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Multiple-symbol detection has recently caught attention in ultrawideband (UWB) communications because of its high performance without requiring explicit channel estimation. In this context, the generalized likelihood ratio test (GLRT) for multiple-symbol detection problem is developed to jointly detect multiple symbols, which exhibits considerable error performance improvement over transmitted reference transmissions methods. Unfortunately, the GLRT is a Boolean quadratic programming (BQP) problem, which is generally nondeterministic polynomial hard (NP-hard). In this paper, we propose two near-optimal detectors with polynomial complexity. The first detector performs semidefinite relaxation to approximately solve the BQP problem (called SDP-MSD). The second detector is based on a sphere-based relaxation of the BQP problem [we refer to this as modified unconstrained relaxation multiple-symbol detector (MUR-MSD)]. Both detectors achieve near-optimal performance, while the SDP-MSD performs slightly better than the MUR-MSD at the price of higher computational complexity. Furthermore, the MUR-MSD can be treated as a further nontight relaxation of SDP-MSD. Simulations are utilized to validate our findings and to demonstrate performance robustness to multiaccess interference.