G. N. Karystinos and D. A. Pados, “Rank-2-optimal adaptive design of binary spreading codes,” IEEE Transactions on information Theory, vol. 53, no. 9, pp. 3075 - 3080, Sept. 2007. doi: 10.1109/TIT.2007.903130
https://doi.org/10.1109/TIT.2007.903130
Over the real/complex field, the spreading code that maximizes the signal-to-interference-plus-noise ratio (SINR) at the output of the maximum-SINR linear filter is the minimum-eigenvalue eigenvector of the interference autocovariance matrix. In the context of binary spreading codes, the maximization problem is NP-hard with complexity exponential in the code length. A new method for the optimization of binary spreading codes under a rank-2 approximation of the inverse interference autocovariance matrix is presented where the rank-2-optimal binary code is obtained in lower than quadratic complexity. Significant SINR performance improvement is demonstrated over the common binary hard-limited eigenvector design which is shown to be equivalent to the rank-1-optimal solution.