Post beam steering techniques as a means to extract horizontal winds from atmospheric radars VN Sureshbabu1, VK Anandan1, Toshitaka Tsuda2 1ISTRAC, Indian Space Research Organisation, Bangalore -58, India 2Research Institute for Sustainable Humanosphere (RISH), Kyoto University, JAPAN (Dated: 30 May 2012) (V.N.SURESHBABU) Abstract 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. The 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 MST 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. The antenna array is also capable of steering the beam electronically using phase shifters in transmit and receive path. The experiment was conducted with full array of transmission (beam width 3.6o) in vertical direction. Signals received from spatially separated antennas are made to interfere constructively by phasing the received signals within the transmit beam width. This technique is used to synthesize the beams in the desired directions and so called as Post Beam Steering Technique (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. The beam steering can be optimized by weighting vectors through beamforming approach like Capon method [2], [9]-[12]. Then 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. The beams are independently synthesized for an off zenith angle (tilt angle) of 1.5o and equally separated 32 different azimuth angles within the transmit beam width (3.6o). The 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. The obtained results are compared with other wind observational methods like DBS and GPS sonde in contiguous time. This 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 The 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. Third, 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 T (1) S(t) = [S1 (t) S 2 (t) S 3 (t) SN (t)] where S(t) is the received signal matrix at time t along zenith direction and the superscript T 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)=( aθ, ) S(t) (2) T where X(t) = [X1 (t) X 2 (t) X 3 (t) XN (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) -j(Φ ) T a(θ, ) = [e12 e e3N e ] (3) -j(Φ ) -j(Φ ) -j(Φ ) where e12 ,e ,...., 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 Φi in the above Eqn.3 can be given as 2π Φ = (D sinθsin +D sinθcos +D cosθ) iλ ix iy iz th where is wavelength of transmitted signal and Dix , D iy , D iz are the components of position vector of i 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). The array covariance matrix R in the forward case can be written as HH R= E X(t)X (t) = a (θ, φ) Rs a (θ, φ)+ Q (5) where Rs and Q are the signal (steered) and noise auto covariance matrices with dimension NN, 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 ∧ 1 m H RXX= (k) (k) (6) m k=1 where m is number of points in the time series signal. The 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. The 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. This 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. The weight vector w is given by -1 Ra(,) w s (8) H -1 a(,)(,) Rs a The 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. The 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.