Design of Spreading Sequences for Lattice-Coded Based Multiple Access

It was shown that by operating over the integer linear combinations (ILCs) of $K$ users' messages, lattice-code based multiple-access (LCMA) offers increased system load and improved error-rate performance over non-lattice based schemes. This paper advances the existing LCMA system by designing the spreading sequences. We first formulate the spreading sequences optimization problem based on the achievable symmetric rate of LCMA. To solve this problem, we develop three new methods, namely target-switching steepest descent (TS-SD), particle swarm (PS) optimization, and Hadamard concatenation (HC). The TS-SD method always targets on the ILC with the lowest computation rate in the SD process. The PS method treats the spreading matrix as a particle and iteratively updates a swamp of particles' positions and velocities, based on the relative distance to the best position that are currently known. To further reduce the complexity, we first obtain a solution in a lower dimension, and then apply Hadamard concatenation (HC) which yields a solution for the required dimension. The PS and HC methods are shown to approach the capacity of the MA channel.