Regularized Lattice Sphere Decoding for Block Data Transmission Systems

This paper presents Lattice Sphere Decoding (LSD) with regularization techniques for block data transmission systems. It has shown that a small condition number ( τ ) results in better detection performance. This paper aims to reduce this value to its smallest possible value. Regularization technique offers reduction in condition number ( τ ) that improves LSD performance. In this work, two regularization techniques are utilized on LSD. First, L 1 -regularization method is introduced, which sums the mixed norms. Second, L 2 - regularization method, which is the most commonly used method of regularization for ill-conditioned problems in mathematics. We derive the exact relationship between the LSD performance and condition number ( τ ) as well as the relationship between LSD initial radius ( d ) and condition number ( τ ). The derived equations show their convergence to the fact that the performance increases as the radius ( d ) increases. Simulation results show that the LSD with L 1 -regularization technique offers smaller condition number ( τ ), and therefore, produces better system performance. From the performance results and the complexity analysis, it is apparent that the proposed techniques achieve a good balance between complexity and performance.