diff options
| author | Andy Walls <awalls.cx18@gmail.com> | 2017-07-24 19:52:29 -0400 |
|---|---|---|
| committer | Andy Walls <awalls.cx18@gmail.com> | 2017-07-24 19:52:29 -0400 |
| commit | ada34c9d6b31ae5e9e3097ce4b088c4ad8d4b0e2 (patch) | |
| tree | bffbdd5feb868376b952a2136ffdb6a21640e931 /gr-digital/lib/clock_tracking_loop.h | |
| parent | 3b3a403e8871bdb83f8cd9bdc904626de14a7cca (diff) | |
digital: Add expected TED gain for computing symbol sync loop gains
The computation of proportional (alpha) and intergal (beta) loop
gains in the symbol synchronizer blocks neglected to account for
the timing error detector gain. Add expected timing error
detector gain as a user configurable parameter.
Diffstat (limited to 'gr-digital/lib/clock_tracking_loop.h')
| -rw-r--r-- | gr-digital/lib/clock_tracking_loop.h | 114 |
1 files changed, 88 insertions, 26 deletions
diff --git a/gr-digital/lib/clock_tracking_loop.h b/gr-digital/lib/clock_tracking_loop.h index 84c77e197a..1a20713c48 100644 --- a/gr-digital/lib/clock_tracking_loop.h +++ b/gr-digital/lib/clock_tracking_loop.h @@ -35,9 +35,9 @@ namespace gr { * which need a symbol clock tracking loop to determine the optimal * instant to sample a received symbol from an input sample * stream (i.e. *_clock_recovery* and *_clock_sync* blocks). - * It takes in a normalized loop bandwidth and damping factor - * as well as clock period bounds and provides the functions that - * control the update of the loop. + * It takes in an expected timing error detector gain, a normalized loop + * bandwidth and damping factor, as well as clock period bounds, and + * provides the functions that control the update of the loop. * * This control loop runs at the rate of the output clock, so * each step of the loop produces estimates about the output clock, @@ -51,9 +51,9 @@ namespace gr { * The loop's low pass filter is a Proportional-Integral (PI) filter. * The proportional and integral gains of the filter are termed alpha * and beta respectively. These gains are calculated using the input - * loop bandwidth and damping factor. If needed, the alpha and beta - * gain values can be set using their respective #set_alpha or #set_beta - * functions. + * expected timing error detector gain, loop bandwidth and damping factor. + * If needed, the alpha and beta gain values can be set using their + * respective #set_alpha or #set_beta functions. * * The class estimates the average clock period, T_avg; the instantaneous * clock period, T_inst; and the instantaneous clock phase, tau; of a @@ -70,20 +70,21 @@ namespace gr { * keeps the phase within +/-T_avg/2). * * The clock tracking loop, with its PI filter, when properly implemented, has - * a digital loop phase-transfer function, in terms of the proportional gain - * \f$\alpha\f$ and the integral gain \f$\beta\f$ as follows: + * a digital loop phase-transfer function, in terms of the timing error + * detector gain, \f$K_{ted}\f$; proportional gain, \f$\alpha\f$; and the + * integral gain, \f$\beta\f$, as follows: * * \f{align*} * H(z) &= \dfrac {\Theta_o(z)}{\Theta_i(z)} - * = (\alpha + \beta)z^{-1} \cdot + * = K_{ted}(\alpha + \beta)z^{-1} \cdot * \dfrac{ * 1 * - \dfrac{\alpha}{\alpha + \beta} z^{-1} * } * { * 1 - * - 2 \left(1 - \dfrac{\alpha + \beta}{2}\right) z^{-1} - * + (1 - \alpha) z^{-2} + * - 2 \left(1 - K_{ted}\dfrac{\alpha + \beta}{2}\right) z^{-1} + * + (1 - K_{ted}\alpha) z^{-2} * } \\ * \f} * @@ -140,23 +141,27 @@ namespace gr { * \\ * \f} * - * The PI filter gains, expressed in terms of the damping factor \f$\zeta\f$, - * the natural radian frequency \f$\omega_{n}\f$, the damped radian frequency of - * oscillation \f$\omega_{d}\f$, and the clock period \f$T\f$ are: + * The PI filter gains, expressed in terms of the damping factor, \f$\zeta\f$; + * the natural radian frequency, \f$\omega_{n}\f$; the damped radian frequency of + * oscillation, \f$\omega_{d}\f$; the timing error detector gain \f$K_{ted}\f$; + * and the clock period \f$T\f$ are: * * \f{align*} - * \alpha &= 2e^{-\zeta\omega_{n}T} \sinh(\zeta\omega_{n}T) \\ + * \alpha &= \dfrac{2}{K_{ted}}e^{-\zeta\omega_{n}T} \sinh(\zeta\omega_{n}T) \\ * \\ * \beta &= * \begin{cases} - * 2 - * -2e^{-\zeta\omega_{n}T} [\sinh(\zeta\omega_{n}T) + \cos(\omega_{d}T)] & - * \text{for} \quad \zeta < 1 \quad (under \: damped)\\ - * 2 - * -2e^{-\zeta\omega_{n}T} [\sinh(\zeta\omega_{n}T) + 1] & - * \text{for} \quad \zeta = 1 \quad (critically \: damped)\\ - * 2 - * -2e^{-\zeta\omega_{n}T} [\sinh(\zeta\omega_{n}T) +\cosh(\omega_{d}T)] & + * \dfrac{2}{K_{ted}} \left(1 - + * e^{-\zeta\omega_{n}T} [\sinh(\zeta\omega_{n}T) + \cos(\omega_{d}T)] + * \right) & + * \text{for} \quad \zeta < 1 \quad (under \: damped)\\ \\ + * \dfrac{2}{K_{ted}} \left(1 - + * e^{-\zeta\omega_{n}T} [\sinh(\zeta\omega_{n}T) + 1] + * \right) & + * \text{for} \quad \zeta = 1 \quad (critically \: damped)\\ \\ + * \dfrac{2}{K_{ted}} \left(1 - + * e^{-\zeta\omega_{n}T} [\sinh(\zeta\omega_{n}T) +\cosh(\omega_{d}T)] + * \right) & * \text{for} \quad \zeta > 1 \quad (over \: damped)\\ * \end{cases} \\ * \\ @@ -179,6 +184,17 @@ namespace gr { * \pi \dfrac{f_{n}}{\left(\dfrac{F_{c}}{2}\right)} * \f} * + * In practice, the timing error detector (TED) of the symbol clock + * tracking loop is implemented with an estimator of symbol clock phase + * error, which has some gain \f$K_{ted}\f$. The gain, \f$K_{ted}\f$, is + * defined as the slope of a TED's S-curve plot at a symbol clock phase + * offset of \f$\tau = 0\f$. The S-curve shape and central slope, and + * hence the gain \f$K_{ted}\f$, depend on the TED's estimator espression, + * the input signal level, the pulse shaping filter, and the \f$E_s/N_0\f$ + * of the incomping signal. The user must determine the TED's + * S-curve by analysis or simulation of the particular situation, in order + * to determine an appropriate value for \f$K_{ted}\f$. + * * * A note on symbol clock phase vs. interpolating resampler sample phase, * since most GNURadio symbol synchronization blocks seem to have the same * implementation error: @@ -263,6 +279,13 @@ namespace gr { // omega_n_norm = omega_n*T = 2*pi*f_n*T = 2*pi*f_n_norm float d_omega_n_norm; + // Expected gain of the timing error detector in use, given the + // TED estimator expression, the expected input amplitude, the + // input pulse shape, and the expected input Es/No. (This value is the + // slope of the TED's S-curve plot at a timing offset of tau = 0, and + // must be determined by analysis and/or simulation by the user.) + float d_ted_gain; + // Proportional gain of the PI loop filter (aka gain_mu) // (aka gain_mu in some clock recovery blocks) float d_alpha; @@ -315,16 +338,27 @@ namespace gr { * Damping in the range (1.0, Inf) yields an over-damped loop. * Damping equal to 1.0 yields a crtically-damped loop. * Under-damped loops are not generally useful for clock tracking. - * This parameter defaults to 2.0, if not specified. + * This parameter defaults to 1.0, if not specified. + * + * \param ted_gain + * Expected gain of the timing error detector, given the TED in use + * and the anticipated input amplitude, pulse shape, and Es/No. + * This value is the slope of the TED's S-curve at timing offset tau = 0. + * This value is normally computed by the user analytically or by + * simulation in a tool outside of GNURadio. + * This value must be correct for the loop filter gains to be computed + * properly from the desired input loop bandwidth and damping factor. + * This parameter defaults to 1.0, if not specified. */ clock_tracking_loop(float loop_bw, float max_period, float min_period, float nominal_period = 0.0f, - float damping = 2.0f); + float damping = 1.0f, + float ted_gain = 1.0f); virtual ~clock_tracking_loop(); - /*! \brief Update the gains from the loop bandwidth and damping factor. + /*! \brief Update the gains from the ted_gain, loop bw and damping factor. * * \details * This function updates the gains based on the loop @@ -445,6 +479,25 @@ namespace gr { void set_damping_factor(float df); /*! + * \brief Set the expected gain of the Timing Error Detector. + * + * \details + * Sets the expected gain of the timing error detector, given the TED in + * use and the anticipated input amplitude, pulse shape, and Es/No. + * This value is the slope of the TED's S-curve at timing offset tau = 0. + * This value is normally computed by the user analytically or by + * simulation in a tool outside of GNURadio. + * This value must be correct for the loop filter gains to be computed + * properly from the desired input loop bandwidth and damping factor. + * + * When a new ted_gain is set, the gains, alpha and beta, + * of the loop are automatcally recalculated. + * + * \param ted_gain expected gain of the timing error detector + */ + void set_ted_gain (float ted_gain); + + /*! * \brief Set the PI filter proportional gain, alpha. * * \details @@ -621,6 +674,15 @@ namespace gr { float get_damping_factor() const; /*! + * \brief Returns the user providded expected gain of the Timing Error + * Detector. + * + * \details + * See the documenation for set_ted_gain() for more details. + */ + float get_ted_gain() const; + + /*! * \brief Returns the PI filter proportional gain, alpha. * * \details |