MT QAM Feedforward Equalizer (LMS) (Specify coefficients)
- Updated2023-02-17
- 8 minute(s) read
MT QAM Feedforward Equalizer (LMS) (Specify coefficients)
Applies adaptive feedforward software equalization using the least-mean-squared (LMS) algorithm to the QAM-demodulated input complex waveform. Sets equalizer coefficients or their initial conditions.
Inputs/Outputs
input complex waveform
The modulated complex baseband waveform data.
t0
Trigger (start) time of the Y array.
Default value: 0.0
dt
Time interval between data points in the Y array.
Default value: 1.0
Y
The complex-valued signal-only baseband modulated waveform. The real and imaginary parts of this complex data array correspond to the in-phase (I) and quadrature-phase (Q) data, respectively.
QAM system parameters
Parameter values defining the QAM system. Wire the QAM system parameters cluster of MT Generate QAM System Parameters (M) or MT Generate QAM System Parameters (map) to this cluster.
samples per symbol
An even number of samples dedicated to each symbol. Multiply this value by the symbol rate to determine the sample rate.
Default value: 16
symbol map
An ordered array that maps each Boolean symbol to its desired coordinates in the complex plane. The number of states in the array must be 2N, where N is the number of bits per symbol.
equalizer coefficients in
The filter coefficients for initializing the feedforward equalizer. The time span of this array (in symbols) is given by the following equation:
size(equalizer coefficients in) / taps per symbol
For best performance and minimization of intersymbol interference, ensure that the time span (in symbols) of the equalizer coefficients filter is greater than the time span (in symbols) of the channel filter.
- The equalizer coefficients in array must contain an odd number of elements.
- The values specified here are used by the equalizer only when reset? is set to TRUE or on the first call to this node. Otherwise, this node maintains an internal buffer of the equalizer coefficients resulting from completion of the previous call.
training bits
The binary-valued training bits that train the feedforward equalizer during the training phase when the reset? parameter is set to TRUE. This parameter is ignored when reset? is set to FALSE.
- Ensure that the duration of training is long enough to allow the feedforward equalizer to converge before switching to a decision-directed adaptation.
- When working with M-ary modulation schemes {M>2, or bits per symbol>1} in which symbols represent groups of bits, the specified training bits must start on a symbol boundary.
error in
Error conditions that occur before this node runs.
The node responds to this input according to standard error behavior.
Default value: No error
feedforward equalizer (lms) parameters
The feedforward equalization parameters, which define the equalizer tap spacing (symbol spaced/fractionally spaced) and convergence rate during training and steady-state.
taps per symbol
The tap-spacing of the equalizer coefficients array, relative to one symbol duration. For error-free operation, set this parameter value to be a factor of the samples per symbol passed from MT Generate System Parameters.
taps per symbol = 1,
which means that every tap of the equalization filter spans the time duration of one symbol.
A fractionally-spaced (T/N-spaced) equalizer has
taps per symbol > 1.
For example, a T/2-spaced equalizer has taps per symbol = 2, meaning that every two taps of the equalization filter span the time duration of one symbol.
Default value: 1
delta (training)
The convergence parameter for feedforward equalization during the training phase. This value adapts the feedforward equalizer coefficients for the duration of the training period when reset? is set to TRUE.
Default value: 0.01
delta (steady state)
The steady-state convergence parameter for adapting the equalizer coefficients during the decision-directed phase. Use this value for adapting the feedforward equalizer coefficients when reset? is set to FALSE.
Default value: 0.01
reset?
A Boolean that determines whether to continue feedforward equalization using the previous iteration states. This node always resets on first call.
TRUE | Resets the internal state, restarts, and trains the equalizer. |
FALSE | Continues feedforward equalization using the previous iteration states. This node assumes that the input complex waveform is phase-continuous with the previous iteration. |
Default value: TRUE
output complex waveform
The equalized oversampled waveform generated from the feedforward equalizer as a result of adaptation. This waveform consists of the oversampled data that are compensated for the channel impulse response with zero intersymbol interference. Wire this parameter to the corresponding instance of MT Measure Quadrature Impairments to make modulation measurements such as modulation error ratio (MER) and error vector magnitude (EVM).
t0
Trigger (start) time of the Y array.
Default value: 0
dt
Time interval between data values in the Y array.
Default value: 1.0
Y
The complex-valued signal-only baseband modulated waveform. The real and imaginary parts of this complex data array correspond to the in-phase (I) and quadrature-phase (Q) data, respectively.
error
The instantaneous per symbol error in the output of the adaptive feedforward equalizer filter.
equalizer coefficients out
The adaptive feedforward equalizer filter coefficients when equalization is complete for the current iteration.
output bit stream
The recovered bit stream generated from the adaptive feedforward equalizer. The recovered bit stream is phase-aligned with the output complex waveform at the equalizer output. Wire this parameter to MT Measure Quadrature Impairments for performing modulation measurements such as modulation error ratio (MER) and error vector magnitude (EVM), or to MT Calculate BER after Trigger for making bit error rate (BER) measurements.
error out
Error information.
The node produces this output according to standard error behavior.
Demodulator-to-Equalizer Data Flow
The input complex waveform is assumed to have undergone matched filtering and carrier frequency offset correction during the demodulation process (the recovered complex waveform returned by a Demodulation node meets these criteria). The adaptive equalization process ensures that the convolution of the channel filter and the equalizer coefficient filter yields a delta function thereby removing any intersymbol interference in the equalized output complex waveform.
The following flow chart illustrates demodulator-to-equalizer data flow.
Duration of Training Mode
Because the feedforward equalizer is adaptive, the adaptation is carried out initially in a training mode and is later switched to a decision-directed mode. In the training mode, a user-supplied training bit sequence trains the equalizer to adapt to the channel conditions. In the decision-directed mode, the equalizer tap adaptation is self-directed, and the current equalizer output adapts the equalizer taps for the next iteration.
The duration of the training mode is set by the number of training bits when reset? is set to TRUE, or when the first instance of this node is called. Training mode equalization is applied to the initial N symbols of the input complex waveform, where N is the number of symbols that can be mapped from the input training bits. Decision-directed equalization is applied to the input complex waveform starting at symbol N+1.
Continuous Data Stream
The equalizer is continuable, that is, the same instance of an equalizer can be called multiple times, with each instance operating on an input complex waveform representing a subsequent frame of the same data stream. To operate in this manner, call the equalizer in a loop with the first iteration setting reset? to TRUE and subsequent iterations setting reset? to FALSE.
Discontinuous Data Stream
The equalizer can also be applied to a discontinuous data stream, in which the same instance of the equalizer operates on input complex waveforms that do not maintain phase continuity from one to the next. To operate in this manner, call the same instance of the equalizer in a loop with reset? set to TRUE for all iterations.
Continuous Equalization on Discontinuous Data
This node allows continuous equalization on discontinuous data. If you are working with discontinuous data and know that your input channel is invariant enough to potentially benefit from continuous equalization, wire equalizer coefficients out to the equalizer coefficients in parameter. To do so, call the equalizer in a loop with reset? set to TRUE and use a feedback node or shift register to wire the output of a previous iteration as the input for the next iteration. This technique also allows continuous training of the equalizer; if supplied with appropriate training bits, the equalizer retrains with every iteration.
In This Section
- Inputs/Outputs
- input complex waveform
- t0
- dt
- Y
- QAM system parameters
- samples per symbol
- symbol map
- equalizer coefficients in
- training bits
- error in
- feedforward equalizer (lms) parameters
- taps per symbol
- delta (training)
- delta (steady state)
- reset?
- output complex waveform
- t0
- dt
- Y
- error
- equalizer coefficients out
- output bit stream
- error out
- input complex waveform
- Demodulator-to-Equalizer Data Flow
- Duration of Training Mode
- Continuous Data Stream
- Discontinuous Data Stream
- Continuous Equalization on Discontinuous Data