Steepest-Descent Optimization of CDMA Signatures for Multiple Correlated Sources With Applications to Joint Source-Channel Coding

An approach to transmitting multiple correlated sources over a Gaussian multiple-access channel (GMAC) using code-division multiple-access (CDMA) is investigated. A block coordinate descent (BCD) algorithm is presented which can be used to optimize CDMA signatures for a given source covariance matrix under individual transmitter power constraints. This algorithm can be used to design non-orthogonal CDMA signatures for GMACs with arbitrary input alphabets, fading, and colored noise. While the main focus has been the design of signatures which minimize the mean square error (MSE) of linear decoding, the algorithm can also be used to design signatures which maximize the input-output mutual information of the channel. This paper investigates the uncoded transmission of Gaussian sources and the coded transmission of binary sources over a GMAC using joint source-channel (JSC) optimized CDMA signatures under constraints on transmitter power and channel bandwidth, scenarios relevant to wireless sensor networks. By using simple coding schemes which only rely on linear multi-user detection and independent channel decoding of a large number of sources, it is demonstrated that CDMA-based JSC coding can exploit inter-source correlation to achieve lower distortion (Gaussian sources) or higher rates (binary sources) compared to conventional separate source-channel (SSC) coding over the same channel bandwidth.