Joint Estimation of DOA and Channel Response Aided by Magnitude Measurements

This paper discusses the joint estimation of direction-of-arrivals (DOAs) and channel responses in a novel magnitude-aided antenna array (MA-AA), where magnitude-only radio frequency (RF) chains are introduced into the classical AA to acquire magnitude observations. Due to the existence of nonlinear magnitude measurements and high-dimensional integration, the joint posterior probability distribution functions (pdfs) of DOAs and channel responses over the hybrid MA-AA measurements have no explicit expression, and neither do their posterior means. Consequently, the Metropolis-Hastings Markov chain Monte Carlo (MH-MCMC) algorithm is modified to handle the magnitude measurements, and then generate samples of DOAs and channel responses obeying their posterior pdfs, based on which, their posterior means are numerically calculated after the burn-in period. In the modified MH-MCMC, the independent proposals of DOAs and channel responses are designed as uniform pdfs and complex Gaussian pdfs, and their hyper-parameters are obtained by multiple signal classification (MUSIC) and least square (LS) based on several complex observations, respectively. Compared with existing estimators, the modified MH-MCMC shows superiorities on DOA and channel response estimation, and computational complexity. With the MH-MCMC estimator, MA-AA is more energy-efficient than the conventional AA.