Abstract-The true Cramér-Rao lower bound (CRLB) for the joint estimation of carrier phase and frequency is derived for transmission bursts with interleaved reference and phase-shift keying/quadrature amplitude modulated data symbols. Results are presented for the special cases of midamble, and preamble and postamble, pilot-symbol insertion. The derivation reveals that the CRLB is a function of the location of the reference symbols in the burst, the number of reference symbols, the number of data symbols, the signal-to-noise ratio and the data-modulation scheme. By distributing the reference symbols symmetrically about the center of the burst and analyzing relative to the middle of the signal vector, the joint frequency and phase estimation can be decoupled, and the optimal phase estimation is achieved. In the decoupled case, the phase CRLB is independent of the location of reference symbols in the burst. In a symmetrical burst, the use of a preamble and postamble is found to provide a lower frequency-estimation CRLB than that with a midamble. It appears that the frequency CRLB is reduced as the reference symbols are symmetrically distributed closer to the ends of the burst.
Abstract-This paper addresses the problem of improving the spurious free dynamic range (SFDR) for digitization by use of antenna arrays. Nonlinearities in the analog-to-digital conversion process give rise to spurious signals (harmonics and intermodulation products) that limit the overall SFDR of the digitization process. When the signal of interest arises from a sensor such as an antenna or hydrophone, the paper addresses the question of whether array processing (ie use of multiple antennas) can improve the resulting SFDR at the beamformer output. The paper argues that significant improvements can be obtained using linear, or more effectively, optimal (minimum variance distortionless response) beamforming.Index Terms-Analog-to-digital conversion, array processing, digital receivers, spurious free dynamic range.
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