%matplotlib inline import matplotlib import numpy as np import matplotlib.pyplot as plt
GPS Timing¶Carrier-phase detection is suppose to yield better timing information than tracking the pseudorandom code stream. The reason for this is supposedly that the higher frequency carrier allows for more accurate measurements of the mismatch between the generated pseduorandom code stream and the broadcasted one. This increase in accuracy comes from sharper peaks in the autocorrelation function.
Lets try this out:
def corr(npoints, repeat): A = np.random.randint(0, 2, npoints) A = np.repeat(A, repeat) xcor = np.correlate(A, A, mode='same') plt.figure() N = len(A) offvec = np.arange(0, N)-N/2 print offvec.size, xcor.size plt.plot(offvec, xcor, 'x-') # generate 5 points each repeating 20 times, a slow signal corr(5,20) # a much faster signal corr(100,1)
100 100 100 100
It is clear that if you were trying to figure out the sample delay, you are much better off with the faster signal because the it is very obvious when you have the timing right. With the slower signal, you can be a little wrong and still get within a few pc of the correct correlation value.
Code Division Multiplexing¶Try out CDM for myself. It is important that -1,1 is used instead of 0,1 because multiplying by 0 is always 0.
def gen_code(N): """ Generatea a random array containing -1 and 1 of size N """ out = np.random.randint(0, 2, N) out *= 2 out -= 1 return out def code_modulate(signal, stretch=5, carrier=None): signal = np.repeat(signal, stretch) if carrier is None: carrier = gen_code(len(signal)) return np.multiply(signal, carrier), carrier sig_1 = gen_code(100) sig_2 = gen_code(100) out_1, c_1 = code_modulate(sig_1) # generate an orthogonal array by flipping every other element c_2 = np.array(c_1) c_2[::2] = -1*c_1[::2] out_2, _ = code_modulate(sig_2, carrier=c_2) out_comb = out_1 + out_2 def plot_sig(s, title=''): plt.figure() plt.stem(s) plt.ylim([min(s)-0.5, max(s)+0.5]) plt.title(title) plot_sig(sig_1, 'sig_1') plot_sig(sig_2, 'sig_2') plot_sig(out_comb, 'combined output')
def code_demodulate(signal, carrier, stretch=5): y = np.multiply(signal, carrier) ysubs = np.split(y, len(y)/5) ysubs = map(sum, ysubs) ysubs = map(lambda x:max(-1, x), ysubs) ysubs = map(lambda x:min(1, x), ysubs) return ysubs x = code_demodulate(out_comb, c_1) plot_sig(x, 'sig_1 recovered') plot_sig(sig_1, 'sig_1 expected') x = code_demodulate(out_comb, c_2) plot_sig(x, 'sig_2 recovered') plot_sig(sig_2, 'sig_2 expected')
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