Sparse code multiple access (SCMA) which is based on a non-linear spreading has received great attention due to its good overloading capability. The current SCMA codewords are non-constant modulus and thus may lead to more stringent requirements than the constant modulus based ones. In this work, we proposed a novel gradient descent based method to optimize the SCMA codebooks with constant modulus constraints. The codewords designed based on the proposed method exhibits significantly larger minimum distance and constant modulus, which renders it more attractive to practical applications.
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