Optimal Joint Channel Estimation And Data Detection By L1-Norm Pca For Streetscape Iot

We prove, for the first time in the literature of communication theory and machine learning, the equivalence of joint maximum-likelihood (ML) optimal channel estimation and data detection (JOCEDD) to the problem of finding the $L_1$-norm principal components of a real-valued data matrix. Optimal algorithms for $L_1$-norm principal component analysis (PCA) are therefore direct solvers to the problem of interest, thus the proposed JOCEDD approach requires a polynomial number of operations. To avoid high computational costs incurred by the exact calculation of optimal $L_1$ principal components, we implement an efficient bit flipping-based algorithm for $L_1$-norm PCA in a software-defined radio. In particular, we carry out experiments with two radios that operate at Wi-Fi frequencies in a multipath indoor radio environment and have no direct line-of-sight. We apply $L_1$-norm PCA for JOCEDD over short frames that are transmitted over the single-input single-output communication link. We compare the performance of supervised data-aided channel estimation techniques versus JOCEDD in terms of bit-error-rate and demonstrate the superiority of the proposed approach across a wide range of signal-to-noise ratios.