pfb_clock_sync_fff.h

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/* -*- c++ -*- */
/*
 * Copyright 2009,2010,2012 Free Software Foundation, Inc.
 *
 * This file is part of GNU Radio
 *
 * GNU Radio is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 3, or (at your option)
 * any later version.
 *
 * GNU Radio is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
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 * the Free Software Foundation, Inc., 51 Franklin Street,
 * Boston, MA 02110-1301, USA.
 */

#ifndef INCLUDED_DIGITAL_PFB_CLOCK_SYNC_FFF_H
#define INCLUDED_DIGITAL_PFB_CLOCK_SYNC_FFF_H

#include <gnuradio/digital/api.h>
#include <gnuradio/filter/fir_filter.h>
#include <gnuradio/block.h>

namespace gr {
  namespace digital {

    /*!
     * \brief Timing synchronizer using polyphase filterbanks
     * \ingroup synchronizers_blk
     *
     * \details
     * 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
     * filterbank 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 block's parameters are:
     *
     * \li \p sps: The clock sync block needs to know the number of
     * samples per symbol, because it defaults to return a single
     * point representing the symbol. The sps can be any positive real
     * number and does not need to be an integer.
     *
     * \li \p loop_bw: The loop bandwidth is used to set the gain of
     * the inner control loop (see:
     * http://gnuradio.squarespace.com/blog/2011/8/13/control-loop-gain-values.html).
     * This should be set small (a value of around 2pi/100 is
     * suggested in that blog post as the step size for the number of
     * radians around the unit circle to move relative to the error).
     *
     * \li \p taps: One of the most important parameters for this
     * block is the taps of the filter. One of the benefits of this
     * algorithm is that you can put the matched filter in here as the
     * taps, so you get both the matched filter and sample timing
     * correction in one go. So create your normal matched filter. For
     * a typical digital modulation, this is a root raised cosine
     * filter. The number of taps of this filter is based on how long
     * you expect the channel to be; that is, how many symbols do you
     * want to combine to get the current symbols energy back (there's
     * probably a better way of stating that). It's usually 5 to 10 or
     * so. That gives you your filter, but now we need to think about
     * it as a filter with different phase profiles in each filter. So
     * take this number of taps and multiply it by the number of
     * filters. This is the number you would use to create your
     * prototype filter. When you use this in the PFB filerbank, it
     * segments these taps into the filterbanks in such a way that
     * each bank now represents the filter at different phases,
     * equally spaced at 2pi/N, where N is the number of filters.
     *
     * \li \p filter_size (default=32): 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.
     *
     * \li \p init_phase (default=0): 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.
     *
     * \li \p max_rate_deviation (default=1.5): The next 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.
     *
     * \li \p osps (default=1): The osps is the number of output
     * samples per symbol. By default, the algorithm produces 1 sample
     * per symbol, sampled at the exact sample value. This osps value
     * was added to better work with equalizers, which do a better job
     * of modeling the channel if they have 2 samps/sym.
     *
     * Reference:
     * f. j. harris and M. Rice, "Multirate Digital Filters for Symbol
     * Timing Synchronization in Software Defined Radios", IEEE
     * Selected Areas in Communications, Vol. 19, No. 12, Dec., 2001.
     *
     * http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.127.1757
     */
    class DIGITAL_API pfb_clock_sync_fff : virtual public block
    {
    public:
      // gr::digital::pfb_clock_sync_fff::sptr
      typedef boost::shared_ptr<pfb_clock_sync_fff> sptr;

      /*!
       * 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).
       * \param osps (int) The number of output samples per symbol (default=1).
       *
       */
      static sptr make(double sps, float gain,
                       const std::vector<float> &taps,
                       unsigned int filter_size=32,
                       float init_phase=0,
                       float max_rate_deviation=1.5,
                       int osps=1);

      /*! \brief update the system gains from omega and eta
       *
       *  This function updates the system gains based on the loop
       *  bandwidth and damping factor of the system.
       *  These two factors can be set separately through their own
       *  set functions.
       */
      virtual void update_gains() = 0;

      /*!
       * Resets the filterbank's filter taps with the new prototype filter
       */
      virtual void set_taps(const std::vector<float> &taps,
                            std::vector< std::vector<float> > &ourtaps,
                            std::vector<gr::filter::kernel::fir_filter_fff*> &ourfilter) = 0;

      /*!
       * Returns all of the taps of the matched filter
       */
      virtual std::vector< std::vector<float> > taps() const = 0;

      /*!
       * Returns all of the taps of the derivative filter
       */
      virtual std::vector< std::vector<float> > diff_taps() const = 0;

      /*!
       * Returns the taps of the matched filter for a particular channel
       */
      virtual std::vector<float> channel_taps(int channel) const = 0;

      /*!
       * Returns the taps in the derivative filter for a particular channel
       */
      virtual std::vector<float> diff_channel_taps(int channel) const = 0;

      /*!
       * Return the taps as a formatted string for printing
       */
      virtual std::string taps_as_string() const = 0;

      /*!
       * Return the derivative filter taps as a formatted string for printing
       */
      virtual std::string diff_taps_as_string() const = 0;


      /*******************************************************************
       SET FUNCTIONS
      *******************************************************************/


      /*!
       * \brief Set the loop bandwidth
       *
       * Set the loop filter's bandwidth to \p bw. This should be
       * between 2*pi/200 and 2*pi/100 (in rads/samp). It must also be
       * a positive number.
       *
       * When a new damping factor is set, the gains, alpha and beta,
       * of the loop are recalculated by a call to update_gains().
       *
       * \param bw    (float) new bandwidth
       */
      virtual void set_loop_bandwidth(float bw) = 0;

      /*!
       * \brief Set the loop damping factor
       *
       * Set the loop filter's damping factor to \p df. The damping
       * factor should be sqrt(2)/2.0 for critically damped systems.
       * Set it to anything else only if you know what you are
       * doing. It must be a number between 0 and 1.
       *
       * When a new damping factor is set, the gains, alpha and beta,
       * of the loop are recalculated by a call to update_gains().
       *
       * \param df    (float) new damping factor
       */
      virtual void set_damping_factor(float df) = 0;

      /*!
       * \brief Set the loop gain alpha
       *
       * Set's the loop filter's alpha gain parameter.
       *
       * This value should really only be set by adjusting the loop
       * bandwidth and damping factor.
       *
       * \param alpha    (float) new alpha gain
       */
      virtual void set_alpha(float alpha) = 0;

      /*!
       * \brief Set the loop gain beta
       *
       * Set's the loop filter's beta gain parameter.
       *
       * This value should really only be set by adjusting the loop
       * bandwidth and damping factor.
       *
       * \param beta    (float) new beta gain
       */
      virtual void set_beta(float beta) = 0;

      /*!
       * Set the maximum deviation from 0 d_rate can have
       */
      virtual void set_max_rate_deviation(float m) = 0;

      /*******************************************************************
       GET FUNCTIONS
      *******************************************************************/

      /*!
       * \brief Returns the loop bandwidth
       */
      virtual float loop_bandwidth() const = 0;

      /*!
       * \brief Returns the loop damping factor
       */
      virtual float damping_factor() const = 0;

      /*!
       * \brief Returns the loop gain alpha
       */
      virtual float alpha() const = 0;

      /*!
       * \brief Returns the loop gain beta
       */
      virtual float beta() const = 0;

      /*!
       * \brief Returns the current clock rate
       */
      virtual float clock_rate() const = 0;
    };

  } /* namespace digital */
} /* namespace gr */

#endif /* INCLUDED_DIGITAL_PFB_CLOCK_SYNC_FFF_H */