A Final Word About Covariance Matrix Estimation
Ctrue = true covariance matrix, unavailable with real data
- for a given s, w= Ctrue-1s maximizes E{SINR}
- for a given w, E{SINR} = |wHs|2 / wH Ctruew
Csamp = sample covariance matrix for computing weights
- as nsamp increases, Csamp provides a better (more accurate) estimate of Ctrue, thus the weights get “better”, i.e., E{SINR} = |wHs|2 / wH Ctruew approaches the maximum
- BUT, samples have to be representative
Ceval = estimate of covariance matrix for evaluating performance
- as nsamp increases, Ceval provides a better (more accurate) estimate of Ctrue, thus |wHs|2 / wH Cevalw provides a more accurate estimate of E{SINR}
If the data samples used in Csamp and Ceval overlap, then the estimate of E{SINR} will be biased... use different samples