Representation and Calculation of Correlation Constraints of One Dimensional Unipolar Orthogonal Codes

The one dimensional unipolar orthogonal codes are employed as signature sequences in spread spectrum modulation schemes like incoherent optical CDMA system. The cardinality or upper bound of code set, containing one dimensional unipolar orthogonal codes of code length 'n' and code weight 'w' and correlation constraint λ, is given by Johnson bounds. Conventionally these codes are represented by weighted position representation (WPR) or position of bit 1's in the code. The auto-correlation and cross-correlation constraints of the unipolar orthogonal codes are calculated using the binary sequences equivalent to these codes in WPR. In this paper two other representations of one dimensional unipolar orthogonal codes are proposed as well as two methods for calculation of correlation constraints of these unipolar orthogonal codes.