Abstract For a Hammerstein system subject to a stochastic input that is spectrally coloured, this study is first in the open literature (to the present authors' best knowledge) to estimate its linear dynamic subsystem. This estimation is achieved without any prior knowledge nor any prior/simultaneous estimation of the preceding non‐linear static subsystem. This proposed estimator can handle any temporally self‐correlated input despite its potentially unknown spectrum, unknown variance and unknown mean—unlike the common assumption that the input is white and zero‐mean. This proposed estimator needs observations only of the Hammerstein system's overall input and consequential output, but not any observation of any intrasubsystem signal. Furthermore, this proposed estimator can handle a linear subsystem whose input and/or output are each corrupted additively by stationary (and possibly coloured) noises of unknown probability distributions, of unknown non‐zero means and of unknown autocovariances. The proposed estimate is analytically proved herein as asymptotically unbiased and as pointwise consistent; and the estimate's finite‐sample convergence rate is also derived analytically.

Abstract This study proposes the first estimator in the open literature (to the present authors' best knowledge) to nonparametrically estimate a Hammerstein system's nonlinear static subsystem when excited by an input that is temporally self‐correlated with an unknown spectrum, an unknown variance and an unknown mean (instead of the input as commonly presumed to be white and zero‐mean). This proposed nonparametric estimator is analytically proved here to be asymptotically unbiased and pointwise consistent. The proposed estimate's associated finite‐sample convergence rate is also derived analytically.

This paper proposes a new way to realize a maximum‐SINR beamformer for block‐based cyclically prefixed single‐carrier modulation. Here, SINR stands for ‘signal to interference plus noise’ ratio, at the beamformer output. This spatial beamformer will ‘blindly’ pass the signal‐of‐interest; and this beamformer will ‘blindly’ null any co‐channel interference, any adjacent‐channel interference, any out‐of‐system interference, and/or any spatio‐temporally correlated additive noises. This proposed scheme is made possible by zero‐padding an in sufficient guard interval, which may be shorter than the temporally spreading channel's order. The proposed receiver will first undergo frequency‐domain equalization, to ‘clear’ the data of any signal‐of‐interest's energy in the zero‐padded guard interval, in order to facilitate the estimation of the interference and noise. This interference‐and‐noise estimate will then be eigen‐subtracted from the signal‐and‐interference‐and‐noise dataset by the aforementioned ‘blind’ beamformer in the spatial dimension.

This study extends an algorithm, previously proposed by the present authors, for ‘linear minimum‐mean‐squared error’ estimation of phase noise of (possibly) temporal non‐stationarity, large magnitude, ‘non’‐identical increments that have a Levy distribution, of which the Wiener distribution represents a special case. This estimator‐taps may be pre‐set to any number, may be pre‐computed offline with no matrix inversion, based on the prior knowledge of only the signal‐to‐(additive)‐noise ratio and the phase‐noise's characteristic function. That estimator may be set to various degrees of latency. This is here generalised to allow observables at irregular time‐instants (e.g. because of the irregular placement of pilot symbols in the transmitted waveform), under which the phase‐noise increments become non‐identically distributed. This study handles this more complicated scenario.

This paper analytically derives an upper bound for the output power of two-sensor branch-selection (a.k.a. "antenna selection," "selection diversity," or "selection combining") reception, based on an empirically proven "geometric model" of the wireless propagation channel. The derived upper bound is explicit in terms of the geometric model parameters. The tightness of this upper bound is verified by Monte Carlo simulations.

This paper is first in the open literature (to the authors' best knowledge) on wireless channel fading to derive the uplink received signal's fourth-order spatial-correlation coefficient function across a receiving sensor-array's aperture. This derivation is mathematically rigorous and is based on idealized geometric relationships among the mobile transmitter, the base-station's receiving antennas, and the scatterers of the channel. The scatterers' spatial locations are modeled as Poisson distributed, with a Gaussian intensity over a two-dimensional space. This scatterer model has previously been empirically verified to produce faithful expressions for the second-order spatial correlation coefficient. The final formula is in closed form, explicit in terms of the simple geometric model's few independent parameters.

For a directional (a.k.a. directive) transceiver misaligned towards an omni-directional transceiver, the multipaths' time-of-arrival (TOA) distribution is herein derived in closed form explicitly in terms of the "geometric modeling" parameters. This derivation allows the directional beamwidth to mis-point to any arbitrary azimuth-direction, even if entirely away from the intended omni-directional transceiver.

The linear minimum-mean-square error (LMMSE) estimator is herein derived to estimate phase-noise of Levy statistics (including Wiener phase-noise) and of arbitrarily large magnitude. This estimator may be pre-set to any latency and any number of tabs. This estimator depends only on the signal-to-(additive)-noise ratio and the phase-noise variance, but requires no matrix-inversion.

Herein proposed is a new frequency domain equalizer (FEQ) to suppress channel induced interference such as ICI and ISI, co-channel interference, and overlaid systems interference. Unlike earlier schemes, this proposed algorithm requires no temporal oversampling nor the use of more than one receive antenna. All the above is achieved by exploiting null subcarriers (a.k.a. virtual/unused/unmodulated subcarriers) inherent in standard multicarrier systems, and by a generalized sidelobe cancellation (GSC) like scheme. This proposed method can offer superior bit error rate over earlier methods as well as simpler computations over another GSC-like scheme.

This paper analytically derives closed-form expressions of the uplink received-signal's polarization-parameterized spatial-correlation-coefficient functions across the basestation antenna-array's spatial aperture, based on a geometrical model of idealized spatial relationships among the transmitter, the scatterers, and the receiving antennas. The derived formulas fit well with some empirical data.

This paper presents a new trivariate joint and bivariate distributions of a landmobile cellular wireless communication system's uplink multipaths' time-of-arrival (TOA) and two-dimensional (2D) azimuth-elevation direction-of-arrival (DOA). These distributions are rigorously derived via thorough mathematics, based on a "geometrical" model of the three-dimensional (3D) spatial relationships among the mobile-station (MS), the scatterers, and the base-station (BS). Unlike earlier "geometric models" that assume the scatterers to have only a 2D spatial density (for example, uniform density within a disc around the mobile), this present "geometric model" have the scatterer spatial density as uniform within a 3D vertical above ground cylinder whose flat bottom circular base centers at the mobile.

Proposed herein is a pre-processing technique applicable to maximum-SINR beamformers for "blind" space-time Rake receivers in "single-user"-type DS-CDMA detection. This smart-antennas signal-processing technique enhances the constructive summation of multipaths and the rejection of co-channel interference, both of which decrease the bit-error-rate and lower the error-floor of the cellular uplink's near-far problem at high SNR. This technique is "blind" in that it needs neither prior knowledge nor explicit estimation of (1) the channel-faded multipaths' arrival angles, relative arrival delays or power profiles, (2) the receiving antenna array's nominal or actual gain-phase-polarization response, and (3) the co-channel multi-access users' signature-spreading codes. Monte Carlo simulations show that the proposed scheme can enhance the output-SINR by 1 - 10 dB. A mathematical analysis shows this proposed pre-processing scheme to always improve the asymptotic output-SINR. A formula is analytically derived to predict this asymptotic output-SINR. This formula lies within 1 dB of limited simulation results at an input-SIR above -7 dB and a chip-rate space time-sampling, but the formula is less accurate otherwise

Speckle noise has been found to rotate an image's homomorphic elliptically distributed complex-wavelet coefficients. This work proposes a counter-rotation of these complex-wavelet coefficients as a means of mitigating speckle noise using principle component analysis. Simulations suggest that the proposed denoising technique offers superior visual quality, though its signal-to-mean-square-error ratio (S/MSE) is numerically comparable to the improvement obtained in customary median filtering and adaptive Wiener filtering.

This letter presents the joint/marginal distributions of the uplink (downlink) multipaths' azimuth angles of arrival and times of arrival at the cellular base station (mobile). These closed-form explicit densities are rigorously derived based on a new "geometrical model" wherein omnidirectional scatterers are modeled as spatially distributed at an inverted parabolic spatial distribution on a two-dimensional disc centered at the mobile. This "inverted parabolic" density, in contrast to the uniform disc density or the rim density, indirectly accounts for scattering power loss. This new model better least-squares-fit some empirical data than its competing models can.

This paper presents the open literature's first closed-form explicit expressions of the trivariate joint and marginal distributions of a land mobile cellular wireless communication system's uplink and downlink multipaths' time-of-arrival (TOA) and two-dimensional (2D) direction-of-arrival (DOA), rigorously derived via thorough mathematics based on a "geometrical" model of the three-dimensional (3D) spatial relationships among the mobile-station (MS), the scatterers, and the base-station (BS). The scatterers are herein modeled to have a uniform 3D spatial distribution in an above-ground hemisphere with a flat circular base (or alternatively, within a sphere) centered at the mobile.

This paper is first in the open literature of wireless landmobile radiowave cellular communication to derive via thorough mathematics explicit closed-form expressions for the uplink received-signal's spatial-correlation-coefficient function across the basestation antenna-array's aperture. This rigorous analytical derivation is based on geometric relationships among the mobile transmitter, the basestation's receiving antennas, and the scatterers. The derived spatial-correlation-coefficient functions are expressed explicitly in terms of the base-station's interantenna spacing and in terms of each scatterer-cluster's distance and spatial angle from the base-station. The scatterers' spatial distribution is herein modeled as stochastic, Poisson-distributed with multiGaussian intensity over a two-dimensional space. This nonhomogeneous stochastic spatial distribution accommodates better the field variability in the scatterers' spatial locations than would deterministic spatial distributions (like the uniform-ring, the uniform-disc, or the Gaussian spatial distributions) that currently dominate the literature.

Wong (2002) has earlier proposed a new transmission-detection scheme to "blindly" detect an M-ary frequency-shift-keying (MFSK) fast frequency-hop (FFH) peer-to-peer code-division multiple-access (CDMA) signal-of-interest (SOI) amid unknown co-channel interferences. That earlier algorithm implements a two-dimensional space-frequency "blind" beamformer over the direction-of-arrival and the frequency-hop set to maximize the beamformer's output signal-to-interference-and-noise ratio (SINR) without prior knowledge of (1) the (possibly overlapping) hop-sequences of the multi-user co-channel interferers, (2) the fading channel (possibly spatially and temporally decorrelated) space-time impulse response, and (3) the mobile receiver antennas' nominal or actual gain/phase responses. A computationally more efficient realization of that earlier algorithm is herein presented. Also herein demonstrated is the efficacy of the proposed scheme for Galois-field-based FFH-CDMA modulation.

Herein presented is a finite-data-record performance analysis of a "blind" space-time RAKE-receiver algorithm previously proposed by Wong, Lok, Lehnert & Zoltowski (WLLZ) [T.F. Wong, T.M. Lok, J.S. Lehnert & M.D. Zoltowski, 1998] for uplink DS-CDMA cellular radiowave wireless communications using only single-user-type "conventional" detectors. Derived are two approximations of the detector's finite sample mean output-SINR. This analysis reveals how the output-SINR depends on the multi-user access cellular system's various system parameters, and the fading-channel's delay spread and temporal variability. Simulations confirm this analysis' validity, except when the detector breaks down in certain small-sample-support situations. Such breakdown is further shown to be alleviated by overlapping time-segments in the estimation of the covariance matrix of the interference-plus-noise delay-segments of the despread signal.

A new algorithm is herein proposed to "blindly" suppress co-channel interference and to detect the signal-of-interest (SOI) for peer-to-peer mobile transceivers using M-ary frequency-shift-keying (MFSK) fast frequency-hop (FFH) code-division multiple-access (CDMA). This algorithm implements a two-dimensional space-frequency "blind" beamformer over the direction-of-arrival and the frequency-hop set. This proposed blind adaptive "smart antennas" signal processing scheme attempts to maximize the beamformer's output signal-to-interference-and-noise ratio (SINR) without prior knowledge of (1) the (possibly overlapping) hop-sequences of the multi-user co-channel interferers, (2) the fading channel's (possibly spatially and temporally decorrelated) space-time impulse response, and (3) the mobile receiver antennas' nominal or actual gain/phase responses. The proposed scheme can also reject "spectral splatter" and can exploit any spatially decorrelated fading across the receiving antennas. This proposed scheme requires no additional bandwidth but assumes (rather reasonably) that the strongest co-channel interferers persist for at least a few information symbols.

This paper develops new quasi-Bayesian statistical models for the geometric deformation of a nominally linear towed array, based on rigorous fluid mechanics. These models of will be expressed in terms of physically meaningful and measurable quantities, which may be calibrated using various empirical tow-array shape deformation studies for diverse oceanic and towing conditions. Towards this end, this paper (1) will advance new statistical models for the towing vessel's temporally correlated motion and the oceanic currents' space-time correlated behavior, and (2) will show how such driving forces influence the towed array's fluid mechanics to produce the array's space-time shape deformation — with “space” referring to length along the array's nominal axis. This present analysis is more comprehensive than earlier works, which consider only the effects of temporally uncorrelated motion of the towing vessel and ignore the oceanic-current effects.

A new “fractional self-decorrelation” technique is herein proposed to enhance the multipath constructive summation capability and the interference rejection capability of single-user-type DS-CDMA detectors at maximum-SINR blind space-time RAKE receivers to tackle the near-far problem in wireless mobile communications. This technique can significantly decrease the error rate and can remove the near-far problem's error floor at high SNR. Moreover, this “blind” space-time processing receiver architecture needs no prior knowledge nor explicit estimation of (1) the channel's multipath arrival angle or arrival delay or power profile — the fading channel's delay spread may be of arbitrary length, even as long as the symbol duration, (2) the receiver's nominal or actual antenna array manifold, and (3) the other DS-CDMA users' signature spreading codes.

A novel "self-decorrelating" technique is proposed to enhance the multipath constructive summation capability and the interference rejection capability of a class of maximum-SINR blind space-time CDMA RAKE receivers designed to tackle the near-far problem. This proposed "self-decorrelating" technique appears to have effectively removed the near-far problem's error floor at high SNR; and the proposed technique can also significant decrease the error rate. Moreover, this "blind" space-time processing receiver architecture needs no prior knowledge nor explicit estimation of (1) the channel's multipath arrival angle or arrival delay or power profile, (2) the receiver's nominal or actual antenna array manifold, and (3) the other CDMA users' signature spreading codes. Preliminary simulations suggest very significant performance improvement realizable from the proposed technique. Though developed for direct-sequence CDMA, the proposed technique might be adopted for frequency-hopping CDMA.

A simple diversely polarized antenna geolocation scheme is herein proposed to upgrade older base-stations' nonadaptive antenna arrays to geolocate approximately mobile users and to perform downlink beamforming. Instead of retrofitting each antenna at an existing base-station with a separate temporal RAKE receiver, this simple technology needs only two horizontally oriented and magnetically small loops (plus an optional vertically oriented dipole), each with one temporal RAKE receiver. The diversely polarized system at the receiver matches the polarization of the handset transmitter's strong vertical electric-field; and novel geolocation algorithms are herein proposed for use with these collocated loops/dipole antenna systems. The estimated approximate azimuth angle of the mobile user then facilitates downlink transmission beamforming at the base-station.

A pulse train of diversely compressed pulses may produce better Doppler-delay resolution than a similar pulse train of identically compressed pulses by reducing the total ambiguity and being more flexible in distributing that reduced ambiguity. This work investigates the design of such a pulse-diverse waveform under a design criterion constraining the allowable sidelobe height in the composite ambiguity function. A genetic algorithm is used to design the pulse modulation parameters for frequency shift keying (FSK) pulse modulation and joint frequency-phase shift keying (FSK-PSK) pulse modulation. Simulation studies verify the superior Doppler-delay resolution and interference rejection capability of these pulse-diverse modulation schemes.

Wavelet packet division multiplexing (WPDM) is a high-capacity, flexible and robust orthogonal multiplexing scheme in which wavelet packet basis functions are chosen as the coding waveforms. In this paper, characterization of the effects of amplifier nonlinearities over the WPDM signal is performed for a 16-QAM signal constellation. An expression for the symbol error probability in the presence of Gaussian noise and amplifier nonlinearities is derived.

This paper introduces an underwater acoustic source localization and blind interference rejection algorithm for multiple non-cooperative wideband fast frequency-hop (FFH) spread spectrum signals of unknown hop sequences and unknown arrival angles. This algorithm avoids the need to adjust beamforming weights to accommodate frequency variations in the frequency-hopping signals. This novel approach deploys one vector-hydrophone, which is composed of two or three spatially colocated but orthogonally oriented velocity-hydrophones plus an optional colocated pressure-hydrophone. The spatial colocation of all component hydrophones comprising such a vector-hydrophone frees the beamforming weights of any dependence on the signals' hopping frequencies.

This paper introduces a novel closed-form ESPRIT-based algorithm for multi-source direction finding using arbitrarily spaced electromagnetic vector-sensors whose locations need not be known. The electromagnetic vector-sensor, already commercially available, consists of six co-located but diversely polarized antennas separately measuring all six electromagnetic-field components of an incident wavefield. In this novel algorithm, ESPRIT exploits the non-spatial inter-relations among the six unknown electromagnetic-field components of each source and produces from the measured data a set of eigenvalues, from which the source's electromagnetic-field vector may be estimated to within a complex scalar. Application of a vector cross-product operation to this ambiguous electromagnetic-held vector estimate: produces an unambiguous estimate of that source's normalized Poynting-vector, which contains as its components the source's Cartesian direction-cosines. Monte Carlo simulation results verify the efficacy and versatility of this innovative scheme.

This paper introduces a sensor-array geolocation and blind interference rejection algorithm for multiple noncooperative wideband fast frequency-hop (FFH) spread spectrum signals of unknown hop sequences and unknown arrival angles. This algorithm avoids the need to adjust beamforming weights to accommodate frequency variations in the frequency-hopping signals. This method also exploits the sources' polarizational diversity in addition to their diversity in spatial angles and temporal characteristics. This novel approach deploys one electromagnetic vector sensor, which is composed of six spatially co-located non-isotropic polarization-sensitive antennas measuring all six electromagnetic-field components of the incident wave-field. The spatial co-location of all component antennas comprising such a vector-sensor frees the beamforming weights of any dependence on the signals' hopping frequencies. This algorithm is also applicable to blind co-channel interference rejection in frequency-hop code-division multiple access (CDMA) wireless communications.

A closed-form multi-dimensional multi-invariance generalization of the ESPRIT algorithm is introduced to exploit the entire invariance structure underlying a (possibly) multiparametric data model, thereby greatly improving estimation performance. The multiple-invariance data structure that this proposed method can handle includes: (1) multiple occurrence of one size of invariance along one or multiple parametric dimensions, (2) multiple sizes of invariances along one or multiple parametric dimensions, and (3) invariances that cross over two or more parametric dimensions. The basic (uni-dimensional uni-invariance) ESPRIT algorithm is applied in parallel to each multiple pair of matrix-pencils characterizing the multiple invariance relationships in the data model, producing multiple sets of cyclically ambiguous estimates over the multi-dimensional parameter space. A weighted least-squares hyper-plane is then fitted to these set of estimates to yield very accurate and unambiguous estimates of the signal parameters.

A novel sparse array geometry embedding two sizes of spatial invariances is proposed for extended-aperture spatial diversity using a new ESPRIT-based algorithm. This novel direction-finding method extends the array aperture without additional antennas, irregular inter-element spacings, nor any cyclic ambiguity in the final arrival angle estimates. The half-wavelength invariance yields unambiguous but high-variance DOA estimates to disambiguate low-variance but cyclically ambiguous estimates obtained using the larger invariance. This novel approach facilitates (1) multipath de-correlation (independent fading), (2) coherent summation of multipaths from the same source, and (3) down-link beamforming from the base-station to the mobile. Under one simulation scenario involving two closely spaced time-delayed multipaths in frequency-selective slow-fading, the proposed algorithm offers an impressive 80% reduction in the standard deviation and bias. Any additional computation needed by this method may be performed in parallel, thereby requiring no serious increase in the overall computational time.

A novel ESPRIT-based 2D angle estimation scheme is proposed involving the use of a right-triangular array of three vector sensors spaced much farther apart than a half-wavelength. A vector sensor is composed of six co-located antennas distinctly measuring all six electromagnetic field components of a multi-component incident wavefield. Information on each source's respective electromagnetic field components is obtained by decoupling the signal eigenvectors via lower dimensional eigenvectors derived from TLS-ESPRIT. This facilitates estimation of each source's respective Poynting vector thereby enabling one to resolve the phase ambiguities in ESPRIT's eigenvalues when the intervector-sensor spacing is greater than a half-wavelength. Simulations are presented showing the sample variance of the direction cosine estimates decreasing linearly on a log-log scale as the intervector-sensor spacing is increased from a half-wavelength to 30 wavelengths, with a factor of 80 reduction in the latter case relative to the former case. The proposed scheme and attendant vector sensor array also outperform a uniformly-spaced array of scalar sensors with the same aperture and same number of component antennas whenever the intervector sensor spacing in the former case is greater than 3 half-wavelengths.