Embedded second-order cone programming with radar applications

Second-order cone programming (SOCP) is required for the solution of underdetermined systems of linear equations with complex coefficients, subject to the minimization of a convex objective function. This type of computational problem appears in compressed radar sensing, where the goal is to reconstruct a sparse image in a generalized space of phase model parameters whose dimension is higher than the number of complex measurements. In order to enforce sparsity in the final rectified radar image, the sum of moduli of a complex vector, called the ℓ₁ norm, must be minimized. This norm differs from what is ordinarily encountered in compressed sensing for digital photographic data and video, in that the convex optimization that must be performed involves an SOCP rather than a linear program. We illustrate the role of this type of optimization in radar signal processing by means of examples. The examples point to a significant generalization that encompasses and unifies a wide class of radar signal processing algorithms that can be implemented in software by means of SOCP solvers. Finally, we show how modern SOCP solvers are optimized for efficient solution of these problems in the context of embedded signal processing on small autonomous platforms.