Squaring Timing Recovery

Recover symbol timing phase using squaring method


Timing Phase Recovery sublibrary of Synchronization


The Squaring Timing Recovery block recovers the symbol timing phase of the input signal using a squaring method. This feedforward, non-data-aided method is similar to the conventional squaring loop. This block is suitable for systems that use linear baseband modulation types such as pulse amplitude modulation (PAM), phase shift keying (PSK) modulation, and quadrature amplitude modulation (QAM).

Typically, the input to this block is the output of a receive filter that is matched to the transmitting pulse shape. This block accepts a column vector input signal of type double or single. The input represents Symbols per frame symbols, using Samples per symbol samples for each symbol. Typically, Symbols per frame is approximately 100, Samples per symbol is at least 4, and the input signal is shaped using a raised cosine filter.

    Note   The block assumes that the phase offset is constant for all symbols in the entire input frame. If necessary, use the Buffer block to reorganize your data into frames over which the phase offset can be assumed constant. If the assumption of constant phase offset is valid, then a larger frame length yields a more accurate phase offset estimate.

The block estimates the phase offset for the symbols in each input frame and applies the estimate uniformly over the input frame. The block outputs signals containing one sample per symbol. Therefore, the size of each output equals the Symbols per frame parameter value. The outputs are as follows:

  • The output port labeled Sym gives the result of applying the phase estimate uniformly over the input frame. This output is the signal value for each symbol, which can be used for decision purposes.

  • The output port labeled Ph gives the phase estimate for each symbol in the input frame. All elements in this output are the same nonnegative real number less than the Samples per symbol parameter value. Noninteger values for the phase estimate correspond to interpolated values that lie between two values of the input signal.

Dialog Box

Symbols per frame

The number of symbols in each frame of the input signal.

Samples per symbol

The number of input samples that represent each symbol. This must be greater than 1.


This block uses a timing estimator that returns


as the normalized phase between -1/2 and 1/2, where x is the input vector, L is the Symbols per frame parameter and N is the Samples per symbol parameter.

For more information about the role that the timing estimator plays in this block's algorithm, see Feedforward Method for Timing Phase Recovery in Communications System Toolbox™ User's Guide.


See Squaring Timing Phase Recovery Example in Communications System Toolbox User's Guide.


[1] Oerder, M. and H. Myer, "Digital Filter and Square Timing Recovery," IEEE Transactions on Communications, Vol. COM-36, No. 5, May 1988, pp. 605-612.

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

[3] Meyr, Heinrich, Marc Moeneclaey, and Stefan A. Fechtel, Digital Communication Receivers, Vol 2, New York, Wiley, 1998.

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