Estimating Jakes' Doppler power spectrum parameters using the whittle approximation

Abstract

We derive methods for asymptotic maximum likelihood (ML) estimation of Jakes' Doppler power spectrum parameters from complex noisy estimates of the fading channel. We consider both single-input single-output (SISO) and smart-antenna scenarios and utilize the Whittle approximation to the likelihood to estimate the Doppler spread, noise variance, and channel covariance parameters. Asymptotic Crame´r-Rao bounds (CRBs) for the unknown parameters are derived. We also discuss the initialization of the proposed methods and their generalization to the Ricean-fading scenario. Numerical simulations demonstrate the performance of the proposed methods. We derive methods for asymptotic maximum likelihood (ML) estimation of Jakes' Doppler power spectrum parameters from complex noisy estimates of the fading channel. We consider both single-input single-output (SISO) and smart-antenna scenarios and utilize the Whittle approximation to the likelihood to estimate the Doppler spread, noise variance, and channel covariance parameters. Asymptotic Cramér-Rao bounds for the unknown parameters are derived. We also discuss the initialization of the proposed methods and their generalization to the Ricean-fading scenario. Numerical simulations demonstrate the performance of the proposed methods.

Serial concatenation of quadratic interleaved codes in different wireless doppler environments

“…5-8, the required ‫ܧ‬ /ܰ to attain the BER ൎ 10 ିହ for SCQIC FECs of section III and IV are presented. As far as Doppler spectrum and ‫ܧ‬ /ܰ are important parameters for assessing the quality and rate of change of wireless channels [44], energy-gap computation and comparison for the discussed channel conditions are provided. Under the assumption that the calculations of ‫ܧ‬ /ܰ take 90% of confidence level when computing the error-rates, the mean average coding gain gap (MACGG) between SCQIC-coded systems and block-interleaved systems with ܴ ൎ ‫ܥ‬ ൎ ඥܰ ூே் for four aforementioned Doppler PSDs are (in order of Rounded, Bell, Gaussian, and Bi-Gaussian) 1.05, 1.2, 0.93, and 1.65 ‫ܤ݀‬ for SISO, 1.5, 1.25, 0.625, and 0.7 ‫ܤ݀‬ for MISO (2Tx-1Rx), 1.325, 1.325, 0.65, and 0.525 ‫ܤ݀‬ for MIMO (2Tx-2Rx), and 1.17, 1.17, 0.4, and 0.4 ‫ܤ݀‬ for MIMO (3Tx-3Rx).…”

A spectrum‐efficient integer frequency offset estimator of mobile OFDM system in double selective channels

“…According to (6), so long as (M − max −1) is large enough, the denominator of ( p) can be approximated as 2 z , then we define l ( p) as:…”

Nonparametric mobile speed estimation in fading channels: Performance analysis and experimental results

“…However, both crossingbased and covariance-based speed estimators are sensitive to noise, especially for small Doppler spreads [2] [3] [9]. Although the ML-based estimators [10] [11] are optimal or near optimal, they are complex to implement, need the knowledge of signal-to-noise-ratio (SNR), and require that the noise be Gaussian. Furthermore, the effects of nonisotropic scattering and line-of-sight (LOS) on ML-based estimators are not investigated in [10] and [11].…”

“…Although the ML-based estimators [10] [11] are optimal or near optimal, they are complex to implement, need the knowledge of signal-to-noise-ratio (SNR), and require that the noise be Gaussian. Furthermore, the effects of nonisotropic scattering and line-of-sight (LOS) on ML-based estimators are not investigated in [10] and [11]. Wavelet and pattern recognition methods are also used for speed estimation [12] [13], but they are computationally intensive.…”