Closed-form Cramer-Rao Lower Bound Research Articles

Closed-form CRLB and LPI power allocation strategies for MIMO radars with unneglectable clutter

This paper studies clutter’s effect on MIMO radar performance through obtaining closed-form Cramer Rao lower bounds (CRLBs) for the range and velocity parameters versus the powers assigned to the transmit antennas which resulted in more calculation’ complexity. To verify extracted CRLBs, the maximum likelihood estimation’s error variance (MLEEV) of range and velocity were derived in attendance of clutter. Based on obtained closed-form CRLBs, four optimized power allocation (PA) strategies are proposed which consider measurement error statistics as the objective function or constraints to improve radar performance. So, the calculated closed-form CRLBs are simplified to the closed-forms versus assigned powers to the transmitters. Simulation results verify the proposed CRLBs’ accuracy, and improvements have been made by proposed power allocations.

Strong homogeneous clutter and random target scattering analysis for closed-form Cramer Rao bound and optimal power allocations in MIMO radars

This paper considers the effects of strong homogeneous clutter and the target's random scattering on radar measurements. The signal model is improved and closed-form Cramer-Rao lower bounds (CRLBs) are calculated for delay and Doppler frequency estimations in attendance of practical clutter, and target's scatterings models. The calculated closed-form CRLBs are simplified to extract the effect of assigned powers to the transmitters for using power allocation (PA) strategies. The maximum likelihood estimation error variances (MLEEVs) are derived for calculated CRLBs' verifications. Four power allocation strategies are defined as mathematical optimization problems that consider the power budget constraints and measurement error statistics as the objective function or constraints. Simulation results verify the proposed simplified closed-form CRLBs accuracies by comparing with exact CRLBs and MLE estimators' performance. It is shown that proposed power allocations not only preserve required performance but also optimize objectives.

On the Performance Gain of Harnessing Non-Line-of-Sight Propagation for Visible Light-Based Positioning

In practice, visible light signals undergo non-line-of-sight (NLOS) propagation, and in visible light-based positioning (VLP) methods, the NLOS links are usually treated as disturbance sources to simplify the associated signal processing. However, the impact of NLOS propagation on VLP performance is not fully understood. In this paper, we aim to reveal the performance limits of VLP systems in an NLOS propagation environment via Fisher information analysis. Firstly, the closed-form Cramer-Rao lower bound (CRLB) on the estimation error of user detector (UD) location and orientation is established to shed light on the NLOS-based VLP performance limits. Secondly, the information contribution from the NLOS channel is quantified to gain insights into the effect of the NLOS propagation on the VLP performance. It is shown that VLP can gain additional UD location information from the NLOS channel via leveraging the NLOS propagation knowledge. In other words, the NLOS channel can be exploited to improve VLP performance in addition to the line-of-sight (LOS) channel. The obtained closed-form VLP performance limits can not only provide theoretical foundations for the VLP algorithm design under NLOS propagation, but also provide a performance benchmark for various VLP algorithms.

Massive MIMO Self-Calibration: Optimal Interconnection for Full Calibration

In time-division duplexing (TDD) massive multiple-input multiple-output (MIMO) systems, the reciprocity between the downlink (DL) and the uplink (UL) channels can be utilized to infer the DL channel state information (CSI) with the acquired uplink (UL) CSI. However, the end-to-end UL and DL channel reciprocity are broken when there are mismatches in the radio frequency (RF) analog circuits among different antennas at the base station (BS). Without accurate calibration, there will be severe system performance degradation. This paper studies the internal self-calibration scheme to recover all the unknown full calibration coefficients when different BS antennas are interconnected via hardware transmission lines. On the one hand, we derive the calibration performance for an arbitrary interconnection network in closed-form and obtain closed-form Cramer-Rao lower bound (CRLB) expressions when $(M-1)$ transmission lines are consumed and $M$ denotes the total number of BS antennas. On the other hand, we prove that the star interconnection network is optimal for internal full self-calibration due to its lowest CRLB. Numerical simulation are carried out to verify our theoretical analyses and results.

Joint User Location and Orientation Estimation for Visible Light Communication Systems With Unknown Power Emission

In this paper, we are interested in the joint estimate of user equipment (UE) position and orientation for visible light communication (VLC) with uncertain emission power. This joint estimation is a non-convex problem with a huge search space. To address this challenge, a novel VLC localization algorithm is proposed, which converges to the stationary solution of the joint estimation problem at an asymptotic quadratic convergence rate due to our problem-specific surrogate function design. A closed-form update rule is obtained via exploiting the hidden convex structure of the non-convex optimization problem. Hence, our algorithm has low complexity compared with the particle swarm-based optimization methods. In addition, the closed-form Cramer-Rao lower bounds (CRLBs) on the estimation errors of the respective UE location, orientation and LED emitting power are derived. Moreover, the effect of critical parameters such as signal-to-noise ratio (SNR), the number of LED transmitters, transmission distance and non-line-of-sight propagation on the VLC localization performance are revealed. The simulation result verifies that the proposed VLC localization algorithm under unknown VLC emitting power can achieve a huge performance gain over the state-of-the-art localization baselines.

Performance Limits of Visible Light-Based User Position and Orientation Estimation Using Received Signal Strength Under NLOS Propagation

In this paper, we aim at providing a unified performance analysis framework for visible light-based positioning (VLP) using received signal strength (RSS), which can be used to gain insights into improving the performance of RSS-based VLP systems. Specifically, we first obtain a closed-form Cramer-Rao lower bound (CRLB) for the user equipment (UE) location and orientation, respectively. Then, we reveal the impact of the signal-to-noise ratio (SNR), transmission distance, prior knowledge and the number of LED sources on the RSS-based VLP performance. Moreover, the impact of the non-line-of-sight (NLOS) propagation on the RSS-based VLP performance is studied. It is shown that the RSS-based VLP performance will hit an error floor caused by the unknown NLOS links. These NLOS-caused UE location and orientation error floors in the high SNR region are analyzed. Finally, the information contribution of each LED source is studied to give an intuitive understanding on the impact of the LED array geometry on the RSS-based VLP performance. The obtained CRLB and the associated VLP performance analysis form a theoretical basis for the design of efficient VLP algorithms and VLP performance optimization strategies (e.g., resource allocation and smart LED source selection).

RSS-AOA-Based Localization via Mixed Semi-Definite and Second-Order Cone Relaxation in 3-D Wireless Sensor Networks

In this paper, the target node localization problems based on hybrid RSS-AOA measurements in both noncooperative and cooperative three-dimensional (3-D) wireless sensor networks (WSNs) are discussed. By using novel error approximate expressions for both received signal strength (RSS) and angle-of-arrival (AOA) measurement models, new estimators based on the least squares (LS) criterion are proposed. These estimators can be transformed into mixed semi-definite programming (SDP) and second-order cone programming (SOCP) problems by applying convex relaxation techniques. In addition, the closed-form Cramer-Rao lower bound (CRLB) of the estimator on hybrid measurements in cooperative WSNs is also derived. Theoretical analysis and simulation results show that the Root Mean Square Error (RMSE) of the proposed hybrid RSS-AOA estimators is lower than that of the discussed estimators in both noncooperative and cooperative cases.

Simultaneous Positioning and Orientating for Visible Light Communications: Algorithm Design and Performance Analysis

Visible light communication (VLC) based simultaneous positioning and orientating (SPAO), using received signal strength (RSS) measurements, is studied in this paper. RSS-based SPAO for VLCs of great challenge as it is essentially a non-convex optimization problem due to the nonlinear RSS model. To address this non-convexity challenge, a novel particle-assisted stochastic search (PASS) algorithm is proposed. The proposed PASS-based SPAO scheme does not require the knowledge of the height of receiver, the perfect alignment of transceiver orientations or inertial measurements. This is a huge technical improvement over the existing VLC localization solutions. The algorithmic convergence is established to justify the proposed PASS algorithm. In addition, a closed-form Cramer–Rao lower bound (CRLB) on localization error is derived and analyzed to gain insights into how the VLC-based SPAO performance is related to system configurations. It is shown that the receiver's position and orientation accuracy is linear with signal-to-noise ratio and direction information. In addition, the position accuracy decays with six powers of the transceiver distance, while the orientation accuracy decays with four powers of the transceiver distance. Finally, simulation results verify the performance gain of the proposed PASS algorithm for VLC-based SPAO.

Compressive Sensing-Based Multiple-Leak Identification for Smart Water Supply Systems

In this paper, the identification of multiple leaks in pipes based on transient waves is studied, which is, however, quite challenging due to its nonconvex nature with lots of local optima. Existing approaches need the number of leaks and suffer from a huge computational complexity that is increased exponentially with the number of leaks. To provide a scalable solution, we propose a compressive sensing (CS) framework to solve the multileaks identification. We first exploit the sparseness nature of leak locations through spatial sampling. Then, we formulate the multileak identification as a CS problem, where the spatial sample-dependent components form a basis matrix and the leak sizes are viewed as a sparse signal. We establish the convergence of spatial sampling mismatch and the two-restricted isometry property of basis matrix to justify the proposed CS framework. The proposed CS framework renders a superior-performance solution to multileak identification and its computational complexity is linear with the number of leaks, which is a significant technical improvement over existing approaches. In addition, a closed-form Cramer-Rao lower bound (CRLB) on the leak localization errors is derived. A geometric insight of CRLB evolution is presented to give us an intuitive understanding of the contribution of new measurements to leak localization performance.

Joint-Bin Monopulse Processing of Rayleigh Targets

Amplitude comparison monopulse systems provide precision angle localization of a target. In practice, the in-phase part of the monopulse ratio is commonly used for direction-of-arrival (DOA) estimation due to simplicity and computational speed, but it suffers poor performance for off-boresight and/or low signal-to-noise ratio (SNR) targets. Target energy is typically assumed to be contained in a single range bin, while in practice the matched filter sampling process often results in multiple adjacent matched filter samples with target energy. In the traditional radar literature, this is called bin straddling and is typically treated as a nuisance—an undesired loss of signal energy. Recent literature has addressed bin straddling for DOA and range estimation for the case of multiple unresolved targets. However, error variance reports on those target estimates, which are required by target tracking algorithms, are not provided. Furthermore, target strength is assumed to be a known parameter, which is often not valid in practice. Here, we explicitly incorporate sampling into the statistical model for sum and difference channel signal samples, and derive estimators for the unknown range and unknown DOA of a single Rayleigh target. Closed-form Cramer-Rao lower bounds (CRLBs) on those estimators are provided. Furthermore, we propose the generalized CRLB (GCRLB) as an error variance report, and SNRs required for statistical efficiency and variance consistency are provided.

On the performance limits of data-aided synchronization

This paper addresses data-aided (DA) synchronization, in which the reference parameter acquisition is aided by a training sequence known to the receiver. The Cramer-Rao lower bound (CRB) for the DA timing and/or carrier phase recovery is presented. For DA parameter estimation, the CRB typically varies with the training sequence. This indicates that different training sequences offer fundamentally different performance. In the literature, the widely cited closed-form CRB for timing and carrier phase recovery was derived under the assumption that the training sequence is independent and identically distributed (i.i.d.) and sufficiently long. We derive a closed-form CRB for timing and carrier phase recovery with respect to an arbitrary training sequence and pulse shaping function for the over and under sampling cases. It turns out that the CRB is a weighted summation of the aperiodic correlation of the training sequence and the weighting factor is determined by the pulse shaping filter. Therefore, this paper reveals the fundamental link between a training sequence and its corresponding performance limit.