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Low-SNR limit of the Cramer-Rao bound for estimating the carrier phase and frequency of a PAM, PSK, or QAM waveform

2001; IEEE Communications Society; Volume: 5; Issue: 5 Linguagem: Inglês

10.1109/4234.922765

2373-7891

Heidi Steendam, Marc Moeneclaey,

Blind Source Separation Techniques

We consider the Cramer-Rao bound (CRB) for the estimation of the carrier phase and frequency of a noisy linearly modulated signal with random data symbols. The observation vector consists of the matched filter output samples taken at the symbol rate, assuming known symbol timing. Because of the presence of the random data, the evaluation of this CRB is quite tedious. Instead, here we derive a simple closed-form expression for the limit of the CRB at low-signal-to-noise ratio (SNR), which holds for arbitrary PAM, PSK, and QAM constellations.