  Bounds on the amplitude of a scale-invariant stochastic primordial magnetic
field (PMF) can be significantly improved by measurements of the Faraday
Rotation (FR) of CMB polarization. The mode-coupling correlations induced by FR
make it possible to extract it from cross-correlations of the B-mode
polarization with the E-mode and the temperature anisotropy. In this paper, we
construct an estimator of the rotation measure that appropriately combines
measurements of the FR from multiple frequency channels. We study the
dependence of the signal-to-noise in the PMF detection on the resolution and
the noise of the detectors, as well as the removal of the weak lensing
contribution and the galactic FR. We show that a recently proposed space-based
experiment PRISM can detect magnetic fields of 0.1 nano-Gauss strength at a 2
sigma level. Higher detection levels can be achieved by reducing the detector
noise and improving the resolution or increasing the number of channels in the
30-70 GHz frequency range.
