Clutter suppression for high resolution atmospheric observations using multiple receivers and multiple frequencies

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1 RADIO SCIENCE, VOL. 45,, doi: /2009rs004330, 2010 Clutter suppression for high resolution atmospheric observations using multiple receivers and multiple frequencies T. Y. Yu, 1 J. I Furumoto, 2 and M. Yamamoto 2 Received 19 November 2009; revised 23 April 2010; accepted 12 May 2010; published 21 August [1] Range imaging (RIM) was developed in 1999 to improve range resolution by transmitting multiple frequencies. Since then, the capability of RIM for resolving fine atmospheric layer embedded in the conventional range gate has been demonstrated by a number of VHF and UHF atmospheric radars around the world. Nevertheless, like conventional radar, RIM is susceptible to clutter contamination that is contributed from antenna sidelobes. This work addresses this important issue in RIM for the first time by capitalizing the capability offered by multiple receivers and multiple frequencies with the goals of maintaining resolution gained by RIM and simultaneously, suppressing clutter contamination. Two techniques are developed where multi receiver signals from the same frequency are initially combined using Fourier or Capon beam forming for clutter suppression, and subsequently, these combined signals from multiple frequencies are processed using RIM for resolution enhancement. The two techniques are abbreviated by FB RIM and CB RIM. The mathematical representation of FB RIM and CB RIM is derived. Moreover, the 3 D atmospheric radar imaging (AIM) is applied to the multi receiver and multi frequency signals to image in the vertical direction. The feasibility of the three techniques is demonstrated and their performances are compared using both simulations and real data collected by the Middle and Upper (MU) radar in Japan. The FB RIM, which is similar to the conventional RIM, has the best performance of reconstructing a single thin layer embedded within the radar volume with high temporal resolution, but is prone to the contamination of moving clutter. On the other hand, although CB RIM and AIM retrieve the thin layer with slightly degraded performance, the clutter contamination can be significantly suppressed. Furthermore, for most cases AIM provides comparable or better performance of both layer reconstruction and clutter mitigation compared to CB RIM. Citation: Yu, T. Y., J. I. Furumoto, and M. Yamamoto (2010), Clutter suppression for high resolution atmospheric observations using multiple receivers and multiple frequencies, Radio Sci., 45,, doi: /2009rs Introduction [2] Many interesting and complex fine layer structures that are related to atmospheric dynamics and instabilities have been shown through the observations 1 School of Electrical and Computer Engineering and Atmospheric Radar Research Center, University of Oklahoma, Norman, Oklahoma, USA. 2 Research Institute for Sustainable Humanosphere, Kyoto University, Uji, Japan. Copyright 2010 by the American Geophysical Union /10/2009RS with Frequency modulated continuous wave (FMCW) radars [e.g., Richter, 1969; Gossard et al., 1971; Eaton et al., 1995; Ince et al., 2003]. However, significant bandwidth is required to achieve such superior range resolution, which is typically not available for pulse radar. Range imaging (RIM) was developed about a decade ago to improve the range resolution of pulse radar by transmitting several shifted frequencies on a pulse by pulse basis [Palmer et al., 1999; Luce et al., 2001]. Signals from multiple frequencies are combined coherently to image atmospheric structure within a conventional range gate. It has been shown that if signals are combined adaptively using the Capon method [Capon, 1969], finer scale 1of15

2 structure can be reconstructed compared to those using the Fourier method. The feasibility of RIM for high resolution observations in the boundary layer, troposphere, and stratosphere has been demonstrated using both UHF and VHF radars [e.g., Palmer et al., 2001; Chilson et al., 2003; Luce et al., 2006; Chen et al., 2009]. Although RIM has become mature, the technique is susceptible to clutter contamination, which hinders its applicability. This work addresses this important issue by exploiting additional signals from spatially separated antenna subarrays. [3] For atmospheric radar, both stationary clutter such as buildings or terrain and non stationary (moving) clutter such as birds and airplanes can significantly bias radar measurements. For conventional radar with a single receiver and frequency, several techniques have been developed to mitigate clutter contamination using signal statistics, wavelet, fuzzy logic, and neural network, just to name a few [e.g., Merritt, 1995; Jordan et al., 1997; Morse et al., 2002; Kretzschmar et al., 2003]. Those can be considering as filtering clutter contribution in time or frequency domains. Moreover, clutter contamination can be mitigated by applying a spatial filter to signals received from spatially separated receivers through a beam forming approach, which is also referred to as coherent radar imaging (CRI) in the atmospheric radar community [Woodman, 1997]. It has been shown that multi receiver offers the capability of suppressing ground clutter [Kamio et al., 2004; Allen and Ghavami, 2005] and moving clutter [Cheong et al., 2006; Chen et al., 2007]. In beam forming, signals received from multiple antenna subarrays with wide and vertically pointing beam patterns are properly phase shifted and summed to produce a focused receiving beam in the direction of interest. The Capon beam forming can adaptively suppress clutter and/or interference from different directions and provide improved angular resolution from the Fourier beam forming [Yu et al., 2000; Cheong et al., 2006]. It should be noted that the Fourier method is more robust compared to the Capon method if the angular distribution of return power to be imaged is relatively uniform. In this work, we capitalize on both RIM and beam forming technologies to develop three imaging techniques based on signals from multiple receivers and multiple frequencies with the goal of resolution enhancement and clutter suppression. [4] The idea of using multiple receivers and frequencies for atmospheric observations has been exploited for different applications and can be categorized into two approaches. In the first approach, signals from multiple receivers and multiple frequencies were considered independently. For example, both spatial and frequency domain interferometry techniques were used for lightning study [Röttger et al., 2000] and system phase calibration [Chen et al., 2002]. Recently, Chen et al. [2008] applied RIM and CRI independently to investigate Kelvin Helmholtz instability. The second approach requires the processing of multi receiver signals in conjunction with multi frequency signals to generate only one product. For example, 3 D atmospheric radar imaging was developed to image the atmospheric structure within the radar resolution volume in both angular and range directions by processing multi receiver and multi frequency signals simultaneously [Yu and Palmer, 2001; Hassenpflug et al., 2008]. In addition, Yu and Brown [2004] applied spaced antenna technique to RIM synthesized signals to obtain high resolution profiles of 3 D wind fields. In this work, three imaging techniques are introduced to combine multi receiver and multi frequency signals so that the resolution enhancement provided by RIM and clutter mitigation offered by beam forming can be achieved simultaneously. The first technique combines signals from multiple receivers using Fourier beam forming to synthesize return from a vertically pointing beam, and subsequently these synthesized signals from multiple frequencies are processed using Capon RIM. It is abbreviated as FB RIM. The second technique is the same as FB RIM except that Capon beam forming is used and thus is termed CB RIM. The third technique applies the Capon 3 D imaging technique [Yu and Palmer, 2001; Hassenpflug et al., 2008] to all the signals to image in the vertical direction and is termed AIM (atmospheric radar imaging). [5] The paper is organized as follows. In section 2, the mathematical representation of the three techniques is presented. In section 3, the three imaging techniques are tested and their resolution enhancement and clutter suppression performance are compared using simulation for two scenarios. In Scenario I, only the presence of a single thin atmospheric layer is considered and in Scenario II, signals from the layer structure are contaminated by moving clutter with different flight paths. In section 4, the application of the three techniques to atmospheric observations is further verified using the Middle and Upper (MU) atmospheric radar in Japan, which was recently upgraded to facilitate transmission of 5 different frequencies with a maximum spacing of 1 MHz and up to 25 digital receivers [Hassenpflug et al., 2008]. Finally, summary and conclusions are provided in section Enhancement of Range Resolution and Clutter Suppression [6] The main goal of this work is to reconstruct atmospheric structure within the conventional range gate when radar measurements are contaminated by moving clutter, by taking advantages of multi receiver and multifrequency configuration. Let the column vector S con- 2of15

3 sists of signals from M frequencies and N receivers in the following form. S ¼ ½s 1 s 2 s M Š T ð1þ where T is the transpose operator and s i =[s i1 s i2 s in ] is a row vector containing signals from N receivers and transmitted frequency f i. In other words, multi receiver and multi frequency signals are organized in the column vector of S with size of NM, where the first N elements are from all the receivers and the first transmitted frequency, the second N elements are from all the receivers and the second frequency, etc. The first and second subscript in s ij denote the respective frequency and receiver the signal is from. Two approaches are proposed in this work. In the first approach, multi receiver and multifrequency signals are processed sequentially as follows. Multi receiver signals are combined using either Fourier or Capon beam forming for each frequency to synthesize signals received from vertically pointing beam. It is expected that the Capon beam forming can adaptively suppress clutter contamination if it is present. Subsequently, these synthesized signals from M frequencies are RIM processed to image in the vertical direction. In the second approach, multi receiver and multi frequency signals are processed simultaneously using the Capon 3 D imaging to achieve both layer reconstruction and clutter mitigation. A detailed description of the two approaches is provided in the following sections Application of RIM to Beam Formed Signals [7] For each frequency, signals from N receivers are combined using the beam forming technique, where multi receiver signals are weighted and summed. As a result, signals S after beam forming can be written in the following equation: V ¼ w H c S ð2þ where H is the transpose conjugate operator of a matrix, V =[V 1 V 2 V M ] T is the column vector containing beam formed signals for M frequencies, and the weighting function w c is shown in the following equation: 2 3 w c w c2 0 0 w c ¼ w cm ð3þ Note that both w ci and 0 are column vectors with length of N, and therefore w c has size NM M. In other words, the beam formed signal from the ith frequency is written in the following equation: V i ¼ w H ci st i ð4þ where w ci is the weighting function for beam forming or CRI [Yu et al., 2000]. The weights for the Fourier beamforming depend on the pointing direction of the synthesized beam pattern a and receiver positions of D j, j =1,2, N as w ci = [exp( jk i a D 1 ) and exp( jk i a D 2 ) exp( jk i a D N )] T, where k i is the wave number for the ith frequency. In this work, only the vertically pointing beam is of interest and implemented, i.e., a = [0 0 0]. As a result, the signals after Fourier beam forming is simply the sum of signals from all receivers. The resultant signals for multiple frequencies V are similar to those from conventional RIM, where only a single receiver is required. The difference is that in this work, the beamforming is applied after signals are received and digitized. It is known that the fixed synthesized pattern produced in Fourier beam forming is susceptible to interference and/or clutter in angular directions. On the other hand, Capon beam forming was designed to minimize interference/clutter from unknown angular directions by adaptively adjusting the synthesized pattern [e.g., Capon, 1969; Palmer et al., 1998]. As a result, the complex valued weights for Capon beam forming are determined using w ci = hs i s i H i 1 e/(e H hs i s i H i 1 e), where hs i s i H i is the correlation matrix of multi receiver signals with size N N at frequency f i, and the steering vector e has the same form as the Fourier weighting vector. It should be noted that if the angular distribution of the power to be imaged is relatively uniform, it is expected that the Fourier method can provide more robust results. In this case, the resolution enhancement is not needed and the inversion in the Capon method is susceptible to statistical fluctuations. [8] Subsequently, the M sets of beam formed signals are subsequently RIM processed to obtain high resolution power distribution in height (range) using (5) and the two steps for weighting multi receiver and multi frequency signals are shown together in (6). P r ðþ¼w z H r hvvh iw r ¼ w H r wh c hssh iw c w r ð5þ ð6þ where w r is the RIM weighting vector of size M 1 and P r (z) is the imaged power at height z [Palmer et al., 1999; Luce et al., 2001]. The high resolution profile of P r (z) is obtained by stepping z through the range gate. Although w r can be obtained by Fourier or Capon method, in this work, only the Capon RIM is used due to its superior performance of resolution enhancement 3of15

4 compared to the Fourier RIM [e.g., Palmer et al., 1999; Luce et al., 2001; Chilson et al., 2003]. The weights for Capon RIM have similar representation to the one in Capon beam forming, but the correlation matrix is replaced by hvv H i and the steering vector has the form e = [exp(j2k 1 z) exp(j2k 2 z) exp(j2k M z)] T. If Capon (Fourier) beam forming is used, then the imaging technique for high resolution observation is termed CB RIM (FB RIM), where RIM implicitly indicates the Capon RIM. CB RIM was briefly discussed by Furumoto et al. [2010] for application of RIM to signals from the Radio Acoustic Sounding System (RASS) for the purpose of high resolution temperature measurements Application of 3 D Imaging Directly [9] The multi frequency and multi receiver signals in (1) can be combined in one step using the 3 D imaging technique so that all NM signals are added coherently at height z [Yu and Palmer, 2001]. P a ðþ¼w z H hss H iw ð7þ where w is the weighting function for 3 D imaging with a size of NM 1 and can be obtained by either Fourier or Capon method. It is interesting to point out that the Fourier 3 D imaging is equivalent to applying Fourier RIM to Fourier beam formed signals. In other words, w in (7) is equal to w c w r in (6). For example, the Fourier 3 D imaging weight for the signal from the ith frequency and jth receiver is the {(i 1)N + j}th element in w and is represented by exp[j(2k i z k i a D j )], which is the product of the Fourier beam forming weight for the jth receiver and the Fourier RIM weight for the ith frequency. Moreover, the Fourier weights for the N receivers and the same frequency are identical if the vertical direction is considered (i.e., a = [0 0 0]). Nevertheless, only the Capon 3 D atmospheric radar imaging as described in equation (16) of Yu and Palmer [2001] was implemented in the vertical direction owing to its high resolution capability and is termed AIM. The weights for AIM involve the inversion of the correlation matrix of hss H i whose size is NM NM. AIM is adaptive to the power distribution in both angle and range directions and has the capability of simultaneously suppressing clutter in angle and providing high resolution in vertical direction. The performance of AIM, CB RIM, and FB RIM is investigated and compared using simulation and real data in the following two sections. 3. Simulation Study [10] The three techniques of FB RIM, CB RIM, and AIM are now demonstrated, tested, and verified using simulation for two scenarios. In Scenario I, a single thin atmospheric layer that is horizontally uniform is used to demonstrate the high resolution capability of the three techniques. In Scenario II, moving clutter with different flight paths is added to test and verify their performance of both layer reconstruction and clutter mitigation. [11] The simulation scheme has been used for various imaging applications such as CRI [Yu et al., 2000; Cheong et al., 2004], RIM [Palmer et al., 1999], and 3 D Imaging [Yu and Palmer, 2001] and is briefly described as follows. A number of scatterers are placed within the radar resolution volume, and moved by mean wind and turbulence. The radar received signal from a specific transmitted frequency and receiver is the sum of signals from those scatterers, whose amplitude and phase are determined from the radar weighting function and atmospheric return, and two way path, respectively. To simulate a moving clutter target, one scatterer is added with independent velocity and reflectivity. After the time series of received signals is generated, a sequence of random noise is added based on a given signal to noise ratio (SNR). For this work, the radar configuration in the simulation is similar to the MU radar experiment in section 4. Five equally spaced frequencies of 46.00, 46.25, 46.50, 46.75, and MHz were used for transmission and all the 25 receivers were employed [Hassenpflug et al., 2008]. The radar resolution volume was centered at 5 km with a half power beam width (HPBW) of 7 and a Gaussian shaped range weighting function of range resolution 150 m [Doviak and Zrnić, 1993]. The mean wind consisting only zonal component of 20 m s 1 and the turbulence fluctuations of 0.5 m s 1 were used. The scatterers locations were updated every inter pulse period (IPP) of s. Although there was no gap among data samples, data were organized so that each record has 128 points. The SNR was set at 20 db. For both scenarios, the return power in height from the layer was modeled by a Gaussian function with the mean height of 4.95 km and standard deviation of 20 m (i.e., layer width of 40 m). In addition, because the resolvability of the three techniques in range direction is of primary interest, the angular power distribution of the layer structure is assumed to be uniform. Therefore, it is expected that the Fourier beam forming is sufficient to combine the signals from multiple receivers to produce the vertically pointing beam Scenario I: A Thin Atmospheric Layer [12] A layer with width much smaller than the range resolution was simulated to test and verify the highresolution capability of the three techniques. The results are exemplified in Figure 1 (left), where the estimated high resolution power from FB RIM, CR RIM, and AIM are denoted by black solid, gray dotted, and black dashed lines, respectively. The signal power from the 4of15

5 Figure 1. (left) One realization of high resolution imaging results from the three different techniques for Scenario I, where a single atmospheric layer was located at 4.95 km with width of 40 m. The model power is shown as a solid gray line, and FB RIM, CB RIM, and AIM results are depicted by solid black, dotted gray, and dashed black lines, respectively. (right) The scattering diagram of RMSE for 800 realization with SNR of 20 db. The results from RMSE for FB RIM vs CB RIM and FB RIM vs AIM are denoted by light gray circles and black circles, respectively. It is evident that the layer structure can be best reconstructed by FB RIM, followed by AIM, and CB RIM. model was obtained by the product of range weighting function (2 way) and the Gaussian shaped return power from the layer. Subsequently, a noise floor was added so that the resulted SNR from the model is 20 db. The total power from the model is denoted by a solid gray line. Note that the Capon method was designed to minimize the contribution from all the interferences under the constraint that the gain at the direction of interest is unity [Capon, 1969]. In other words, unlike the Fourier method, the power estimated from the Capon method is not necessarily conserved. Specifically, the power estimated from FB RIM, CR RIM, and AIM is not at the same level. For easy comparison, their estimated power and the model power shown in Figure 1 were normalized so that the maximum power is 0 db. The correlation matrix corresponding to the three techniques was averaged over 3 records, resulting in a time resolution of approximately 24.6 s. It can be observed that the thin layer embedded in the resolution volume can be revealed through the three proposed imaging techniques. In addition, FB RIM and AIM provide results that agree better with the model compared to CB RIM. This will be discussed in more detail later. [13] The root mean squared error (RMSE) is introduced to quantify the performance of resolution enhancement in terms of how well the layer is reconstructed. The RMSE is defined by { i [P x (i ) P m (i)] 2 / [P x (i)p m (i)]} 1/2, where P x (i) is the normalized power estimated by one of the three techniques at height z i and P m (i) is the normalized model power. The summation was performed over the range (i.e., ±180 m from the center of the gate) shown in Figure 1 (left). Moreover, 800 realizations, each with an independent noise sequence, were generated for statistical analysis. The scattering diagram of RMSE from FB RIM (abscissa) and CB RIM and AIM (ordinate) is shown in Figure 1 (right). It is evident that for this scenario, FB RIM has the best performance of layer reconstruction manifested by the lowest RMSE among the three techniques and is followed by AIM. For the comparison of FB RIM and CB RIM, it is noted that the only difference of the two techniques lies in the beam forming step. In this scenario the model power distribution in angle is determined by the antenna pattern, which is relatively smooth, and no clutter is present. In other words, the more intuitive Fourier beam forming is sufficient, where multi receiver signals (s i ) are directly summed to produce the synthesized signal V i for the ith frequency in (4). In other words, the weights in w ci are all unity. On the other hand, the weights for Capon beamforming are generally complex valued and obtained without any knowledge of the vertical structure of the layer. Thus, additional phase shifts can be introduced into the synthesized signal V i. It can be thought of as increasing phase error in the correlation matrix of hvv H i and as a result, the RIM image becomes blurry. This is demonstrated by the overestimated layer structure using 5of15

6 Figure 2. The eight flight paths of clutter are superimposed on the contour of the angular distribution of the normalized model power. The speed of the clutter is approximately m s 1 from southwest to northeast for all the paths. The length of the path indicates the angular distance of clutter target traveling over the period for three incoherent averages (24.58 s). The mean location over the period is indicated by a solid circle for each path. CB RIM in Figure 1 (left). For AIM, one would expect a similar result to FB RIM, because both angular and range distribution of the power are considered. As a result, AIM will automatically adjust its weights to produce high resolution range profile and maintain relatively uniform result in angle. However, AIM involves the inversion of matrix, while the FB RIM only inverts a 5 5 matrix in RIM processing, which is less susceptible to noise effect. Although it is not shown, the following result was observed. If the number of records for averaging increases, the RMSE of both FB RIM and AIM as well as the difference between the two techniques decrease. This suggests that FB RIM can provide the same quality of layer reconstruction as AIM with higher temporal resolution Scenario II: Atmosphere and Clutter [14] In this scenario, a moving clutter target was added to Scenario I by including one scatterer with its own velocity and reflectivity in the simulation. Eight flight paths were simulated and are depicted in angular domain in Figure 2. The initial range of the moving target was set to 5080 m for all the paths, which determines the corresponding height of the moving target for each path. Subsequently, the scatterer was moving at the constant height from southwest to northeast with both zonal and meridional velocities of 40 m s 1. The normalized model power in angles for Scenario I is represented by the underlying contours. Each solid line denotes the flight path over the period of 3 records (24.58 s), which is the number of incoherent averages used for the three techniques. In other words, the location of the moving clutter in the CRI images will be smeared over its flight path. Each flight path can be characterized by two variables, the zenith angle of the mean location ( c ) and the model clutter to signal ratio (CSR). The zenith angle of the mean location is denoted by a solid circle in Figure 2. The model CSR was obtained using the following approach. The power of atmospheric signal was obtained from Scenario I (clutter free), while the power for signal plus clutter was obtained from Scenario II. Both powers were estimated before the noises were added and averaged over all the available frequencies and receivers. The zenith angle and the model CSR are provided in Table 1 for two cases. For each case, the reflectivity of the moving target was kept the same for the 8 paths. Additionally, in Case II, the reflectivity from the moving clutter was increased by 10 db compared to Case I and the rest of parameters were unchanged. It is shown that the model CSR decreases with increasing c. This is because that the received power from the moving clutter target is mainly determined by the flight path across the antenna pattern. Therefore, when the path is located away from the beam center, the received power decreases. [15] The results of FB RIM, CB RIM, and AIM for Scenario II are exemplified in Figure 3 for the two cases with selected paths. Figures 3 (top) and 3 (bottom) depict Cases I and II, respectively, and Figures 3 (left), 3 (middle), and 3 (right) show paths 2, 5, and 8, respec- 6of15

7 Table 1. Zenith Angle of the Mean Location, c, for Eight Flight Paths Shown in Figure 2 a Path c ( ) Case I: CSR (db) Case II: CSR (db) a The model CSR values for the two cases are also provided. The model CSR values for Case II are approximately 10 db higher than those for Case I. tively. The model CSR and zenith angle of the mean location are provided on the top of each plot. The model power was normalized to its maximum return and is denoted by thick light gray lines. The results from FB RIM, CB RIM, and AIM are denoted by black solid, gray dotted, and black dashed lines, respectively. All the results are normalized so that the reconstructed power profile at the location of maximum model power is 0 db. It is apparent that FB RIM is susceptible to clutter contamination which is manifested by strong return at a height of approximately 5.02 km for all the paths. In other words, unlike in Scenario I, the fixed synthesized beam pattern produced by the Fourier beam forming is no longer sufficient to combine multi receiver signals if signals are contaminated by clutter and clutter suppression is desirable. On the other hand, CB RIM and AIM can suppress the moving clutter by adaptively putting a null in the location of the clutter and at the same time, grossly reconstruct the layer structure for paths 5 and 8 in both cases (Figures 3 (middle) and 3 (right)). [16] To further quantitatively compare the performance of three imaging techniques for Scenario II, two measures of that how much the atmospheric component is reconstructed and how well the clutter is suppressed are introduced. The former is quantified using the RMSE defined in section 3.1, except that the summation is limited to the power from the lower half of the gate, where the atmospheric layer is located. The latter is defined by the suppression factor (db), which is defined by the ratio of the sum of model power to the sum of imaged power over the vicinity heights (i.e., ±20 m) of the moving clutter. If the clutter is suppressed by the imaging technique, the imaged power at the clutter location should be significantly reduced and is similar to the model power. For each path and case, 50 realizations were generated and the mean of RMSE and suppression factor is shown in Figures 4 (top) and 4 (bottom), respectively, for the three techniques. It is observed for the three techniques that generally RMSE decreases with c and the suppression factor increases with c. CSR increases with increasing c as shown in Table 1. Figure 3. Selected examples from (top) Case I and (bottom) Case II. The atmospheric layer is the same as described in Figure 1 and is depicted by thick gray solid lines. The flight paths of the clutter are the path numbers (left) 2, (middle) 5, and (right) 8. The results of FB RIM, CB RIM, and AIM are denoted by solid, dotted, and dashed lines, respectively. 7of15

8 Figure 4. RMSE as a function of the clutter zenith angles for (top left) FB RIM, (top middle) CB RIM, and (top right) AIM. (bottom) The suppression factor for the three techniques. Each result is the mean of 50 realizations, and the SNR is 20 db for all cases. [17] Note that FB RIM has no clutter suppression ability, and that therefore the clutter is always present in the imaged power, even when the layer structure can be obtained at large c. The dependence of suppression factor on c for FB RIM simply reflects the decrease of model CSR. Thus, we focus on the comparison of CB RIM and AIM because both the clutter suppression and layer reconstruction are of interest. Generally speaking, the performance of both CB RIM and AIM in terms of clutter suppression and layer reconstruction increases as c (CSR decreases). Moreover, the performance degrades with the increase of model CSR from Cases I to II for all the paths, except for CB RIM of path 1. Specifically, for the path 3 to 8 in Case I, AIM provides slightly lower RMSE (0.13 in average) and higher suppression factor (1.5 db in average) than CB RIM. This is also demonstrated by the slightly wider layer structure and higher returns at the height of clutter from CB RIM than AIM, as shown in Figures 3 (top middle) and 3 (top right). However, such a differences becomes insignificant in Case II, except for path 8, where AIM still shows slightly better performance than CB RIM. For paths 1 and 2, the clutter target passed across with c = 0.62 and 1.18 as depicted in Figure 2, where the flight path is near the direction of beam forming (i.e., zenith). As a result, the suppression of such contamination is limited because nulling out the clutter presented in the angle close to the beam forming direction becomes difficult. For these cases, AIM produces results resemble to FB RIM as shown in Figure 3 (left), because the weights of both AIM and FB RIM are dominated by the clutter. Note that CB RIM has lower RMSE and higher suppression ratio than AIM for paths 1 and 2 in both cases. However, the saturation effect begins to appear, where the resulting image becomes a uniform profile. This can be clearly observed in Figure 3 (bottom left). Although the location of the layer might be determined, the layer width is significantly over estimated. 4. MU Radar Experiment [18] To demonstrate the application of the three techniques to atmospheric observations, a MU radar experiment was conducted on LT 15 July of15

9 The MU radar is located in Shigaraki, Japan (34.85 N, E) [Fukao et al., 1985a, 1985b] and was upgraded in 2004 to be capable of transmitting 5 frequencies and receiving with a maximum of 25 digital receivers [Hassenpflug et al., 2008]. In this experiment, two modes of imaging and wind measurements using Doppler Beam Swinging (DBS) were alternated. However, we will focus on the results from the imaging mode, where 5 uniformly spaced frequencies between 46 and 47 MHz, and 25 receivers were used. Moreover, only the center 7 groups of antennas were used for transmission resulting a one way HPBW of approximately 6.9 [Hassenpflug, 2006]. Each record consisted of 125 sets of multi receiver and multi frequency signals after 32 coherent averaging of raw signals from an IPP of 400 ms, and each set has 128 data points. Every 30 record of imaging mode (4.1 min) was interlaced with one DBS wind mode of approximately 0.96 min. The minimum height is 1.05 km and 160 ranges gates were used with range resolution of 150 m. A 16 bit spano code [Spano and Ghebrebrhan, 1996] was also used in the imaging mode. [19] Before the implementation of the imaging techniques, a calibration of range delay caused by the radar system was applied to the three techniques. The scheme is similar to the one proposed by Chen and Zecha [2009] and Chen et al. [2009], where the imaging powers at common ranges estimated from adjacent gates are assumed to be the same. Specifically, a range delay was determined from the minimization of difference in those powers at each range gate. Consequently, the calibration range was determined from the mean of range delays from all the gates below 5 km over the experiment period. The calibration for range delays of 133.5, 112.8, and m was used in FB RIM, CB RIM, and AIM respectively. Note that the range delay of 50 m for conventional RIM was reported by Chen et al. [2009] for MU radar. The difference could be caused by radar setting, system status, and number of receiving channels, for example. The range weighting function is also corrected using the method described by Chen and Zecha [2009]. Moreover, in order to increase the robustness of the matrix inversion, the correlation matrixes were averaged over 3 records, resulting in a time resolution of approximately 24.6 s. A standard processing (i.e., no RIM processing) was also applied to the signals combined by the Fourier beam forming for the central frequency of MHz to represent the conventional product from a single receiver and frequency. [20] The height time intensity (HTI) plots of return power estimated from standard, FB RIM, CB RIM, and AIM are shown in Figures 5a 5d. The contamination by moving clutter is apparent in both standard and FB RIM processed results at heights above approximately 6 km. The instance of clutter manifested themselves as pointlike and typically strong returns, and are likely airplanes or birds. Note that FB RIM is similar to the conventional RIM processing where a single receiver is used. The gain of range resolution by RIM over the standard processing is evident, with more clear and detailed layer structures revealed, such as those at heights between 2.5 and 5.0 km and LT and those at 6 8 km and LT. The resolution enhancement using FB RIM is consistent with previous work [Chilson et al., 2003; Palmer et al., 2001; Luce et al., 2006; Chen et al., 2009]. More importantly, CB RIM and AIM can provide similar resolution enhancement and simultaneously, suppress clutter contamination as demonstrated in Figures 5c and 5d. Generally speaking, the complex layer structures from the previous two FB RIM examples are maintained by both CB RIM and AIM, while the point like echoes from clutter are significantly suppressed. As a result, a clearer HTI can be obtained from CB RIM and AIM. [21] To better compare the performance of the three imaging techniques, the HTI plots from km and LT are shown in Figure 6, where a couple of cases of clutter are also included. It can be clearly observed that FB RIM and AIM produced similar results demonstrating the evolution of multiple layer structures. However, the image from CB RIM is not as sharp as the other two techniques. These results agree with the simulation result of Scenario I. The clutter appearing at a height of 6.7 km and 1725 LT is used to demonstrate the capability of clutter mitigation in Figure 7. The results of imaging techniques as well as standard processing are shown in four consecutive time frames. The FB RIM, CB RIM, AIM and standard processing are denoted by black solid, dotted, dashed, and thick gray lines, respectively. The boundaries of each gate are depicted by horizontal dashed lines. No normalization was used for imaging techniques so that difference in power can be observed. Two weak layer structures can be observed at heights of 6.25 and 6.5 km for the four time frames using the three imaging techniques, but not in the standard processing. The clutter contamination can be clearly observed in both standard and FB RIM at heights around 6.7 km in the time frames for 17:25:40 LT and 17:26:04 LT in Figure 7. On the other hand, CB RIM and AIM can significantly suppress the clutter contribution and produce profiles of imaging power which are consistent in time. [22] Statistical comparison of the performance of the three techniques was carried out. The simulation results in section 3.1 indicated that the FB RIM provides the best performance in reconstructing high resolution profiles of atmospheric structure for Scenario I. Therefore, the model power in the RMSE calculation was replaced by the FB RIM processed power in the experiment. The RMSE was calculated only for heights below 5 km, where no moving clutter was present, over the entire period of the experiment. The scattering diagram of the RMSE from 9of15

10 Figure 5. (a) The height time intensity plot of echo power (db) obtained from standard processing with 150 m range resolution, and (b) the FB RIM processed results for LT 15 July Results obtained using (c) CB RIM and (d) AIM. 10 of 15

11 Figure 6. Comparison of FB RIM, CB RIM, and AIM for selected heights and time. Apparent layer structures can be observed using all three techniques, and these are generally consistent with each other. The CB RIM results are not as clear as the other two methods as shown between 3.5 and 4.5 km and LT. 11 of 15

12 Figure 7. Example of the three imaging techniques applied to clutter located at the height of approximately 6.6 km and 17:25:40 and 17:26:04 LT. The echo power from the standard mode is denoted by thick gray lines, while the FB RIM, CB RIM, and AIM results are denoted by solid, dotted, and dashed lines, respectively. The suppression of clutter by CB RIM and AIM is apparent at the location of the clutter, while the FB RIM remains susceptible to clutter contamination. CB RIM and AIM for SNR larger than 5 db is shown in Figure 8a. Approximately 84% of AIM results have RMSE smaller than the one from CB RIM, which further verifies that AIM and FB RIM provide similar resolution for the case of atmospheric component only and have better performance than CB RIM. In order to evaluate the performance of clutter suppression, the gates where clutter was present were determined by applying a simple Figure 8. Scattering diagram of (a) RMSE and (b) suppression factor for the comparison of CB RIM and AIM. The location of the moving clutter is determined by a simple detection of point target. The RMSE is calculated based on the difference of CB RIM (or AIM) and the FB RIM at heights below 5 km over the entire period. 12 of 15

13 point target detection to range corrected power obtained from standard processing. The point target is detected if the range corrected power is larger than the background returns by a given threshold. The power from the background is defined by the average power over the time frames prior to and after at the gate of interest. The threshold for detection was set at 15 db. Moreover, if detections were made at more than 6 consecutive ranges at any given time, all the detections were disregarded because those are not likely from clutter like airplanes or birds. As a result, 845 gates were detected. Since FB RIM can observe the clutter with high resolution, the height of the clutter was subsequently refined using the height of the maximum FB RIM power in the detected gate. The clutter power after CB RIM and AIM suppression was determined by summing their imaged power over a 30 m interval centered at the clutter height. The background power for CB RIM and AIM was determined by the average of 2 pixels prior to and after the time frame of interest and over the same 30 m interval. The suppression factor was then determined by the ratio of background power and the imaged power, and is shown in Figure 8b. The result indicates that AIM performs better than CB RIM in terms of clutter suppression in approximately 93% of data. The reason may be that the path of most moving clutter was located far from the zenith, as suggested in section Summary and Conclusions [23] In this work, three imaging techniques were proposed to achieve the goal of high range resolution and clutter suppression using signals from multiple receivers and multiple frequencies. Multi receiver signals can be first combined using beam forming techniques to synthesize returns from a vertically pointing beam. Subsequently, these beam formed signals from different frequencies were processed to obtain high resolution profile using Capon RIM. If the Fourier beam forming was used to combine multi receiver signals, then this approach is termed FB RIM. On the other hand, if the Capon beam forming was used, it is termed CB RIM. The third imaging technique is to apply 3 D imaging technique that processes signals from multi receiver and multi frequency simultaneously to form a constructive interference pattern in the vertical direction. The mathematical formulas for the three techniques were presented. The FB RIM is similar to the conventional RIM where only a single channel receiver is used. [24] The three imaging techniques were first demonstrated and verified using simulation for Scenario I of atmospheric layer only and Scenario II of layer and moving clutter. The layer with width of 40 m was embedded in a 150 m gate and the return power from the layer in angle was assumed to be uniform. Eight different flight paths and two cases of model CSRs were considered for the moving clutter in Scenario II. The RMSE and suppression factor were introduced to quantify the performance of resolution enhancement and clutter mitigation, respectively. Statistical analysis showed that for Scenario I, FB RIM has the best performance in reconstructing layer structure. AIM can provide similar results to FB RIM if the number of averages increases, which results in the degradation of temporal resolution. Additionally, CB RIM produced over estimated layer width owing to the additional and undesirable phases introduced at the stage of Capon beam forming. From Scenario II, it is clear that FB RIM is prone to clutter contamination for all the cases. On the other hand, CB RIM and AIM can recover the thin layer structure and suppress the clutter for cases where the clutter flight path is away from zenith and not too strong. AIM generally has comparable or better performance compared to CB RIM in terms of both layer reconstruction and clutter mitigation. When the clutter is located close to zenith, CB RIM provides better value of RMSE and suppression ratio than AIM, but the dynamic range of the imaged power is greatly reduced. [25] The application of the three techniques to atmospheric observations was further demonstrated using data collected by the MU radar with 25 receivers and 5 frequencies. It is shown qualitatively that FB RIM and AIM provide similar performance of layer reconstruction. The appearance of clutter in FB RIM images is clear and the range of the clutter can be better obtained compared to those from standard processing due to improved range resolution. The capability of clutter suppression offered by CB RIM and AIM was clearly seen from their images. In addition, the statistical analysis indicates that AIM provides better performance of layer reconstruction and clutter suppression than CB RIM for most cases. The results are consistent with those from simulation study. [26] It is worth emphasizing that adding the multireceiver capability to conventional RIM offers the flexibility of clutter suppression. In other words, AIM or CB RIM can be applied if the signals are contaminated by clutter/interference and FB RIM can be used if only signals from the atmosphere are present. Moreover, FB RIM requires fewer number of samples than AIM does to obtain similar layer reconstruction. In other words, the evolution of atmospheric layer can be revealed at higher temporal resolution by FB RIM if no clutter contamination is present. However, how to switch among the three imaging techniques in a practical system is not trivial and more work is needed to address this issue. [27] In this work, all the three methods were implemented off line. For real time implementation, the computational cost for each method depends on the number of receivers (N) and frequencies (M) and the number of sub gates in RIM. Moreover, FB RIM demands the least computational 13 of 15

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