Phase-locked Loop

The synchronization of the carrier frequencies is the most important piece of the communication system. In a wireless communication channel, various channel imperfections like ISI and Rayleigh fading due to multi-path effect exist. Without a synchronized local oscillator, data cannot be extracted correctly from the received QPSK signal. Implementing a phase-locked loop (PLL) is a standard method used to regenerate carrier frequency and correct for the channel imperfections introduced during transmission.
   The QPSK waveform carries phase information that represents data. By performing the following computation

                                               (2)

where  Δϕ  denotes the phase error, X(n) and Y(n) are the outputs from decimators. I(n) and Q(n) are the in-phase and quadrature hard-decoded data.
    The phase error (Δϕ) in Fig. 1 is calculated and then used to adjust the frequency and phase of the local oscillator. As the error is reduced to zero, the transmitter and receiver frequencies become synchronized, allowing for extraction of data from the  I and Q channels.

Fig. 1.  QPSK constellation grid.

      Equation (2) is calculated for every data sample, meaning that this must be implemented in hardware and run at the symbol rate. The phase error calculation is illustrated in Fig. 5. This rapid calculation is occurring in the “Carrier Recovery” block of the system block diagram, and serves as a feedback controller for the adjustment of the local oscillator.

Fig. 5.  Phase-locked loop.

   Crucial to the design of the PLL is the loop filter, which provides direct control over the PLL bandwidth. The bandwidth of a PLL is the measure of the PLL’s ability to track the input clock and jitter. A high bandwidth provides a fast lock time and tracks jitter on the reference clock source, passing it through to the PLL output, whereas a low bandwidth filters out reference clock jitter, but increases lock time [4].
     To control phase error, proportional and integral (PI) control techniques are used via a loop filter. PI control is implemented by selecting values for K_p and K_i, which provide the user with control over bandwidth and a damping factor. By optimizing these parameters, the system can achieve carrier synchronization with both a fast locking time and reduced jitter. First, the bandwidth for desired operation is chosen and then K_p and K_i values are derived using the following equations.

                                                                       (3)

                                                                       (4)

            where θ=2π*BW and BW is the bandwidth.