Approximate Message Passing for Joint Activity Detection and Decoding in Non-orthogonal CDMA

In Compressive Sensing, the knowledge of an unknown vector's statistical properties together with a small number of linear measurements makes it possible to reconstruct the vector with high accuracy in terms of minimum mean-squared error. A popular statistical property is sparsity of the unknown vector. The model can thus be applied to multi-user systems, where only a small number of users is active at a given time. In this paper, we show how the properties of the users channel code and approximate knowledge of the fraction of active users can be used to simultaneously detect user activity and the transmitted codeword, when the users code-symbols are transmitted by nonorthogonal spreading sequences. The main goal is to provide a unified framework (based on compressed-sensing techniques) in which to describe and solve the joint detection-and-decoding problem by a single computationally highly efficient algorithm.