Abstract: The present invention is a machine or method used in digital communications. Symbols are selected in periodic fashion from at least two different symbol constellations. At least one of the symbol constellations has a non-conjugated second moment not equal to zero. The non-conjugated second moment is a second-order statistic. Symbol selection leads to second-order input statistics having cyclostationary phase, and thus to second-order output statistics having cyclostationary phase. These statistics can be used for low-complexity identification and equalization of both linear and nonlinear channels. The invention allows for low-complexity identification and equalization of linear channels and of nonlinear channels without requiring constant-modulus constellations.

Abstract: A machine or method used in signal processing transforms involving computing one or more sums each of one or more products. A multiplier has one or both of its two inputs restricted to limited sets of numbers having given finite-precision numeric formats. The multiplier is not a constant multiplier capable only of computing the product of any first number and a constant. The multiplier is not a general multiplier capable of computing the product of any pair of numbers. The multiplier has lower complexity than a general multiplier, but more flexibility than a constant multiplier. The invention can be used to reduce the overall computational complexity of signal processing transforms. The invention can be used when transform weights are fixed and known. The invention can be used when transform inputs, though random, come from small, known sets, as is the case in digital communications.