Bamrung Tau Sieskul

A Hybrid SS–ToA Wireless NLoS Geolocation Based on Path Attenuation: ToA Estimation and CRB for Mobile Position Estimation

We propose a new hybrid wireless geolocation scheme that requires only one observation quantity, namely, the received signal. The attenuation model is explored herein to capture the propagation features from the received signal. Thus, it provides a more accurate approach for wireless geolocation. To investigate geolocation accuracy, we consider the time-of-arrival (ToA) estimation in the presence of path attenuation. The maximum-correlation (MC) estimator is revisited, and the exact maximum-likelihood (ML) estimator is derived to estimate the ToA. The error performance of the ToA estimates is derived using a Taylor expansion. It is shown that the ML estimate is unbiased and has a smaller error variance than the MC estimate. Numerical results illustrate that, for a low effective bandwidth, the ML estimator well outperforms the MC estimator. Afterward, we derive the Cramer-Rao bound (CRB) for the mobile position estimation. The obtained result, which is applicable to any value of path loss exponents, gives a generalized form of the CRB for the ordinary geolocation approach. In seven hexagonal cells, numerical examples show that the accuracy of the mobile position estimation exploring the path loss is improved compared with that obtained by the usual geolocation.

Time-of-arrival estimation in path attenuation

We consider a time-of-arrival (ToA) estimation in the presence of path attenuation. Maximum correlation (MC) is revisited and maximum likelihood (ML) is newly derived to estimate the ToA. It reveals that for low effective bandwidth, short distance and large path loss exponent, the ML has a smaller error variance than the MC. Numerical examples illustrate that the ML outperforms the MC.

Cramer-Rao bound for TOA estimations in UWB positioning systems

This paper deals with time delay estimation for a UWB positioning system. We consider the a priori model in which the distributions of path gain and the desired time delay are known. Joint probability density functions for both parameters are cast into explicit form. Then, we address parameter estimations based on maximum likelihood as well as maximum a posteriori. The Fisher information matrix (FIM) of the ordinary Cramer-Rao bound (CRB) is available from maximum likelihood criterion. For three possible cases of a priori knowledge, the inherent accuracy are provided by a posteriori CRBs, which can be derived from three possible assumptions. All theoretical results are unconditioned on any specification of UWB pulse and hence are plausible to extend to further performance analysis.

Spatial Fading Correlation for Local Scattering: A Condition of Angular Distribution

Local scattering in the vicinity of the receiver or the transmitter leads to the formation of a large number of multipath components along different spatial angles. A condition of angular distribution, which is valid for only a uniform linear array, is proposed in this paper to justify whether the spatial fading correlation (SFC) remains simple as a Bessel function. If an angular distribution satisfies the condition, a class of angular distributions is revealed and results in simplifying the analysis of the SFC. To demonstrate its practical use, we apply the condition to several angular distributions that are considered in previous works. It is found that cosine and von Mises distributions follow the condition, whereas uniform, Gaussian, and Laplacian distributions do not satisfy the condition, and then, one needs to calculate the sinusoidal coefficients in the SFC computation.

On Parameter Estimation of Ricean Fading MIMO Channel: Correlated Signals and Spatial Scattering

The purpose of this paper is to account for estimating the MIMO channel parameters in the presence of stochastically correlated signals, spatial scattering and Ricean fading. A parametric framework based on the second-order statistic is developed herein. As manipulated a few of reduced parameterizations, we derive an explicit form of the array covariance matrix, an alternative expression of the Cramer-Rao bound (CRB), and two asymptotically efficient estimators. Numerical simulation is conducted to demonstrate the estimation possibility of three important parameters in wireless communication, such as the nominal direction, the angular spread and the generalized Rice factor. It appears that for a large number of temporal snapshots, the performance of both estimators can attain the CRB, while the asymptotic maximum likelihood estimator outperforms the weighted least squares criterion in non-asymptotic region

A Hybrid SS-ToA Wireless NLoS Geolocation Based on Path Attenuation: Mobile Position Estimation

The mobile position estimation using time-of-arrival (ToA) is considered for the wireless NLoS geolocation exploring a signal strength (SS) based on path loss. As exploited the path attenuation, a hybrid SS-ToA approach indicates a performance improvement compared with the usual ToA method. To realize this prospect, it calls for an estimator to determine the mobile position from the time delay. In this paper, we show that the use of line-of-sight (LoS) time delay provides the same performance as that given by using both the LoS and non-LoS (NLoS) time delays. We then propose least squares (LS), weighted least squares (WLS) and maximum likelihood (ML) to estimate the mobile position. Theoretical performance of the LS and WLS is analyzed. It reveals that for different LoS time delay error variances, the LS error variance is larger than the WLS error variance, which is equal to the Cramer-Rao bound (CRB). Numerical results illustrate that the time delay performance analysis is accurate when the time delay estimate is close to its true value, i.e. for small time delay error variance. For high SNR and large effective bandwidth, the LS cannot provide the performance compared with the CRB, whereas the WLS and ML are statistically efficient.

Spatial fading correlation for semicircular scattering: Angular spread and spatial frequency approximations

Spatial frequency approximation (SFA) of spatial fading correlation (SFC) is addressed for the case that the exact infinite summation of Bessel functions is inconvenient or infeasible. The angular spread is derived for semicircular scattering, especially characterized by uniform, Gaussian, Laplacian, and von Mises distributions. The semicircular scattering on the range (−1over2π, 1over2π] happens, e.g., when the antenna is placed on the wall. In the usual SFA of the SFC, a characteristic function is involved with the infinite integration range due to a small angular spread and a near broadside nominal angle. In this paper, we propose a new SFA of the SFC with a finite integration range. Considering the Laplacian angular distribution, numerical examples illustrate that for a moderate angular spread, the new SFA yields higher accuracy in computing the SFC than the conventional SFA. For the von Mises distribution, the new SFA is able to approximate the SFC, while the ordinary SFA provides discrete solutions, which are unreliable to the SFC approximation.

An Introduction to Multiple Antennas for UWB Communication and Localization

Wireless ultra-wideband (UWB) systems are characterized by an enormous bandwidth of up to several GHz and are therefore a promising candidate for high data rate indoor communications and for precise localization of UWB signal-objects. Multiple antennas are another approach for improving the performance of a wireless link with respect to data rate, coverage, or, in a localization scenario, accuracy. Within this contribution we introduce the topic of UWB communication and localization where either the transmitter, the receiver or both are equipped with multiple antennas.

A Hybrid SS-ToA Wireless NLoS Geolocation Based on Path Attenuation: Cramer-Rao Bound

Non-line-of-sight propagation in wireless localization systems leads to a challenging problem for the estimation of a mobile position. A hybrid idea has been considered as a promising approach to increase estimation accuracy. Existing methods, however, are formulated using separate measurements, neces- sitating different observation quantities, e.g. received signal and received signal strength, thus making the parameter estimation cumbersome. In this paper, we propose a new hybrid wireless ge- olocation model requiring only one observation quantity, namely the received signal. The attenuation model for transmit power from base stations is explored herein to capture propagation features in the received signal model. Fortunately, it also provides a more realistic approach to wireless geolocation. To investigate geolocation accuracy, the Cram´ er-Rao bound (CRB) is derived for the estimation error of the mobile position. For any value of path loss exponent, the obtained result provides a generalized form of the CRB for the usual time delay case. In small cells, e.g. office building picocells, numerical examples illustrate that the accuracy of mobile position estimation exploring path loss is improved comparing with that provided by the usual time delay method. Index Terms—Parameter estimation, non-line-of-sight propa- gation, path loss.

On the Effect of Shadow Fading on Wireless Geolocation in Mixed LoS/NLoS Environments

This paper considers the wireless non-line-of-sight (NLoS) geolocation in mixed LoS/NLoS environments by using the information of time-of-arrival. We derive the Cramer-Rao bound (CRB) for a deterministic shadowing, the asymptotic CRB (ACRB) based on the statistical average of a random shadowing, a generalization of the modified CRB (MCRB) called a simplified Bayesian CRB (SBCRB), and the Bayesian CRB (BCRB) when the a priori knowledge of the shadowing probability density function is available. In the deterministic case, numerical examples show that for the effective bandwidth in the order of kHz, the CRB almost does not change with the additional length of the NLoS path except for a small interval of the length, in which the CRB changes dramatically. For the effective bandwidth in the order of MHz, the CRB decreases monotonously with the additional length of the NLoS path and finally converges to a constant as the additional length of the NLoS path approaches the infinity. In the random shadowing scenario, the shadowing exponent is modeled by sigmav = usigma, where u is a Gaussian random variable with zero mean and unit variance and sigma is another Gaussian random variable with mean musigma and standard deviation sigmasigma. When musigma is large, the ACRB considerably increases with sigmasigma, whereas the SBCRB gradually decreases with sigmasigma. In addition, the SBCRB can well approximate the BCRB.