Spatial polarimetric time-frequency distributions for direction-of-arrival estimations

Time-frequency distributions (TFDs) are traditionally applied to a single antenna receiver with a single polarization. Recently, spatial time-frequency distributions (STFDs) have been developed for receivers with multiple single-polarized antennas and successfully applied for direction-of-arrival (DOA) estimation of nonstationary signals. In this paper, we consider dual-polarized antenna arrays and extend the STFD to utilize the source polarization properties. The spatial polarimetric time-frequency distributions (SPTFDs) are introduced as a platform for processing polarized nonstationary signals, which are received by an array of dual-polarized double-feed antennas. This paper deals with narrow-band far-field point sources that lie in the plane of the receiver array. The source signals are decomposed into two orthogonal polarization components, such as vertical and horizontal. The ability to incorporate signal polarization empowers the STFDs with an additional degree of freedom, leading to improved signal and noise subspace estimates for direction finding. The polarimetric time-frequency MUSIC (PTF-MUSIC) method for DOA estimation based on the SPTFD platform is developed and shown to outperform the time-frequency, polarimetric, and conventional MUSIC techniques, when applied separately.     

Spatial signature estimation for uniform linear arrays with unknownreceiver gains and phases

The problem of spatial signature estimation using a uniform linear array (ULA) with unknown receiver gain and phase responses is studied. Sufficient conditions for identifying the spatial signatures are derived, and a closed-form ESPRIT-like estimator is proposed. The performance of the method is investigated by means of simulations and on experimental data collected with an antenna array in a suburban environment. The results show that the absence of receiver calibration is not critical for uplink signal waveform estimation using a plane wave model     

Improved coherent DOA estimation algorithm for uniform linear arrays

An improved algorithm on coherent direction-of-arrival (DOA) estimation is presented in this article, with the objective to overcome the unsatisfactory performances of estimation of signal parameter via rotational invariance techniques (ESPRIT)-like algorithms (Han and Zhang, IEEE Antennas and Wireless Propagation Letters 2005;4:443–446). On the basis of trilinear model by reconstructing a series of Toeplitz matrix from the co-variance matrix of array output, our proposed algorithm is to resolve the DOAs of coherent signals, which not only has much better DOA estimation performance than algorithms of ESPRIT-like and multi-invariance ESPRIT but also identifies more DOAs than ESPRIT-like algorithm. Simulation results demonstrate its validity.     

DESIGN OF VIRTUAL UNIFORM LINEAR ARRAYS FOR EFFICIENT DIRECTION FINDING

The problem considered in this paper is to interpolate a virtual uniform array froma real two-dimensional array with arbitrary geometry via an interpolation matrix. The key to thisproblem is how to arrange these virtual sensors. It is shown that the virtual uniform linear arrayshould have the same main-lobe beam-pattern as the real array over an angular sector of interest.Simulation results are presented to illustrate the application of virtual array in direction finding.     

An automatically paired two-dimensional direction-of-arrival estimation method for two parallel uniform linear arrays

In two-dimensional (2-D) direction-of-arrival (DOA) estimation, paring the azimuth and elevation angles of multiple sources is an important issue. In this letter, we propose a new automatically paired 2-D DOA estimation method by designing the geometry of two antenna subarrays and using the propagator method (PM). A special geometry between two parallel uniform linear arrays (ULAs) with a position displacement on the axial direction is proposed to facilitate the elevation and azimuth pairing and estimation. The simulation results have shown that the proposed method can achieve the same 2-D DOA estimation performance as the existing methods, while the complexity is reduced considerably.     

Kernel decomposition of time-frequency distributions

Bilinear time-frequency distributions (TFDs) offer improved time-frequency resolution over linear representations, but suffer from difficult interpretation, higher implementation cost, and the lack of associated low-cost signal synthesis algorithms. In the paper, the authors introduce some new tools for the interpretation and quantitative comparison of high-resolution TFDs. These tools are used in related work to define low-cost high-resolution TFDs and to define linear, low-cost signal synthesis algorithms associated with high-resolution TFDs. First, each real-valued TFD is associated with a self-adjoint linear operator ψ. The spectral representation of ψ expresses the TFD as a weighted sum of spectrograms (SPs). It is shown that the SP decomposition and Weyl correspondence do not yield useful interpretations for high-resolution TFDs due to the fact that ψ is not positive     

Principal decomposition of time-frequency distributions

The authors present a novel time-frequency analysis technique which uses principal components analysis to map any given time-frequency distribution (TFD) of a signal into a set of three 1-D principal decomposition functions. These three functions may then be considered to be `separable' components of a time-frequency function which they refer to as the principal approximation function for the original TFD. They show how principal decomposition analysis is useful for the enhancement and frequency-tracking of nonstationary harmonic signals     

Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains

Formulas for the potentials due to uniform and Linearly varying source distributions defined on simply shaped domains are systematically developed and presented. Domains considered are infinite planar strips, infinite cylinders of polygonal cross sections, planar surfaces with polygonal boundaries, and volumetric regions with polyhedral boundaries. The expressions obtained are compact in form and their application in the numerical solution of electromagnetics problems by the method of moments is illustrated.     

Robust adaptive beamforming for wide-band, moving, and coherentjammers via uniform linear arrays

The problem of providing robustness to the conventional narrow-band uniform linear array configuration so as to handle wide-band and moving jammers is addressed. This robustness is achieved via the use of derivative constraints in jammer directions. However, since the jammer directions are not known a priori, these constraints are incorporated with a maximum likelihood characterization of the so-called jammer subspace. This formulation does not need to assume the availability of signal-free observations, as stipulated in earlier work. Computer simulation results are presented, which show that the algorithms proposed here yield significantly better performance as compared to the previous algorithms of Gershman et al. (see ibid., vol.44, p.361-6, 1996, and IEEE Trans. Signal Processing, vol.45, p.1878-85, 1997) and Hung and Turner (1983) in a variety of situations required to handle wide-band, moving, and coherent jammers     

Volterra series representation of time-frequency distributions

This paper addresses a Volterra series representation of bilinear (or quadratic) time-frequency distributions that belong to Cohen's class, whereby the analogy of the bilinear class with a second-order double Volterra series is utilized. In addition, a different viewpoint for the bilinear kernel and a complementary interpretation concerning the quadratic time-frequency distributions are provided.     

Efficient detection in uniform linear and planar arrays MIMO systems under spatial correlated channels

In this paper, the efficiency of various multiple‐input multiple‐output (MIMO) detectors was analyzed from the perspective of highly correlated channels, where MIMO systems have a lack of performance, besides in some cases, an increasing complexity. Considering this hard but a useful scenario, various MIMO detection schemes were accurately evaluated concerning complexity and bit error rate performance. Specifically, successive interference cancellation, lattice reduction, and the combination of them were associated with conventional linear MIMO detection techniques. To demonstrate effectiveness, a wide range of the number of antennas and modulation formats have been considered aiming to verify the potential of such MIMO detection techniques according to their performance‐complexity trade‐off. We have also studied the correlation effect when both transmit and receiver sides are equipped with uniform linear array and uniform planar array antenna configurations. The performance of different detectors is carefully compared when both antenna array configurations are deployed considering a different number of antennas and modulation order, especially under near‐massive MIMO condition. We have also discussed the relationship between the array factor and the bit error rate performance of both antenna array structures.     

Multiple-pattern linear antenna arrays with single prefixedamplitude distributions: modified Woodward-Lawson synthesis

The authors describe the design of linear antenna arrays that generate multiple radiation patterns by switching between different excitation phase distributions while maintaining a constant pre-established amplitude distribution. Examples are given of antennas with uniform or Gaussian amplitude distributions that, depending on their phase distribution, generate a sum pattern, a flat-topped beam or a cosec-squared pattern     

Virtues and vices of quartic time-frequency distributions

We present results concerning three different types of quartic (fourth order) time-frequency distributions (TFDs). First, we present new results on the previously introduced local ambiguity function and show that it provides more reliable estimates of instantaneous chirp rate than the Wigner distribution. Second, we introduce the class of quartic, shift-covariant, time-frequency distributions and investigate distributions that localize quadratic chirps. Finally, we present a shift covariant distribution of time and chirp rate     

Shift covariant time-frequency distributions of discrete signals

Many commonly used time-frequency distributions are members of the Cohen (1989) class. This class is defined for continuous signals, and since time-frequency distributions in the Cohen class are quadratic, the formulation for discrete signals is not straightforward. The Cohen class can be derived as the class of all quadratic time-frequency distributions that are covariant to time shifts and frequency shifts. We extend this method to three types of discrete signals to derive what we call the discrete Cohen classes. The properties of the discrete Cohen classes differ from those of the original Cohen class. To illustrate these properties, we also provide explicit relationships between the classical Wigner distribution and the discrete Cohen classes     

Realisability of uniform aperture distributions

Physical realisability of uniform aperture distributions in planar-aperture antennas has been discussed in the light of Rhodes' interpretation of the volume integrals in the complex Poynting theorem.     

An analysis of some time-frequency and time-scale distributions

This paper presents an analysis of the representation of instantaneous frequency and group delay using time-frequency transforms or distributions of energy density domain. The time-frequency distributions which ideally represent the instantaneous frequency or group delay (itfd) are defined. Closeness to the itfd is chosen as a criterion for comparison of various commonly used distributions. It is shown that the Wigner distribution is the best among them, with respect to this criterion. The wavelet and scaled forms of the Wigner distribution are defined and analyzed. In the second part of the paper we extended the analysis to the multicomponent signals and cross terms effects. On the basis of that analysis, an efficient method, derived from the analysis of the Wigner distribution defined in the frequency domain, is proposed. This method provides some substantial advantages over the Wigner distribution. The theory is illustrated on numerical examples.     

Interference mitigation in spread spectrum communication systemsusing time-frequency distributions

The capability of the time-frequency distributions (TFDs) to properly represent a single as well as multiple component signals in time and frequency permits the application of a new approach for interference excision in spread spectrum communication systems. The instantaneous frequency (IF) estimate from the TFD is used to construct a finite impulse response filter that reduces the interference power with a minimum possible distortion of the desired signal. The proposed technique is therefore a case of open-loop adaptive filtering. Three- and five-coefficient zero-phase excision filters are considered. Closed-form expressions of the improvement of SNR at the receiver correlator output using the TFD-based adaptive filtering are derived for two extreme cases of time-varying interferers, namely, those of fixed frequency sinusoids and randomly changing instantaneous frequencies. Simulation results including the bit error rates are presented for both swept and frequency hopping jammers     

Minimum-redundancy linear arrays for cyclostationarity-based sourcelocation

The problem of designing minimum-redundancy linear arrays (MRLAs) and appropriate augmentation techniques to be utilized with cyclostationarity-exploiting (cyclic) methods for source location is addressed. The MRLA geometries proposed in the literature for the conventional case, which apply equally well when the signals of interest exhibit cyclostationarity are not appropriate when they exhibit conjugate cyclostationarity. In this case, the problem of finding optimal MRLAs is restated as the problem of number theory that is commonly referred to as the postage stamp problem. Results of computer simulations show that in densely crowded environments, the use of cyclic methods with MRLA geometries and appropriate matrix augmentation techniques can offer a significant performance improvement on cyclic methods that do not resort to matrix augmentation techniques     

Phase weighting for linear antenna arrays

A novel method for introducing an amplitude taper onto a linear array is described, using equal amplitude elements with randomised phase reversals to create an effective taper.