Post beam steering techniques as a means to extract horizontal winds from atmospheric radars VN Sureshbabu 1, VK Anandan 1, oshitaka suda 2 1 ISRAC, Indian Space Research Organisation, Bangalore -58, India 2 Research Institute for Sustainable Humanosphere (RISH), Kyoto University, JAPAN (Dated: 30 May 2012) Abstract (V.N.SURESHBABU) Postset Beam Steering (PBS) technique has been used to extract horizontal winds from the data collected from multi receiver phased array atmospheric radar (Middle and Upper (MU) atmospheric radar). PBS includes various signal processing algorithms such as beamforming, spectral estimation, moments estimation and etc. Capon beamformer is used for beam synthesizing in the desired direction within the radar beam width. Using the synthesized beam, the power spectrum is obtained through various power spectral estimation methods such as Fourier (non-parametric), Multiple Signal Classification (MUSIC) and Eigenvector (EV) methods. A study has been carried out to analyze the performances of the spectral estimators for better moments computation and thus wind estimations. Results suggest that EV based spectral estimation is a best approach (among three) for complete wind profiling up to the maximum height about 20 km with a temporal resolution about 1.3 min. he analyzed results are in good agreement with other wind observational methods in contiguous time. 1. Introduction Over the past few decades, radar remote sensing of winds is of interest in the tropospheric and upper atmospheric profiling communities. Doppler beam swinging (DBS) is one of the simplest observational methods in which radar antenna main beams are directed in the vertical or near vertical direction to measure the wind components i.e. zonal, meridional and zenith. Zonal and meridian components are generally called as horizontal wind velocities along east-west and north-south directions respectively and zenith component as vertical velocity. In DBS based observations, the wind components are obtained by using line of sight angles and radial velocities of the incoming signals. A minimum of three beams are formed by introducing phases electronically at corresponding antenna elements to derive wind vectors by DBS based method. Also, five beams (one as vertical beam and four as oblique beams) are used for 3-D wind estimation in MS and other wind profiling atmospheric radars. PBS technique was initially demonstrated in wind profiling [6] as a means of software steering using multi receiver data. Since these measurements typically involve reception on minimum three spatially separated arrays, a systematic phase shift can be applied to the signals to produce a two-way beam pattern in any arbitrary direction within the volume illuminated by the transmitted beam. In this article, a comparative study has been carried out using spectral based techniques on data received from middle and upper atmospheric (MU) radar [5] at Shigaraki, Japan. MU radar, mono static pulsed phased array radar, operates at 46.5 MHz with a peak power of 1 MW. he antenna array is also capable of steering the beam electronically using phase shifters in transmit and receive path. he experiment was conducted with full array of transmission (beam width 3.6 o ) in vertical direction. Signals received from spatially separated antennas are made to interfere constructively by phasing the received signals within the transmit beam width. his technique is used to synthesize the beams in the desired directions and so called as Post Beam Steering echnique (PBS) [3]-[4], [6]-[7], [12]-[14]. As these measurements typically involve reception of signals by minimum three spatially separated arrays, the vertically received signals are steered along the desired line of sight angle by introducing systematic phase shifts in the received signals themselves. he beam steering can be optimized by weighting vectors through beamforming approach like Capon method [2], [9]-[12]. hen the weighted steered signals are combined linearly to produce a two-way beam pattern in the desired line of sight angle within the transmit beam volume. he beams are independently synthesized for an off zenith angle (tilt angle) of 1.5 o and equally separated 32 different azimuth
angles within the transmit beam width (3.6 o ). he power spectrum in the desired AOA is obtained by various spectral estimation methods, such as Periodogram (Fourier), MUSIC [1], [9]-[10] and EV, from the synthesized beam in a given direction. As the power spectrum is obtained by various power spectral estimation methods, a comparative study has been carried out to analyze the performances of the spectral estimators for better moments computation [15] and thus wind estimations. Results suggest that EV based spectral estimation is a best approach (among three) for complete wind profiling up to the maximum height about 20 km with a temporal resolution about 1.3 min. he obtained results are compared with other wind observational methods like DBS and GPS sonde in contiguous time. his paper is organized as follows. Mathematical background of the work is given in section-2. System description and data processing are given in section-3. Result analysis with discussion and conclusion are given in the section-4 and section-5 respectively. 2. Mathematical background A. Signal Model he development of a signal model is based on several assumptions. First, multiple incident sources are assumed to be narrowband sources and located in the field far from the array elements. Second, incident sources are considered as point sources. hird, the propagation medium is homogeneous, and the signal arriving at the array is considered to be as a plane wave. Consider two dimensional arbitrary phased array radar composed of N receivers. For an N- element antenna array of arbitrary geometry, the signals (as a function of time) received by N elements along zenith direction at time t can be represented in a column matrix as S(t) = [S 1 (t) S 2 (t) S 3 (t) S N (t)] (1) where S(t) is the received signal matrix at time t along zenith direction and the superscript denotes the transpose of the matrix. In this section, bold letters indicate to vector or matrix representation. Now, the signals (as a function of time) steered along the desired direction (, ), within the transmit beam width, at time t can be modeled as [8]- [10] X(t) = a(θ, ) S(t) (2) where X(t) = [X 1 (t) X 2 (t) X 3 (t) X N (t)] is the steered signal matrix at time t along the desired direction (, ) using vertically received signal at time t (given in Eqn.1) and a (, ) is the steering vector. For an arbitrary array, the steering vector a(, ) takes the form as -j(φ ) -j(φ ) -j(φ ) 1 2 3 -j(φ N ) a (θ, ) = [e e e e ] (3) -j(φ ) -j(φ ) -j(φ ) where e 1,e 2,..., e N are complex phase shift required at the array elements 1,2.,N respectively to steer the vertically received signals in the desired direction during the beam synthesizing in post processing. For example, the phase angle Φ i in the above Eqn.3 can be given as 2π Φ i = (D ix sinθsin +D iy sinθcos +D iz cosθ) λ where is wavelength of transmitted signal and D ix, D iy, D iz are the components of position vector of ith element along x, y, z axes with respect to origin or center of the array. From Eqn.1, the steered signal X(t) along the desired direction (, ) results in a scalar product of steering vector a(, ) and vertically received signal S(t). In the presence of an additive noise n(t), we now get the model commonly used in array processing as X(t) a(, ) S(t) n(t) (4) where n(t) has the same dimension of S(t). he array covariance matrix R in the forward case can be written as R H H = E X(t)X (t) = a (θ, φ) R s a (θ, φ)+ Q (5) where R s and Q are the signal (steered) and noise auto covariance matrices with dimension N N, E denotes statistical expectation and the superscript H represents conjugate transpose of the matrix. A natural estimate R [8] is the sample auto covariance matrix R, which is given as
R 1 m H = (k) (k) m k=1 X X (6) where m is number of points in the time series signal. he auto covariance matrix given above plays an important factor in both parametric and non-parametric spectral estimation methods. For an arbitrary radar array, this beamformer maximizes the power of the beamforming output in the desired direction (within the transmitting beam width) for a given signal X(t) and hence acts as a spatial filter. he spatially filtered signal is obtained as H Y(t) = w X(t) (7) B. Capon Beamformer Capon s minimum variance method [12] is a AOA estimation technique. It is a beamformer developed to overcome the poor performance of conventional beamformers when multiple narrow band sources present from different AOAs. In this case, the array output power contains a contribution from the desired signal as well as the undesired ones from other AOA estimations. his property will limit the resolution of the conventional beamformer. Capon proposed to minimize the contribution of undesired AOAs by minimizing the total output power while maintaining the gain along the look direction as constant. he weight vector w is given by -1 R a(, ) w s (8) H -1 a (, ) Rs a(, ) he weight obtained by the above equation is also called the Minimum Variance Distortionless Response (MVDR). Substituting (8) in (7), one can get optimized time series signal in the desired direction within the transmitting beam width. he Capon s method gives better performance than the conventional beamformer. However, Capon s method still depends on the number of element array and on the SNR. C. Spectral estimation Frequency estimation is the process of estimating the complex frequency components of a signal in the presence of noise. Now, let us consider the time series signal, as given in Eqn (7), in a vector form as Y = [Y(t 1 ) Y(t 2 ) Y(t 3 ) Y(t m)] (or) Y = [Y(1) Y(2) Y(3) Y(m)] Using the time domain signal (above equation), the power spectrum is obtained in spectral domain by periodogram, MUSIC and EV, which have been discussed in literature. ' In subspace methods, in the case of atmospheric radar signals, the normalized eigenvalues ( λ ) of auto covariance matrix (Eqn. 6) are sequenced in descending order. he response curve is obtained by taking gradient on the normalized eigenvalues. he valley point is identified such that magnitude of gradient of eigenvalues increases abruptly (10 db and above) and also the order (p) is minimum. Since sub space methods assume the signal into signal sub space and noise subspace, p numbers of eigenvalues and corresponding eigenvector sets (sinusoids) are assigned into signal sub space and rest of things are assigned into noise subspace. It was observed that MUSIC, one of the subspace methods, can be useful to de-noise the signal (like atmospheric radar signals) and may not be useful for parameter (spectrum width) retrieval. hough EV is derived from MUSIC through eigenvalue weighting, its performance in obtaining parameters is observed to be efficient due to the contribution of eigenvalues which are not uniform or zero valued numbers for atmospheric radar signals. It is noted that there exists much uncertainty in parameters if the number of sinusoids are chosen lesser or greater than p. It is observed that number of sinusoids less than p leads to line spectrum and that more than p leads to unwanted multiple peaks within spectrum width. 3. System description and data processing MU radar located in Shigaraki, Japan ( 34 85 N,136 10 E ) has a large circular antenna array of 110 m in diameter with 475 crossed Yagi elements, the peak transmission power of 1 MW, and the bandwidth of 3.5 MHz. his frequency band is divided into five overlapping sub bands with the interval of 0.25 MHz and the bandwidth of 1.65 MHz. hese sub bands are alternatively switched by pulse-to-pulse manner for obtaining phase information about targets. For receiving, the antenna array can be separated to 25 sub-arrays (channels) that have independent signal processing and storage units for spatial interferometry. he observation is conducted with full array of transmission (beam width 3.6 o ) in vertical direction for PBS technique. A 1 s transmitted pulse is used for 150 m range resolution. he sampling time including all coherent integrations is set to be 0.1024 s and each record of 256 time series points are obtained for 25 channels.he data collected from 25 channels are subjected to PBS technique
to synthesize new beams at 1.5o tilt angle with 32 equally spaced azimuth positions. he power spectra at different line of sight angles are independently obtained as mentioned in the sections II for 5 overlapping sub bands and the sequence are repeated for three times. In this way, 15 power spectra is obtained from one record itself. All the fifteen (5x3) spectra are integrated to improve the SNR. From the average spectrum, zeroth order (total power) and first order (mean velocity) moments are calculated through adaptive moments estimation method [10]. hus, radial velocities from corresponding line of sight angles are readily obtained. As a result, the horizontal wind components i.e. zonal and meridional velocities are derived by least squares sense. 4. Results and discussion In this section, the horizontal wind components derived by PBS technique (1.5o tilt angle with 32 beam configuration) using Capon beamforming method have been compared with DBS and GPS sonde estimated winds in near time. As the moments are obtained through frequency domain, performances of various spectral estimation methods, in deriving atmospheric winds are quantitatively analyzed. he comparison of performances of spectral estimators in deriving winds is given in Fig.1. It is observed that PBS derived winds are shown in comparison with standard DBS derived winds up to a height about 20 km. In DBS observational method, tilt angle was 10 o. Fig.1 reveals that horizontal wind velocities can be derived reliably by tilting the beam at 1.5o itself say within transmit beam width. Earlier study has reported [17] wind profiling from 6 to 15 km with a temporal resolution of 10 min using Imaging Doppler Interferometry (IDI) technique and about 10 km height with a temporal resolution of 5 min by Coherent Radar Imaging (CRI) using Capon s method [12] in time domain analysis. In simulation study, it has been realized that subspace methods improve SNR for atmospheric signals compared to Fourier based method. Particularly MUSIC improves SNR of the signal compared to other two spectral estimators. In the case of atmospheric signal, the power spectral distribution is of Gaussian shaped. But, the power spectrum produced by MUSIC is sharply peaked (line/pseudo spectrum) at the frequencies of the sinusoidal components of the signal. hough it is an advantage by de-noising the noise fluctuations in atmospheric signals through eigen-decomposition, the retrieval of spectrum width by MUSIC is not reliably observed to be same as Fourier based method. he spectrum width derived by Fourier based method can be reliable and so it has been Fig.1 Vertical profile of horizontal winds derived using PBeribuge g-13(d)-5( )160(co)6(e/pa-5(o)-5(v)7(ed)-7l )-37(w-10(5(s)3( )-98(3
considered as a reference in this paper. he impact of error in spectrum width retrieval by MUSIC has led to uncertainty in the measurement of radial Doppler frequency and thus horizontal winds. So, there are derivations in winds estimated by MUSIC in comparison with standard DBS observed winds. Hence, MUSIC could not be considered as a best spectral estimation method for wind estimation on atmospheric radar data. It is clearly noticed in Fig.1. In addition, Fourier based spectral estimation methods are more suitable for atmospheric radar signals. But,
5. Conclusion PBS technique has been used to derive horizontal winds using MU radar data. A detailed study has been investigated to encompass the best spectral estimator suitable for PBS wind estimates. In this study, the best performance and accuracy of EV in wind estimation have been revealed to identify and trace the atmospheric signals in noisy environment, which help the complete wind profiling up to the maximum height and is an alternate method to Fourier based spectral estimation. he winds derived using EV spectral estimator are in very good agreements with standard DBS and GPS sonde observed winds in near time. he systematic improvements done for PBS based wind observation have revealed the complete wind profiling up to the maximum height about 20 km with a temporal resolution about 1.3 minutes. Statistical analyses have also shown the consistency and reliability of EV in deriving the winds. he study has brought out the advantage of wind profiling using PBS for high temporal resolution compared to DBS based wind estimation with almost same height coverage. Such high temporal estimation can be reliably used to study the fast changing non-homogeneous wind fields during disturbed atmospheric condition. References [1] E Boyer., M. Petitdidier., W. Corneil., C. Adnet., P. Larzabal, 2001: Application of model-based spectral analysis to wind-profiler radar observations. Ann. Geophys., 19, 815-824. [2] M.Y Chen.,.Y. Yu, Y.H. Chu, W.O.J. Brown., S. A. Cohn., 2007: Application of Capon technique to mitigate bird contamination on a spaced antenna wind profiler. Radio Sci., 42, 1-12. [3] B.L Cheong., M.W Hoffman., R.D Palmer., S.J Frasier., F.J Lopez-Dekker., 2004: Pulse pair beamforming and the effects of reflectivity field variation on imaging Radars. Radio Sci., 39. [4] B.L Cheong.,.Y Yu., R. D Palmer., K.F Yang., M. W Hoffman., S. J Frasier., F. J Lopez- Dekker., 2008: Effects of wind field inhomogeneities on Doppler beam swinging revealed by an imaging radar. J. Atmos. Oceanic echnol., 25, 1414-1422. [5] S Fukao., Sato., suda., SEB1 0 0 1 218.69 40EB4(ys)] JEh