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The M-PSK Phase Recovery block recovers the carrier phase of the input signal using the M-Power method. This feedforward, non-data-aided, clock-aided method is suitable for systems that use baseband phase shift keying (PSK) modulation. It is also suitable for systems that use baseband quadrature amplitude modulation (QAM), although the results are less accurate than those for comparable PSK systems. The alphabet size for the modulation must be an even integer.

For PSK signals, the **M-ary number** parameter
represents the alphabet size. For QAM signals, the **M-ary
number** should be 4 regardless of the alphabet size because
the 4-power method is the most appropriate for QAM signals.

The M-Power method assumes that the carrier phase is constant
over a series of consecutive symbols, and returns an estimate of the
carrier phase for the series. The **Observation interval** parameter
is the number of symbols for which the carrier phase is assumed constant.
This number must be an integer multiple of the input signal's vector
length.

This block accepts a scalar or column vector input signal of
type `double` or `single`. The input
signal represents a baseband signal at the symbol rate, so it must
be complex-valued and must contain one sample per symbol.

The outputs are as follows:

The output port labeled

`Sig`gives the result of rotating the input signal counterclockwise, where the amount of rotation equals the carrier phase estimate. The`Sig`output is thus a corrected version of the input signal, and has the same sample time and vector size as the input signal.The output port labeled

`Ph`outputs the carrier phase estimate, in degrees, for all symbols in the observation interval. The`Ph`output is a scalar signal.

The block's algorithm requires it to collect symbols during
a period of length **Observation interval** before
computing a single estimate of the carrier phase. Therefore, each
estimate is delayed by **Observation interval** symbols
and the corrected signal has a latency of **Observation interval** symbols,
relative to the input signal.

**M-ary number**The number of points in the signal constellation of the transmitted PSK signal. This value as an even integer.

**Observation interval**The number of symbols for which the carrier phase is assumed constant. The observation interval parameter must be an integer multiple of the input signal vector length.

When this parameter is exactly equal to the vector length of the input signal, then the block always works. When the integer multiple is not equal to

`1`, select**Simulation**>**Configuration Parameters**>**Solver**and set

**Tasking mode for periodic sample times**to`SingleTasking`.

If the symbols occurring during the observation interval are x(1), x(2), x(3),..., x(L), then the resulting carrier phase estimate is

where the arg function returns values between -180 degrees and 180 degrees.

[1] Mengali, Umberto, and Aldo N. D'Andrea, *Synchronization
Techniques for Digital Receivers*, New York, Plenum Press,
1997.

[2] Moeneclaey, Marc, and Geert de Jonghe,
"ML-Oriented NDA Carrier Synchronization for General Rotationally
Symmetric Signal Constellations," *IEEE Transactions on
Communications*, Vol. 42, No. 8, Aug. 1994, pp. 2531-2533.

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