Exact SMP Algorithms for Integer-Forcing Linear MIMO Receivers

To obtain the optimal coefficient matrix for the integer-forcing (IF) linear receiver, the successive minima problem (SMP) on lattices needs to be solved. By decomposing SMP into a series of subspace avoiding problems (SAP) and developing a modified sphere-decoding (SD) algorithm based on the Schnorr-Euchner (SE) enumeration strategy to solve each instance of SAP, two practical algorithms are constructed to solve SMP exactly for real and complex lattices respectively. The initial radius and the starting position on the search-tree of the SAP algorithm are optimized by exploiting the intermediate results obtained in previous rounds. As compared to the Minkowski reduction algorithm, the proposed complex SMP algorithm brings not only more freedom in lattice code design, but also computation reduction in finding the coefficient matrix. Moreover, benefiting from the tree-search initialization optimization, the proposed real SMP algorithm can bring even more computation reduction when the system size is large. However, the proposed algorithms achieve practically the same performance as Minkowski reduction for the IF linear receiver, as the Minkowski-reduced basis approximates successive minima very closely.