synchronization

A Digital Communications Synchronization and PLLs Function Module

A collection of useful functions when studying PLLs and synchronization and digital comm

Copyright (c) March 2017, Mark Wickert All rights reserved.

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sk_dsp_comm.synchronization.DD_carrier_sync(z, M, BnTs, zeta=0.707, mod_type='MPSK', type=0, open_loop=False)[source]

z_prime,a_hat,e_phi = DD_carrier_sync(z,M,BnTs,zeta=0.707,type=0) Decision directed carrier phase tracking

z = complex baseband PSK signal at one sample per symbol M = The PSK modulation order, i.e., 2, 8, or 8.

BnTs = time bandwidth product of loop bandwidth and the symbol period,

thus the loop bandwidth as a fraction of the symbol rate.

zeta = loop damping factor type = Phase error detector type: 0 <> ML, 1 <> heuristic

z_prime = phase rotation output (like soft symbol values)
a_hat = the hard decision symbol values landing at the constellation

values

e_phi = the phase error e(k) into the loop filter

Ns = Nominal number of samples per symbol (Ts/T) in the carrier

phase tracking loop, almost always 1

Kp = The phase detector gain in the carrier phase tracking loop;

This value depends upon the algorithm type. For the ML scheme described at the end of notes Chapter 9, A = 1, K 1/sqrt(2), so Kp = sqrt(2).

Mark Wickert July 2014 Updated for improved MPSK performance April 2020 Added experimental MQAM capability April 2020

Motivated by code found in M. Rice, Digital Communications A Discrete-Time Approach, Prentice Hall, New Jersey, 2009. (ISBN 978-0-13-030497-1).

sk_dsp_comm.synchronization.NDA_symb_sync(z, Ns, L, BnTs, zeta=0.707, I_ord=3)[source]
z = complex baseband input signal at nominally Ns samples

per symbol

Ns = Nominal number of samples per symbol (Ts/T) in the symbol

tracking loop, often 4

BnTs = time bandwidth product of loop bandwidth and the symbol period,

thus the loop bandwidth as a fraction of the symbol rate.

zeta = loop damping factor

I_ord = interpolator order, 1, 2, or 3

e_tau = the timing error e(k) input to the loop filter

Kp = The phase detector gain in the symbol tracking loop; for the

NDA algoithm used here always 1

Mark Wickert July 2014

Motivated by code found in M. Rice, Digital Communications A Discrete-Time Approach, Prentice Hall, New Jersey, 2009. (ISBN 978-0-13-030497-1).

sk_dsp_comm.synchronization.PLL1(theta, fs, loop_type, Kv, fn, zeta, non_lin)[source]

Baseband Analog PLL Simulation Model

Parameters:

  • theta – input phase deviation in radians

  • fs – sampling rate in sample per second or Hz

  • loop_type – 1, first-order loop filter F(s)=K_LF; 2, integrator with lead compensation F(s) = (1 + s tau2)/(s tau1), i.e., a type II, or 3, lowpass with lead compensation F(s) = (1 + s tau2)/(1 + s tau1)

  • Kv – VCO gain in Hz/v; note presently assume Kp = 1v/rad and K_LF = 1; the user can easily change this

  • fn – Loop natural frequency (loops 2 & 3) or cutoff frquency (loop 1)

  • zeta – Damping factor for loops 2 & 3

  • non_lin – 0, linear phase detector; 1, sinusoidal phase detector

Returns:

theta_hat = Output phase estimate of the input theta in radians, ev = VCO control voltage, phi = phase error = theta - theta_hat

Notes

Alternate input in place of natural frequency, fn, in Hz is the noise equivalent bandwidth Bn in Hz.

Mark Wickert, April 2007 for ECE 5625/4625 Modified February 2008 and July 2014 for ECE 5675/4675 Python version August 2014

sk_dsp_comm.synchronization.PLL_cbb(x, fs, loop_type, Kv, fn, zeta)[source]

Baseband Analog PLL Simulation Model

Parameters:

  • x – input phase deviation in radians

  • fs – sampling rate in sample per second or Hz

  • loop_type – 1, first-order loop filter F(s)=K_LF; 2, integrator with lead compensation F(s) = (1 + s tau2)/(s tau1), i.e., a type II, or 3, lowpass with lead compensation F(s) = (1 + s tau2)/(1 + s tau1)

  • Kv – VCO gain in Hz/v; note presently assume Kp = 1v/rad and K_LF = 1; the user can easily change this

  • fn – Loop natural frequency (loops 2 & 3) or cutoff frequency (loop 1)

  • zeta – Damping factor for loops 2 & 3

Returns:

theta_hat = Output phase estimate of the input theta in radians, ev = VCO control voltage, phi = phase error = theta - theta_hat

Mark Wickert, April 2007 for ECE 5625/4625 Modified February 2008 and July 2014 for ECE 5675/4675 Python version August 2014

sk_dsp_comm.synchronization.phase_step(z, ns, p_step, n_step)[source]

Create a one sample per symbol signal containing a phase rotation step Nsymb into the waveform.

Parameters:

  • z – complex baseband signal after matched filter

  • ns – number of sample per symbol

  • p_step – size in radians of the phase step

  • n_step – symbol sample location where the step turns on

Returns:

the one sample symbol signal containing the phase step

Mark Wickert July 2014

sk_dsp_comm.synchronization.time_step(z, ns, t_step, n_step)[source]

Create a one sample per symbol signal containing a phase rotation step Nsymb into the waveform.

Parameters:

  • z – complex baseband signal after matched filter

  • ns – number of sample per symbol

  • t_step – in samples relative to Ns

  • n_step – symbol sample location where the step turns on

Returns:

the one sample per symbol signal containing the phase step

Mark Wickert July 2014