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
 *
 * SPDX-License-Identifier: GPL-3.0-or-later
 *
 */
 
#ifndef INCLUDED_DIGITAL_PFB_CLOCK_SYNC_FFF_H
#define INCLUDED_DIGITAL_PFB_CLOCK_SYNC_FFF_H
 
#include <gnuradio/block.h>
#include <gnuradio/digital/api.h>
#include <gnuradio/filter/fir_filter.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 std::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 update_taps(const std::vector<float>& taps) = 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 */