Synchronization and Clock Recovery

As I talked before, we will use 2nd Order Costas Loop as Carrier Wave Recovery (synchronization) and M&M Clock Recovery to recover the Symbol Clock. GNU Radio provides blocks for both algorithms. Let’s start with Costas Loop.

Costas Loop

For the parameters we will only need 0.00199 as Loop Bandwidthand 2 as Order. After that we should have our virtual carrier in the base band. Now we only need to synchronize our samples with clock using M&M Clock Recovery.

M&M Clock Recovery

For the M&M Parameters we will use Omega as 4.25339that is basically our symbols per sample rate, or sample_rate / symbol_rate. That is the first symbolrate guess for M&M. For Gain Omega we use (alpha ^ 2) / 4, that is alpha = 3.7e-3, so our Gain Omega be 3.4225e-6, Mu as 0.5, Gain Mu as alpha (or 3.7e-3), Omega Relative Limit as 5e-3.

So you can notice that I called a new parameter alphain M&M that is not a direct parameter of the block. That alpha is a parameter to adjust how much the M&M clock recovery can deviate from the initial guess. You can experiment with your own values, but 3.7e-3 was the best option to me.

Now at the output of M&M we will have our Complex Symbols pumped out with the correct rate. Now we only need to extract our values.