diff options
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 |