Performance Analysis of Discrete-valued Vector Reconstruction Based on Box-constrained Sum of L1 Regularizers

In this paper, we analyze the asymptotic performance of a convex optimization-based discrete-valued vector reconstruction from linear measurements. We firstly propose a box-constrained version of the conventional sum of absolute values (SOAV) optimization, which uses a weighted sum of ℓ
₁
regularizers as a regularizer for the discrete-valued vector. We then derive the asymptotic symbol error rate (SER) performance of the box-constrained SOAV (Box-SOAV) optimization theoretically by using convex Gaussian min-max theorem. Simulation results show that the empirical SER performances of Box-SOAV and the conventional SOAV are very close to the theoretical result for Box-SOAV when the problem size is sufficiently large.