Design of unimodular sequences using generalized receivers

This paper reviews recent advances in designing unimodular sequences with good auto/cross correlation properties along with a new approach that emphasizes on independent receiver design. The general problem is to design single or multiple sequences with constant modulus in the time-domain such that their respective matched filter outputs ideally resemble delta functions and the cross-matched filter outputs are zeros. In this context CAN (cyclic-algorithm new) and WeCAN (Weighted CAN) have been proposed for designing such sequences with good auto-cross correlation properties. In this paper, the equivalence of the CAN algorithms and the classic Gerchberg-Saxton (GS) algorithm involving the sequential magnitude substitution operations in the time and frequency domain is demonstrated. The design of unimodular sequences is further generalized here by considering the receiver design to be more general than the respective matched input sequences. The receiver design is carried out by taking care of the desired output requirements and the freedom present at the input can be used to further minimize the output side-lobe level.