Noncircular Interferences Research Articles

Non-circular interference fit analysis in harmonic reducer based on sequential assembling and loading simulation

The flexible bearing is usually connected to the cam with an interference fit in harmonic reducers. Studies show that interference fit can cause changes in the structural parameters of the bearing and lead to changes in the service performance of the bearing and its supporting system. This paper proposes a general simulation method to investigate the influence of interference fit in harmonic reducers with the concept of the equivalent interference for non-circular fit between the flexible bearing and cam. Then, the four steps based on the sequential assembling and loading process are designed to ensure assembly concentricity and simulation convergence. The analysis results indicate that appropriately increasing the equivalent interference can improve the service life of the flexspline without degrading the meshing performance and, at the same time, increase the number of loaded balls to make the operation of the harmonic reducer more stable. Moreover, an optimal equivalent interference can be designed to ensure the harmonic reducer operates at its best, where the number of loaded balls and the maximum Mises stress of the inner ring appear inflection point, and the number of meshing tooth pairs reaches the maximum.

Widely Linear Null Broadening GNSS Anti-Interference for Polarization-Sensitive Arrays

In this correspondence, we consider suppressing non-circular interferences for Global Navigation Satellite Systems (GNSS) receivers utilizing polarization sensitive arrays, regarding high dynamic scenarios. We model the widely linear array receive signal corrupted by potentially non-circular interferences. We analyze the second-order statistics of the widely linear receive signal and extend the covariance matrix taper (CMT) methodology to cope with the widely linear receive signal. We further develop widely linear null broadening algorithms to suppress high-dynamic non-circular interferences. Simulation results validate the superior performance of the proposed algorithms in suppressing high-dynamic non-circular interferences.

Third-order Volterra MMSE receivers for enhanced single and multiple antenna interference cancellation

Data-like interference mitigation in wireless communications systems, and in mobile cellular networks in particular, has always been a challenging problem which is becoming even more so for 5G networks and beyond including the Internet of things (IoT), to support a massive number of low data rate devices for given spectral resources. A promising solution to this problem consists in using one dimensional signaling (i.e., real-valued modulations) jointly with widely linear (WL) processing at the receiver, which has the capability to process up to 2N−1 data-like interference from N antenna receivers, and to fulfill, for N=1, single antenna interference cancellation (SAIC) of a one-dimensional interference in particular. However, when the signal of interest (SOI) and observations are jointly non-Gaussian, which is the case for most of digital radiocommunications systems, WL receivers become sub-optimal and optimal receivers become non-linear. It is then of interest to propose new non-linear receivers to improve performance of WL receivers. In this context, the paper aims at introducing, for small-scale systems, third-order complex Volterra (CV) minimum mean square error (MMSE) receivers, for the reception of a digital linearly modulated SOI whose waveform is known, corrupted by potentially non-Gaussian and non-circular interference, omnipresent in practical situations. Properties, performance and adaptive implementation of these receivers in the presence of non-Gaussian and potentially non-circular interference up to the 6th-order are analyzed in this paper. In particular, some of these receivers are shown to enhance WL receiver performance for SAIC of one rectilinear interference such as binary phase-shift keying (BPSK) interference. Whereas some other receivers allow us to fulfill SAIC of 4th-order non-circular interference such as quadrature phase-shift keying (QPSK) interference, which is not possible using WL receivers. These new receivers open new perspectives for cancellation of non-Gaussian and potentially non-circular interference up to 6th-order in radiocommunication networks.

A Full Second-Order Analysis of the Widely Linear MVDR Beamformer for Noncircular Signals

A full performance analysis of the widely linear (WL) minimum variance distortionless response (MVDR) beamformer is introduced. While the WL MVDR is known to outperform its strictly linear counterpart, the Capon beamformer, for noncircular complex signals, the existing approaches provide limited physical insights, since they explicitly or implicitly omit the complementary second-order (SO) statistics of the output interferences and noise (IN). To this end, we exploit the full SO statistics of the output IN to introduce a full SO performance analysis framework for the WL MVDR beamformer. This makes it possible to separate the overall signal-to-interference plus noise ratio (SINR) gain of the WL MVDR beamformer w.r.t. the Capon one into the individual contributions along the in-phase (I) and quadrature (Q) channels. Next, by considering the reception of the unknown signal of interest (SOI) corrupted by an arbitrary number of orthogonal noncircular interferences, we further unveil the distribution of SINR gains in both the I and Q channels, and show that in almost all the spatial cases, these performance advantages are more pronounced when the SO noncircularity rate of the interferences increases. Illustrative numerical simulations are provided to support the theoretical results.

On the sensitivity of third-order Volterra MVDR beamformers to interference-pulse shaping filter

Linear beamformers are optimal, in a mean square (MS) sense, when the signal of interest (SOI) and observations are jointly Gaussian and circular. Otherwise, optimal beamformers become non-linear with a structure depending on the unknown joint probability distribution of the SOI and observations. In this context, third-order Volterra minimum variance distortionless response (MVDR) beamformers have been proposed recently to improve the performance of linear beamformers in the presence of non-Gaussian and potentially non-circular interference, omnipresent in practical situations. High performance gains have been obtained for binary phase shift keying (BPSK) and quadrature phase shift keying (QPSK) interference having a square pulse shaping filter in particular. However in practice, for spectral efficiency reasons, most of signals use non-square pulse shaping filters, such as square root raised cosine filter. It is then important to analyze the sensitivity of third-order MVDR beamformers to interference pulse shaping filter, which is the purpose of this paper.

Third-Order Volterra MVDR Beamforming for Non-Gaussian and Potentially Non-Circular Interference Cancellation

Linear beamformers are optimal, in a mean square (MS) sense, when the signal of interest (SOI) and observations are jointly Gaussian and circular. Otherwise, linear beamformers become suboptimal. When the SOI and observations are zero-mean, jointly Gaussian and noncircular, optimal beamformers become widely linear (WL). They become nonlinear with a structure depending on the unknown joint probability distribution of the SOI and observations when the latter are jointly nonGaussian, assumption which is very common in radiocommunications. In this context, the paper aims at introducing, for small-scale systems, third-order Volterra minimum variance distortionless response (MVDR) beamformers, for the reception of an SOI, whose waveform is unknown but whose steering vector is known, corrupted by nonGaussian and potentially noncircular interference, omnipresent in practical situations. Properties, performance, complexity, and adaptive implementation of these beamformers in the presence of nonGaussian and potentially noncircular interference are analyzed in this paper. These new beamformers are shown to always improve, in the steady state, the performance of Capon beamformer for nonGaussian/circular interference, whereas some of them improve the performance of the WL MVDR beamformer for nonGaussian/noncircular interference. These new beamformers open new perspectives for spectrum monitoring of nonGaussian signals and for radiocommunication networks using such signals.

Robust Capon beamforming exploiting the second-order noncircularity of signals

This paper extends the worst-case performance optimization based robust Capon beamformer (RCB) to the generalized case with possible noncircular signal-of-interest (SOI) and/or noncircular interferences. The proposed widely linear (WL) beamformer exploits the second-order noncircularity of the SOI and interferences simultaneously, and it is robust against the errors in the steering vector, sample covariance matrix and estimated noncircularity coefficient of the SOI. Further, a theoretical performance analysis for the class of WL beamformers using generalized loading in the presence of steering vector errors is presented. The superior performance of the proposed beamformer over the RCB is demonstrated by the theoretical results and various numerical experiments.

A class of diagonally loaded robust Capon beamformers for noncircular signals of interest

Diagonal loading is a simple and effective method for robustness enhancement of the Capon beamformer against perturbation in the presumed steering vector of the signal-of-interest (SOI). However, the determination of an appropriate diagonal loading level is not a trivial task. Three noncircularity restoral based methods are herein proposed for selecting the diagonal loading level to recover a noncircular SOI buried in circular and/or noncircular interferences plus circular background noise. Monte Carlo simulations are performed to verify the efficacy of the proposed methods.

GLRT-based array receivers for the detection of a known signal with unknown parameters corrupted by noncircular interferences

The detection of a known signal with unknown parameters in the presence of noise plus interferences (called total noise) whose covariance matrix is unknown is an important problem which has received much attention these last decades for applications such as radar, satellite localization or time acquisition in radio communications. However, most of the available receivers assume a second order (SO) circular (or proper) total noise and become suboptimal in the presence of SO noncircular (or improper) interferences, potentially present in the previous applications. The scarce available receivers which take the potential SO noncircularity of the total noise into account have been developed under the restrictive condition of a known signal with known parameters or under the assumption of a random signal. For this reason, following a generalized likelihood ratio test (GLRT) approach, the purpose of this paper is to introduce and to analyze the performance of different array receivers for the detection of a known signal, with different sets of unknown parameters, corrupted by an unknown noncircular total noise. To simplify the study, we limit the analysis to rectilinear known useful signals for which the baseband signal is real, which concerns many applications.

Performance analysis of LRT/GLRT-based array receivers for the detection of a known real-valued signal corrupted by noncircular interferences

A performance analysis of likelihood ratio test (LRT)-based and generalized likelihood ratio test (GLRT)-based array receivers for the detection of a known real-valued signal corrupted by a potentially noncircular interference is considered in this paper. The distribution of the decision statistics associated with the LRT and GLRT is studied. This allows us to give exact closed-form expressions of the probability of detection ( P D) and false alarm ( P FA) for two LRT-based receivers. Then, asymptotic (with respect to the data length) closed-form expressions are given for P D and P FA for four GLRT-based receivers. Finally, in order to strengthen the obtained results, some illustrative examples are presented.

Widely Linear MVDR Beamformers for the Reception of an Unknown Signal Corrupted by Noncircular Interferences

For nonstationary observations, potentially second-order (SO) noncircular, the SO optimal complex filters are time variant (TV) and, under some conditions of noncircularity, widely linear (WL). Moreover, for applications such as spectrum monitoring or passive listening, the sources' waveforms are unknown and no training sequence or spreading code is a priori available. In this context, this paper aims at introducing the time invariant (TI) WL minimum variance distortionless response (MVDR) beamformer for the optimal reception of an unknown signal, whose waveform is unknown but whose steering vector is known, corrupted by potentially noncircular interferences. Its properties, performance, and adaptive implementation in noncircular contexts are analyzed in this paper. This optimal beamformer is shown to always improve, in the steady state, the performance of the well-known Capon's beamformer for noncircular interferences. Moreover, it should be noticed that this optimal beamformer allows the processing of up to 2 (N-1) rectilinear interferences from an array of N sensors. Finally, at the end of this paper, a TV extension of this TI WL MVDR beamformer is presented to process SO noncircular interferences having a nonnull carrier residue or frequency offset.

Second-Order Optimal Array Receivers for Synchronization of BPSK, MSK, and GMSK Signals Corrupted by Noncircular Interferences

The synchronization and/or time acquisition problem in the presence of interferences has been strongly studied these last two decades, mainly to mitigate the multiple access interferences from other users in DS/CDMA systems. Among the available receivers, only some scarce receivers may also be used in other contexts such as F/TDMA systems. However, these receivers assume implicitly or explicitly circular (or proper) interferences and become suboptimal for noncircular (or improper) interferences. Such interferences are characteristic in particular of radio communication networks using either rectilinear (or monodimensional) modulations such as BPSK modulation or modulation becoming quasirectilinear after a preprocessing such as MSK, GMSK, or OQAM modulations. For this reason, the purpose of this paper is to introduce and to analyze the performance of second-optimal array receivers for synchronization and/or time acquisition of BPSK, MSK, and GMSK signals corrupted by noncircular interferences. For given performances and in the presence of rectilinear signal and interferences, the proposed receiver allows a reduction of the number of sensors by a factor at least equal to two.

New insights into optimal widely linear array receivers for the demodulation of BPSK, MSK, and GMSK signals corrupted by noncircular interferences-application to SAIC

For nonstationary observations, potentially second-order (SO) noncircular, the SO optimal complex filters are time variant and, under some conditions of noncircularity, widely linear (WL). For more than a decade, there has been an increasing interest in optimal WL filters in radiocommunications contexts involving rectilinear signals such as binary phase-shift keying (BPSK) signals. In particular, it has been pointed out that single antenna interference cancellation (SAIC) may be performed by such filters in the context of BPSK cellular networks. Recently, it has been shown that, by a simple algebraic operation of demodulation on the baseband signal, the minimum shift keying (MSK) and Gaussian MSK (GMSK) modulations can be made to approximately correspond to a BPSK modulation, allowing the application of the SAIC concept to the GSM cellular network at the mobile level, being currently studied for standardization, and offering significant improvements of the network's capacity. Despite the increasing interest in optimal WL filters in rectilinear or quasi-rectilinear contexts, many questions about their behavior and their performance have still arisen. The purpose of this paper is to gain insight into the behavior, properties, and performance of optimal WL array receivers, and thus of the SAIC technology, for the demodulation of BPSK, MSK, and GMSK signals corrupted by noncircular interferences.