## The Costas loop

#### A commonly used variant of the squaring-based carrier recovery method is the Costas loop (Costas (1956)).
The Costas loop is essentially two phase-locked loops operating in parallel, with a common VCO giving quadrature outputs to each loop. The squaring process necessary to make the PSK modulation modulo 2p is inherent within the Costas loop by virtue of the third mixer.

There are two main advantages to the Costas loop. Firstly, it does not implicitly generate a twice carrier frequency component and thus does away with the need for a 'divide by two' circuit. Secondly, it performs the required coherent data detection in one of the branches of the dual PLL system, eliminating the need for extra detection circuitry. (A separate matched filter is used for data recovery as the filtering within the Costas loop is usually made very narrow in order to achieve good noise averaging of the coherent reference. |