This model shows symbol timing recovery for an 8-PSK modulated and filtered signal transmitted over a varying delay channel.
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The example uses various blocks from the Communications System Toolbox™ DSP System Toolbox™, and Simulink® to model an 8-PSK transmitted signal.
The model includes the following blocks:
An M-PSK Modulator BasebandM-PSK Modulator Baseband block followed by a Raised Cosine Transmit FilterRaised Cosine Transmit Filter block that modulates, upsamples, and applies pulse shaping to the signal stream for transmission.
The channel consisting of a Variable Integer Delay block and an AWGN ChannelAWGN Channel block. The Variable Integer Delay block introduces random integer delays less than the upsampling factor, and the AWGN ChannelAWGN Channel block can vary the SNR level based on user input.
At the receiver end, a receive filter matched to the raised cosine pulse shape is followed by the Gardner Symbol Synchronizer subsystem block. After appropriate demodulation, the output is fed to the displays for analysis.
As the introduced delay of the channel is changed for every frame, the error signal shows periodic bursts where the synchronizer has to retrack the signal.
You can increase the size of the frame to observe the settling period. A stable value of the error is a measure of the percent difference in the transmitter and receiver frequencies that the synchronizer has recovered from.
On running the simulation model, the scatter plot shows the recovered signal points before demodulation.
The BER meter shows the error performance for the level of noise selected. The Symbol Clock scope shows the recovered clock at the symbol rate. Note the initial jitter and the subsequent gradual settling phase over a frame that indicates the tracking behavior.
On loading, the model initializes a set of variables that control the simulation. You are encouraged to play with the values of these variables to see their effects on the model.
The following are some possibilities for modifying the model:
Vary transmit and receive filter characteristics, such as the Rolloff factor and Group delay.
Vary the receiver symbol frequency to see if the block can still track the signal and demodulate appropriately.
Vary the AWGN noise levels.
Vary the simulation frame size. Change the delay to be constant for the length of the simulation or multiple frames.
Use a different modulation scheme, such as QPSK or 16QAM (this might require you to change some of the blocks).