This paper presents an analytical approach to evaluate the expected complexity of a generalized sphere decoding (GSD) algorithm, GSDλ − , for underdetermined integer leastsquares (ILS) problems. The analytical approach is used to derive the closed-form formulas to approximate the expected complexity of the GSDλ − 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 GSDλ − and can serve as reference for other GSD algorithms.