On the use of linear programming for spectral estimation

This paper provides an interpretation of linear programming for spectral estimation [1,2] as building an MLM-like data-adaptive filter with separate weights on each pair of sensors rather than on each sensor individually. It is shown that this estimate becomes MLM when a positive semi-definiteness constraint is imposed on the matrix of weights and becomes linear programming when a non-negative response to sinusoids constraint is imposed on the matrix of weights. It is shown that, for some sensor array configurations, linear programming does indeed provide tighter bounds on the spectral power than MLM, linear programming can pick up lower level sources than MLM, and linear programming can reject more interfering sources than MLM.