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. Cancellation of interference and
noise can also be accomplished by exploiting eigenvalue shape or by designing the codes and amplitudes of the transmitted
signal and using the reduced rank
Wiener filter to filter interference and
noise from the receive
signal. The techniques enable the use of code design and
power control for the control of
system complexity and bandwidth.