Uniquely decodable codes for overloaded synchronous CDMA with two sets of orthogonal signatures

In this paper, a new system model is proposed for synchronous overloaded code division multiple access (CDMA), where the errorless transmission is guaranteed over noiseless channel for a total number users (M) being greater than the spreading gain (N). The first N users are accommodated within a code subspace, which is an antipodal orthogonal Hadamard Sylvester (HS) matrix. In contrast, the rest (M-N) number of users are assigned with an orthogonal ternary subset. The proposal aims at the existence of orthogonal derived subset, which if replaced with the quasi orthogonal sequences of O/O CDMA can achieve significant improvement in error performance without any further increase in receiver complexity. The proposed signature matrix has a maximum achievable overloading capacity of 150%. The overall decoding process involves two stages of matched filters (MF) for each subset followed by an intermediate stage of interference cancellation. The extended HS (EHS) matrix in spite of being uniquely decodable (UD) facilitates the use of conventional MF, which unlike any other set of UD codes add more simplicity to the overall design.