Abstract: A system and method are disclosed that substantially reduce the complexity of receivers in digitally modulated wireless communication systems such as systems that use CDMA and similar multi-access coding. Transmitted signals are designed to use orthogonal or non-orthogonal codes with specific amplitudes that reduce the number of distinct eigenvalues in a code correlation matrix or in a code-plus-interference-plus-noise correlation matrix, so that a few steps of a conjugate direction calculation will compute a reduced rank Wiener filter that can be used to provide approximate de-correlation type receivers in a substantially reduced number of steps when compared to inverse correlation matrix calculations, or when compared to conjugate direction computations run on correlation matrices with un-shaped eigenvalues. These techniques can also be applied to active or passive imaging systems such as sonar, ultrasound and radar imaging systems and phased array systems that use beam forming.