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Synchronizer

__init__(fs=128000, Rb=400, sync_word='2BEEEEBF', channel_encode=('nrz', 'man'), sync_window=None)

Initializes the symbol synchronizer to identify the moment of maximum correlation between the received signal and the synchronization signal.

pageplot

Parameters:

Name Type Description Default
fs int

Sampling frequency of the received signal.

 128000
Rb int

Transmission rate of the received signal.

 400
sync_word str

Synchronization word.

 '2BEEEEBF'
channel_encode tuple

Tuple with the type of encoding of the I and Q channels respectively.

 ('nrz', 'man')

Examples:

>>> import argos3
>>> import numpy as np 
>>> 
>>> Si, Sq = argos3.Preamble(preamble_hex="2BEEEEBF").generate_preamble()
>>> 
>>> X = np.random.randint(0,2,20)
>>> Y = np.random.randint(0,2,20)
>>> X, Y = argos3.Multiplexer().concatenate(Si, Sq, X, Y)
>>> 
>>> Xn = argos3.Encoder().encode(X)
>>> Yn = argos3.Encoder().encode(Y)
>>> 
>>> formatterI = argos3.Formatter(type="RRC", channel="I", bits_per_symbol=1)
>>> formatterQ = argos3.Formatter(type="Manchester", channel="Q", bits_per_symbol=2)
>>> 
>>> mfI = argos3.MatchedFilter(type="RRC-Inverted", channel="I", bits_per_symbol=1)
>>> mfQ = argos3.MatchedFilter(type="Manchester-Inverted", channel="Q", bits_per_symbol=2)
>>> 
>>> dI = mfI.apply_filter(formatterI.apply_format(Xn))
>>> dQ = mfQ.apply_filter(formatterQ.apply_format(Yn))
>>> 
>>> sync = argos3.Synchronizer()
>>> delayQ_min, delayQ_max, delayQ, corr_vec = sync.correlation(dQ, "Q")
>>> 
>>> print(delayQ_min)
0.079984375
>>> print(delayQ_max)
0.117484375
>>> print(delayQ)
0.098734375
  • Time Domain: pageplot

create_sincronized_word(sync_word)

Creates the vectors of symbol \(S_I(t)\) and \(S_Q(t)\), corresponding to the synchronization word of channel \(I\) and \(Q\), respectively. The length of the synchronization word is given by \(\Delta \tau\), according to the expression below.

\[ \Delta \tau = L_{sync} \cdot \frac{f_s}{R_b} \]
Where
  • \(\Delta \tau\) is the length of the synchronization word.
  • \(L_{sync}\) is the length of the synchronization word of \(S_I(t)\) and \(S_Q(t)\).
  • \(R_b\) is the bit rate.
  • \(f_s\) is the sampling frequency.

Parameters:

Name Type Description Default
sync_word str

Synchronization word.

 required

Examples:

  • Time Domain: pageplot

correlation(signal, channel)

Performs the cross-correlation between the received signal \(s(t)\) and the synchronization word \(d(t)\), for each time index \(t\).

\[ c[k] = \sum_{t=0} s[t] d[t - k] \]
Where
  • \(s(t)\) and \(d(t)\) are the symbol vectors of the received signal and the synchronization word, respectively.
  • \(k\) is the time index in the cross-correlation vector.
  • \(c[k]\) is the cross-correlation value for the index \(k\).

Subsequently, the index of \(c[k]\) with the highest value is located, resulting in \(k_{max}\), this is the sample index with the highest correlation between the received signal and the synchronization word, finally, the delay \(\tau\) is calculated.

\[ \tau = \frac{k_{max}}{f_s} \]
Where
  • \(\tau\): Delay between the received signal and the synchronization word.
  • \(f_s\): Sampling frequency of the received signal.
  • \(k_{max}\): Sample index with the highest correlation between the received signal and the synchronization word.

Parameters:

Name Type Description Default
signal ndarray

Received signal.

 required
channel str

Channel of reception, \(I\) or \(Q\).

 required

Returns:

Name Type Description
delay tuple

Tuple containing the delay \(\tau\), the delay \(\tau_{min}\) and the delay \(\tau_{max}\).

Examples:

  • Correlation Factor: pageplot