Optimal Joint Channel Estimation and Data Detection by L1-norm PCA for Streetscape IoT

Abstract

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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm principal components of a real-valued data matrix. Optimal algorithms for L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> principal components, we implement an efficient bit flipping-based algorithm for L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -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.