Analysis of a signal estimation algorithm for diversely polarizedarrays

The problem of separating and estimating the waveforms of superimposed signals received by a diversely polarized array is considered. Signal estimation is accomplished by a two-step procedure: (1) The directions of arrival and polarization parameters of all the signals are estimated using an eigenstructure-based technique; (2) The estimated signal is obtained as a linear combination of the array outputs, with weights that are computed from the estimated direction/polarization parameters. The objective is to analyze the quality of the estimated signal in terms of the output signal-to-interference ratio (SIR) and output signal-to-noise ratio (SNR). Closed-form expressions are derived for the output SIR and SNR of a general diversely polarized array. By evaluating these expressions for selected test cases it is shown that polarization sensitive arrays can provide significantly higher output SIR and SNR than uniformly polarized arrays. The performance improvement is especially significant for closely spaced sources with sufficiently different polarization characteristics     

Fading effects on antenna arrays in cellular communications

In future application of antenna arrays to wireless communications, it is envisioned that known signal waveforms (e.g., synchronization data stream) will be used for estimating the array response for all the relevant links. Once the array response is known, it will be used for separation and reconstruction of the unknown data stream. Since the array response matrix is estimated with finite precision, we examine the error effects on the signal reconstruction errors. The results are presented in the form of output signal-to-interference ratio (SIR) and output signal-to-noise ratio (SNR) for uncorrelated signals. We obtain closed-form expressions for the average output SNR and SIR for Rayleigh, Ricean, and Nagakami fading. It is shown that in the presence of slowly fading channels, the diversity advantage of the array decreases as the number of signals (or interferers) increases     

Performance analysis of diversely polarized antenna arrays

The performance of direction finding systems utilizing diversely polarized antenna arrays is investigated. The Cramer-Rao bound (CRB) is used to evaluate the accuracy of the estimated directions of arrival. The resolving power of the array is evaluated by analyzing the performance of a likelihood ratio detector designed to determine whether the signals observed by the array originate from a single source or from two closely spaced sources. Numerical examples and analysis of some special cases provide insights into the improvement in direction finding accuracy and in the resolving power of the array due to polarization diversity. The case of a signal in the presence of an interferer is studied in some detail. The CRB and the probability of detection are evaluated as functions of the spatial separation and the polarization difference between signal and interferer, signal-to-noise ratio, and signal-to-interference ratio. Performance comparisons are made between uniformly polarized and diversity polarized arrays. It is shown that improved direction finding performance can be obtained by using polarization diversity, with no increase in hardware complexity     

Performance analysis of the minimum variance beamformer

We present an analysis of the signal-to-interference-plus-noise ratio (SINR) at the output of the minimum variance beamformer. The analysis is based on the assumption that the signals and noise are Gaussian and that the number of samples is large compared to the array size, and it yields an explicit expression for the SINR in terms of the different parameters affecting the performance, including signal-to-noise ratio (SNR), interference-to-noise ratio (INR), signal-to-interference ratio (SIR), angular separation between the desired signal and the interference, array size and shape, correlation between the desired signal and the interference, and finite sample size     

The effect of a finite-distance signal source on a far-fieldsteering Applebaum array-two dimensional array case

Approximate expressions are obtained for the output signal-to-noise ratio (SNR) expressed in terms of the finite signal distance and signal direction for a finite-distance signal source's effect on the performance of a far-field steering two-dimensional Applebaum-type adaptive array. The expression is shown to be consistent with the actual simulated value. Using that expression, a simplified rule is obtained to determine the distance between the signal source and the array center at which the output SNR loss is given by a specific value. The SNR value so obtained varied with two-dimensional signal direction. The analysis for the case of an arbitrarily located array is presented, followed by the cases for rectangular, circular and elliptical arrays. It was found that this distance associated with the given SNR value is always less for a rectangular array than that of a linear array when the total number of array elements for both are equal and the performances of an elliptical array are similar to those of a circular array     

Minimum-noise-variance beamformer with an electromagnetic vectorsensor

We study the performance of the minimum-noise-variance beamformer employing a single electromagnetic (EM) vector sensor that is capable of measuring the complete electric and magnetic fields induced by EM signals at one point. Two types of signals are considered: one carries a single message, and the other carries two independent messages simultaneously. The state of polarization of the interference under consideration ranges from completely polarized to unpolarized. We first obtain explicit expressions for the signal to interference-plus-noise ratio (SINR) in terms of the parameters of the signal, interference, and noise. Then, we discuss some physical implications associated with the SINR expressions. These expressions provide a basis for effective interference suppression as well as generation of dual-message signals of which the two message signals have minimum interference effect on one another. We also analyze the characteristics of the main-lobe and side-lobe of the beampattern of an EM vector sensor and compare them with other types of sensor arrays     

Maximal-ratio combining architectures and performance with channel estimation based on a training sequence

Maximum-ratio combining (MRC) is a simple and effective combining scheme for adaptive antenna arrays to combat noise, fading, and to a certain degree, cochannel interference. However, it requires estimation of the spatial signature (i.e., the channel gain and phase at each antenna element) of the desired signal across the array. Assuming that this estimate is obtained by correlation using a known training sequence of K symbols embedded in the useful signal, we proceed to develop a fully analytical assessment of the impact of estimation error on the output signal-to-noise ratio (SNR) of the array. The originality of the approach revolves around the derivation of the distribution of the normalized SNR, that is the real SNR normalized to the ideal (i.e., perfect estimation) SNR. The end result is a set of distributions which can potentially reduce or in certain cases eliminate the need for simulation to determine certain design parameters such as array size, training sequence length, etc. These are then applied to find closed-form expressions for the outage probability and the error probability in differential phase-shift keying and quarternary phase-shift keying after training in uncorrelated Rayleigh fading.     

Performance analysis of the minimum variance beamformer in thepresence of steering vector errors

We present an analysis of the signal-to-interference-plus-noise ratio (SINR) at the output of the minimum variance beamformer in the presence of steering vector errors. The analysis yields an explicit expression for the SINR in terms of the variance of the steering vector errors and the other parameters affecting performance, including signal-to-noise ratio (SNR), interference-to-noise ratio (INR), signal-to-interference ratio (SIR), angular separation between desired signal and interference, array size and shape, correlation between desired signal and interference, and finite sample size     

Adaptive arrays: A new approach to the steady-state analysis

Our main goal is a closed-form expression for the steady-state output signal-to-noise ratio (SNR) of ann-element adaptive array excited by one desired narrow-band signal andK - 1narrowband jammers. This is facilitated by representing each excitation by a complexn-dimensional vector-the excitation vector. We show that the important system parameters are functions of scalar products of pairs of these exctiation vectors. In particular, the normalized output SNR of the array is shown to be the ratio of determinants whose elements involve these scaler products. Such determinants are also shown to be involved in the expressions for the optimal array weights.     

信号DOA和极化信息联合估计的降维四元数MUSIC方法

基于简化电磁矢量传感器阵列,该文提出了一种新的降维四元数MUSIC估计方法。文中引用了四元数的概念,利用四元数的正交特性能够很好地描述矢量传感器阵元的正交结构这一优点,建立了电磁矢量传感器阵列的四元数模型,利用降维Q-MUSIC (Quaternion-MUSIC)方法先对极化信号DOA进行估计,通过已经估计出来的DOA信息,再借助传统的V-MUSIC (long-MUSIC)方法估计极化信息。从而依次获得极化信号的4个参数。仿真实验验证了算法的可行性。     

Shortwave Infrared Polarization Imaging and Monolithic Integrated Polarization Amplification Systems Based on Aligned Carbon Nanotube Arrays

Next-generation shortwave infrared (SWIR) imaging systems generally require a multidimensional information sensing capability (including intensity, wavelength, polarization, phase, etc.), a highly integrated photodetector unit, and information processing, allowing for miniaturization and low-cost production. However, traditional polarized SWIR imaging systems with integrated polarizer arrays as supplementary filters and silicon-based amplifying circuits are complicated and very expensive. Here, a SWIR polarization-sensitive photodetector and a monolithic integrated polarization amplification system (MIPAS) based on well-aligned carbon nanotube (CNT) arrays are demonstrated. The polarization-sensitive CNT photodetector exhibits anisotropic ratios of ≈5.18 and ≈7.56 at 1800 and 2000 nm wavelengths, respectively, and high-resolution characteristics that can be utilized to image SWIR laser spots with a radius of less than 10 µm. Furthermore, MIPAS including a CNT field-effect transistor, a CNT loading resistor, and a polarization-sensitive CNT photodetector is used to increase the anisotropic ratio of the CNT photodetector. The amplified anisotropic ratio is improved up to 173 and 243 at 1800 and 2000 nm wavelengths, respectively, which is the maximum reported in the SWIR band.  Our work demonstrates that the CNT polarization-sensitive photodetector has the potential for SWIR polarization imaging with a monolithic integrated polarization amplification system.     

基于双旋转单偶极子阵列的谱参数估计方法

提出了一种基于双旋转单偶极子阵列的联合谱参数估计算法.通过旋转阵元及修正极化多重信号分类(multiple signal classification, MUSIC)算法中谱函数的导向矢量, 便能实现用两阵元进行多目标测向, 回避了传统算法中要求信号源个数小于阵元数的问题.仿真结果表明:在小快拍数、低信噪比的影响下, 该算法在测向性能上优于阵元数为6的极化空间谱估计算法, 且所用通道数少, 可降低成本.该算法所述的单偶极子阵列可用任意极化敏感天线单元或组合进行构造, 可移植性较强.     

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.     

Calculation of the signal-to-noise ratio for simple surface coilsand arrays of coils [magnetic resonance imaging]

Describes a new method to calculate the signal-to-noise ratio (SNR) of MR signals obtained from single receiver coils and arrays of receiver coils. The coils are assumed to be placed on the surface of a conducting half-space and the SNR is sample-noise dominated. While in conventional methods line integrals over the electric currents in the coils are chosen to calculate the electric and magnetic fields, this new method uses surface integrals over magnetic dipoles covering the area enclosed by the antenna to derive these fields. Using this method, the SNR for simple circular and square coils was analytically calculated. The calculations show that the theoretical difference in SNR between circular and square antennas is very low. Furthermore, based on the new method, a derivation of the ultimate gain in SNR for arrays of surface coils is presented. The SNR of such an array approaches a limit even if the total number of coils is increased to infinity. This ultimate SNR of a coil array is 35.8% above that of a single circular-shaped, size-optimized and linear polarized coil     

Subspace fitting with diversely polarized antenna arrays

Diversely polarized antenna arrays are widely used in RF applications. The diversity of response provided by diversely polarized antenna arrays can greatly improve direction-finding performance over arrays sensitive to only one polarization component. For d emitters, directly implementing a multidimensional estimation algorithm would require a search for 3d parameters: d directions of arrival (DOAs), and 2d polarization parameters. A more efficient solution is presented based on the noise subspace fitting (NSF) algorithm. It is shown how to decouple the NSF search into a two-step procedure, where the DOAs are estimated separately. The polarization parameters are then obtained by solving a linear system of equations. The advantage of this approach is that the search dimension is reduced by a factor of three, and no initial polarization estimate is required. The algorithm can be shown to yield asymptotically minimum variance estimates: provided no perfectly coherent signals are present. Simulation examples are included     

Removal of the finite-distance source effect on the Applebaum array

The effect of a finite-distance signal source on the performance of an Applebaum array has been studied extensively in the literature. It has been concluded that unless the Applebaum array is focused at the exact source location, the degradation of the output signal-to-noise ratio (SNR) becomes unacceptable. The automatic focusing technique (AFT), developed for long-wavelength imaging systems using nonadaptive linear arrays, is extended here to focus adaptive arrays such as the Applebaum type. Thereafter, the far-field steering vector is used successfully to form a beam approaching the desired signal while suppressing the interferences. Substantial improvements in data processing have been achieved through the use of a partial convolution in the frequency domain. It is also demonstrated that the AFT can be used when the signal source range lies in the beginning of the Fresnel region of a nonadaptive linear array with negligible loss in the output SNR     

Novel fiber sensor arrays using erbium-doped fiber amplifiers

We examine the signal-to-noise ratio (SNR) performance of a novel type of time domain multiplexed sensor arrays in which low gain (1-10 dB) fiber amplifiers are incorporated to compensate for splitting losses between sensors. The system noise figure for passive and amplified sensor arrays is presented, along with expressions to optimize the array parameters for high SNRs. We show that practical amplified sensor arrays exhibit low system noise figures that allow much larger arrays (hundreds of sensors) than passive arrays     

极化域-空域联合谱估计精度研究

研究了极化域-空域联合谱估计的精度问题。用克拉美-劳限(CRB)来衡量信号到达角和极化角的估计精度;利用Fisher信息矩阵求逆导出信号到达角和极化角CRB的解析表达式,得出采样点数和阵元数目对估计精度的影响; 通过单个信号源和两个信号源情形下的研究,得出估计精度与信号源位置、信噪比、信干比、信号特征参量之间的关系。     

Cramér-Rao bound for multiple parameters estimation using a polarization sensitive array

In this paper, new Cramér-Rao lower bounds (CRB) of the estimates of frequencies, two-dimensional arrival angles and polarization parameters of multiple incident signals are derived for a polarization sensitive array. The incident sources have distinct carrier-frequencies, in contrast to the modeling of all sources to be at the same known carrier-frequency, which has been investigated in the existing research literature on the Cramér-Rao bounds (CRB) for polarization sensitive direction finding. The derived CRBs are compact closed-form expressions and applicable to an arbitrary array geometry. Numerical examples and analysis of some special cases provide insights into the fact that the estimation accuracy of all parameters is enhanced with the increasing signal-to-noise ratio (SNR) and number of snapshots. In addition, they are hardly influenced by the sampling frequency and independent of the initial phase of incident sources. These insights offer guidelines to the system engineer on how to improve parameters’ estimation accuracy.     

Joint parameter estimation of DOD/DOA/polarization for bistatic MIMO radar

In the paper,polarization-sensitive array is exploited at the receiver of multiple input multiple output (MIMO) radar system,a novel method is proposed for joint estimation of direction of departure (DOD),direction of arrival (DOA) and polarization parameters for bistatic MIMO radars. A signal model of polarimetric MIMO radar is developed,and the multi-parameter estimation algorithm for target localization is described by exploiting polarization array processing and the invariance property in both transmitter array and receiver array. By making use of polarization diversity techniques,the proposed method has advantages over traditional localization algorithms for bistatic MIMO radar. Simulations show that the performance of DOD and DOA estimation is greatly enhanced when different states of polarization of echoes is fully utilized. Especially,when two targets are closely spaced and cannot be well separated in spatial domain,the estimation resolution of traditional algorithms will be greatly degraded. While the proposed algorithm can work well and achieve high-resolution identification and accurate localization of multiple targets.