Final Project: Symbol timing recovery for Square 16 QAM

The file baseproject.m is a Matlab script file that simulates a transmitter and AWGN channel.  The samples of the received signal are given in the variable "r" at the end of the loop.  Your assignment is to use the techniques we discussed in class to synchronize with the data embedded in the received signal.

Some simulation parameters are:

• N = 4 (number of samples per symbol period)
• Square-root raised cosine pulse with 35% excess bandwidth
• Square 16 QAM modulation

Other parameters can be found in the baseproject.m file.

Do the following:

• Build a receiver assuming using known symbol timing information.  Plot an eye diagram for the in-phase and quadrature branches.  Show a scatter plot of the sampled match filtered output when there is a small amount of noise.
• Design a derivative matched filter (DMF) and add a DMF to the in-phase and quadrature branches in your system.  Does the eye diagram at the DMF output appear as you expected?  The derivative filter adds delay to the DMF output.  Add a corresponding delay to the matched filter (MF) branches.  Make sure that the eye diagrams at the MF and DMF outputs are "in phase".  The DMF and MF outputs will be used in the next part to build the timing error detector.
• Implement the maximum likelihood timing error detector (MLTED).  Add a proportional-plus-integral loop filter to low pass filter the error signal.  Does the filtered error signal appear as you expected?
  
• Build a symbol timing synchronizer using the MLTED and polynomial interpolation.  Use second or third order interpolation.
  
• Build a symbol timing synchronizer using the MLTED and up-sampling to perform interpolation.  Up-sample by at least a factor of Q=4.
  
• Explain how you selected the PLL parameters: Kp, K0, K1, and K2.  Use BnTs = 0.0001 and damping factor of 1/sqrt(2).
  
• Show a plot of the fractional interval as a function of time.
• Show a plot of the timing error signal.
• Show a plot of the sampled match filter outputs over time for both the in-phase and quadrature branches.