The Cramér-Rao lower bound (CRLB) is widely used in the design of magnetic resonance (MR) experiments for parameter estimation. Previous work has considered only Gaussian or Rician noise distributions in this calculation. However, the noise distribution for multiple-coil acquisitions, such as in parallel imaging, obeys the noncentral χ-distribution under many circumstances. Here, we present the general mathematical expression for the CRLB calculation for parameter estimation from multiple-coil acquisitions. Our results indicate that the CRLB calculation must account for the noncentral χ-distribution of noise in multi-coil acquisitions, especially in the low-to-moderate signal-to-noise ratio (SNR) regime.
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