The block diagram of the QPSK system is shown below:
First, random four-digit integers are generated, which are then mapped to the constellation diagram through the QPSK Modulator Baseband. After pulse shaping and modulation, the signal is sent to the Gaussian band channel. At the receiving end, demodulation is performed first, converting the band signal into a baseband signal, followed by symbol synchronization and carrier synchronization processing.
The baseband QPSK signal waveform is
Using Gray code, the phase shift is $\frac{\pi}{4}$.
Up-conversion Module#
After sampling at four times the symbol rate, the signal is converted into I and Q signals through the Complex to Real-Imag module. A raised cosine filter with a roll-off factor of 0.5 is used for pulse shaping, and the amplitude response of the raised cosine filter is shown in the figure:
The signal after the raised cosine filter is
The spectrum is
Since the raised cosine filter is set to 4 samples per symbol, the sampling rate becomes 16MHz.
Then, it is multiplied by the high-frequency carrier signal, and the multiplied signal and spectrum are
It can be seen that the center frequency of the spectrum has changed to the frequency of the carrier.
Gaussian Channel#
The spectrum of the signal is
Down-conversion#
The spectrum after multiplication and the spectrum after low-pass filtering are shown below
The time-domain signal waveform is
Digital Baseband Receiver#
First, it goes through the raised cosine reception filter, then performs bit synchronization and carrier synchronization, and finally outputs to the demodulator.
It can be seen that the eye diagram is larger and more regular after time recovery and carrier recovery.
Timing Recovery#
It consists of a Farrow structure interpolation filter, timing error detection, loop filter, and interpolation controller.
The internal structure of the interpolation controller is
The output of the interpolation controller is
Carrier Synchronization#
