  We consider signature waveform design for synchronous code division
multiplexing in the presence of interference and wireless multipath fading
channels. The adaptive real/complex signature that maximizes the
signal-to-interference-plus-noise ratio (SINR) at the output of the
maximum-SINR filter is the minimum-eigenvalue eigenvector of the disturbance
autocovariance matrix. In digital communication systems, the signature alphabet
is finite and digital signature optimization is NP-hard. In this paper, first
we convert the maximum-SINR objective of adaptive binary signature design into
an equivalent minimization problem. Then we present an adaptive binary
signature design algorithm based on modified Fincke-Pohst (FP) method that
achieves the optimal exhaustive search performance with low complexity. In
addition, with the derivation of quaternary-binary equivalence, we extend and
propose the optimal adaptive signature design algorithm for quaternary
alphabet. Numerical results demonstrate the optimality and complexity reduction
of our proposed algorithms.
