Complementary Set Matrices Satisfying a Column Correlation Constraint

Motivated by the problem of reducing the peak-to-average power ratio (PAPR) of transmitted signals, we consider a design of complementary set matrices whose column sequences satisfy a correlation constraint. The design algorithm recursively builds a collection of 2^t+1 mutually orthogonal (MO) complementary set matrices starting from a companion pair of sequences. We relate correlation properties of column sequences to that of the companion pair and illustrate how to select an appropriate companion pair to ensure that a given column correlation constraint is satisfied. For t = 0, companion pair properties directly determine matrix column correlation properties. The proposed companion pair-based design can construct binary complementary sets with either a minimum out-of-phase autocorrelation magnitude or a minimum sum-of-out-of-phase autocorrelation magnitude for column sequences of length at least up to 28. For t ges 1, reducing correlation merits of the companion pair may lead to improved column correlation properties. Exhaustive search for companion pairs satisfying a column correlation constraint is infeasible for medium length and long sequences. We instead search for two shorter length sequences by minimizing a cost function in terms of their autocorrelation and cross-correlation merits. In addition, by exploiting the well-known Welch bound, sufficient conditions for the existence of companion pairs which satisfy a set of column correlation constraints are given.