On the Expected Complexity Analysis of a Generalized Sphere Decoding Algorithm for Underdetermined Linear Communication Systems

This paper presents an analytical approach to evaluate the expected complexity of a generalized sphere decoding (GSD) algorithm, lambda - GSD, for underdetermined integer least- squares (ILS) problems. The analytical approach is used to derive the closed-form formulas to approximate the expected complexity of the lambda - GSD algorithm, by utilizing special statistical properties in the transformed channel matrix. Analytical and simulation results in various scenarios are in good agreement, indicating that the proposed complexity analysis can be used as reliable complexity estimation for practical implementation of lambda - GSD and can serve as reference for other GSD algorithms.