equalisation

Adaptive equaliser routines

Adaptive equaliser functions

Functions for adaptive equalisation and filer application.

The following adaptive equaliser methods are provided:

Non-decision based:

• Constant Modulus Algorithm (CMA) after [1]

• Radius Directed Error (RDE) [1]

• Modfied Constant Modulus Algorithm (MCMA) after [2]

• Modified Radius Directed Error (MRDA) after [3]

• Signed based CMA [1]

Decision based:

• Symbol Based Decision (SBD) after [3]

• Modified Decision Directed Modulus Algorithm (MDDMA) after [4]

• Decision-directed LMS after [1]

Adaptive Step Size Algorithms:

In addition algorithms can use a adaptive stepsize based on the step size adoption in [5] It is possible to use an adaptive step for all equalisers using the adaptive_stepsize keyword parameter

Real-valued equalisers:

A subset of the equalisers can be run as real-valued equalisers.

Data aided:

In addition there is a data aided SBD algorithm and real_valued DD algorithm

The available methods are specified in the following sets

qampy.equalisation.DATA_AIDED = ('dd_data_real', 'sbd_data')

Data-aided equalisation methods

qampy.equalisation.TRAINING_FCTS = ('sbd', 'mddma', 'dd', 'sbd_data', 'dd_real', 'dd_data_real', 'cma', 'cma2', 'mcma', 'rde', 'mrde', 'cma_real', 'sgncma_real', 'sgncma')

All available equaliser method#:

qampy.equalisation.NONDECISION_BASED = ('cma', 'cma2', 'mcma', 'rde', 'mrde', 'cma_real', 'sgncma_real', 'sgncma')

Non-decision based equalisation methods

qampy.equalisation.DECISION_BASED = ('sbd', 'mddma', 'dd', 'sbd_data', 'dd_real', 'dd_data_real')

Decision based equalisation methods

qampy.equalisation.REAL_VALUED = ('cma_real', 'dd_real', 'dd_data_real', 'sgncma_real')

Real-valued equalisation methods

References

[1] (1,2,3,4)

Faruk, M.S. and Savory, J.S. “Digital Signal Processing for Coherent Transceivers Employing Multilevel Formats”, Journal of Lightwave Technology, vol. 35, no. 5, pp. 1125–1141, Mar. 2017, doi: 10.1109/JLT.2017.2662319.

[2]

Oh, K. N., & Chin, Y. O. “Modified constant modulus algorithm: blind equalization and carrier phase recovery algorithm”. Proceedings IEEE International Conference on Communications ICC ’95, 1, 498–502 (1995) http://doi.org/10.1109/ICC.1995.525219

[3] (1,2)

Filho, M., Silva, M. T. M., & Miranda, M. D. “A FAMILY OF ALGORITHMS FOR BLIND EQUALIZATION OF QAM SIGNALS”. In 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (pp. 6–9) (2011).

[4]

Fernandes, C. A. R., Favier, G., & Mota, J. C. M. “Decision directed adaptive blind equalization based on the constant modulus algorithm. Signal, Image and Video Processing”, 1(4), 333–346. (2007) http://doi.org/10.1007/s11760-007-0027-2

[5]

Ashmawy, D., Banovic, K., Abdel-Raheem, E., Youssif, M., Mansour, H., and Mohanna, M. “Joint MCMA and DD blind equalization algorithm with variable-step size,” Proc. 2009 IEEE Int. Conf. Electro/Information Technol. EIT 2009, no. 1, pp. 174–177, 2009.

qampy.equalisation.DATA_AIDED = ('dd_data_real', 'sbd_data')

Data-aided equalisation methods

qampy.equalisation.DECISION_BASED = ('sbd', 'mddma', 'dd', 'sbd_data', 'dd_real', 'dd_data_real')

Decision based equalisation methods

qampy.equalisation.NONDECISION_BASED = ('cma', 'cma2', 'mcma', 'rde', 'mrde', 'cma_real', 'sgncma_real', 'sgncma')

Non-decision based equalisation methods

qampy.equalisation.REAL_VALUED = ('cma_real', 'dd_real', 'dd_data_real', 'sgncma_real')

Real-valued equalisation methods

qampy.equalisation.TRAINING_FCTS = ('sbd', 'mddma', 'dd', 'sbd_data', 'dd_real', 'dd_data_real', 'cma', 'cma2', 'mcma', 'rde', 'mrde', 'cma_real', 'sgncma_real', 'sgncma')

All available equaliser method#:

qampy.equalisation.apply_filter(sig, wxy, method='pyt', frames=[0])

Apply the equaliser filter taps to the input signal.

Parameters:

• sig (SignalObject) – input signal to be equalised

• wxy (tuple(array_like, array_like,optional)) – filter taps for the x and y polarisation

• method (basestring) – which apply filter method to use (pyx=cython, py=python)

• frames (list(int), optional) – if signal object is a pilot signal the frames to be equalised. If False, empty or None, do not perform a frame sync and apply filter to the whole signal.

Returns:

sig_out – equalised signal

Return type:

SignalObject

qampy.equalisation.dual_mode_equalisation(sig, mu, Ntaps, TrSyms=(None, None), Niter=(1, 1), methods=('mcma', 'sbd'), adaptive_stepsize=(False, False), symbols=None, modes=None, apply=True, **kwargs)

Blind equalisation of PMD and residual dispersion, with a dual mode approach. Typically this is done using a CMA type initial equaliser for pre-convergence and a decision directed equaliser as a second to improve MSE.

Parameters:

• sig (SignalObject) – single or dual polarisation signal field (2D subclass of SignalBase)

• mu (tuple(float, float)) – step size parameter for the first and second equaliser method

• Ntaps (int) – number of filter taps. Either this or wxy need to be given. If given taps are initialised as [00100]

• TrSyms (tuple(int,int) optional) – number of symbols to use for filter estimation for each equaliser mode. Default is (None, None) which means use all symbols in both equaliser.

• Niter (tuple(int, int), optional) – number of iterations for each equaliser. Default is one single iteration for both

• method (tuple(string,string), optional) – equaliser method for the first and second mode has to be one of cma, rde, mrde, mcma, sbd, mddma, sca, dd_adaptive, sbd_adaptive, mcma_adaptive

• adaptive_stepsize (tuple(bool, bool), optional) – whether to adapt the step size upon training for each of the equaliser modes

• modes (array_like, optional) – array or list of modes to equalise over (default=None equalise over all modes of the input signal)

• apply (Bool, optional) – whether to apply the filter taps and return the equalised signal

Returns:

• if apply –

  sig_outSignalObject

  equalised signal X and Y polarisation

• (wx, wy) (tuple(array_like, array_like)) – equaliser taps for the x and y polarisation

• (err1, err2) (tuple(array_like, array_like)) – estimation error for x and y polarisation for each equaliser mode

• if apply is False do not return sig_out

qampy.equalisation.equalise_signal(sig, mu, wxy=None, Ntaps=None, TrSyms=None, Niter=1, method='mcma', adaptive_stepsize=False, symbols=None, modes=None, apply=False, **kwargs)

Blind equalisation of PMD and residual dispersion, using a chosen equalisation method. The method can be any of the keys in the TRAINING_FCTS dictionary.

Parameters:

• sig (SignalObject) – single or dual polarisation signal field (2D complex array first dim is the polarisation)

• mu (float) – step size parameter

• wxy (array_like, optional) – the wx and wy filter taps. Either this or Ntaps has to be given.

• Ntaps (int) – number of filter taps. Either this or wxy need to be given. If given taps are initialised as [00100]

• TrSyms (int, optional) – number of symbols to use for filter estimation. Default is None which means use all symbols.

• Niter (int, optional) – number of iterations. Default is one single iteration

• method (string, optional) – equaliser method has to be one of cma, rde, mrde, mcma, sbd, mddma, sca, dd_adaptive, sbd_adaptive, mcma_adaptive

• adaptive_stepsize (bool, optional) – whether to use an adaptive stepsize or a fixed

• modes (array_like, optional) – array or list of modes to equalise over (default=None equalise over all modes of the input signal)

• apply (Bool, optional) – whether to apply the filter taps and return the equalised signal

Returns:

• if apply –

  sig_outSignalObject

  equalised signal X and Y polarisation

• (wx, wy) (tuple(array_like, array_like)) – equaliser taps for the x and y polarisation

• err (array_like) – estimation error for x and y polarisation

qampy.equalisation.pilot_equaliser(signal, mu, Ntaps, apply=True, foe_comp=True, wxinit=None, frame=0, verbose=False, **eqkwargs)

Pilot based equalisation on a single frame

Parameters:

• signal (SignalObject) – Pilot-based signal object, has to be synced already

• mu (float) – Step size parameter

• Ntaps (int) – Number of equaliser taps

• apply (bool, optional) – Apply the filter to the signal

• foe_comp (bool, optional) – Do frequency offset compensation

• wxinit (array_like, optional) – Initialisation taps for the equaliser. If this is given Ntaps will not be used

• frame (int, optional) – Which frame to equalise, frame numbers start at 0

• verbose (bool, optional) – Return verbose output

• **eqkwargs – Dictionary of values to pass to the equaliser functions

Returns:

• taps (array_like) – filter taps

• if apply also return –

  out_sigSignalObject

  equalised signal

• if verbose also return –

  foe_allarray_like

  estimated frequency offset

  ntapstuple

  Tuple of equaliser and synchronization taps

qampy.equalisation.pilot_equaliser_nframes(signal, mu, Ntaps, apply=True, foe_comp=True, frames=[0], wxinit=None, verbose=True, **eqkwargs)

Pilot based equalisation over multiple frames

Parameters:

• signal (SignalObject) – Pilot-based signal object, has to be synced already

• mu (float) – Step size parameter

• Ntaps (int) – Number of equaliser taps

• apply (bool, optional) – Apply the filter to the signal

• foe_comp (bool, optional) – Do frequency offset compensation

• frames (array_like, optional) – List of frames to process the first frame is frame 0

• **eqkwargs – Dictionary of values to pass to the equaliser functions

Returns:

• taps (array_like) – filter taps for each frame

• if apply also return –

  out_sigSignalObject

  equalised signal per frame

• if verbose also return –

  foe_allarray_like

  estimated frequency offset per frame

  ntapstuple

  Tuple of equaliser and synchronization taps per frame