  In this letter, we propose a new symbol detection method for
faster-than-Nyquist signaling (FTNS) systems. Based on frame theory, we
formulate a symbol detection problem as a under-determined linear equation on a
finite set. The problem is reformulated as a sum-of-absolute-values (SOAV)
optimization that can be efficiently solved by the fast iterative shrinkage
thresholding algorithm (FISTA). The proximity operator for the convex
optimization is derived analytically. Simulation results are given to show that
the proposed method can successfully detect symbols in faster-than-Nyquist
signaling systems and has lower complexity in terms of computation time.
