*
* \ingroup filter_blk
*
+ * This block performs timing synchronization for PAM signals by minimizing the
+ * derivative of the filtered signal, which in turn maximizes the SNR and
+ * minimizes ISI.
+ *
+ * This approach works by setting up two filterbanks; one filterbanke contains the
+ * signal's pulse shaping matched filter (such as a root raised cosine filter),
+ * where each branch of the filterbank contains a different phase of the filter.
+ * The second filterbank contains the derivatives of the filters in the first
+ * filterbank. Thinking of this in the time domain, the first filterbank contains
+ * filters that have a sinc shape to them. We want to align the output signal to
+ * be sampled at exactly the peak of the sinc shape. The derivative of the sinc
+ * contains a zero at the maximum point of the sinc (sinc(0) = 1, sinc(0)' = 0).
+ * Furthermore, the region around the zero point is relatively linear. We make
+ * use of this fact to generate the error signal.
+ *
+ * If the signal out of the derivative filters is d_i[n] for the ith filter, and
+ * the output of the matched filter is x_i[n], we calculate the error as:
+ * e[n] = (Re{x_i[n]} * Re{d_i[n]} + Im{x_i[n]} * Im{d_i[n]}) / 2.0
+ * This equation averages the error in the real and imaginary parts. There are two
+ * reasons we multiply by the signal itself. First, if the symbol could be positive
+ * or negative going, but we want the error term to always tell us to go in the
+ * same direction depending on which side of the zero point we are on. The sign of
+ * x_i[n] adjusts the error term to do this. Second, the magnitude of x_i[n] scales
+ * the error term depending on the symbol's amplitude, so larger signals give us
+ * a stronger error term because we have more confidence in that symbol's value.
+ * Using the magnitude of x_i[n] instead of just the sign is especially good for
+ * signals with low SNR.
+ *
+ * The error signal, e[n], gives us a value proportional to how far away from the zero
+ * point we are in the derivative signal. We want to drive this value to zero, so we
+ * set up a second order loop. We have two variables for this loop; d_k is the filter
+ * number in the filterbank we are on and d_rate is the rate which we travel through
+ * the filters in the steady state. That is, due to the natural clock differences between
+ * the transmitter and receiver, d_rate represents that difference and would traverse
+ * the filter phase paths to keep the receiver locked. Thinking of this as a second-order
+ * PLL, the d_rate is the frequency and d_k is the phase. So we update d_rate and d_k
+ * using the standard loop equations based on two error signals, d_alpha and d_beta.
+ * We have these two values set based on each other for a critically damped system, so in
+ * the block constructor, we just ask for "gain," which is d_alpha while d_beta is
+ * equal to (gain^2)/4.
+ *
+ * The clock sync block needs to know the number of samples per second (sps), because it
+ * only returns a single point representing the sample. The sps can be any positive real
+ * number and does not need to be an integer. The filter taps must also be specified. The
+ * taps are generated by first conceiving of the prototype filter that would be the signal's
+ * matched filter. Then interpolate this by the number of filters in the filterbank. These
+ * are then distributed among all of the filters. So if the prototype filter was to have
+ * 45 taps in it, then each path of the filterbank will also have 45 taps. This is easily
+ * done by building the filter with the sample rate multiplied by the number of filters
+ * to use.
+ *
+ * The number of filters can also be set and defaults to 32. With 32 filters, you get a
+ * good enough resolution in the phase to produce very small, almost unnoticeable, ISI.
+ * Going to 64 filters can reduce this more, but after that there is very little gained
+ * for the extra complexity.
+ *
+ * The initial phase is another settable parameter and refers to the filter path the
+ * algorithm initially looks at (i.e., d_k starts at init_phase). This value defaults
+ * to zero, but it might be useful to start at a different phase offset, such as the mid-
+ * point of the filters.
+ *
+ * The final parameter is the max_rate_devitation, which defaults to 1.5. This is how far
+ * we allow d_rate to swing, positive or negative, from 0. Constraining the rate can help
+ * keep the algorithm from walking too far away to lock during times when there is no signal.
+ *
*/
class gr_pfb_clock_sync_fff : public gr_block
private:
/*!
* Build the polyphase filterbank timing synchronizer.
+ * \param sps (double) The number of samples per second in the incoming signal
+ * \param gain (float) The alpha gain of the control loop; beta = (gain^2)/4 by default.
+ * \param taps (vector<int>) The filter taps.
+ * \param filter_size (uint) The number of filters in the filterbank (default = 32).
+ * \param init_phase (float) The initial phase to look at, or which filter to start
+ * with (default = 0).
+ * \param max_rate_deviation (float) Distance from 0 d_rate can get (default = 1.5).
+ *
*/
friend gr_pfb_clock_sync_fff_sptr gr_make_pfb_clock_sync_fff (double sps, float gain,
const std::vector<float> &taps,
void set_taps (const std::vector<float> &taps,
std::vector< std::vector<float> > &ourtaps,
std::vector<gr_fir_fff*> &ourfilter);
+
+ /*!
+ * Returns the taps of the matched filter
+ */
std::vector<float> channel_taps(int channel);
+
+ /*!
+ * Returns the taps in the derivative filter
+ */
std::vector<float> diff_channel_taps(int channel);
/*!
* Print all of the filterbank taps to screen.
*/
void print_taps();
+
+ /*!
+ * Print all of the filterbank taps of the derivative filter to screen.
+ */
void print_diff_taps();
+ /*!
+ * Set the gain value alpha for the control loop
+ */
void set_alpha(float alpha)
{
d_alpha = alpha;
}
+
+ /*!
+ * Set the gain value beta for the control loop
+ */
void set_beta(float beta)
{
d_beta = beta;
}
+ /*!
+ * Set the maximum deviation from 0 d_rate can have
+ */
void set_max_rate_deviation(float m)
{
d_max_dev = m;
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