Symbol Synchronizer
Adjustments to character synchronisation.
Description
Block Symbol Synchronizer corrects the symbol synchronisation clock shift between transmitter and receiver with a single carrier for PAM, PSK, QAM or OQPSK modulation schemes. For more information, refer to Symbol Synchronisation Overview.
| The input signal operates based on the sampling frequency and the output signal operates based on the symbol frequency. |
Ports
Input
Samp - input samples
scalar | vector-column
Input samples specified as a scalar or column vector of a modulated single channel PAM, PSK, QAM or OQPSK signal.
This port has no name on the block icon.
Data types: Float32, Float64, Int64, Int32
Support for complex numbers: Yes
Output
Sym - symbols of the output signal
scalar | vector-column
Output signal type symbols returned as a variable dimension scalar or column vector, having the same data type as the input signal. For input data with dimensionality by 1, the output data Sym has dimensionality by 1, where is approximately equal to , divided by . The value of is equal to the value of the Samples per symbol parameters. The length of the output signal is truncated if it exceeds the maximum output signal size, which is defined as
.
Data types: Float32, Float64
Support for complex numbers: Yes
Err - calculated synchronisation error
scalar | vector-column
Synchronisation error estimate for each input sample, returned as a scalar or column vector with values in the range [0, 1]. The synchronisation error estimate is normalised to the input sample time. Err has the same data size as the input signal.
Dependencies
To use this port, set the Normalised timing error output port parameters to `enabled'.
Data types: Float32, Float64
Complex Number Support: Yes
Parameters
Modulation type - modulation type
PAM/PSK/QAM (by default) | OQPSK.
Modulation type, options to select PAM/PSK/QAM or OQPSK.
If OQPSK is selected for the Modulation type parameters, demodulate the symbol rate synchronised signals with the unit QPSK Modulator Baseband, as the unit outputs a symbol rate QPSK modulated signal for an OQPSK modulated input signal.
|
Timing error detector - type of synchronisation error detector
Early-Late (non-data-aided) (by default) | Zero-Crossing (decision-directed) | Gardner (non-data-aided) | Mueller-Muller (decision-directed)
Type of synchronisation error detector. Options for selection:
-
Zero-Crossing (decision-directed). -
Gardner (non-data-aided). -
Early-Late (non-data-aided). -
Mueller-Muller (decision-directed).
This parameter specifies the synchronisation error detection scheme used in the synchroniser.
For more information, see Synchronisation Error Detection.
Samples per symbol - Samples per symbol
2 (by default) | `positive integer greater than 1'.
Samples per symbol , set as positive integer greater than 1.
For more information about , see Contour Filter.
Damping factor - attenuation factor for the loop filter
1 (By default) | positive scalar
Samples per character , specified as a positive integer greater than 1.
For more information about , see Contour Filter.
Normalised loop bandwidth - normalised loop bandwidth for the loop filter
0.01 (by default) | positive scalar less than 1
The normalised loopwidth bandwidth of the loop filter, specified as a positive scalar less than 1. The loop bandwidth is normalised to the symbol rate of the input signal.
For more information about , see Contour Filter.
To ensure that the symbol synchroniser is locked, set the Normalised loop bandwidth parameters to a value less than 0.1.
|
Detector gain - the gain of the phase detector
2.7 (By default) | Positive scalar
Phase detector gain , set as a positive scalar.
For more information about , see Contour Filter.
Normalised timing error output port - use the calculated timing error output port
enabled (By default) | disabled.
Select the checkbox to output normalised timing error data to the Err output port.
Algorithms
Symbol synchronisation overview
The symbol time synchronisation algorithm is based on the phased lock loop (PLL) algorithm, which consists of four components:
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Timing error detector (TED).
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Interpolator.
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Interpolation control.
-
Contour filter.
With OQPSK modulation, the in-phase and quadrature signal components are first aligned (as with QPSK modulation) using a state buffer to accumulate the last half-symbol of the previous input. After the initial alignment, the rest of the synchronisation process is the same as with QPSK modulation.
The block diagram shows an example synchroniser. In the figure, PLL symbol synchronisation works with , obtained by sampling signal after matched filtering. The PLL symbol synchroniser outputs the symbol signal after clock mismatch correction between transmitter and receiver.
Synchronisation error detection
The Symbol Timer supports the types of synchronisation error detector without usage and with decision. This table shows the time estimation expressions for different types of synchronisation error detector.
| Timing error detector | Expression |
|---|---|
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The non-data-aided synchronisation error detector methods (Gardner (non-data-aided) and Early-late (non-data-aided)) use the samples obtained without knowledge of the transmitted signal or the channel estimation results. Non-data-aided synchronisation error detector methods are used to estimate the synchronisation error of signals with modulation schemes in which constellation points are aligned with the in-phase or quadrature synchronisation axis. Examples of signals suitable for these methods include QPSK-modulated signals with zero phase shift that have points in the and BPSK modulated signals with zero phase shift.
The Early-late (non-data-aided) method is similar to the Gardner (non-data-aided) method, but the Gardner (non-data-aided) method performs better in high signal-to-noise ratio systems because it has less intrinsic noise than the Early-late (non-data-aided) method.
-
The
Gardner (non-data-aided)method is a non-data-aided feedback Gardner method that does not depend on carrier phase recovery. It is used for baseband systems and modulated carrier systems. Strictly speaking, this method is used for systems using a linear type of modulation with Nyquist pulses that have excess bandwidth in the range of 40 to 100 per cent. Examples are systems using PAM, PSK, QAM or OQPSK modulation and shaping the signal using boosted cosine filters with a drop factor between 0.4 and 1. In the presence of noise, the performance of this method of synchronisation recovery improves as the excess bandwidth (or the falloff ratio in the case of the boosted cosine filter) increases. The Gardner method is similar to the leading and lagging gating methods. -
The
Early-late (non-data-aided)method is a leading and lagging feedback gating method without data transmission. It is used in systems with a linear modulation type such as PAM, PSK, QAM or OQPSK. For example, systems using a boosting cosine filter with Nyquist pulses. In the presence of noise, the performance of this method of synchronisation recovery improves as the excess bandwidth of the pulse (or attenuation coefficient in the case of the boosted cosine filter) increases.
The decision-directed synchronisation error detector methods (Zero-crossing (decision-directed) and Mueller-Muller (decision-directed)) use the `sign' function to estimate the in-phase and quadrature components of the received samples, resulting in less computational complexity than the non-decision-directed methods.
-
The
Zero-crossing (decision-directed)method is a decision-directed zero-crossing method that requires 2 samples per symbol at the input of the synchroniser. It is used under low signal-to-noise ratio conditions for all excess bandwidth values and under moderate signal-to-noise ratio conditions for moderate excess bandwidth coefficients in the approximate range [0.4, 0.6]. -
The
Mueller-Muller (decision-directed)method is a Miller-Muller (decision-directed) feedback method that requires prior carrier phase recovery. When the input signal has Nyquist pulses (e.g., by usage of a boosted cosine filter), the Miller-Muller method has no intrinsic noise. For narrowband signalling in the presence of noise, the performance of the Miller-Mueller method improves as the excess pulse bandwidth factor decreases.
Since the Zero-crossing (decision-directed) and Mueller-Muller (decision-directed) methods estimate the synchronisation error based on the sign of the in-phase and quadrature components of the signals transmitted to the synchroniser, they are not recommended for constellations that have points with zero in-phase or quadrature components.
The in-phase and quadrature components of the input signals to the synchronisation error detector, where is the estimated synchronisation error. The coefficients of the Miller-Muller method and are estimates of and . Temporal estimates are derived by applying the sign function to the in-phase and quadrature components and are only used in decision-based synchronisation error detector methods.
Interpolator
The time delay is estimated from fixed matched filter samples that are asynchronous to the symbol transmission frequency. Since the resulting samples do not coincide with the symbol boundaries, an interpolator is used to "move" them. Since the time delay is unknown, the interpolator must be adaptive. Furthermore, since the interpolator is a linear combination of the available samples, it can be considered as the output of a filter.
A piecewise parabolic interpolator with Farrow structure and coefficient (see [1]) is used as an interpolator.
Interpolation control
The interpolation control provides the interpolator with a base point index and a fractional interval. The base point index is the nearest sample index to the interpolator. The fractional interval is the ratio of the time between the interpolator and its base point index to the interpolation interval.
Interpolation is performed for each sample, and a strobe signal is used to determine the output of the interpolator. The synchroniser uses modulo 1 counter interpolation control to provide gating and fractional interval for usage with the interpolator.
Contour Filter
The synchroniser uses a proportional-integral (PI) loop filter. The proportional gain and the integration gain are calculated as follows:
и
.
The intermediate term is defined as follows:
,
where
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- is the number of samples per symbol;
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- attenuation coefficient;
-
- loop bandwidth , normalised to the symbol rate ;
-
- detector gain.
