GNU Radio Manual and C++ API Reference  3.7.13.4
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pfb_clock_sync_fff.h
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22 
23 #ifndef INCLUDED_DIGITAL_PFB_CLOCK_SYNC_FFF_H
24 #define INCLUDED_DIGITAL_PFB_CLOCK_SYNC_FFF_H
25 
26 #include <gnuradio/digital/api.h>
28 #include <gnuradio/block.h>
29 
30 namespace gr {
31  namespace digital {
32 
33  /*!
34  * \brief Timing synchronizer using polyphase filterbanks
35  * \ingroup synchronizers_blk
36  *
37  * \details
38  * This block performs timing synchronization for PAM signals by
39  * minimizing the derivative of the filtered signal, which in turn
40  * maximizes the SNR and minimizes ISI.
41  *
42  * This approach works by setting up two filterbanks; one
43  * filterbank contains the signal's pulse shaping matched filter
44  * (such as a root raised cosine filter), where each branch of the
45  * filterbank contains a different phase of the filter. The
46  * second filterbank contains the derivatives of the filters in
47  * the first filterbank. Thinking of this in the time domain, the
48  * first filterbank contains filters that have a sinc shape to
49  * them. We want to align the output signal to be sampled at
50  * exactly the peak of the sinc shape. The derivative of the sinc
51  * contains a zero at the maximum point of the sinc (sinc(0) = 1,
52  * sinc(0)' = 0). Furthermore, the region around the zero point
53  * is relatively linear. We make use of this fact to generate the
54  * error signal.
55  *
56  * If the signal out of the derivative filters is d_i[n] for the
57  * ith filter, and the output of the matched filter is x_i[n], we
58  * calculate the error as: e[n] = (Re{x_i[n]} * Re{d_i[n]} +
59  * Im{x_i[n]} * Im{d_i[n]}) / 2.0 This equation averages the error
60  * in the real and imaginary parts. There are two reasons we
61  * multiply by the signal itself. First, if the symbol could be
62  * positive or negative going, but we want the error term to
63  * always tell us to go in the same direction depending on which
64  * side of the zero point we are on. The sign of x_i[n] adjusts
65  * the error term to do this. Second, the magnitude of x_i[n]
66  * scales the error term depending on the symbol's amplitude, so
67  * larger signals give us a stronger error term because we have
68  * more confidence in that symbol's value. Using the magnitude of
69  * x_i[n] instead of just the sign is especially good for signals
70  * with low SNR.
71  *
72  * The error signal, e[n], gives us a value proportional to how
73  * far away from the zero point we are in the derivative
74  * signal. We want to drive this value to zero, so we set up a
75  * second order loop. We have two variables for this loop; d_k is
76  * the filter number in the filterbank we are on and d_rate is the
77  * rate which we travel through the filters in the steady
78  * state. That is, due to the natural clock differences between
79  * the transmitter and receiver, d_rate represents that difference
80  * and would traverse the filter phase paths to keep the receiver
81  * locked. Thinking of this as a second-order PLL, the d_rate is
82  * the frequency and d_k is the phase. So we update d_rate and d_k
83  * using the standard loop equations based on two error signals,
84  * d_alpha and d_beta. We have these two values set based on each
85  * other for a critically damped system, so in the block
86  * constructor, we just ask for "gain," which is d_alpha while
87  * d_beta is equal to (gain^2)/4.
88  *
89  * The block's parameters are:
90  *
91  * \li \p sps: The clock sync block needs to know the number of
92  * samples per symbol, because it defaults to return a single
93  * point representing the symbol. The sps can be any positive real
94  * number and does not need to be an integer.
95  *
96  * \li \p loop_bw: The loop bandwidth is used to set the gain of
97  * the inner control loop (see:
98  * http://gnuradio.squarespace.com/blog/2011/8/13/control-loop-gain-values.html).
99  * This should be set small (a value of around 2pi/100 is
100  * suggested in that blog post as the step size for the number of
101  * radians around the unit circle to move relative to the error).
102  *
103  * \li \p taps: One of the most important parameters for this
104  * block is the taps of the filter. One of the benefits of this
105  * algorithm is that you can put the matched filter in here as the
106  * taps, so you get both the matched filter and sample timing
107  * correction in one go. So create your normal matched filter. For
108  * a typical digital modulation, this is a root raised cosine
109  * filter. The number of taps of this filter is based on how long
110  * you expect the channel to be; that is, how many symbols do you
111  * want to combine to get the current symbols energy back (there's
112  * probably a better way of stating that). It's usually 5 to 10 or
113  * so. That gives you your filter, but now we need to think about
114  * it as a filter with different phase profiles in each filter. So
115  * take this number of taps and multiply it by the number of
116  * filters. This is the number you would use to create your
117  * prototype filter. When you use this in the PFB filerbank, it
118  * segments these taps into the filterbanks in such a way that
119  * each bank now represents the filter at different phases,
120  * equally spaced at 2pi/N, where N is the number of filters.
121  *
122  * \li \p filter_size (default=32): The number of filters can also
123  * be set and defaults to 32. With 32 filters, you get a good
124  * enough resolution in the phase to produce very small, almost
125  * unnoticeable, ISI. Going to 64 filters can reduce this more,
126  * but after that there is very little gained for the extra
127  * complexity.
128  *
129  * \li \p init_phase (default=0): The initial phase is another
130  * settable parameter and refers to the filter path the algorithm
131  * initially looks at (i.e., d_k starts at init_phase). This value
132  * defaults to zero, but it might be useful to start at a
133  * different phase offset, such as the mid-point of the filters.
134  *
135  * \li \p max_rate_deviation (default=1.5): The next parameter is
136  * the max_rate_devitation, which defaults to 1.5. This is how far
137  * we allow d_rate to swing, positive or negative, from
138  * 0. Constraining the rate can help keep the algorithm from
139  * walking too far away to lock during times when there is no
140  * signal.
141  *
142  * \li \p osps (default=1): The osps is the number of output
143  * samples per symbol. By default, the algorithm produces 1 sample
144  * per symbol, sampled at the exact sample value. This osps value
145  * was added to better work with equalizers, which do a better job
146  * of modeling the channel if they have 2 samps/sym.
147  *
148  * Reference:
149  * f. j. harris and M. Rice, "Multirate Digital Filters for Symbol
150  * Timing Synchronization in Software Defined Radios", IEEE
151  * Selected Areas in Communications, Vol. 19, No. 12, Dec., 2001.
152  *
153  * http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.127.1757
154  */
155  class DIGITAL_API pfb_clock_sync_fff : virtual public block
156  {
157  public:
158  // gr::digital::pfb_clock_sync_fff::sptr
159  typedef boost::shared_ptr<pfb_clock_sync_fff> sptr;
160 
161  /*!
162  * Build the polyphase filterbank timing synchronizer.
163  * \param sps (double) The number of samples per second in the incoming signal
164  * \param gain (float) The alpha gain of the control loop; beta = (gain^2)/4 by default.
165  * \param taps (vector<int>) The filter taps.
166  * \param filter_size (uint) The number of filters in the filterbank (default = 32).
167  * \param init_phase (float) The initial phase to look at, or which filter to start
168  * with (default = 0).
169  * \param max_rate_deviation (float) Distance from 0 d_rate can get (default = 1.5).
170  * \param osps (int) The number of output samples per symbol (default=1).
171  *
172  */
173  static sptr make(double sps, float gain,
174  const std::vector<float> &taps,
175  unsigned int filter_size=32,
176  float init_phase=0,
177  float max_rate_deviation=1.5,
178  int osps=1);
179 
180  /*! \brief update the system gains from omega and eta
181  *
182  * This function updates the system gains based on the loop
183  * bandwidth and damping factor of the system.
184  * These two factors can be set separately through their own
185  * set functions.
186  */
187  virtual void update_gains() = 0;
188 
189  /*!
190  * Resets the filterbank's filter taps with the new prototype filter.
191  */
192  virtual void update_taps(const std::vector<float> &taps) = 0;
193 
194  /*!
195  * Used to set the taps of the filters in the filterbank and
196  * differential filterbank.
197  *
198  * WARNING: this should not be used externally and will be moved
199  * to a private function in the next API.
200  */
201  virtual void set_taps(const std::vector<float> &taps,
202  std::vector< std::vector<float> > &ourtaps,
203  std::vector<gr::filter::kernel::fir_filter_fff*> &ourfilter) = 0;
204 
205  /*!
206  * Returns all of the taps of the matched filter
207  */
208  virtual std::vector< std::vector<float> > taps() const = 0;
209 
210  /*!
211  * Returns all of the taps of the derivative filter
212  */
213  virtual std::vector< std::vector<float> > diff_taps() const = 0;
214 
215  /*!
216  * Returns the taps of the matched filter for a particular channel
217  */
218  virtual std::vector<float> channel_taps(int channel) const = 0;
219 
220  /*!
221  * Returns the taps in the derivative filter for a particular channel
222  */
223  virtual std::vector<float> diff_channel_taps(int channel) const = 0;
224 
225  /*!
226  * Return the taps as a formatted string for printing
227  */
228  virtual std::string taps_as_string() const = 0;
229 
230  /*!
231  * Return the derivative filter taps as a formatted string for printing
232  */
233  virtual std::string diff_taps_as_string() const = 0;
234 
235 
236  /*******************************************************************
237  SET FUNCTIONS
238  *******************************************************************/
239 
240 
241  /*!
242  * \brief Set the loop bandwidth
243  *
244  * Set the loop filter's bandwidth to \p bw. This should be
245  * between 2*pi/200 and 2*pi/100 (in rads/samp). It must also be
246  * a positive number.
247  *
248  * When a new damping factor is set, the gains, alpha and beta,
249  * of the loop are recalculated by a call to update_gains().
250  *
251  * \param bw (float) new bandwidth
252  */
253  virtual void set_loop_bandwidth(float bw) = 0;
254 
255  /*!
256  * \brief Set the loop damping factor
257  *
258  * Set the loop filter's damping factor to \p df. The damping
259  * factor should be sqrt(2)/2.0 for critically damped systems.
260  * Set it to anything else only if you know what you are
261  * doing. It must be a number between 0 and 1.
262  *
263  * When a new damping factor is set, the gains, alpha and beta,
264  * of the loop are recalculated by a call to update_gains().
265  *
266  * \param df (float) new damping factor
267  */
268  virtual void set_damping_factor(float df) = 0;
269 
270  /*!
271  * \brief Set the loop gain alpha
272  *
273  * Set's the loop filter's alpha gain parameter.
274  *
275  * This value should really only be set by adjusting the loop
276  * bandwidth and damping factor.
277  *
278  * \param alpha (float) new alpha gain
279  */
280  virtual void set_alpha(float alpha) = 0;
281 
282  /*!
283  * \brief Set the loop gain beta
284  *
285  * Set's the loop filter's beta gain parameter.
286  *
287  * This value should really only be set by adjusting the loop
288  * bandwidth and damping factor.
289  *
290  * \param beta (float) new beta gain
291  */
292  virtual void set_beta(float beta) = 0;
293 
294  /*!
295  * Set the maximum deviation from 0 d_rate can have
296  */
297  virtual void set_max_rate_deviation(float m) = 0;
298 
299  /*******************************************************************
300  GET FUNCTIONS
301  *******************************************************************/
302 
303  /*!
304  * \brief Returns the loop bandwidth
305  */
306  virtual float loop_bandwidth() const = 0;
307 
308  /*!
309  * \brief Returns the loop damping factor
310  */
311  virtual float damping_factor() const = 0;
312 
313  /*!
314  * \brief Returns the loop gain alpha
315  */
316  virtual float alpha() const = 0;
317 
318  /*!
319  * \brief Returns the loop gain beta
320  */
321  virtual float beta() const = 0;
322 
323  /*!
324  * \brief Returns the current clock rate
325  */
326  virtual float clock_rate() const = 0;
327  };
328 
329  } /* namespace digital */
330 } /* namespace gr */
331 
332 #endif /* INCLUDED_DIGITAL_PFB_CLOCK_SYNC_FFF_H */
Timing synchronizer using polyphase filterbanks.
Definition: pfb_clock_sync_fff.h:155
#define DIGITAL_API
Definition: gr-digital/include/gnuradio/digital/api.h:30
boost::shared_ptr< pfb_clock_sync_fff > sptr
Definition: pfb_clock_sync_fff.h:159
Include this header to use the message passing features.
Definition: logger.h:695
static const float taps[NSTEPS+1][NTAPS]
Definition: interpolator_taps.h:9
The abstract base class for all &#39;terminal&#39; processing blocks.A signal processing flow is constructed ...
Definition: block.h:65