instrumental noise on the relevant angular scales.

### Covariance estimation and conditioning {#sec:cov}

The bandpower covariance matrix accounts for sample variance and instrumental noise variance. As in R12, the sample variance is estimated from the signal-only simulations (see Section \[sec:sims\]), and the noise variance is calculated from the distribution of the cross-spectrum bandpowers $D^{\nu_i\times\nu_j,AB}_b$ between observations A and B, and frequencies $\nu_i$ and $\nu_j$. At $\ell > 5000$, where the signal is strongly noise dominated, we ensure the covariance matrix remains positive definite by using only the first term in eqn. A15 in L10. This term scales with the variance of the cross spectra, and is an accurate estimate of the covariance in the noise-dominated regime. There is statistical uncertainty on elements of the estimated bandpower covariance matrix that can degrade parameter constraints [see, e.g., @dodelson13]. We “condition” the covariance matrix to reduce this uncertainty following the prescription in R12. We find in simulations that this conditioning significantly reduces the degradation in parameter constraints.

The covariance matrix is a set of thirty-six square blocks, with the six on-diagonal blocks corresponding to the covariances of 95 x 95, 95 x 150, ... 220 x 220 GHz spectra. The covariance matrix includes 