Algorithms for the Construction of Incoherent Frames Under Various Design Constraints

A Frame-Theoretic Scheme for Robust Millimeter Wave Channel Estimation

“…This scheme, referred to as sequential iterative decorrelation via convex optimization (SIDCO), was originally introduced in [20] only for frames in R M . More recently, a strategy to generalize SIDCO to frames in C M , referred to as complex SIDCO (C-SIDCO), was reported by [26]. An explicit and complete mathematical formulation of C-SIDCO was, however, not given in [26].…”

“…More recently, a strategy to generalize SIDCO to frames in C M , referred to as complex SIDCO (C-SIDCO), was reported by [26]. An explicit and complete mathematical formulation of C-SIDCO was, however, not given in [26]. A variation of the latter based on an explicit quadratic program is offered below.…”

“…Consider an existent unit-norm frame F ∈ C M ×N . The strategy of C-SIDCO [26] is to minimize mutual coherence by iteratively solving the problem…”

“…1] with the quadratic program given by equation ( 14), and the direct interlacing from C M to R 2M achieved in our formulation via the matrices D M , A R,1 , A R,2 , A I,1 and A A,2 , C-SIDCO becomes here a simple extension of the original SIDCO algorithm, which converges (absolutely) to the local minimum coherence points since the original concept of M -ball packings is preserved. For all the above, the explicit quadratic reformulation of C-SIDCO offered above is original, and can be directly coded on top of optimized standard quadratic solvers, unlike the formulation presented in [26].…”