This docuent is provided by JAXA. > REPACE TIS INE WIT YOUR PAPER IDENTIFICATION NUMBER (DOUBE-CICK ERE TO EDIT) < 2 detais of the PAWR have been pres

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1 This docuent is provided by JAXA. > REPACE TIS INE WIT YOUR PAPER IDENTIFICATION NUMBER (DOUBE-CICK ERE TO EDIT) < 1 Bea Foring on Fast-Scanning Phased Array Weather Radar Eiichi Yoshikawa, Tooo Ushio, Zen Kawasaki, Satoru Yoshida, Takeshi Morioto, Fuihiko Mizutani, and Masakazu Wada, Meber, IEEE Abstract A fast-scanning phased array weather radar (PAWR) with a digita bea foring receiver is under deveopent. It is iportant in bea foring for weather radar observation with teporay high resoution to for a stabe and robust ainobe and adaptivey suppress sideobes with a sa nuber of puses in order to accuratey estiate precipitation profies (refectivity, ean Dopper veocity, and spectra width). A iniu ean-square error () foruation with a power constraint, proposed in this paper, gives us adaptivey fored beas that satisfy these deands. The bea-foring ethod is copared in various precipitation radar signa siuations with traditiona bea-foring ethods, Fourier and Capon ethods, which have been appied in atospheric research to observe distributed targets such as precipitation, and it is shown that the ethod is appropriate to this fast-scanning PAWR concept. Inde Ters Phased array digita bea foring, distributed targets, fast-scanning weather radar I. INTRODUCTION IN the quest to rapidy detect hazardous weather phenoena and provide warning inforation, a weather radar syste using a phased array antenna syste that achieves high speed scans has been attracting attention. The Coaborative Adaptive Sensing of Atosphere (CASA) project has proposed a phased array radar network to efficienty observe precipitation by eectronic scan, steering beas for weather phenoena adaptivey [1], [2]. In [3], a uti-function phased array radar for not ony detecting weather phenoena but controing air traffic and tracking non-cooperative airpanes by using a rapid scan has been proposed. For the fast scanning purpose, CASA Manuscript received January 10, This work is supported by Toshiba Corporation and the Nationa Institute of Inforation and Counications Technoogy (NICT). Eiichi Yoshikawa was with Osaka University, Osaka, Japan and Coorado State University, CO, USA, and now is with Japan Aerospace Eporation Agency (JAXA), Tokyo, Japan (phone: +81-(0) ; e-ai: yoshikawa.eiichi@jaa.jp). Tooo Ushio is with Osaka University, Osaka, Japan. Zen Kawasaki is with Osaka University, Osaka, Japan and Egypt-Japan University of Science and Technoogy (E-JUST), Aeandria, Egypt. Satoru Yoshida is with Osaka University, Osaka, Japan. Takeshi Morioto was with Osaka University, Osaka, Japan, and now is with Kinki University, Osaka, Japan. Fuihiko Mizutani and Masakazu Wada are with Toshiba Corporation, Tokyo, Japan. Fig. 1. Antenna array of PAWR. 128 sotted waveguide antennas are aigned verticay for rapid scanning. IP1 radar, Rapid-Scan DOW, Atospheric Iaging Radar, RaPo, MWR-05XP, and so on has been proposed and deveoped [4], [5], [6], [7], [8]. At present we are deveoping a phased array weather radar (PAWR) to rapidy scan in 3-D and finey detect hazardous weather phenoena such as tornadoes and downbursts with a ifetie beow 60 in and horizonta scae on the order of D array antenna (horizonta poarization) consisting of 128 eeents for eevation is instaed in the PAWR, as shown in Fig. 1. A fan bea is transitted via feeding power (430 W) into 12 to 24 eeents. After receiving and saping scattered signas with a 128 eeents into 128 anaog-to-digita converters (ADC; 14 bits, 48 Mz), adaptive digita bea foring (DBF) is perfored to sharpen the fan bea. Thus, precipitation at severa eevation anges is siutaneousy observed and tepora resoution is drasticay iproved. Athough the PAWR is under deveopent and any specifications are not fied, the transitting fan and receiving sharp bea widths are epected as 10 and 1 deg, respectivey, for eevation, which achieves a D esh with a sensitivity of 18 dbz (equivaent to about 0.5 /h) at the aiu range of about 25 k and 10 sec per voue scan whie transitting around 16 puses for a direction. Other

2 This docuent is provided by JAXA. > REPACE TIS INE WIT YOUR PAPER IDENTIFICATION NUMBER (DOUBE-CICK ERE TO EDIT) < 2 detais of the PAWR have been presented in [9] (These paraeters ay change in the future). A significant probe with fan bea transission is huge sideobes of strong echoes fro strong precipitation ces or cutter, which are aost two ties stronger than a sharp bea transission and reception in db. For eape, whie a sharp bea transission and reception has a first sideobe eve of -26 db fro the ain obe for the center direction, a configuration of unifor and sharp beas has a first sideobe eve of -13 db in the sae ange. Many adaptive DBF ethods have been proposed to achieve sideobe reduction in a phased array antenna syste. In atospheric radars observing a scattering voue fied with partices, the Capon ethod has been used [10], [11], [12], [13], [14], [15] for both bea foring and ranging. The Capon approach requires a sufficient nuber of sapes (puses) to estiate accuratey and cannot work we with 16 puses in the PAWR. Aternativey, a direction-of-arriva (DOA) approach for point targets based on the iniu ean-square error () fraework has been proposed [16]. This approach does not epoy spatia sape covariance inforation, which degrades DOA estiation in the Capon or soe other DOA ethods in cases correated signas are scattered in different directions, on the prior assuption that they are uncorreated. Therefore, the nuber of puses is not essentia in this fraework. In this paper, a odified approach for sideobe reduction and accurate estiation for distributed targets with fewer puses on the PAWR is proposed and evauated. For eteoroogica appication, not ony DOA but aso estiation of received power and shifted phase fro distributed targets is iportant, which derive physica paraeters of precipitation. By the odifications, gain constraint and convergence criteria, these received power and phase are correcty estiated. This paper is organized as foows. In Section II, the signa ode of phased array radar and the agorith are eaborated. Two traditiona ethods, Fourier and Capon bea foring, are introduced and are used for perforance coparisons in the foowing sections. In Section III, estiation accuracies of these three ethods are evauated and copared with the use of nuerica siuations, in which signas are generated by a precipitation radar signa siuator. In Section IV, estiation resuts for precipitation are described with the use of easureents fro the CSU-CI radar. II. METODOOGY A. Signa Mode Assuing that a inear-spaced phased array antenna with N antenna eeents, th tie sape of a received cope apitude y (N-vector) is epressed by an associated cope apitude (M 1-vector, M N) in an arbitrary range bin, an N M-vector S which consists of spatia steering vector s(θ), and an additiona Gaussian noise vector v as y S v, (1) y y y, (2) y T, 0,1, N 1 T, 0,1, M 1, (3) S s s s, (4) 0 1 M 1 ep j j s 1 1 ep N 1, (5) and n 2 dnsin. (6) [ ] T is a transpose. λ is waveength and d is spacing of neighboring antenna eeents. In the PAWR, θ eans eevation ange, and corresponds to M-separated precipitation profies in eevation anges. In adaptive array signa processing, estiated precipitation profies are cacuated as ˆ ˆ ˆ, (7) ˆ T, 0,1, M 1 y ˆ, w, (8) w is an N cope weighting vector for received cope apitudes of each antenna eeent. [ ] is a cope-conjugate transpose. B. Fourier Bea Foring (FR) Fourier bea foring (FR), aso known as a atched fiter, is the ost basic ethod in phased array radars for steering a bea in a direction by unifor phase shift. In FR, the weighting cope vector (FR weight) is epressed as w FR s N. (9) Thus, a precipitation profie estiated by using FR weight is equivaent to the resut of a Fourier transfor of y. C. Capon Bea Foring (CP) The Capon bea-foring ethod (CP) iniizes received power subject to a constraint in which a desired direction is constant [10], [11], [12], [13], [14], [15]. In CP, weighting cope vector is epressed as 1 R y s w CP, 1 s R y s (10) R 1 y y. (11) y 1 is the nuber of tie sapes. D. Bea Foring bea foring for adaptive phased array was proposed in [16], it is based on the sae concept as an adaptive puse copression (APC) agorith [17], [18], [19]. To estiate received power accuratey, we appy a concept of gain-constrained APC [20], whose constrained cost function is 2 J E Re 1 w y w s, (12) E[ ] is epectation, Re{ } is the rea part, and λ is a T

3 This docuent is provided by JAXA. > REPACE TIS INE WIT YOUR PAPER IDENTIFICATION NUMBER (DOUBE-CICK ERE TO EDIT) < 3 agrange utipier. Miniizing Eq. (12), the weighting cope vector of bea foring ( weight) is epressed as 1 R s w, (13) 1 s R s R SR S R v. (14) R is a covariance atri of as 1 R E I M M. (15) 1 is the adaard product and I M M is an M M identity atri. Eq. (15) is based on the assuption that signa sources fro different positions are teporay uncorreated. R v is a noise covariance atri epressed as 2 R v Evv v I M M (16) σ 2 v is variance of thera noise, which is assued as a white noise. Coparing Eqs. (14) and (15) to Eqs. (10) and (11), it is cear that the cost function with gain constraint reaches the sae soution as CP. The advantages of beaforing is derived fro a way to deterine the covariance atri as indicated in Eqs. (15) and (16), an unknown vector is incuded. weight and soution are cacuated iterativey with the use of prior inforation as foows. 1) Prior Inforation As prior inforation, the soution of FR is substituted in Eq. (15). (0) 1 R ˆ FR ˆ FR 1 I M M, (17) ˆ ˆ ˆ ˆ, (18) (23) TABE I CARACTERISTICS OF NUMERICA SIMUATION Paraeter 4) Re-iteration i+1-iterative R is cacuated by i-iterative soutions. 1 R i ˆ ˆ 1 1 I M M, (24) And then, return to 2). In this paper, the iteration is terinated with a threshod of noraized ean square errors (NMSE) between i-iterative and i-1-iterative soutions, ( i1) 2 ˆ ˆ M,, 1 1 i, (25) M 1 ( i 1) 2 ˆ, 1 NMSEs in each range bin are averaged. ereafter, an i-iterative is caed (i), and, if it satisfies Eq. (25), it is caed c(i) as a converged resut. T III. NUMERICA SIMUATIONS FR FR,0 FR,1 FR, M 1 To evauate the perforance of bea foring and to ˆ FR w y, FR. (19) copare it with other traditiona bea-foring ethods, radar is the nuber of tie sapes as in CP ethod. signa siuations were carried out. The siuation signas were generated by a procedure described by Chandrasekar et a. 2) Deterination of Weights [21] that generates a tie series of received signas having a M weights are deterined by i-iterative R. Gaussian spectra shape with window effect and randoness 1 (see aso [22]). Eevation profies of power, ean radia R s w, (20) veocity, and spectra width, which are corresponding to, are 1 s R s deterined in each siuation ode. Then, received signas, y, are cacuated as Eq. (1) with thera noise (noise eves are aso deterined arbitrariy in each ode). ere, each antenna R SR S R v. (21) eeent is assued as onidirectiona. Characteristics of this siuation are shown in Tabe I. Frequency, the nuber of 3) Coputation of soutions antenna eeents, interva of neighboring antenna eeents, tit M soutions are cacuated by i-iterative w. ange of antenna, and puse repetition frequency are designed ˆ ˆ ˆ ˆ T paraeters of PAWR (they ay change because the syste is,0,1, M 1 under deveopent). Athough 256 puse sapes woud not be, (22) transitted in the PAWR observation, this siuation is carried out to ake a coparison with CP, which is not appropriate with a sa nuber of puses. A wide range of eevations fro ˆ w y,. -30 to 90 deg is considered. Since the PAWR transits a fan Vaue frequency 9.4 Gz nuber of antenna eeents (N) 128 spacing of neighboring antenna 16.5 eeents (d) tit ange of antenna 30 deg puse repetition frequency 5.4 kz nuber of puses () 16 and 256 nuber of associated eevation anges (M) 1201 (every 0.1 deg fro -30 to 90 deg) convergence criteria δ i < or 20th iteration count

4 This docuent is provided by JAXA. > REPACE TIS INE WIT YOUR PAPER IDENTIFICATION NUMBER (DOUBE-CICK ERE TO EDIT) < 4 Fig. 2. Eapes of ean power estiates and fored bea patterns for two-point targets and distributed targets. Pane (a-1) shows the ean power estiates for two targets paced at eevations of 25 and 5 deg, respectivey, in which bue soid, green soid, red dotted, and red soid ines indicate resuts of FR, CP, (1), and c, respectivey. Back circes and a dashed ine indicate truth and given noise eve. In Pane (a-2), a fored bea pattern grazing at an eevation ange of 25 deg (indicated by a back dashed ine) in the case with the two point targets are shown, in which four coored ines indicate each ethod, as Pane (a-1). In Panes (b-1) and (b-2), respectivey, those for the distributed targets are shown. A back soid ine in Pane (b-1) is accuuated truth, which is derived fro convoution between truth and the ainobe of FR. bea with -3-dB bea width of about 10 deg, we ay dea with a narrower range of eevation, which gives us ess coputationa cost. owever, the fan bea is not considered here because these bea-foring ethods are signa processing ony for the receiver side and are independent on transission. Additionay, the siuation with this wide range of eevation obviousy shows the differences in these ethods. The threshod of δ i for convergence of is set to beow (-30 db). Even if it does not satisfy the standard, the agorith is terinated in the 20th iteration. A. Point Targets and Distributed Targets The Capon and ethods were originay designed for detection of point targets such as aircraft. It is iportant to understand the differences in their perforance for distributed targets such as precipitation. In Panes (a-1) of Fig. 2, an Agorith TABE II MEAN POWER ESTIMATES FOR TE POINT TARGETS For the eft Target (db) For the Right Target (db) FR CP (1) c Truth eape of ean power estiates for two point targets is shown. It is assued that the two targets are paced at eevations of 25 and 35 deg, respectivey, in the sae range and aziuth bin with ean received power of 20 and 50 db, ean Dopper veocities of 8 and 10 /sec, and spectra widths of 1 /sec, as indicated by the back circes. The ean power of additiona white noise is assued to about 10 db as indicated by the back dashed ine. To show the resuts of CP, 256 puses are given. The bue, green soid, red dot, and red soid ines are FR, CP, (1), and c, respectivey. The estiated resuts of the two eevations are suarized in Tabe II (the truths do not stricty agree with the input paraeters indicated above because the radar signa siuator gives randoness). FR correcty estiates the received power of the right (strong) target; however, it has the poorest resoution and highest sideobes. The eft (weak) target is aost hidden and its received power is overestiated by about 2.4 db by sideobes of the right (strong) target. Athough the CP correcty detects both targets with high resoution and sufficienty suppresses sideobes under the noise eve, both received powers are underestiated, with 2.7 and 3.1 db for the eft and right targets, respectivey. This underestiation is caused by a correation between both the signas (it is we known that CP works when received signas are independent). Therefore, this probe is resoved with the use of ore puses. c shows high resoution and ow sideobes equivaent to CP and

5 This docuent is provided by JAXA. > REPACE TIS INE WIT YOUR PAPER IDENTIFICATION NUMBER (DOUBE-CICK ERE TO EDIT) < 5 Fig. 3. Eapes of ean power, ean Dopper veocity, and spectra width estiates cacuated with 16 and 256 puses. Those with 16 puses are shown in Panes (a-1), (a-2), and (a-3), and those with 256 puses are shown in Panes (b-1), (b-2), and (b-3), respectivey. Bue soid, green soid, red dotted, red soid, back dotted, back soid, and back dashed ines are FR, CP, (1), c, truth, accuuated truth, and noise eve, as in Fig. 1. the best power estiation resuts for both the targets. A oss of signa-to-noise ratio (SNR) is aso not seen. It is shown that the soutions converge step by step through FR, (1) to c(8). In Pane (a-2), fored bea patterns of each ethod for an eevation of 25 deg are shown. CP and c for a nu at an eevation of 35 deg. That is why detection and power estiates of the eft target are not affected by the right target in these ethods. In contrast to Pane (a-1), in which resoution of CP and c(8) ook very sharp, it is shown that their bea widths are aost equivaent to FR. This eans that these bea-foring ethods never sharpen ainobes, which are essentiay deterined by antenna size, and ony suppress sideobes adaptivey. In Pane (b-1), an eape of ean power estiates for distributed targets is shown. Aso, the ean power of additiona white noise is assued to about 10 db as indicated by the back dashed ine. FR shows sideobes beow an eevation of 27 deg, and a correct shape of distributed targets with about +9 db offset fro the truth (corresponding absoute square of ) beyond the eevation, which is caused by a convoution between a fored bea pattern and the truth. Accuuated truth, which is cacuated by a convoution of ainobes of FR and distributed target, agrees with FR beyond 27 deg eevation. Athough CP suppresses the sideobes that FR has beow 27 deg eevation, it underestiates caused by correations between signas ean power in a eevations. Though the CP soutions get coser to the accuuated truth with ore puses as in the point-target siuation, this characteristic of CP is a serious probe for precipitation radars because the distributed targets change continuousy, and a correation between narrow-band rando signas with siiar frequencies is high. Copared with these ethods, c correcty estiates ean power without underestiation, sideobes, and oss of SNR. As shown in Pane (b-2), CP and c suppress sideobes adaptivey and ainobes are not sharpened for distributed targets as in the point-target siuation. For distributed targets, these bea-foring ethods estiate an accuuated ean power with weights of their ainobes different fro those for point targets, and this is copetey consistent with the theory of radar equation for distributed targets. B. Estiation Accuracy for Distributed Targets Estiation accuracies of these ethods are copared in three paraeters ean power, ean Dopper veocity, and spectra width by a radar signa siuation assuing distributed targets with two precipitation ces. Eapes of ean power, ean Dopper veocity, and spectra width estiates with 16 and 256 puses are shown in Fig. 3. ere, the ean power of additiona white noise is assued to about -10 db as indicated by the back dashed ine as in Panes (a-1) and (b-1). Mean power, ean Dopper veocity, and spectra width estiates of these ethods and accuuated truth are cacuated with the use of the ost genera ethods based on a tie series, which is eaborated in Chapter 5 (5.10 and 5.11) of [23]. In Panes (a-1) and (b-1), FR shows high sideobes in

6 This docuent is provided by JAXA. > REPACE TIS INE WIT YOUR PAPER IDENTIFICATION NUMBER (DOUBE-CICK ERE TO EDIT) < 6 Fig. 4. Eapes of eevation Dopper veocity spectrographs at 16 and 256 puses. In Panes (a-1), (a-2) and (a-4), spectrographs of accuuated truth, FR, and c are shown. Spectrograph of CP, corresponding to Pane (a-3), is not shown because of the over arge underestiation with 16 puses. Those of accuuated truth, FR, CP, and c with 256 puses are shown in Pane (b-1), (b-2), (b-3), and (b-4), respectivey. ean power estiates, and correcty estiates the ony in two yeow coored areas in eevations fro 20 to 30 or fro 55 to 65 deg, in which strong distributed targets eist. As ean power, Panes (a-2) and (b-2) show that ean Dopper veocity estiates of FR are cose to accuuated truth in the yeow coored areas. Spectra widths of FR are correcty estiated ony in the right yeow coored area as shown in Panes (a-3) and (b-3). It sees that the nuber of puses is aost independent of estiated accuracies of FR. There is an obvious difference between CPs with 16 and 256 puses. In Panes (a-1), CP has too arge underestiations and is not described in the pot range. Therefore, estiated ean Dopper veocities and spectra widths in Panes (a-2) and (a-3), respectivey, are ikey eaningess. As shown in Panes (b-1), (b-2), and (b-3), CP resuts are better with a arger nuber of puses. owever, underestiations sti reain. c has good resuts, as in previous siuations, regardess of the nuber of puses. Since received power fro targets are uch saer than the additiona white noise in eevations beow 10 or above 70 deg, spectra widths of c are very arge, which corresponds to spectra width of white noise. Throughout Panes in Fig. 3, c s perforance is obviousy superior. A quantitative evauation of estiate accuracies appies to two regions of eevation; 1) beyond additive noise eve in TABE III ESTIMATION ACCURACIES beyond additive noise eve in eevations fro 13 to 77 deg (bue coored area) beyond additive noise eve in eevations fro 20 to 30 and 55 to 65 deg (yeow coored areas) = 16 = 256 = 16 = 256 ean bias Standard deviation ean bias Standard deviation ean bias Standard deviation ean bias Standard deviation ean power (db) FR ean Dopper veocity (/sec) spectra width (/sec) ean power (db) CP ean Dopper veocity (/sec) spectra width (/sec) ean power (db) c ean Dopper veocity (/sec) spectra width (/sec) Note: A bias of ean power is that a difference between an estiated power in db and an accuuated truth in db.

7 This docuent is provided by JAXA. > REPACE TIS INE WIT YOUR PAPER IDENTIFICATION NUMBER (DOUBE-CICK ERE TO EDIT) < 7 Fig. 5. Eapes of eevation Dopper veocity spectrographs 16 and 256 puses with anticipated strong ground cutters. In Panes (a-1), (a-2) and (a-4), spectrographs of accuuated truth, FR, and c are shown. Spectrograph of CP, corresponding to Pane (a-3), is not shown because of the too over underestiation with 16 puses. Those of accuuated truth, FR, CP, and c with 256 puses are shown in Pane (b-1), (b-2), (b-3), and (b-4), respectivey. eevation anges fro 13 to 77 deg (indicated by the bue area in Fig. 3), 2) beyond sideobes of FR in eevation anges fro 20 to 30 deg and 55 and 65 deg (indicated by two yeow areas). Estiation accuracies are vaidated by ean bias errors (ean of differences between estiated powers in db and accuuated truths in db) and standard deviations copared with accuuated truth with the use of 256 siuations signas with different rando nubers for both the radar signa siuator and additiona noise. In Tabe III, estiation accuracies with 16 and 256 puses in the two vaidated regions are suarized. Whie there are arge errors in the bue coored area, FR indicates good estiation accuracies in the yeow coored areas without affections of sideobes. On the other hand, FR s ean Dopper and spectra width estiates are worse than the other two ethods. The reason for this is shown in an eape of Dopper spectrograph shown ater. CP cannot output vaid resuts with 16 puses. Since ean power estiates have arge negative bias errors ess than -200 db, the other two estiates are no onger worthy of discussion. With 256 puses, the CP resuts are iproved, and it is cear that CP is not affected by sideobes. owever, CP s ean power estiates have negative biases. This negative bias is suppressed with a greater nuber of puses, as stated above. Spectra width estiates of CP have arge bias errors and standard deviations, which are not resoved with ore puses. c resuts indicate eceent accuracies. Regardess of the nuber of puses, c correcty estiates these three paraeters without sideobes. c has a bias error of db with 16 puses in the yeow areas, which is 2.2 ties higher than that of FR. Since c aso has a negative bias of -0.3 db even with 256 puses in the bue area, c tends to sighty underestiate ean powers with a arge agnitude. The eevation-dopper veocity spectrographs shown in Fig. 4 are very hepfu for understanding the characteristics of these ethods. Panes (a-2) and (b-2) show that signas containate each other by their sideobes in FR. This is why ean Dopper veocity and spectra width estiates are biased even if the arge signas do not appear to be containated in Panes (a-1) and (b-1) in Fig. 3. Pane (b-3) shows that the CP s Dopper spectrus in every eevation are stretched wider than the accuuated truth of Pane (b-1), which ead to the arge biases indicated in Tabe III. Focusing Dopper veocities around 0 /sec, spectrus are weakened because high correations between these signas affect CP s perforance. CP s spectrograph with 16 puses is not shown here because underestiations are too arge, as stated above. Copared with the, spectrographs of c in Pane (a-4) and (b-4) are very siiar to those of the accuuated truth in Panes (a-1) and (b-1). C. Ground Cutter The PAWR is designed to observe precipitation in urban areas in which it is anticipated that strong ground cutter and its sideobes significanty containate the desired signas. Ground cutter appears at eevations in which ground, trees, or

8 This docuent is provided by JAXA. > REPACE TIS INE WIT YOUR PAPER IDENTIFICATION NUMBER (DOUBE-CICK ERE TO EDIT) < 8 Fig. 6. Convergence processes of the agorith. Pane (a-1) shows convergence processes of δi aong iteration count, in which square and diaond sybos indicate those for Modes 1 and 2 with 16 puses, respectivey, and a back dashed ine is the threshod to judge if a soution is converged. Pane (a-2) shows convergence processes of ean NMSE between accuuated truth and soutions with 16 puses. Panes (b-1) and (b-2) shows those processes in the case with 256 puses. buidings eist in a desired range bin. Furtherore, ground cutter in other range bins around the desired one aso shoud affect the signas by tais of oduated puses by a receiver band width [23], [24] or their range sideobes if it s a puse copression radar [25], [26]. These bea-foring ethods never suppress ground cutter itsef but can itigate its sideobes. Additionay, with strong cutter signas, estiated resuts of coud be worse because it is obvious that the condition nubers of atri R is arge. In this section, estiated resuts are evauated with the use of the two-ce ode, as in the forer section, with the addition of ground cutter signas. The ground cutter eeents have a ean power of a Gaussian shape whose peak is positioned at 0 deg eevation with about 110 db peak power. Their ean Dopper veocities and spectra widths are 0 /sec and 0.2 /sec, respectivey, in a the eevations. This cutter signa is aso generated by the radar signa siuator stated above. Spectrographs of the three ethods with 16 and 256 puses are shown in Fig. 5. In this case, FR in Panes (a-2) and (b-2) has TABE IV NUMBER OF ITERATIONS FOR CONVERGENCE = 16 = 256 Mode 1 Mode 2 Mode 1 Mode 2 a in ean standard deviation sideobes too arge to detect the distributed signas, and CP in Pane (b-3) aso has arger underestiations than the no cutter case. c in Panes (a-4) and (b-4) correcty suppresses the sideobes of the strong ground cutter and ets the distributed signas appear regardess of the nuber of puses. Tabe III indicates estiated accuracies of c in this case. Mean biases and standard deviations are cacuated estiation resuts in eevations fro 20 to 30 deg and 55 and 65 deg (the two yeow areas). A the paraeters are aost the sae as Tabe II. D. Convergence of the Agorith It is iportant to know how to converge soutions in the iterations and to confir whether the converge condition for the terination, Eq (25), is correct. Of course, a process of convergence is dependent on distribution of signas. In this section, using the sae siuation odes as those in Subsections B and C (caed Modes 1 and 2), convergence processes of the agorith are vaidated. In Fig. 6, eapes of convergence processes are shown. Panes (a-1) and (b-1) show convergence processes of δ i, indicated in Eq. (25), with 16 and 256 puses, respectivey. Corresponding ean NMSEs in each range bin between (i) and accuuated truth are shown in Panes (a-2) and (b-2). In each case, δ i and the corresponding ean NMSEs decrease aong the iteration count, and the ean NMSEs sufficienty converge when δ i is under the threshod of -30 db (see Tabe I). Tabe IV

9 This docuent is provided by JAXA. > REPACE TIS INE WIT YOUR PAPER IDENTIFICATION NUMBER (DOUBE-CICK ERE TO EDIT) < 9 Fig. 7. Range-eevation cross sections of refectivity in a siuation based on data coected by the CSU-CI radar. Panes (a-1), (a-2), and (a-4) are refectivities with 16 puses of accuuated truth, FR, and c, respectivey. Pane (a-3), which is for CP, is not shown because of its etree underestiation. Those with 256 puses are in Panes (b-1) through (b-4). suarizes the nuber of iteration counts for convergence with 16 and 256 puses in the two siuation odes. The aiu, iniu, ean, and standard deviation of the nuber of iterations are derived fro 256 siuations, as in Subsections B and C. The ean vaue depends on the odes. converges faster in Mode I because the initia soution in Mode 2 is farther fro truth than Mode 1. The siuation with ground cutter with 16 puses takes the ost nuber of interactions, and the agorith reached the aiu nuber of 20 in 4 of 256 siuations. IV. APPICATION TO TE CSU-CI MEASUREMENTS To describe the perforance of these ethods, a siuation with precipitation data observed on the CSU-CI radar was carried out. The CSU-CI radar data provide ore reaistic profie of precipitation, which is not described in the forer siuations (for eape, arge gradients of refectivity). Additionay, the estiated resuts indicate which parts of precipitation structure works better than other ethods in. In an RI observation on Aug. 1, 2011, refectivity, ean Dopper veocity, spectra width, etc., were obtained in eevations fro to deg (aost 0.15 deg spacing) with -3-dB bea width of 1 deg. inear interpoation for each obtained paraeter gave precipitation profies with 0.1 deg spacing. Tie-series data with 16 and 256 puses were generated fro these paraeters by the radar signa siuator. Fig. 7 shows a range-eevation cross section of refectivity of accuuated truth, FR, CP, and c with 16 and 256 puses. This coparison ceary iustrates that c correcty detects precipitation profies. It is very difficut to visuay find out differences between accuuated truth (Panes (a-1) and (b-1)) and c (Panes (a-4) and (b-4)). In FR (Panes (a-2) and (b-2)), precipitation is not observed correcty beyond and beow strong echoes, especiay in ranges fro 20 to 35 k, due to high sideobes. The resuts of c indicate that c contributes to accurate detection of precipitation. One iportant advantage of c is that echo tops are ceary identified. In addition, precipitation structures at ow atitudes, in which precipitation has ore variabiity due to interactions with the ground surface, are accuratey estiated. It is aso cear that anvis in ranges fro 35 to 40 k are separatey described. In this data, CP s perforance (Pane (b-3)) is worse than the forer siuations because input Dopper veocities are siiar aong eevations (Pane (a-3) is not shown because of arge underestiation as above). Even in a convective rain ike this sape, signas fro precipitation are highy correated and, therefore, CP needs a arger nuber of puses. It is aso shown here that the c perforance is not dependent on the nuber of puses. V. CONCUSION At present we are deveoping a phased array weather radar (PAWR) to rapidy scan and finey detect hazardous weather phenoena with spatia resoution of D esh and

10 This docuent is provided by JAXA. > REPACE TIS INE WIT YOUR PAPER IDENTIFICATION NUMBER (DOUBE-CICK ERE TO EDIT) < 10 tepora resoution of 10 sec per voue scan. The ain concept of this radar is fan bea transission and sharp bea reception, which drasticay acceerate scan speed. Transitting and receiving beas are fored by anaog phase shift and DBF, respectivey. To accopish this stye of observation, it is very iportant to suppress bea sideobes because the sideobes of the two-way antenna pattern are aost two ties higher than fora sharp bea transission and reception. Though any digita bea-foring ethods to suppress sideobes have been proposed, aost a of the are designed for target detection. Not ony sideobe suppression but aso estiation accuracy is necessary in weather radar observation. In this paper, a bea-foring ethod based on is proposed, and its perforance for the distributed targets such as precipitation is evauated. Because the bea foring proposed in [16] does not have any constraint for iniization, the power of fored ainobe is unstabe. In this paper, estiation accuracies are iproved by the addition of a gain constraint as in [20] and a convergence condition based on NMSE. Perforances are vaidated by nuerica siuation. Generated data siuate precipitation, which has narrow band rando signas whose Dopper spectru is a Gaussian shape with a center frequency and spectra width corresponding to otions of radiated precipitation partices. Siuation resuts indicate that the agorith adaptivey suppresses sideobes and correcty estiates power, ean Dopper veocity, and spectra width. It is aso confired that those perforances are superior to FR and CP, which are traditionay appied to phased array radars for distributed targets. Though CP aso suppresses sideobes of undesired signas, it needs a arge nuber of puses to avoid underestiations. In contrast, shows eceent perforance even with 16 puses; therefore, is appropriate for the PAWR, which obtains around 16 puses per singe direction to scan rapidy. In 256 siuations of two precipitation ces with 16 puses, ean biases of ean power, ean Dopper veocity, and spectra width are db, 0.05 /sec, and 1.53 /sec, and standard deviations of ean power, ean Dopper veocity, and spectra width are 2.17 db, 1.58 /sec, and 2.11 /sec, respectivey (beyond additiona nose eve). Additionay, it is anticipated that strong ground cutter containates the desired distributed signas because the PAWR is designed to be instaed in urban area. In nuerica siuations with strong ground cutter, shows perforance as good as siuations without ground cutter. Though the ethod never suppresses ground cutter itsef, sideobes of ground cutters, which significanty containate in high eevation anges, are itigated. This heps a foowing ground cutter fiter work we. Siuations with data obtained by the CSU-CI radar were aso carried out. Though this evauation with data obtained in the CSU-CI radar does not assure that the agoriths perfor as we as with rea data obtained in the PAWR, shows eceent perforance even with these radar signas data representing precipitation ore reaisticay. These resuts indicate that this approach can be appied to puse copression weather radars for ranging with high resoution [27], [28], [29]. In range signa processing, signas outside of processing window often containate estiation resuts ore than in DBF processing. This probe coud be soved by appying the approach with an etended processing window, as shown in [17]. For practica use, any kinds of additiona noises such as caibration errors in each eeent, utua couping between eeents or between an antenna syste and a radoe, diffraction of a water coated radoe, quantization error in digita saping, and so on, disturbs the signa ode, Eq. (1). owever, these errors coud be soved by appying a odified signa ode as indicated in [16]. As a future work, we wi carry out these error anayses, which are indicative for designing the PAWR. Aso, coputationa cost is an iportant issue in practica. Roughy estiating fro Eq. (20), the approach has a coputationa cost 20 ties ore than the CP with 20 iterations. As a faster approach instead of soe etent of deterioration, a odified approach has been proposed [19]. We wi ake a feasibiity study about this with the PAWR specification fied in near future. ACKNOWEDGMENT This work is supported by Toshiba Corporation and the Nationa Institute of Inforation and Counications Technoogy (NICT). The authors acknowedge Dr. V. Chandrasekar at Coorado State University, and Pat Kennedy, and Ji George at the CSU-CI Nationa Radar Faciity for providing the data fro the CSU-CI radar and for productive discussions. The authors aso acknowedge Dr. Toshio Iguchi and Dr. Shinsuke Satoh at NICT for productive discussions. REFERENCES [1] D. J. Mcaughin, et a., Short-Waveength Technoogy and the Potentia For Distributed Networks of Sa Radar Systes, Buetin of the Aerican Meteoroogica Society, vo. 90, Dec. 2009, pp [2] F. Junyent and V. Chandrasekar, Theory and characterization of weather radar networks, J. Atos. Oceanic. Techno., vo. 26, Ju. 2008, pp [3] D. S. Zrnic, J. M. Kipe, D. E. Forsyth, A. Shapiro, G. Crain, R. Ferek, J. eier, W. Benner, T. J. McNeis, and R. J. Vogt, Agie-bea phased array radar for weather observations, Buetin of Aerican Meteoroogica Society, vo. 88, Nov. 2007, pp [4] F. Junyent and V. Chandrasekar, The CASA integrated project 1 networked radar syste, J. Atos. Oceanic. Techno., vo. 27, Ju. 2009, pp [5] J. Wuran and M. Randa, An Inepensive, Mobie, Rapid-Scan radar, in 30th Int. Conf. on Radar Meteor. Soc., Oct [6] B. Iso et a., The Atospheric Iaging Radar (AIR) for igh-resoution Observations of Severe Weather, in 2011 IEEE Radar Conf., Kansas City, [7] A.. Pazany and. B. Buestein, Mobie Rapid-Scanning X-band Poarietric (RaPo) Dopper Radar, in 35th Conf. on Radar Meteor., Pittsburgh, [8]. B. Buestein, Michae M. French, Ivan PopStefanija, Robert T. Buth, and Jeffrey P. Knorr, A obie, phased-array Dopper radar for the study of severe convective stors, Bu. Aer. Meteor. Soc., vo. 91, , [9] F. Mizutani, M. Wada, T. Ushio, E. Yoshikawa, S. Satoh, and T. Iguchi, Deveopent of Active Phased Array Weather Radar, in 35th Conf. on Radar Meteor., Pittsburgh, [10] J. Capon, igh-resoution frequency-wavenuber spectru anaysis, in Proc. IEEE, 1969, pp [11] R. D. Paer, S. Gopaa, T.-Y. Yu, and S. Fukao, Coherent radar iaging using Capon s ethod, Radio Science, vo. 33, Dec. 1998, pp

11 This docuent is provided by JAXA. > REPACE TIS INE WIT YOUR PAPER IDENTIFICATION NUMBER (DOUBE-CICK ERE TO EDIT) < 11 [12] R. D. Paer, T-Y. Yu, and P. B. Chison, Range iaging using frequency diversity, Radio Science, vo. 34, Nov.-Dec. 1999, pp [13]. uce, M. Yaaoto, S. Fukao, D. ea, and M. Crochet, A frequency doain radar interferoetric iaging (FII) technique based on high-resoution ethods, Journa of Atospheric and Soar-Terrestria Physics, vo. 63, Mar. 2001, pp [14] B.. Cheong, M. W. offan, R. D. Paer, S. J. Frasier, and F. J. opez-dekker, Puse pair beaforing and the effects of refectivity fied variations on iaging radars, Radio Science, vo. 39, Jun [15] B.. Cheong, M. W. offan, and R. D. Paer, Efficient Atospheric Siuation for igh-resoution Radar Iaging Appications, J. Atos. Oceanic. Techno., vo. 21, Feb. 2004, pp [16] S. D. Bunt, T. Chan, and K. Gerach, Robust DOA Estiation: The Reiterative Superresoution (RISR) Agorith, IEEE Trans. Aerospace and Eectronic Syste, vo. 47, Jan. 2011, pp [17] S. D. Bunt and K. Gerach, Adaptive puse copression via estiation, IEEE Trans. Aerospace and Eectronic Syste, vo. 42, Apr. 2006, pp [18] K. Gerach and S. D. Bunt, Radar puse copression repair, IEEE Trans. Aerospace and Eectronic Syste, vo. 43, Apr. 2007, pp [19] S. D. Bunt and T. iggins, Achieving rea-tie efficiency for adaptive radar puse copression, in Proc IEEE Radar Conf., Boston, 2007, pp [20] T. iggins, S. D. Bunt and K. Gerach, Gain-constrained adaptive puse copression via an MVDR fraework, in Proc IEEE Radar Conf., Pasadena, 2009, pp [21] V. Chandrasekar, V. N. Bringi, and P. Brockwe, Statistica properties of dua-poarized radar signas, in Proc. 23rd Conf. on Radar Meteoroogy., Snowass, 1986, pp [22] D. S. Zrnic, Siuation of weatherike Dopper spectra and signas, J. App. Meteor., Vo. 14, Jun. 1975, pp [23] V. N. Bringi and V. Chandrasekar, Poarietric Dopper Weather Radar: Principes and Appications. Cabridge, U.K.: Cabridge Univ. Press, 2001, pp [24] R. J. Doviak and D. S. Zrnic, Dopper Radar and Weather Observations. San Diego, CA: Acadeic, 1993, pp [25] M. Skonik, Radar andbook. New York, NY: McGraw-i, 2008, pp [26] P. J. Peebes, Radar Principes. New York, NY: John Wiey & Sons, 1998, pp [27] T. Mega, K. Monden, T. Ushio, K. Okaoto, Z. Kawasaki, and T. Morioto, A ow-power high-resoution broad-band radar using a puse copression technique for eteoroogica appication, IEEE Geosci. Reote Sens. ett., vo. 4, Ju. 2007, pp [28] E. Yoshikawa, T. Ushio, Zen Kawasaki, T. Mega, S. Yoshida, T. Morioto, K. Iai, and S. Nagayaa Deveopent and initia observation of high-resoution voue-scanning radar for eteoroogica appication, Trans. IEEE Geosci. Reote Sens., vo. 48, Aug. 2010, pp [29] D V. Chandrasekar, M. Schwaer, M. Vega, J. Carswe, K.V. Mishra, R. Meneghini, and C. M. Nguywn, Scientific and engineering overview of the NASA Dua-Frequency Dua-Poarized Dopper Radar (D3R) syste for GPM Ground Vaidation, in Proc IEEE Internationa Geosci. And Reote Sens. Syposiu, onouu, 2010, pp Eiichi Yoshikawa (M 09) received B.S. degree in Aerospace Engineering fro Osaka Prefecture University, Japan, in 2005 and M.S. and Ph.D. degrees in Division of Eectrica, Eectric and Inforation Engineering fro Osaka University, Japan, in 2008 and 2010, respectivey. e was with Osaka University and Coorado State University, CO, USA as a post-doctora researcher in Currenty, he is with Japan Aerospace Eporation Agency (JAXA). is research speciaties are radar-based reote sensing, signa processing, and atospheric science. Tooo Ushio (M 00) received the B.S, M.S., and Ph.D. degree in eectrica engineering fro Osaka University in 1993, 1995, 1998, respectivey. e was with the Goba ydroogy and Ciate Center, untsvie A USA as a Postdoctorate Researcher fro 1998 to In 2000, he joined the Departent of Aerospace Engineering, Osaka Prefecture University. After being an assistant professor at Osaka Prefecture University, in 2006, he joined the Division of Eectrica, Eectric and Inforation Engineering, Osaka University Japan he is currenty an associate professor. is research speciaties are radar-based reote sensing, passive and active reote sensing of atosphere fro space-born patfors, and atospheric eectricity. Zen Kawasaki (M 72) received B.S., M.S., and Dr. Eng. Degrees in counications engineering fro Osaka University in 1973, 1975, and 1978, respectivey. In 1989, he joined the Departent of Eectrica Engineering, Osaka University. At present, he is a professor of the Division of Eectrica, Eectronic and Inforation Engineering. e is the dean advisor of Egypt Japan University of Science and Technoogy (E-JUST). is research ainy concerns the eectroagnetic copatibiity and atospheric eectricity. e is the feow of IEE Japan, and the president of Internationa Coission on Atospheric Eectricity (ICAE). Satoru Yoshida received the B.S degree in Physics fro Kobe University in 2001 and the M.S. degree in Counications Engineering fro Osaka University in e received the Ph.D. degree in Eectrica, Eectronic, and Inforation Engineering in 2008 fro Osaka University. After he was a research feow of the Japan Society for the Prootion of Science (JSPS Research Feow) fro 2008 to 2009, he joined the Frontier Research Base for Goba Young Researchers, Osaka University he is currenty an assistant professor. is research ainy concerns atospheric eectricity. Takeshi Morioto received the B.S and M.S. degrees in eectrica engineering and the Ph.D. degree in counications engineering fro Osaka University in 2000, 2002, and 2005, respectivey. In 2005, he joined the sae departent as a facuty eber. After being an associate professor at Osaka University, in 2012, he joined the Departent of Eectric and Eectronic Engineering, Facuty of Science and Engineering, Kinki University, Osaka Japan he is currenty an associate professor. is ain interests are in reote sensing and reative engineering. Fuihiko Mizutani received the B.S degree in science fro Kyushu University in 2001, and the M.S degree in science fro Nagoya University in In 2003, he joined Toshiba Corporation he is currenty a speciaist. is work ainy concerns weather observation and forecast syste. Masakazu Wada received the B.S and M.S. degrees in eectrica engineering fro Musashi Institute of Technoogy in 1992 and 1994, respectivey. e received the Ph.D. degree in Eectrica, Eectronic Engineering in 1997 fro Osaka University. In 1997, he joined Toshiba Corporation he is currenty a chief speciaist. is work ainy concerns weather observation and forecast syste.