Carrier%20Phase%20Tracking,%20Timing%20Synchronization,%20Equalization

1
Carrier Phase Tracking, Timing Synchronization,
Equalization
2
Turing the received baseband waveform into bits

• The received baseband waveform is hard to figure
  out.
• Problems to solve include
• Deal with the carrier frequency difference (the
  phase drift)
• Figure out when to take samples to avoid
  Inter-symbol interference
• Deal with multi-path
• As we will see, the solutions are just some
  heuristic algorithms that usually work. The
  constraint is that they can use only a very
  limited time to compute.
• Divide and conquer. Solve these problems one by
  one.
• http//www.gnuradio.org/trac/browser/gnuradio/trun
  k/gnuradio-core/src/lib/general/gr_mpsk_receiver_c
  c.cc?rev7389

3
Carrier Phase Tracking

• First, lets try to remove the frequency offset
  and turn the waveform into a waveform where the
  real component is none zero and the imaginary
  component is all zero.
• The idea is to use the decision, while assuming
  that the decisions are correct (may not be
  correct!)
• Use the current sample to figure out the
  difference.
• Current phase error is the phase difference
  between the current sample with the decision
  (assuming the decision is correct).

4
Carrier Phase Tracking

• First, get the phase error
• phase_error (this.d_phase_error_detector)(samp
  le)
• for BPSK, -arg(sampleconj(d_constellationd_curr
  ent_const_point))
• Basically, if the sample falls in the x line,
  there is no phase error

Im
Re
5
Carrier Phase Tracking

• Then, adjust the phase based on the error value
• d_freq d_betaphase_error             
• d_phase d_freq d_alphaphase_error 
• If error is positive, the phase will be
  increased, if the error is negative, the phase
  will be decreased 
• Thats it.

6
Sample Time

• You need to take samples at the right time.
• Designed algorithms to figure out the right time
  to take the samples.
• The current implementation uses an optimized
  Mueller and Muller algorithm.
• http//ieeexplore.ieee.org/xpl/freeabs_all.jsp?arn
  umber392689

7
The Basic Idea

• The basic Mueller and Muller algorithm ua_k-1
  x_k a_k x_k-1.
• u is the timing error.
• Consider the pulse shape. Recall that if the
  input is 1, the output is h(t), where h(t) is the
  impulse response of the low pass filter. (-h(t)
  if the input is -1).
• In this example, if off by a delta, x_k-1 will
  be deducted by the impulse response at Tdelta,
  which is negative, while x_k will be added by
  the impulse response at -Tdelta, which is
  positive.

k-1
k