A linear algebra approach to systems of polynomial equations with application to digital communications
Jérôme Lebrun, Pierre Comon · 2004
We introduce in this paper a new algebraic approach to some prob-lems arising in signal processing and communications that can be described as or reduced to systems of multivariate quadratic poly-nomial equations. Based on methods from computational algebraic geometry, the approach achieves a full description of the solution space and thus avoids the local minima issue of adaptive algo-rithms. Furthermore, unlike most symbolic methods, the compu-tational cost is kept low by a split of the problem into two stages. First, a symbolic pre-computation is done offline once for all, to get a more convenient parametric trace-matrix representation of the problem using normal forms. The solutions of the problem are then easily obtained from this representation by solving a single univari-ate polynomial equation. This approach is quite general and can be applied to a wide variety of problems: SISO channel identification of PSK modulations but also filter design and possibly MIMO blind source separation by deflation. 1.