Costas loop

A Costas loop is a phase-locked loop (PLL) based circuit which is used for carrier frequency recovery from suppressed-carrier modulation signals (e.g. double-sideband suppressed carrier signals) and phase modulation signals (e.g. BPSK, QPSK). It was invented by John P. Costas at General Electric in the 1950s.^[1]^[2] Its invention was described^[3] as having had "a profound effect on modern digital communications". The primary application of Costas loops is in wireless receivers. Its advantage over other PLL-based detectors is that at small deviations the Costas loop error voltage is $\sin(2(\theta _{i}-\theta _{f}))$ as compared to $\sin(\theta _{i}-\theta _{f})$ . This translates to double the sensitivity and also makes the Costas loop uniquely suited for tracking Doppler-shifted carriers, especially in OFDM and GPS receivers.^[3]

^ Costas, John P. (1956). "Synchronous communications". Proceedings of the IRE. 44 (12): 1713–1718. doi:10.1109/jrproc.1956.275063.
^ Costas, John P. (August 2002) [1956]. "Synchronous Communications". Proceedings of the IEEE. 90 (8): 1461–1466. doi:10.1109/JPROC.2002.800876.
^ ^a ^b Taylor, D. (August 2002). "Introduction to 'Synchronous Communications', A Classic Paper by John P. Costas". Proceedings of the IEEE. 90 (8): 1459–1460. doi:10.1109/jproc.2002.800719.

[1] Costas, John P. (1956). "Synchronous communications". Proceedings of the IRE. 44 (12): 1713–1718. doi:10.1109/jrproc.1956.275063.

[2] Costas, John P. (August 2002) [1956]. "Synchronous Communications". Proceedings of the IEEE. 90 (8): 1461–1466. doi:10.1109/JPROC.2002.800876.

[Taylor-3] Taylor, D. (August 2002). "Introduction to 'Synchronous Communications', A Classic Paper by John P. Costas". Proceedings of the IEEE. 90 (8): 1459–1460. doi:10.1109/jproc.2002.800719.

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