0.1 A telecommunication system  (Page 12/15)

Synchronization: good times bad times

Synchronization may occur in several places in the digital receiver:

• Symbol phase synchronization—choosing when (within each interval $T$ ) to sample.
• Symbol frequency synchronization—accounting for different clock (oscillator) rates at the transmitter and receiver.
• Carrier phase synchronization—aligning the phase of the carrier at the receiver with the phase of the carrier at the transmitter.
• Carrier frequency synchronization—aligning the frequency of the carrierat the receiver with the frequency of the carrier at the transmitter.
• Frame synchronization—finding the “start” of each message data block.

In digital receivers, it is important to sample the received signal at the appropriate time instants.Moreover, these time instants are not known beforehand; rather, they must be determined from the signal itself.This is the problem of clock recovery. A typical strategy samples several times per pulse and then uses some criterionto pick the best one, to estimate the optimal time, or to interpolate an appropriate value.There must also be a way to deal with the situation when the oscillator defining the symbol clock at the transmitterdiffers from the oscillator defining the symbol clock at the receiver.Similarly, carrier synchronization is the process of recovering the carrier (in both frequency and phase)from the received signal. This is the same task in a digital receiver as in an analog design (recall that the cosine waveused to demodulate the received signal in [link] was aligned in both phase and frequency with the modulating sinusoidat the transmitter), though the details of implementation may differ.

In many applications (such as cell phones), messages come in clusters called packets, and each packethas a header (that is located in some agreed-upon place within each data block) that contains important information.The process of identifying where the header appears in the received signal is calledframe synchronization, and is often implemented using a correlation technique.

The point of view adopted in Software Receiver Design is that many of these synchronization tasks can be stated quite simply asoptimization problems. Accordingly, many of the standard solutions to synchronization tasks can be viewed assolutions to these optimization problems:

• The problem of clock (or timing) recovery can be stated as that of finding a timing offset $\tau$ to maximize the energy of the received signal. Solving thisoptimization problem via a gradient technique leads to a standard algorithm for timing recovery.
• The problem of carrier phase synchronization can be stated as that of finding a phase offset $\theta$ to minimize a particular function of the modulated received signal.Solving this optimization problem via a gradient technique leads to the Phase Locked Loop, a standardmethod of carrier recovery.
• Carrier phase synchronization can also be stated using an alternative performance function that leads directly to theCostas loop, another standard method of carrier recovery.