Linear transformation of multi-level signal set in multi-code CDMA

We propose a technique that linearly transforms a multi-level multi-code CDMA signal into an antipodal set. The transformation is, equivalent to a linear block code with elements from the real space. Unlike precoding (which also results in constant envelope signals) there is no loss in data rate due to redundancy since the code rate is 1. Using geometrical arguments, we show that our transformation is equivalent to a rotation or reflection of signal space. We also show that precoding can be classified as a special case of our proposed scheme. In fact, we show that precoding is equivalent to a parity-check linear block code with a modified Hadamard matrix. We also show a close relation between two seemingly different multi-rate schemes of OVSF-CDMA and multi-code CDMA.