Asynchronous Timing in a Bit Timing Recovery Model


This example shows how to model the time-varying drifting of clocks in the transmitter and receiver of a communication system. The example is based on the Timing Recovery Using Fixed-Rate Resampling example in the Communications System Toolbox™ product.

Furthermore, the model exploits asynchronous behavior, which is more efficient than the original example's technique of tracking zero crossings of a voltage-controlled oscillator (VCO) in continuous time.

To learn about the underlying communication system, ways to explore the example, and what the plots mean, see the description of the original Timing Recovery Using Fixed-Rate Resamplingoriginal Timing Recovery Using Fixed-Rate Resampling example. The rest of this section describes how this example differs from the original and how the example implements time-varying drifting of clocks.

Comparison with Original Example

Unlike the original example, this example:

  • Uses a discrete-event function-call generator instead of a continuous-time VCO within the QPSK Transmitter subsystem.

  • Omits a carrier offset, instead focusing more on the timing recovery process. You can see the difference in the QPSK Transmitter subsystem's Carrier Offset and Conversion to Continuous Time subsystem and also in the absence of the Enable carrier recovery option in the Adjust Settings block.

  • Enhances the ability to model clock drift between the transmitter and receiver. This example adds a sinusoidally varying error in symbol timing to the original example's constant error.

The sinusoidal error causes an error in symbol timing that varies smoothly and assumes positive and negative values. The drift in the transmitter's symbol clock causes the timing recovery component in the receiver to continually change the rate at which it drifts in response.

If you run the original example with a carrier offset of 0 and run this example with a sinusoidal error of 0, you get equivalent results.

Calling a Subsystem at Arbitrary Times

The figure below, which shows part of the QPSK Transmitter subsystem's DES Voltage Controlled Sample Rate subsystem, illustrates how this example calls a function-call subsystem at arbitrary times during the simulation. The arbitrary times do not need to be multiples of a fundamental sample time.

During the simulation, blocks in the figure behave as follows:

1. At time T0=0, the Function-Call Generator block generates a function call.

2. The function call at time T0 causes the Signal-Based Event to Function-Call Event block to read the current value, t0, of the t input signal. The block then schedules an event for time T1=T0+t0.

    In this model, the t signal is the reciprocal of the sum of the
    reference frequency, constant frequency error, and sinusoidal
    frequency error.

3. When the scheduled event is processed at time Ti (i=1,2,3,...), the Signal-Based Event to Function-Call Event block issues two function calls:

    a. The function call at the f1 output port connects to a Mux block,
       which in turn connects to the same Signal-Based Event to
       Function-Call Event block. In other words, the Signal-Based Event
       to Function-Call Event calls itself. (The purpose of this Mux
       block is to create a union of function calls from more than one
       This function call causes the block to read the current value,
       ti, of the t input signal. The block then schedules an event for
       time Ti+1=Ti+ti.
    b. The function call at the f2 output port calls the function-call
       subsystem that connects to the outport. The function-call
       subsystem does not appear because it is in the upper level of the
       block diagram.

4. The process in step 3 repeats throughout the simulation. In effect, the Signal-Based Event to Function-Call Event block uses the t input signal as an intergeneration time for generating function calls, uses the f1 output port to iterate, and uses the f2 output port to call the function-call subsystem at the desired times.

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