Scaled and Decoupled Cholesky and QR Decompositions with Application to Spherical MIMO Detection

Motivated by the need for the Cholesky factorization in implementing a spherical MIMO detector, this paper considers Cholesky and QR decompositions suitable for fixed-point implementation. In particular, we reformulate the decompositions to avoid the many square-root and division operations required in their natural form. This is achieved by decoupling the numerator and denominator calculations and applying scaling by powers of 2 (corresponding to bit shifts) to ensure numerical stability in the recursions. We consider the impact on the spherical detector formulation.