Symbol Detection for Faster-Than-Nyquist Signaling by Sum-of-Absolute-Values Optimization

In this letter, we propose a new symbol detection method in faster-than-Nyquist signaling for effective data transmission. Based on the frame theory, the symbol detection problem is described as underdetermined linear equations on a finite alphabet. While the problem is itself NP (nondeterministic polynomial-time) hard, we propose convex relaxation using the sum-of-absolute-values optimization, which can be efficiently solved by proximal splitting. Simulation results are shown to illustrate the effectiveness of the proposed method compared to a recent ℓ
_∞
-based (ellinfinity-based) method.