Optimized Spreading Sequences and Multi-Stage Receiver for Lattice-Code Multiple-Access

It was shown that by operating over the integer linear combinations (ILCs) of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> 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 in two aspects. 1) We 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. 2) We put forth a new multi-stage LCMA receiver. In each stage, the receiver attempts to compute as many ILCs as possible. Then, from these ILCs, generalized matrix inversion (GMI) is introduced to recover a subset of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> users’ messages. These recovered messages are cancelled from the original received signal, yielding an equivalent system with less users for the next stage. Such operation continues successively until all <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> users’ messages are recovered. System loads of up to 400% and near capacity performance are demonstrated for various MA models.