"plt.plot(abs(OFDM_TX), label='TX signal')\n",
"plt.plot(abs(OFDM_RX), label='RX signal')\n",
"plt.legend(fontsize=10)\n",
"plt.xlabel('Time'); plt.ylabel('$|x(t)|$');\n",
"plt.grid(True);"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def get_bits_ground_truth(OFDM_RX, pilotCarriers, pilotValue, CP, K, dataCarriers, allCarriers):\n",
" OFDM_RX_noCP = removeCP(OFDM_RX, CP, K)\n",
" OFDM_demod = DFT(OFDM_RX_noCP)\n",
" Hest = channelEstimate(OFDM_demod, pilotCarriers, pilotValue, allCarriers)\n",
" equalized_Hest = equalize(OFDM_demod, Hest)\n",
" QAM_est = get_payload(equalized_Hest, dataCarriers)\n",
" PS_est, hardDecision = Demapping(QAM_est)\n",
" \n",
" for qam, hard in zip(QAM_est, hardDecision):\n",
" plt.plot([qam.real, hard.real], [qam.imag, hard.imag], 'b-o')\n",
" plt.plot(hardDecision.real, hardDecision.imag, 'ro')\n",
" plt.grid(True)\n",
" plt.xlabel('Real part')\n",
" plt.ylabel('Imaginary part')\n",
" plt.title('Hard Decision demapping')\n",
" plt.show()\n",
"\n",
" bits_est = PS(PS_est)\n",
" return bits_est\n"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def removeCP(signal, CP, K):\n",
" return signal[CP:(CP+K)]\n",
"\n",
"def DFT(OFDM_RX):\n",
" return np.fft.fft(OFDM_RX)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def channelEstimate(OFDM_demod, pilotCarriers, pilotValue, allCarriers):\n",
" \n",
" pilots = OFDM_demod[pilotCarriers] # extract the pilot values from the RX signal\n",
" Hest_at_pilots = pilots / pilotValue # divide by the transmitted pilot values\n",
" \n",
" #print Hest_at_pilots\n",
" #print np.mean(pilots)\n",
"\n",
" # Perform interpolation between the pilot carriers to get an estimate\n",
" # of the channel in the data carriers. Here, we interpolate absolute value and phase \n",
" # separately\n",
"\n",
" Hest_abs = scipy.interpolate.interp1d(pilotCarriers, abs(Hest_at_pilots), kind='linear')(allCarriers)\n",
" Hest_phase = scipy.interpolate.interp1d(pilotCarriers, np.angle(Hest_at_pilots), kind='linear')(allCarriers)\n",
" Hest = Hest_abs * np.exp(1j*Hest_phase)\n",
" \n",
" plt.plot(allCarriers, abs(H_exact), label='Correct Channel')\n",
" plt.stem(pilotCarriers, abs(Hest_at_pilots), label='Pilot estimates')\n",
" plt.plot(allCarriers, abs(Hest), label='Estimated channel via interpolation')\n",
" plt.grid(True); plt.xlabel('Carrier index'); plt.ylabel('$|H(f)|$'); plt.legend(fontsize=10)\n",
" plt.ylim(0,2)\n",
" plt.show()\n",
" \n",
" return Hest\n"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def equalize(OFDM_demod, Hest):\n",
" return OFDM_demod / Hest\n",
"\n",
"def get_payload(equalized,dataCarriers):\n",
" return equalized[dataCarriers]\n",
"\n",
"def PS(bits):\n",
" return bits.reshape((-1,))"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def Demapping(QAM):\n",
" # array of possible constellation points\n",
" constellation = np.array([x for x in demapping_table.keys()])\n",
" \n",
" # calculate distance of each RX point to each possible point\n",
" dists = abs(QAM.reshape((-1,1)) - constellation.reshape((1,-1)))\n",
" \n",
" # for each element in QAM, choose the index in constellation \n",
" # that belongs to the nearest constellation point\n",
" const_index = dists.argmin(axis=1)\n",
" \n",
" # get back the real constellation point\n",
" hardDecision = constellation[const_index]\n",
" \n",
" # transform the constellation point into the bit groups\n",
" return np.vstack([demapping_table[C] for C in hardDecision]), hardDecision"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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2IP+2vyb8yqBlgzixy5vEpT/C5TpAIpUrh1O+/GgsFl/q1SuYBo3GbPtZOAVf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\nZmalnCzMzKyUk4WZmZX6GwK9Q3resMY5AAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10fdbbe50>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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VL5+5KO0rLhOK0n+U9IUMjBG4Z79/czYVHvxUbEwlDTknk4aMUXZWSEPOKOZCzijL9mxB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\nRwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10ff43dd0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"bits_est = get_bits_ground_truth(OFDM_RX, pilotCarriers, pilotValue, CP, K, dataCarriers, allCarriers)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now, that all bits are decoded, let's calculate the bit error rate:"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"('Obtained Bit error rate: ', 0.0)\n"
]
}
],
"source": [
"print (\"Obtained Bit error rate: \", np.sum(abs(bits-bits_est)) / float(len(bits)))"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def channelEstimate_raf(OFDM_demod, pilotCarriers, allCarriers):\n",
" pilots = OFDM_demod[pilotCarriers] # extract the pilot values from the RX signal\n",
" Hest_at_pilots = pilots / np.mean(pilots) # divide by the average transmitted pilot values\n",
" \n",
" # Perform interpolation between the pilot carriers to get an estimate\n",
" # of the channel in the data carriers. Here, we interpolate absolute value and phase \n",
" # separately\n",
" \n",
" Hest_abs = scipy.interpolate.interp1d(pilotCarriers, abs(Hest_at_pilots), kind='linear')(allCarriers)\n",
" Hest_phase = scipy.interpolate.interp1d(pilotCarriers, np.angle(Hest_at_pilots), kind='linear')(allCarriers)\n",
" \n",
" \n",
" Hest = Hest_abs * np.exp(1j*Hest_phase)\n",
" \n",
" plt.plot(allCarriers, abs(H_exact), label='Correct Channel')\n",
" plt.stem(pilotCarriers, abs(Hest_at_pilots), label='Pilot estimates')\n",
" plt.plot(allCarriers, abs(Hest), label='Estimated channel via interpolation')\n",
" plt.grid(True); plt.xlabel('Carrier index'); plt.ylabel('$|H(f)|$'); plt.legend(fontsize=10)\n",
" plt.ylim(0,2)\n",
" plt.show()\n",
" \n",
" return Hest\n",
"\n",
"def complex_autocorrelation(OFDM_demod):\n",
" data_ft = np.fft.fft(OFDM_demod)\n",
" data_ac = np.fft.ifft(data_ft * np.conjugate(data_ft))\n",
" return data_ac"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from __future__ import division, print_function\n",
"import numpy as np\n",
"\n",
"__author__ = \"Marcos Duarte, https://github.com/demotu/BMC\"\n",
"__version__ = \"1.0.4\"\n",
"__license__ = \"MIT\"\n",
"\n",
"\n",
"def detect_peaks(x, mph=None, mpd=1, threshold=0, edge='rising',\n",
" kpsh=False, valley=False, show=False, ax=None):\n",
"\n",
" \"\"\"Detect peaks in data based on their amplitude and other features.\n",
"\n",
" Parameters\n",
" ----------\n",
" x : 1D array_like\n",
" data.\n",
" mph : {None, number}, optional (default = None)\n",
" detect peaks that are greater than minimum peak height.\n",
" mpd : positive integer, optional (default = 1)\n",
" detect peaks that are at least separated by minimum peak distance (in\n",
" number of data).\n",
" threshold : positive number, optional (default = 0)\n",
" detect peaks (valleys) that are greater (smaller) than `threshold`\n",
" in relation to their immediate neighbors.\n",
" edge : {None, 'rising', 'falling', 'both'}, optional (default = 'rising')\n",
" for a flat peak, keep only the rising edge ('rising'), only the\n",
" falling edge ('falling'), both edges ('both'), or don't detect a\n",
" flat peak (None).\n",
" kpsh : bool, optional (default = False)\n",
" keep peaks with same height even if they are closer than `mpd`.\n",
" valley : bool, optional (default = False)\n",
" if True (1), detect valleys (local minima) instead of peaks.\n",
" show : bool, optional (default = False)\n",
" if True (1), plot data in matplotlib figure.\n",
" ax : a matplotlib.axes.Axes instance, optional (default = None).\n",
"\n",
" Returns\n",
" -------\n",
" ind : 1D array_like\n",
" indeces of the peaks in `x`.\n",
"\n",
" Notes\n",
" -----\n",
" The detection of valleys instead of peaks is performed internally by simply\n",
" negating the data: `ind_valleys = detect_peaks(-x)`\n",
" \n",
" The function can handle NaN's \n",
"\n",
" See this IPython Notebook [1]_.\n",
"\n",
" References\n",
" ----------\n",
" .. [1] http://nbviewer.ipython.org/github/demotu/BMC/blob/master/notebooks/DetectPeaks.ipynb\n",
"\n",
" Examples\n",
" --------\n",
" >>> from detect_peaks import detect_peaks\n",
" >>> x = np.random.randn(100)\n",
" >>> x[60:81] = np.nan\n",
" >>> # detect all peaks and plot data\n",
" >>> ind = detect_peaks(x, show=True)\n",
" >>> print(ind)\n",
"\n",
" >>> x = np.sin(2*np.pi*5*np.linspace(0, 1, 200)) + np.random.randn(200)/5\n",
" >>> # set minimum peak height = 0 and minimum peak distance = 20\n",
" >>> detect_peaks(x, mph=0, mpd=20, show=True)\n",
"\n",
" >>> x = [0, 1, 0, 2, 0, 3, 0, 2, 0, 1, 0]\n",
" >>> # set minimum peak distance = 2\n",
" >>> detect_peaks(x, mpd=2, show=True)\n",
"\n",
" >>> x = np.sin(2*np.pi*5*np.linspace(0, 1, 200)) + np.random.randn(200)/5\n",
" >>> # detection of valleys instead of peaks\n",
" >>> detect_peaks(x, mph=0, mpd=20, valley=True, show=True)\n",
"\n",
" >>> x = [0, 1, 1, 0, 1, 1, 0]\n",
" >>> # detect both edges\n",
" >>> detect_peaks(x, edge='both', show=True)\n",
"\n",
" >>> x = [-2, 1, -2, 2, 1, 1, 3, 0]\n",
" >>> # set threshold = 2\n",
" >>> detect_peaks(x, threshold = 2, show=True)\n",
" \"\"\"\n",
"\n",
" x = np.atleast_1d(x).astype('float64')\n",
" if x.size < 3:\n",
" return np.array([], dtype=int)\n",
" if valley:\n",
" x = -x\n",
" # find indices of all peaks\n",
" dx = x[1:] - x[:-1]\n",
" # handle NaN's\n",
" indnan = np.where(np.isnan(x))[0]\n",
" if indnan.size:\n",
" x[indnan] = np.inf\n",
" dx[np.where(np.isnan(dx))[0]] = np.inf\n",
" ine, ire, ife = np.array([[], [], []], dtype=int)\n",
" if not edge:\n",
" ine = np.where((np.hstack((dx, 0)) < 0) & (np.hstack((0, dx)) > 0))[0]\n",
" else:\n",
" if edge.lower() in ['rising', 'both']:\n",
" ire = np.where((np.hstack((dx, 0)) <= 0) & (np.hstack((0, dx)) > 0))[0]\n",
" if edge.lower() in ['falling', 'both']:\n",
" ife = np.where((np.hstack((dx, 0)) < 0) & (np.hstack((0, dx)) >= 0))[0]\n",
" ind = np.unique(np.hstack((ine, ire, ife)))\n",
" # handle NaN's\n",
" if ind.size and indnan.size:\n",
" # NaN's and values close to NaN's cannot be peaks\n",
" ind = ind[np.in1d(ind, np.unique(np.hstack((indnan, indnan-1, indnan+1))), invert=True)]\n",
" # first and last values of x cannot be peaks\n",
" if ind.size and ind[0] == 0:\n",
" ind = ind[1:]\n",
" if ind.size and ind[-1] == x.size-1:\n",
" ind = ind[:-1]\n",
" # remove peaks < minimum peak height\n",
" if ind.size and mph is not None:\n",
" ind = ind[x[ind] >= mph]\n",
" # remove peaks - neighbors < threshold\n",
" if ind.size and threshold > 0:\n",
" dx = np.min(np.vstack([x[ind]-x[ind-1], x[ind]-x[ind+1]]), axis=0)\n",
" ind = np.delete(ind, np.where(dx < threshold)[0])\n",
" # detect small peaks closer than minimum peak distance\n",
" if ind.size and mpd > 1:\n",
" ind = ind[np.argsort(x[ind])][::-1] # sort ind by peak height\n",
" idel = np.zeros(ind.size, dtype=bool)\n",
" for i in range(ind.size):\n",
" if not idel[i]:\n",
" # keep peaks with the same height if kpsh is True\n",
" idel = idel | (ind >= ind[i] - mpd) & (ind <= ind[i] + mpd) \\\n",
" & (x[ind[i]] > x[ind] if kpsh else True)\n",
" idel[i] = 0 # Keep current peak\n",
" # remove the small peaks and sort back the indices by their occurrence\n",
" ind = np.sort(ind[~idel])\n",
"\n",
" if show:\n",
" if indnan.size:\n",
" x[indnan] = np.nan\n",
" if valley:\n",
" x = -x\n",
" _plot(x, mph, mpd, threshold, edge, valley, ax, ind)\n",
"\n",
" return ind\n",
"\n",
"\n",
"def _plot(x, mph, mpd, threshold, edge, valley, ax, ind):\n",
" \"\"\"Plot results of the detect_peaks function, see its help.\"\"\"\n",
" try:\n",
" import matplotlib.pyplot as plt\n",
" except ImportError:\n",
" print('matplotlib is not available.')\n",
" else:\n",
" if ax is None:\n",
" _, ax = plt.subplots(1, 1, figsize=(8, 4))\n",
"\n",
" ax.plot(x, 'b', lw=1)\n",
" if ind.size:\n",
" label = 'valley' if valley else 'peak'\n",
" label = label + 's' if ind.size > 1 else label\n",
" ax.plot(ind, x[ind], '+', mfc=None, mec='r', mew=2, ms=8,\n",
" label='%d %s' % (ind.size, label))\n",
" ax.legend(loc='best', framealpha=.5, numpoints=1)\n",
" ax.set_xlim(-.02*x.size, x.size*1.02-1)\n",
" ymin, ymax = x[np.isfinite(x)].min(), x[np.isfinite(x)].max()\n",
" yrange = ymax - ymin if ymax > ymin else 1\n",
" ax.set_ylim(ymin - 0.1*yrange, ymax + 0.1*yrange)\n",
" ax.set_xlabel('Data #', fontsize=14)\n",
" ax.set_ylabel('Amplitude', fontsize=14)\n",
" mode = 'Valley detection' if valley else 'Peak detection'\n",
" ax.set_title(\"%s (mph=%s, mpd=%d, threshold=%s, edge='%s')\"\n",
" % (mode, str(mph), mpd, str(threshold), edge))\n",
" # plt.grid()\n",
" plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def smooth_estimate_pilot(pilotCarriers_est, K):\n",
" pilots_ = np.array(sorted(pilotCarriers_est))\n",
"\n",
" diff_series = np.ediff1d(pilots_)\n",
"\n",
" counts = np.bincount(diff_series)\n",
"\n",
" pilot_gap = np.argmax(counts)\n",
"\n",
" loc = np.where(diff_series > pilot_gap)[0][0]\n",
"\n",
" final = list(pilots_[0:loc]) + list(np.arange(pilots_[loc], K, pilot_gap))\n",
" return np.array(sorted(final)) "
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def get_bits_raf(OFDM_RX, CP, K, threshold=300, pilotCarriers=None, dataCarriers=None):\n",
" \n",
" allCarriers = np.arange(K) \n",
"\n",
" \n",
" OFDM_RX_noCP = removeCP(OFDM_RX, CP, K)\n",
" OFDM_demod = DFT(OFDM_RX_noCP)\n",
" \n",
" \n",
" data_ac = complex_autocorrelation(OFDM_demod) \n",
"\n",
" # We can possibly Tune to be better\n",
" X_i = set(np.where(data_ac.imag >= threshold)[0])\n",
" X_r = set(np.where(data_ac.real >= threshold)[0])\n",
" \n",
" plt.plot(data_ac.real)\n",
" plt.show()\n",
" \n",
" \n",
" plt.plot(data_ac.imag)\n",
" plt.show()\n",
" \n",
" ind = detect_peaks(data_ac.real, show=True)\n",
" \n",
" ind_set = set(ind)\n",
" \n",
" local_max_set = set(argrelextrema(data_ac, np.greater)[0])\n",
"\n",
" #print(ind_set, local_max_set)\n",
"\n",
"\n",
" if pilotCarriers == None:\n",
" pilotCarriers = list(ind_set) #list((X_i.union(X_r)))\n",
" pilotCarriers.append(K-1)\n",
" pilotCarriers.append(0)\n",
" \n",
" pilotCarriers = smooth_estimate_pilot(pilotCarriers, K)\n",
"\n",
" \n",
" if dataCarriers == None:\n",
" dataCarriers = np.delete(allCarriers, pilotCarriers)\n",
"\n",
" \n",
" Hest = channelEstimate_raf(OFDM_demod, pilotCarriers, allCarriers)\n",
" \n",
" equalized_Hest = equalize(OFDM_demod, Hest)\n",
" QAM_est = get_payload(equalized_Hest, dataCarriers)\n",
" PS_est, hardDecision = Demapping(QAM_est)\n",
" \n",
" \n",
" for qam, hard in zip(QAM_est, hardDecision):\n",
" plt.plot([qam.real, hard.real], [qam.imag, hard.imag], 'b-o')\n",
" plt.plot(hardDecision.real, hardDecision.imag, 'ro')\n",
" \n",
" plt.grid(True)\n",
" plt.xlabel('Real part')\n",
" plt.ylabel('Imaginary part')\n",
" plt.title('Hard Decision demapping')\n",
" plt.show()\n",
"\n",
" bits_est = PS(PS_est)\n",
" return bits_est, pilotCarriers"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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cCWedFScCITEM1vt79FHr+ZU9H1gC/JJLLBFZRH1jPnasNbJFC+1VFYGsGzdQ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\nJOA4juMML4ZVYrjdJpKJyM0i0iMiTyS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"text/plain": [
"<matplotlib.figure.Figure at 0x11074cf90>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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Yl40xx4BNwOVpDtDKbiJ3Pl/LoCwxcOf3cRHB5FmqBw9aIfXJyAij2WIQNrp3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\nbI298ycQXYUAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11036b790>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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rVfdYTN8wDMNo7BSK6fdA323fAzge+AJ9uc1Q7+884HPgxBLXsU4w975hGIbR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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x110969d90>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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8fPD397/qfFxcHDNmzGDr1q3ccMMNDB06NMdrlttnzZ6KPSsiwubNm69K3Z5J9jT0Wa+p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\nU3iZE9kQ381j6LtwGOni/lluSZeTeH7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"text/plain": [
"<matplotlib.figure.Figure at 0x110826590>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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cfX0D3ty81pcv/5TX1b3bDzvsdG9uXut9fQPu7uO2Z4iybMtyCtslDOauLd3D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\nRKTKqRCIiFQ5FQIRkSqnQiAiUuX+P3JKFWwWCuG+AAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x110004290>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"bits_est, pilotCarriers_est = get_bits_raf(OFDM_RX, CP, K, threshold=200, dataCarriers=None, pilotCarriers=None)"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Obtained Bit error rate: 0.0\n"
]
}
],
"source": [
"print (\"Obtained Bit error rate: \", np.sum(abs(bits-bits_est)) / float(len(bits)))"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.13"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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