# Documentation

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# CPM Phase Recovery

Recover carrier phase using 2P-Power method

 Note:   CPM Phase Recovery will be removed in a future release. Use the Carrier Synchronizer block instead.

## Library

Carrier Phase Recovery sublibrary of Synchronization

## Description

The CPM Phase Recovery block recovers the carrier phase of the input signal using the 2P-Power method. This feedforward, non-data-aided, clock-aided method is suitable for systems that use these types of baseband modulation: continuous phase modulation (CPM), minimum shift keying (MSK), continuous phase frequency shift keying (CPFSK), and Gaussian minimum shift keying (GMSK). This block is suitable for use with blocks in the Baseband Continuous Phase Modulation library.

If you express the modulation index for CPM as a proper fraction, h = K / P, then P is the number to which the name "2P-Power" refers. The observation interval parameter must be an integer multiple of the input signal vector length.

The 2P-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.

### Input and Output Signals

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.

 Note   Because the block internally computes the argument of a complex number, the carrier phase estimate has an inherent ambiguity. The carrier phase estimate is between -90/P and 90/P degrees and might differ from the actual carrier phase by an integer multiple of 180/P degrees.

### Delays and Latency

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.

## Parameters

P

The denominator of the modulation index for CPM (h = K / P) when expressed as a proper fraction.

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 clear the Treat each discrete rate as a separate task checkbox.

## Algorithm

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

`$\frac{1}{2P}\mathrm{arg}\left\{\sum _{k=1}^{L}{\left(x\left(k\right)\right)}^{2P}\right\}$`

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

## References

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