Communications Blockset™

Gardner Timing Recovery - Recover symbol timing phase using Gardner's method

Library

Timing Phase Recovery sublibrary of Synchronization

Description

The Gardner Timing Recovery block recovers the symbol timing phase of the input signal using Gardner's method. This block implements a non-data-aided feedback method that is independent of carrier phase recovery. The timing error detector that forms part of this block's algorithm requires at least two samples per symbol, one of which is the point at which the decision can be made.

Inputs

By default, the block has one input port. Typically, the input signal is the output of a receive filter that is matched to the transmitting pulse shape. For best results, the input signal power should be less than 1. The input must be a scalar or a frame-based column vector. The input uses N samples to represent each symbol, where N > 1 is the Samples per symbol parameter. If the input is frame-based, then its vector length is N*R, where R is a positive integer that indicates the number of symbols per frame. If the input is sample-based, then its sample time is 1/N times the underlying symbol period.

If the Reset parameter is set to On nonzero input via port, then the block has a second input port, labeled Rst. The Rst input determines when the timing estimation process restarts, and must be a scalar. The sample time of the Rst input equals the symbol period if the input signal is sample-based, and the frame period if the input signal is frame-based.

Outputs

The block has two output ports, labeled Sym and Ph:

The Sym output is the result of applying the estimated phase correction to the input signal. This output is the signal value for each symbol, which can be used for decision purposes. The values in the Sym output occur at the symbol rate:
- If the input signal is a frame-based column vector of length N*R, then the Sym output is a frame-based column vector of length R having the same frame period.
- If the input signal is a sample-based scalar with sample time T/N, then the Sym output is a sample-based scalar with sample time T.

The Ph output gives the phase estimate for each symbol in the input.

The Ph output contains nonnegative real numbers less than N. Noninteger values for the phase estimate correspond to interpolated values that lie between two values of the input signal. The sample time or frame period of the Ph output is the same as that of the Sym output.

Note If the Ph output is very close to either zero or Samples per symbol, or if the actual timing phase offset in your input signal is very close to zero, then the block's accuracy might be compromised by small amounts of noise or jitter. The block works well when the timing phase offset is significant rather than very close to zero.

Delays

This block incurs a delay of two symbols when the input is frame-based and three symbols when the input is sample-based.

Dialog Box

Samples per symbol: The number of samples, N, that represent each symbol in the input signal. This must be greater than 1.
Error update gain: A positive real number representing the step size that the block uses for updating successive phase estimates. Typically, this number is less than 1/N, which corresponds to a slowly varying phase.
Reset: Determines whether and under what circumstances the block restarts the phase estimation process. Choices are None, Every frame, and On nonzero input via port. The last option causes the block to have a second input port, labeled Rst.

Algorithm

This block uses a timing error detector whose result for the kth symbol is e(k), given by

where

y_I and y_Q are the in-phase and quadrature components, respectively, of the block's input signal
T is the symbol period
d_k is the phase estimate for the kth symbol

Notice from the expressions in curly braces above that the timing error detector approximates the derivative of y using finite differences.

For more information about the role that e(k) plays in this block's algorithm, see Feedback Methods for Timing Phase Recovery in Communications Blockset™ User's Guide.

Examples

The commgardnerphrecov demonstration model uses this block.

References

[1] Gardner, F. M., "A BPSK/QPSK Timing-Error Detector for Sampled Receivers", IEEE Transactions on Communications, Vol. COM-34, No. 5, May 1986, pp. 423-429.

[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.

[4] Oerder, M., "Derivation of Gardner's Timing-Error Detector from the ML principle", IEEE Transactions on Communications, Vol. COM-35, No. 6, June 1987, pp. 684-685.