Channel parameter estimation in mobile radio environments using the SAGE algorithm

TLDR

The dominant waves estimated by the algorithm can be linked to scatterers or reflectors in the propagation environment. The study investigates using the SAGE algorithm to jointly estimate delay, azimuth, Doppler, and complex amplitude of impinging waves in mobile radio environments. The authors evaluate the SAGE scheme’s high‑resolution capability, accuracy, and convergence in synthetic and real macro‑ and pico‑cellular channels. Results show the SAGE algorithm surpasses classical Fourier or beam‑forming limits, separating waves with minimal azimuth differences when delays or Doppler differ, achieving mean‑squared errors near the Cramér‑Rao bounds within fewer than 20 iterations and converging after about ten iterations, proving it a powerful high‑resolution tool for channel modeling from extensive measurement data.

Abstract

This study investigates the application potential of the SAGE (space-alternating generalized expectation-maximization) algorithm to jointly estimate the relative delay, incidence azimuth, Doppler frequency, and complex amplitude of impinging waves in mobile radio environments. The performance, i.e., high-resolution ability, accuracy, and convergence rate of the scheme, is assessed in synthetic and real macro- and pico-cellular channels. The results indicate that the scheme overcomes the resolution limitation inherent to classical techniques like the Fourier or beam-forming methods. In particular, it is shown that waves which exhibit an arbitrarily small difference in azimuth can be easily separated as long as their delays or Doppler frequencies differ by a fraction of the intrinsic resolution of the measurement equipment. Two waves are claimed to be separated when the mean-squared estimation errors (MSEEs) of the estimates of their parameters are close to the corresponding Cramer-Rao lower bounds (CRLBs) derived in a scenario where only a single wave is impinging. The adverb easily means that the MSEEs rapidly approach the CLRBs, i.e., within less than 20 iteration cycles. Convergence of the log-likelihood sequence is achieved after approximately ten iteration cycles when the scheme is applied in real channels. In this use, the estimated dominant waves can be related to a scatterer/reflector in the propagation environment. The investigations demonstrate that the SAGE algorithm is a powerful high-resolution tool that can be successfully applied for parameter extraction from extensive channel measurement data, especially for the purpose of channel modeling.