comm.CarrierSynchronizer
Compensate for carrier frequency offset
Description
The comm.CarrierSynchronizer
System object™ compensates for carrier frequency and phase offsets in
signals that use single-carrier modulation schemes. The carrier synchronizer algorithm is
compatible with BPSK, QPSK, OQPSK, 8-PSK, PAM, and rectangular QAM modulation schemes.
Note
This System object does not resolve phase ambiguities created by the synchronization algorithm. As indicated in this table, the potential phase ambiguity introduced by the synchronizer depends on the modulation type:
Modulation Phase Ambiguity (degrees) 'BPSK'
or'PAM'
0, 180 'OQPSK'
,'QPSK'
, or'QAM'
0, 90, 180, 270 '8PSK'
0, 45, 90, 135, 180, 225, 270, 315 The Examples demonstrate carrier synchronization and resolution of phase ambiguity.
For best results, apply carrier synchronization to non-oversampled signals, as demonstrated in Correct Phase and Frequency Offset for 16-QAM Using Coarse and Fine Synchronization.
To compensate for frequency and phase offsets in signals that use single-carrier modulation schemes:
Create the
comm.CarrierSynchronizer
object and set its properties.Call the object, as if it were a function.
To learn more about how System objects work, see What Are System Objects?.
Creation
Description
creates
a System object that compensates for carrier frequency offset and phase offset in signals
that use single-carrier modulation schemes.carrSynch
= comm.CarrierSynchronizer
sets properties using one or more name-value pairs. Enclose each property name in
quotes.carrSynch
= comm.CarrierSynchronizer(Name
,Value
)
Properties
Usage
Description
Input Arguments
Output Arguments
Object Functions
To use an object function, specify the
System object as the first input argument. For
example, to release system resources of a System object named obj
, use
this syntax:
release(obj)
Examples
Algorithms
The comm.CarrierSynchronizer
System object is a
closed-loop compensator that uses the PLL-based algorithm described in [1]. The output of the
synchronizer, yn, is a frequency-shifted version of
the complex input signal, xn, for the nth sample.
The synchronizer output is
where λn is the output of the direct digital synthesizer (DDS). The DDS is the discrete-time version of a voltage-controlled oscillator and is a core component of discrete-time phase locked loops. In the context of this System object, the DDS works as an integration filter.
To correct for the frequency offset, first the algorithm determines the phase error, en. The value of the phase error depends on the modulation scheme.
Modulation | Phase Error |
---|---|
QAM or QPSK | For a detailed description of this equation, see [1]. |
BPSK or PAM | For a detailed description of this equation, see [1]. |
8-PSK | For a detailed description of this equation, see [2]. |
OQPSK |
To ensure system stability, the phase error passes through a biquadratic loop filter governed by
where ψn is the output of the loop filter at sample n, and gI is the integrator gain. The integrator gain is determined from the equation
where θ, d, K0, and Kp are determined from the System object properties. Specifically,
where Bn is the normalized loop bandwidth, and ζ is the damping factor. The phase recovery gain, K0, is equal to the number of samples per symbol. The modulation type determines the phase error detector gain, Kp.
Modulation | Kp |
---|---|
BPSK, PAM, QAM, QPSK, or OQPSK | 2 |
8-PSK | 1 |
The output of the loop filter is then passed to the DDS. The DDS is another biquadratic loop filter whose expression is based on the forward Euler integration rule
where gP is the proportional gain that is expressed as
The info
object function of this System object returns estimates of the
normalized pull-in range, the maximum frequency lock delay, and the maximum phase lock delay.
The normalized pull-in range, (Δf)pull-in, is expressed in radians and estimated as
The expression for (Δf )pull-in becomes less accurate as approaches 1.
The maximum frequency lock delay, TFL, and phase lock delay, TPL, are expressed in samples and estimated as
References
[1] Rice, M. Digital Communications: A Discrete-Time Approach. Upper Saddle River, NJ: Prentice Hall, 2009, pp. 359–393.
[2] Zhijie, H., Y. Zhiqiang, Z. Ming, and W. Kuang. “8PSK Demodulation for New Generation DVB-S2.” 2004 International Conference on Communications, Circuits and Systems. Vol. 2, 2004, pp. 1447–1450.
Extended Capabilities
Version History
Introduced in R2015a