Article Type:
Research Article

Orthogonal Channel Coding for Simultaneous Co- and Cross-Polarization Measurements

V. Chandrasekar Colorado State University, Fort Collins, Colorado

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Nitin Bharadwaj Colorado State University, Fort Collins, Colorado

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Print Publication:
01 Jan 2009
DOI:
https://doi.org/10.1175/2008JTECHA1101.1
Page(s):
45–56
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Abstract

Dual-polarization weather radars typically measure the radar reflectivity at more than one polarization state for transmission and reception. Historically, dual-polarization radars have been operated at copolar and cross-polar states defined with respect to the transmit polarization states. Recently, based on the improved understanding of the propagation properties of electromagnetic waves in precipitation media, the simultaneous transmit and receive (STAR) mode has become common to simplify the hardware. In the STAR mode of operation, horizontal and vertical polarization states are transmitted simultaneously and samples of both horizontal and vertical copolar returns are obtained. A drawback of the current implementation of STAR mode is its inability to measure parameters obtained from cross-polar signals such as linear depolarization ratio (LDR). In this paper, a technique to obtain cross-polar signals with STAR mode waveform is presented. In this technique, the horizontally and vertically polarized transmit waveforms are coded with orthogonal phase sequences. The performance of the phase-coded waveform is determined by the properties of the phase codes. This orthogonal phase coding technique is implemented in the Colorado State University–University of Chicago–Illinois State Water Survey (CSU–CHILL) radar. This paper outlines the methodology and presents the performance of the cross-polar and copolar parameter estimation based on the simulation as well as data collected from the CSU–CHILL radar.

Corresponding author address: V. Chandrasekar, Colorado State University, 1373 Campus Delivery, Fort Collins, CO 80523. Email: chandra@engr.colostate.edu

Abstract

Dual-polarization weather radars typically measure the radar reflectivity at more than one polarization state for transmission and reception. Historically, dual-polarization radars have been operated at copolar and cross-polar states defined with respect to the transmit polarization states. Recently, based on the improved understanding of the propagation properties of electromagnetic waves in precipitation media, the simultaneous transmit and receive (STAR) mode has become common to simplify the hardware. In the STAR mode of operation, horizontal and vertical polarization states are transmitted simultaneously and samples of both horizontal and vertical copolar returns are obtained. A drawback of the current implementation of STAR mode is its inability to measure parameters obtained from cross-polar signals such as linear depolarization ratio (LDR). In this paper, a technique to obtain cross-polar signals with STAR mode waveform is presented. In this technique, the horizontally and vertically polarized transmit waveforms are coded with orthogonal phase sequences. The performance of the phase-coded waveform is determined by the properties of the phase codes. This orthogonal phase coding technique is implemented in the Colorado State University–University of Chicago–Illinois State Water Survey (CSU–CHILL) radar. This paper outlines the methodology and presents the performance of the cross-polar and copolar parameter estimation based on the simulation as well as data collected from the CSU–CHILL radar.

Corresponding author address: V. Chandrasekar, Colorado State University, 1373 Campus Delivery, Fort Collins, CO 80523. Email: chandra@engr.colostate.edu

Keywords: Radars; Precipitation; Bias

1. Introduction

A fully polarimetric radar is defined as the one that can measure the full covariance matrix of the precipitation medium (Tragl 1990; Bringi and Chandrasekar 2001). The full covariance matrix is composed of both copolar and cross-polar components. Pulse Doppler weather radars with polarization diversity can transmit and/or receive in two orthogonally polarized channels. Dual-polarization weather radars transmit and receive at more than one polarization state. Circular and linear polarization states are the most commonly used polarization states of operation. In a dual-polarized radar operating on a linear basis, the transmitted pulses are at horizontally (H) and vertically (V) polarized states. Polarization diversity refers to the ability of the system to transmit/receive orthogonally polarized waves. Such systems transmit a single polarization state and can receive co- and cross-polar components with dual-channel receivers. Thus, with a combination of both polarization agility on transmit and polarization diversity on receive, the copolar and cross-polar returns can be measured at both polarization states. Historically, weather radars have operated to make measurements at copolar and cross-polar states of the covariance matrix elements. Over two decades of measurements in this basis has led to an improved understanding of propagation characteristics in the precipitation medium (Chandrasekar et al. 1990). The cost and advancement of receiver technology over time led to implementation of different measurement schemes over a period of three decades. For example, in the early 1980s before the digital revolution, receivers were expensive, and this led to single-receiver radars with high-power transmitter switches, to enable only copolar measurements. Over the last two decades, receivers have become very advanced and primarily driven by the marketplace revolution in communication technology, making it cheaper to use multiple receivers; this has led to the introduction of the simultaneous transmit and receive (STAR) mode (Doviak et al. 2000; Bringi and Chandrasekar 2001). However, this mode prevents measurements of cross-polar returns. This paper presents a phase-coding technology such that copolar and cross-polar measurements can be obtained simultaneously.

This paper is organized as follows: a brief description of the received signal and precipitation covariance matrix is given in section 2. Section 3 introduces waveform coding, the codes used to retrieve the cross-polarized signals, and gives a brief description of the properties of cross-polar received signals. Parameter estimation using advanced processing methods is described in section 4, while section 5 describes the statistics of these estimators in retrieving the cross-polar signal-based parameter. In section 6, analysis of the waveform coding with data collected from the Colorado State University–University of Chicago–Illinois State Water Survey (CSU–CHILL) radar is presented followed by the summary and conclusions in section 7.

2. The received signal and the precipitation covariance matrix

The weather radar equation at single polarization is expressed as a well-known scalar equation whereas the corresponding equation for dual-polarization radar becomes a matrix equation expressed as (Bringi and Chandrasekar 2001)
i1520-0426-26-1-45-e1
where 𝗧 is the transmission matrix of the uniform precipitation medium and is included for completeness to account for the propagation of electromagnetic waves through the precipitation medium but does not affect waveform coding; 𝗦 is the 2 × 2 backscattering matrix; Mh and Mυ are the transmitter excitation states in horizontal and vertical ports of a dual-polarized antenna with an antenna gain G, transmit power Pt, and operating at a wavelength λ. Thus it can be seen that the received signal (υh and υυ) is a vector depending on the transmit polarization state. In a switched or alternate polarization mode the transmit states are vectors
i1520-0426-26-1-45-e2
resulting in a sequence of length four vector
i1520-0426-26-1-45-e3
corresponding to the two orthogonal transmit states. The subscripts υh (hυ) refer to transmit horizontal (vertical) polarization and receive vertical (horizontal) polarization. The properties of this signal vector z can be described in terms of the covariance matrix 𝗖:
i1520-0426-26-1-45-e4
where H is the Hermitian operator, * indicates complex conjugate, and E represents the expectation operator. This 4 × 4 matrix can be reduced to 3 × 3 invoking reciprocity. This covariance matrix measurement corresponds to the covariance matrix of the scatterers in the precipitation medium defined by (Bringi and Chandrasekar 2001)
i1520-0426-26-1-45-e5
where Shh, Shυ, and Sυυ are the elements of the scattering matrix, n is the number of particles per unit volume, and the angle brackets denote ensemble averaging. The intrinsic backscattering properties of the hydrometeors at the two polarization states enable the measurement of characteristics such as mean size, shape, and spatial orientation of the precipitation particles in the radar resolution volume. These characteristics are described in terms of the backscattering matrix elements. The elements of the backscattering covariance matrix or some combination of them are used to compute the polarimetric variables such as differential reflectivity (Zdr) and linear depolarization ratio (LDR). The differential reflectivity and linear depolarization ratio are defined as
i1520-0426-26-1-45-e6
i1520-0426-26-1-45-e7
where 〈|υhh|2〉(〈|υυυ|2〉) and 〈|υhυ|2〉 are the copolar and cross-polar signal power, respectively. Polarization diversity enables us to measure differential reflectivity, differential propagation phase (or specific differential phase), and linear depolarization ratio. These multiparameter radar observations have been used to measure the bulk properties of hydrometeors in a resolution volume. These polarimetric parameters are an essential part of algorithms for improved rainfall rate estimation, attenuation correction, and hydrometeor identification (Bringi and Chandrasekar 2001).
The linear depolarization ratio provides valuable information in rain–ice mixtures as well as high-density ice regions. Measurements of LDR are very useful for the hydrometeor classification (Liu et al. 2000; Straka et al. 2000; Lim et al. 2005), studying mixed phase precipitation, and electrification studies (Caylor and Chandrasekar 1996). In addition, cross-polar signal contamination introduces biases in measurements (Doviak et al. 2000; Wang and Chandrasekar 2006). The biases introduced by the cross-polar signal get larger with increases in operating frequency (Wang and Chandrasekar 2006). In a polarization diverse system operating under the STAR mode of operation, simultaneous observations of the resolution volume are made with both horizontal and vertical polarization states. STAR mode reduces hardware complexity by avoiding switching of the transmitter (switching between H and V polarization on a pulse-to-pulse basis) (Doviak et al. 2000; Bringi and Chandrasekar 2001). The radar equation for STAR mode is
i1520-0426-26-1-45-e8
Equation (8) is obtained from Eq. (1) by choosing Mh = Mυ = 1. It can be observed in Eq. (8) that the received signal in the h port (v port) is a linear function of Shh and Shυ (Sυυ and Sυh). Therefore, cross-polar signals υυh (or υhυ) cannot be directly measured in STAR mode and hence measurements of LDR are not available. This paper presents a technique to separate out the copolar and cross-polar signals. The separation of copolar and cross-polar signals enables the retrieval of the linear depolarization ratio in STAR mode. In addition to the retrieval of linear depolarization ratio, the polarimetric variables are unbiased. Coding the transmit waveforms in the H and V channel on a pulse-by-pulse basis enables the retrieval of linear depolarization ratio.

3. Orthogonal channel coding for dual-polarized radars

Phase coding of transmitted signals has been suggested for various applications such as pulse compression, range ambiguity mitigation, digital communication, and cryptography. However, the implementation of phase coding requires a transmitter that is capable of controlling the phase of the transmitted pulse. Klystrons, traveling wave tube (TWT), and solid-state transmitters can control the transmit phase while magnetron-based systems cannot control the transmit phase (Skolnik 1990).

Radars with a single transmitter operate at two polarizations either by alternating between polarization states from pulse to pulse or transmit a slant 45° polarizationand receive on two channels. Orthogonal channel coding for a single-transmitter radar operating in STAR mode would require a radio frequency (RF) phase shifter to enable phase coding. However, with a two-transmitter radar system (Klystron, TWT, or solid state) phase codes can be applied on each channel independently without an RF phase shifter. RF phase shifters traditionally have poor phase noise characteristics, and large phase errors degrade the performance of phase coding. The CSU–CHILL radar system is capable of transmitting horizontal and vertical polarization states simultaneously. Two orthogonally polarized waves are transmitted using two separate but identical Klystron transmitters with dual-channel reception of orthogonally polarized waves. Recent advances in digital technology have enabled the use of digital transmit controllers capable of generating arbitrary waveforms; the CSU–CHILL radar uses a 16-bit arbitrary waveform generator (George et al. 2006). Systems using a digital arbitrary waveform generator with two transmitters such as CSU–CHILL (Fig. 1) can generate and transmit orthogonally coded pulses in the horizontal and vertical polarization channels. The CSU–CHILL radar’s Klystron transmitters enable the use of phase coding to transmit orthogonal waveforms.

Random phase coding the transmit pulses for suppressing range overlaid echoes for weather radars was proposed in Siggia (1983). Giuli et al. (1993) suggested orthogonal signal using chirp waveforms to measure the cross-polar signal while Mudukutore et al. (1998) used independent phase coding to implement pulse compression for weather radars at both polarizations. Sachidananda and Zrnić (1999) proposed a systematic phase-coding technique to resolve range overlaid echoes and its evaluation for polarimetric radars has been described in Bharadwaj and Chandrasekar (2007). A different coding mechanism at the high-power RF side is suggested by Stagliano et al. (2006). In this paper, the two channels (H and V) are orthogonally coded using phase sequences. The transmit polarization state for the kth transmit pulse is given by
i1520-0426-26-1-45-e9
where ψh and ψυ are the switching phase codes that are tagged to each transmit pulse in the horizontal and vertical polarization channel, respectively. The received signal from an orthogonally coded H-channel and V-channel transmit pulse is given by
i1520-0426-26-1-45-e10
The received signals after decoding are given by
i1520-0426-26-1-45-e11
The received signal can now be written in terms of the copolar and cross-polar signal samples as
i1520-0426-26-1-45-e12
i1520-0426-26-1-45-e13
Therefore, the cross-polar signals are phase modulated by ϕh(k) = ψυ(k) − ψh(k) and ϕυ(k) = ψh(k) − ψυ(k) in the H and V channels, respectively, after recohering with the appropriate codes. The effect of decoding on the received signal depends on properties of the cross-polar signal and the codes used. In this paper we consider orthogonal systematic codes based on Hadamard matrices (Proakis 2001).

a. Properties of cross-polarized signals

The power levels of cross-polar signal backscattered from hydrometeors are always significantly less than the copolar signal. The lower bound for the cross-polar signal power is dictated by the polarization isolation of the antenna. The estimation of the bounds for LDR based on the antenna pattern is described by Chandrasekar and Keeler (1993). In this paper we will use the notation for estimated LDR and for mean LDR. The mean Doppler velocity of both the copolar and cross-polar signal is identical, but it has been observed that copolar spectrum is generally narrower than the cross-polar spectrum. The linear depolarization ratio is estimated from the copolar and cross-polar signal samples as
i1520-0426-26-1-45-e14
where N is the total number of samples used in the integration cycle. The variance of LDR can be obtained from the perturbation approximation of the power ratios as (Bringi and Chandrasekar 2001)
i1520-0426-26-1-45-e15
where
i1520-0426-26-1-45-e16
The parameter α is the broadening factor of the cross-polar spectrum compared to the copolar spectrum and ρcx is the copolarization-to-cross-polarization correlation coefficient. For most types of precipitation, |ρcx(n)| ≈ 0; however, |ρcx(n)| can be greater than zero for precipitation with a nonzero canting angle (Ryzhkov 2001; Moisseev et al. 2002). The standard deviation of as a function of the number of samples used in the integration is shown in Fig. 2. The standard deviations obtained from (15) are shown along with errors obtained from simulations. The procedure described by Chandrasekar et al. (1986) was extended to simulate time series data with both copolar and cross-polar signals. The standard errors in from copolar and cross-polar signals are similar to the error obtained from (15). It can be observed that the errors in are on the same order as the error in the estimated reflectivity.

b. Walsh–Hadamard code

A Walsh–Hadamard code is obtained from a Hadamard matrix 𝗛n (n × n matrix) (Proakis 2001) whose elements are either +1 or −1 with the property that any row differs from the other rows in exactly n positions. The rows of the Hadamard matrix are mutually orthogonal to each other forming Walsh codes and can be used to phase code the horizontal and vertical polarization channels. The Walsh–Hadamard code is generated as
i1520-0426-26-1-45-e17
where n is the complement of 𝗛n. For example, when n = 1, the Walsh–Hadamard code is
i1520-0426-26-1-45-e18
The binary phase codes for the H and V channels are obtained by selecting a pair of rows from the Walsh–Hadamard code matrix. The modulation property of phase sequences derived from the Walsh–Hadamard code depends on the pair of sequences selected from 𝗛2n. In this paper the phase sequences selected are the Walsh–Hadamard codes with modulation code ϕh(k) and ϕυ(k) so that modulation translates the signal by π in the spectral domain. It is important to note that there can be more than one pair of phase codes with the modulation property of translating the signal by π in the spectral domain. For example, a phase code for N = 128 pulses is obtained by selecting rows 63 and 64 from 𝗛128. The received signals after decoding can be rewritten from (11) in terms of the copolar and cross-polar signal as given in (13). The cross-polar signal in the H and V channel is modulated by exp[jϕh(k)] and exp[jϕυ(k)], respectively. For example, consider the received signal with two components such that the cross-polar signal is 20 dB below the copolar signal, a slightly wider spectral width, and centered at 10 m s−1 Doppler velocity. Let the spectral coefficients of υhh(k) and υhυ(k) be Vhh(Ωk) and Vhυ(Ωk), respectively. In the absence of any coding, the spectral coefficients of the received signals are given by
i1520-0426-26-1-45-e19
i1520-0426-26-1-45-e20
Since Vhh(Ωk) and Vhυ(Ωk) have identical mean Doppler velocities of 10 m s−1 and Vhυ(Ωk) is significantly weaker than Vhh(Ωk), cross-polar and copolar signals are indistinguishable in the spectral domain as shown in Fig. 3 (thick line). The same explanation as described above holds for the received signal in the V channel. In case of a Walsh–Hadamard coded waveform, the spectral coefficients of the recohered received signal are given by
i1520-0426-26-1-45-e21
i1520-0426-26-1-45-e22
It can be observed in Fig. 3 (thin line) that the modulated cross-polar signal Vhυ(Ωk + π) is displaced by the Nyquist velocity to −17 from 10 m s−1 and is clearly separable from the stronger copolar signal in the spectral domain. A very nice feature of the code is that it provides maximum separation between the copolar and cross-polar signal in the spectral domain (i.e., π). This feature can be used for an explicit estimation of the cross-polar signal power with narrow Doppler spectrum and it has been observed that median spectrum width for widespread showers, stratiform rain, snow, and isolated severe storms is less than about 2 m s−1 (Fang et al. 2004).

4. Copolar and cross-polar signal parameter estimation

The observed shape of the Doppler spectrum of copolar and cross-polar signal can be approximated to be Gaussian (Doviak and Zrnić 1993; Bringi and Chandrasekar 2001). Therefore, we model the observed signal as having two Gaussian spectral components, one for copolar signal and one for cross-polar signal. Let 𝗦 (v, θ) denote the Gaussian spectrum model. The parameter vector θ = (pco υco σco pcx υcx σcx)T describes the spectral moments of the copolar and cross-polar signals. The subscripts co and cx indicate copolar and cross-polar signals, respectively. The spectral model can be written as (Bringi and Chandrasekar 2001)
i1520-0426-26-1-45-e23
where pn is the noise power. The corresponding covariance matrix is given by
i1520-0426-26-1-45-e24
where Ts and λ are the pulse repetition time (PRT) and wavelength, respectively, and δ is the Kronecker delta function.

a. Spectral processing

The continuing advances in digital computing make the application of spectral processing in weather radars possible. For example, spectral processing is used in real time on the first-generation Collaborative Adaptive Sensing of the Atmosphere (CASA) X-band radar network (Bharadwaj et al. 2007). Advantages of spectral processing algorithms with polarimetric radars have been shown with data collected by CSU–CHILL (Seminario et al. 2001; Moisseev et al. 2006; Moisseev and Chandrasekar 2007). The modulation property of the Walsh–Hadamard code is one of the key elements in spectral processing for the retrieval of cross-polarized signal. As described in section 3b, properly selected Walsh–Hadamard codes modulates the cross-polar signal such that the cross-polar signal is translated by π (or Nyquist velocity) with respect to the copolar signal in the spectral domain as given by (22).

The dwell time of the radar results in a finite length of received signal and this finite length of the signal naturally applies a rectangular window function. The application of a rectangular window leads to the spreading of power in the spectral domain through the sidelobes of the window function (spectral leakage). Spectral leakage broadens the power spectrum of the signal and masks weaker signals in the spectrum. A window function is used to minimize spectral leakage due to the finite length window effect. The increase in the standard deviation of the spectral moments depends on the sidelobe suppression ability and main-lobe spectral broadening of the window function.

Since the copolar signal is always stronger than the cross-polar signal, the copolar signal is identified by a spectral peak detection. It has been observed that for Gaussian-shaped echoes this methodology provided good results. The spectral peak is used to notch filter the copolar signal with normalized width nw. A spectral notch filter is used to remove the copolar signal by removing the copolar spectral coefficients. However, the spectral peak detection and notch filter are not effective when the Doppler spectrum is bimodal, flat topped, or very wide. In cases where the spectrum is bimodal or flat topped, the location of the notch filter may be incorrectly chosen, which results in partial filtering of the copolar signal. The analysis of the impact of the bimodal and flat topped spectrum is beyond the scope of this paper. The normalized filter width is defined as the fraction of the total Nyquist band {[−λ/(4Ts), λ/(4Ts)]}. Here nw = 0.5 is used because the Walsh–Hadamard codes separate the signal by π and the two narrowband signals can be considered to be in the two halves of the spectral domain relative to the copolar signal. For example, a λ = 10 cm radar with Ts = 1 ms will have a Nyquist range (−25, 25) m s−1 and a recohered signal with copolar signal centered at 12.5 m s−1 will have the cross-polar signal centered at −12.5 m s−1. Therefore, the copolar signal will be in (0, 25) m s−1 and the cross-polar signal will be in (−25, 0) m s−1. The cross-polar signal power is estimated from the notch filtered signal. The inverse of the notch filter used to remove the copolar signal is used to filter out the cross-polar signal from the received signal. The copolar signal parameters are obtained from the inverse notch filtered signal. The linear depolarization ratio is then estimated from the copolar and cross-polar signal powers using (14). The impact of spectral processing with phase-coded waveform on polarimetric variables is described in section 5.

b. Maximum likelihood estimate

Maximizing the likelihood that θ fits the estimated covariance matrix is a standard technique in estimation theory. It is assumed that the received signals are circularly symmetric complex Gaussian random vectors. The moments of the copolar signal and cross-polar signal are obtained by maximizing the log-likelihood function given by
i1520-0426-26-1-45-e25
where 𝗥(θ) and are the model covariance matrix and sample covariance matrix, and |.| and Tr{.} represent the determinant and trace operator, respectively. The estimated moments are given by the solution of the nonlinear optimization problem given by
i1520-0426-26-1-45-e26
A more detailed description of the maximum likelihood method is provided by Boyer et al. (2003). The optimization problem in (26) is solved numerically to estimate the moments. The feasibility and performance of such a parametric time domain method for spectral moment estimation and clutter mitigation has been described in Nguyen et al. (2008). The likelihood function in (25) does not have a global minimum and the solution is more sensitive to the initializing seed values of the nonlinear optimizations problem in (26). It has been observed that the convergence of the minimization problem in (26) is sensitive to the mean Doppler velocities of the copolar signal. Since the range of Doppler velocities is not very large, the likelihood function in (25) is estimated at sample points uniformly spread between the Nyquist velocities. The sample points that give the minimum log-likelihood are selected as seed values for mean Doppler velocity.

5. Evaluation based on simulation study

A simulation at λ = 11 cm (corresponds to the operating wavelength of the CSU–CHILL radar) was performed to evaluate the performance of the coding scheme to retrieve the linear depolarization ratio. The procedure described by Chandrasekar et al. (1986) was extended to simulate time series data with the cross-polar signal. The lag-0 copolar correlation coefficient ρhυ = 0.99 in the simulations and the coto-cross polarization correlation coefficient are set to a low value between 0.2 and 0.4. A longer time series is truncated to provide the window effect. The simulated time series were phase coded with Walsh–Hadamard code, and the copolar and cross-polar signals were superimposed on a sample-by-sample basis to form the received signal. A phase error of 0.5° standard deviation is added to the transmit pulses in the two channels and true phase codes are used in decoding the received signals.

a. LDR retrieval

The spectral moments are estimated using spectral processing and the maximum likelihood method after the received signal is decoded. The error in is used to evaluate the performance of the two methods. The bias in with simultaneous transmission mode as a function of LDR is shown in Fig. 4. The cross-polar signal spectral width is generally larger than the copolar signal spectral width. Hence, the cross-polar signal spectral width is set to α = 1.2 times the spectral width of the copolar signal (σco = 4 m s−1). The bias in indicates that both spectral processing and the maximum likelihood method have similar performances in estimating the mean LDR. The bias in is within 1 dB for both the spectral and maximum likelihood method. However, the standard deviations of estimated from spectral processing are higher than the maximum likelihood method as shown in Fig. 5. The standard deviations from spectral processing are 0.6 dB higher than the standard deviation from the maximum likelihood method. Although the bias indicates that LDR below −34 dB can be estimated within 1 dB, the lower bound of measurable LDR is limited by the antenna integrated cross-polarization ratio (ICPR) (Chandrasekar and Keeler 1993). The CSU–CHILL system has a lower bound of −34 dB (Brunkow et al. 2000) based on the antenna pattern and measurements have shown values in the −33- to −34-dB range.

b. Impact on polarimetric variables

A simulation study is conducted to study the impact of phase coding on the polarimetric variables. A comparison is made between the retrievals of polarimetric variables for a phase-coded waveform and an uncoded waveform in STAR mode. It is important to note that the copolar signals from an uncoded waveform are always superimposed with the cross-polar signal. The uncoded waveform is processed with the traditional covariance algorithm to obtain the polarimetric variables. However, the phase-coded waveform is processed with spectral processing. The maximum likelihood approach for polarimetric radars is beyond the scope of this paper and is not considered in this section. The errors in the estimated polarimetric variables with phase-coded waveform and uncoded waveform in STAR mode are shown in Fig. 6 for σco = 4 m s−1 and α = 1.2. It can be observed in Fig. 6a that the standard deviation of with a coded waveform is higher than the uncoded waveform. This increase in the standard deviation is due to the application of the window function for spectral processing. A Chebyshev window with 80-dB suppression was used in the processing. The same explanation holds for the increased standard deviation of estimated differential propagation phase shift () and lag-0 copolar correlation coefficient () shown in Figs. 6b and 6c. There is no bias in obtained from phase-coded waveform while there is a very small bias in obtained from uncoded waveform when LDR is high. The biases and increase for an uncoded waveform when LDR is high, while and remain unbiased for a phase-coded waveform. The errors in polarimetric variables are comparable to those described in Bringi and Chandrasekar (2001).

6. Waveform coding with CSU–CHILL radar

Orthogonally coded horizontal and vertical polarization channels were used to collect data from a CSU–CHILL radar. Modulated RF drive pulses for each transmitter are synthesized by the transmitter controller. The transmitter controller uses a digital upconverter chip to synthesize a modulated intermediate frequency (IF) and the resulting IF signal is upconverted to S band. All internal data paths are 16 bits or greater and this allows the phase error to be small (determined to be 0.5°). This was verified by observing the hard target with a phase-coded waveform and decoding the received signal (see Fig. 7). Radar data on a stratiform event with a phase-coded waveform were collected from the CSU–CHILL radar on 29 May 2007. In addition, data using an alternate transmission mode were also collected. The alternate mode of operation enables the direct measurement of linear depolarization ratio. Both alternate mode and phase-coded waveform data were collected with a range–height indicator (RHI) scan at an azimuth of 80°. Figures 8a and 8c show the RHI of estimated reflectivity from the alternate mode and phase-coded simultaneous transmission mode. The increase in reflectivity from the surface up to the melting layer clearly indicates an occurrence of a bright band at an altitude of 1.8 km. The received signals near the ground are contaminated with ground clutter. The cross-polarized signals from the ground are 0–15 dB below the copolar signal from the ground and since signals close to the ground are very strong, the cross-polarized ground clutter is also significantly stronger. However, because of properties of the Walsh–Hadamard code the cross-polar clutter is not at zero velocity but is spread around ±λ/(4Ts), as shown in an example Doppler spectrum from CSU–CHILL in Fig. 9. Ground clutter is easily filtered in spectral processing because the position of the clutter spectral coefficients is known exactly. Therefore, a bandpass finite impulse response (FIR) filter with a frequency response as shown in Fig. 10 can be used to suppress both copolar and cross-polar ground clutter. The FIR filter shown in Fig. 10 is on the order of 81 and Fig. 9 shows an illustration of the result of filtering. The spectral moments can then be estimated using the maximum likelihood method.

The LDR estimated from the alternate mode and simultaneous mode with the Walsh–Hadamard code using spectral processing is shown in Figs. 8b and 8d, respectively. The bright band can be clearly identified by the enhance depolarization ratio in Figs. 8b and 8d. The alternate mode is used as a reference to compare the estimated from the phase-coded waveform. The absolute difference in measurements between alternate mode and simultaneous mode is attributed to the time difference between data collections. There is about a 4-min difference between data collection, and the precipitation event has changed in the 4 min and therefore is not an exact match. The estimated from Walsh–Hadamard coded waveform is very similar to estimated from the alternate mode. An infinite impulse response (IIR) filter is used to remove ground clutter in the alternate mode. The LDR measured from coded waveforms in simultaneous mode closely matches the LDR from the alternate mode and can retrieve LDR up to −30 dB.

7. Conclusions

Phase coding the transmit waveform in the horizontal and vertical polarization channels on a pulse-to-pulse basis can be used to retrieve the linear depolarization ratio in simultaneous transmission mode. Walsh–Hadamard coded waveforms were considered in this paper for retrieving LDR. Two methods for estimating LDR with phase-coded waveforms were presented. A spectral method and a time domain method that used the maximum likelihood principle were presented in this paper. A simulation study was performed to evaluate the ability of the phase-coded waveform to retrieve LDR using the two methods mentioned above. Based on results from the simulation, it is found that the bias in estimated LDR is within 1 dB for both spectral processing and the maximum likelihood method. However, it is observed that the standard deviation of estimates from the maximum likelihood method was lower than the spectral processing estimates by 0.6 dB. The impact of phase coding and associated processing on the retrieval of polarimetric variables was evaluated. Based on the results from the simulation study it can be concluded that unbiased estimates of polarimetric variables can be obtained from orthogonally phase-coded waveform. However, the standard deviations of the polarimetric variables are slightly higher because of the application of the window function.

The estimation of LDR in simultaneous transmission mode was tested with data collected by the CSU–CHILL radar. Estimates of LDR with phase-coded waveform were compared to the estimates from alternate mode. The ability to retrieve LDR is limited by the cross-polar isolation of the antenna. LDR measurements obtained by CSU–CHILL with alternate mode show values in the −32- to −34-dB interval. Data collected by the CSU–CHILL radar show that LDR estimated from phase-coded waveform is comparable to LDR estimated from the alternate mode and can retrieve LDR up to −30 dB. Based on the results from simulations and experimental data from CSU–CHILL it can be concluded that phase-coded waveforms provide a viable means to estimate both copolar and cross-polar signals in simultaneous transmission mode.

Acknowledgments

This work was supported by the National Science Foundation (NSF) through the NSF ITR program and ATM 0313881. The authors would like to acknowledge Jim George at Colorado State University and the Colorado State University CHILL facility staff for their assistance in obtaining data with waveform coding.

REFERENCES

  • Bharadwaj, N., and Chandrasekar V. , 2007: Phase coding for range ambiguity mitigation in dual-polarized Doppler weather radars. J. Atmos. Oceanic Technol., 24 , 1351–1363.

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  • Bharadwaj, N., Chandrasekar V. , and Junyent F. , 2007: Evaluation of first generation CASA radar waveforms in the IP1 testbed. Proc. Geoscience and Remote Sensing Symp., IGARSS’07, Barcelona, Spain, IEEE, 2742–2745.

    • Search Google Scholar
    • Export Citation

  • Boyer, E., Larzabal P. , Adnet C. , and Petitdidier M. , 2003: Parameteric spectral moments estimation for wind profiling radar. IEEE Trans. Geosci. Remote Sens., 41 , 1859–1868.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Bringi, V. N., and Chandrasekar V. , 2001: Polarimetric Doppler Weather Radar: Principles and Applications. Cambridge University Press, 636 pp.

    • Search Google Scholar
    • Export Citation

  • Brunkow, D., Bringi V. N. , Kennedy P. C. , Rutledge S. A. , Chandrasekar V. , Mueller E. A. , and Bowie R. K. , 2000: A description of the CSU–CHILL national radar facility. J. Atmos. Oceanic Technol., 17 , 1596–1608.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Caylor, I., and Chandrasekar V. , 1996: Time-varying ice crystal orientation in thunderstorms observed with multiparameter radar. IEEE Trans. Geosci. Remote Sens., 34 , 847–858.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Chandrasekar, V., and Keeler R. J. , 1993: Antenna pattern analysis and measurements for multiparameter radars. J. Atmos. Oceanic Technol., 10 , 674–683.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Chandrasekar, V., Bringi V. N. , and Brockwell P. J. , 1986: Statistical properties of dual-polarized radar signals. Proc. 23rd Conf. on Radar Meteorology, Snowmass, CO, Amer. Meteor. Soc., 193–196.

    • Search Google Scholar
    • Export Citation

  • Chandrasekar, V., Bringi V. N. , Balakrishnan N. , and Zrnić D. S. , 1990: Error structure of multiparameter radar and surface measurements of rainfall. Part III: Specific differential phase. J. Atmos. Oceanic Technol., 7 , 621–629.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Doviak, R. J., and Zrnić D. S. , 1993: Doppler Radar and Weather Observations. Academic Press, 562 pp.

  • Doviak, R. J., Bringi V. N. , Ryzhkov A. , Zahrai A. , and Zrnić D. S. , 2000: Polarimetric upgrades to operational WSR-88D radars. J. Atmos. Oceanic Technol., 17 , 257–278.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Fang, M., Doviak R. J. , and Melnikov V. , 2004: Spectrum width measured by WSR-88D: Error sources and statistics of various weather phenomena. J. Atmos. Oceanic Technol., 21 , 888–904.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • George, J., Brunkow D. , and Chandrasekar V. , 2006: Networking CSU-CHILL and CSU-Pawnee to form a bistatic radar system. Proc. IGARSS, Denver, CO, IEEE, 656–659.

    • Search Google Scholar
    • Export Citation

  • Giuli, D., Fossi M. , and Facheris L. , 1993: Radar target scattering matrix measurement through orthogonal signals. IEE Proc., 140 , 233–242.

    • Search Google Scholar
    • Export Citation

  • Lim, S., Chandrasekar V. , and Bringi V. , 2005: Hydrometeor classification system using dual-polarization radar measurements: Model improvements and in situ verification. IEEE Trans. Geosci. Remote Sens., 43 , 792–801.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Liu, H., Chandrasekar V. , and Bringi V. N. , 2000: Classification of hydrometeors based on polarimetric radar measurements: Development of fuzzy logic and neuro-fuzzy systems and in situ verification. J. Atmos. Oceanic Technol., 17 , 140–164.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Moisseev, D. N., and Chandrasekar V. , 2007: Nonparametric estimation of raindrop size distributions from dual-polarization radar spectral observations. J. Atmos. Oceanic Technol., 24 , 1008–1018.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Moisseev, D. N., Unal C. M. H. , Russchenberg H. W. J. , and Ligthart L. P. , 2002: Improved polarimetric calibration for atmospheric radars. J. Atmos. Oceanic Technol., 19 , 1968–1977.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Moisseev, D. N., Chandrasekar V. , Unal C. M. H. , and Russchenberg H. W. J. , 2006: Dual-polarization spectral analysis for retrieval of effective raindrop shapes. J. Atmos. Oceanic Technol., 23 , 1682–1695.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Mudukutore, A. S., Chandrasekar V. , and Keeler R. J. , 1998: Pulse compression for weather radars. IEEE Trans. Geosci. Remote Sens., 36 , 125–142.

  • Nguyen, C. M., Moisseev D. N. , and Chandrasekar V. , 2008: A parametric time domain method for spectral moment estimation and clutter mitigation for weather radars. J. Atmos. Oceanic Technol., 25 , 83–92.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Proakis, J. G., 2001: Digital Communications. 4th ed. McGraw-Hill, 1002 pp.

  • Ryzhkov, A. V., 2001: Interpretation of polarimetric radar covariance matrix for meteorological scatterers: Theoretical analysis. J. Atmos. Oceanic Technol., 18 , 315–328.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Sachidananda, M., and Zrnić D. , 1999: Systematic phase codes for resolving range overlaid signals in a Doppler weather radar. J. Atmos. Oceanic Technol., 16 , 1351–1363.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Seminario, M., Gojara K. , and Chandrasekar V. , 2001: Noise correction of polarimetric radar measurements. Preprints, 30th Conf. on Radar Meteorology, Munich, Germany, Amer. Meteor. Soc., 38–40.

    • Search Google Scholar
    • Export Citation

  • Siggia, A., 1983: Processing phase coded radar signals with adaptive digital filters. Preprints, 21st Conf. on Radar Meteorology, Edmonton, AB, Canada, Amer. Meteor. Soc., 513–518.

    • Search Google Scholar
    • Export Citation

  • Skolnik, M. I., 1990: Radar Handbook. 2nd ed. McGraw-Hill, 1200 pp.

  • Stagliano, J. J., Helvin R. J. , Alford L. J. , and Nelson D. , 2006: Measuring the linear depolarization ratio simultaneously with the other polarimetric variables. Proc. Fourth European Conf. on Radar in Meteorology and Hydrology, Barcelona, Spain, Servei Meteorològic de Catalunya, 80–83.

    • Search Google Scholar
    • Export Citation

  • Straka, J. M., Zrnić D. S. , and Ryzhkov A. V. , 2000: Bulk hydrometeor classification and quantification using polarimetric radar data: Synthesis of relations. J. Appl. Meteor., 39 , 1341–1372.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Tragl, K., 1990: Polarimetric radar backscattering from reciprocal random targets. IEEE Trans. Geosci. Remote Sens., 8 , 856–864.

  • Wang, Y., and Chandrasekar V. , 2006: Polarization isolation requirements for linear dual-polarization weather radar in simultaneous transmission mode of operation. IEEE Trans. Geosci. Remote Sens., 44 , 2019–2028.

    • Crossref
    • Search Google Scholar
    • Export Citation

Fig. 1.
Fig. 1.

Simplified block diagram of a two-transmitter radar system with dual-channel waveform generator.

Citation: Journal of Atmospheric and Oceanic Technology 26, 1; 10.1175/2008JTECHA1101.1

Fig. 2.
Fig. 2.

Standard deviation of as a function of the number of samples for copolar Doppler spectral widths of 2 and 4 m s−1.

Citation: Journal of Atmospheric and Oceanic Technology 26, 1; 10.1175/2008JTECHA1101.1

Fig. 3.
Fig. 3.

Illustration of the effect of orthogonal coding on the copolar signal spectrum contaminated with the cross-polar signal. Spectrum of received signal without any coding (thick line) and spectrum of recohered Walsh–Hadamard coded signal (thin line) at S band. Code length N = 128.

Citation: Journal of Atmospheric and Oceanic Technology 26, 1; 10.1175/2008JTECHA1101.1

Fig. 4.
Fig. 4.

Bias in using phase coding as a function of true LDR with an rms phase error of 0.5° at λ = 11.01 cm.

Citation: Journal of Atmospheric and Oceanic Technology 26, 1; 10.1175/2008JTECHA1101.1

Fig. 5.
Fig. 5.

Standard deviation of using phase coding as a function of true LDR with an rms phase error of 0.5° at λ = 11.01 cm.

Citation: Journal of Atmospheric and Oceanic Technology 26, 1; 10.1175/2008JTECHA1101.1

Fig. 6.
Fig. 6.

Error in estimated copolar parameters with and without phase coded waveform for wco = 4 m s−1 and α = 1.2 at λ = 11 cm. (a) Differential reflectivity, (b) differential propagation phase shift, and (c) lag-0 copolar correlation coefficient.

Citation: Journal of Atmospheric and Oceanic Technology 26, 1; 10.1175/2008JTECHA1101.1

Fig. 7.
Fig. 7.

Histogram of phase error measured with the CSU–CHILL radar.

Citation: Journal of Atmospheric and Oceanic Technology 26, 1; 10.1175/2008JTECHA1101.1

Fig. 8.
Fig. 8.

Comparison of reflectivity and LDR measurements from alternate mode and simultaneous mode. Data collected from CSU–CHILL radar on 29 May 2007 with alternate mode (2034:00 UTC) and Walsh-coded simultaneous mode (2028:51 UTC) (a) reflectivity from alternate mode, (b) LDR from alternate mode, (c) reflectivity from simultaneous mode with Walsh–Hadamard code, and (d) LDR estimated from simultaneous mode with Walsh–Hadamard code.

Citation: Journal of Atmospheric and Oceanic Technology 26, 1; 10.1175/2008JTECHA1101.1

Fig. 9.
Fig. 9.

Illustration of Doppler spectrum of signal contaminated with clutter (solid line) and clutter filtered spectrum (dashed line). Data collected from CSU–CHILL radar on 29 May 2007 with Walsh–Hadamard code.

Citation: Journal of Atmospheric and Oceanic Technology 26, 1; 10.1175/2008JTECHA1101.1

Fig. 10.
Fig. 10.

Frequency response of ground clutter filter for Walsh–Hadamard coded waveform.

Citation: Journal of Atmospheric and Oceanic Technology 26, 1; 10.1175/2008JTECHA1101.1

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Cover Journal of Atmospheric and Oceanic Technology
Journal of Atmospheric and Oceanic Technology

  • Bharadwaj, N., and Chandrasekar V. , 2007: Phase coding for range ambiguity mitigation in dual-polarized Doppler weather radars. J. Atmos. Oceanic Technol., 24 , 1351–1363.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Bharadwaj, N., Chandrasekar V. , and Junyent F. , 2007: Evaluation of first generation CASA radar waveforms in the IP1 testbed. Proc. Geoscience and Remote Sensing Symp., IGARSS’07, Barcelona, Spain, IEEE, 2742–2745.

    • Search Google Scholar
    • Export Citation

  • Boyer, E., Larzabal P. , Adnet C. , and Petitdidier M. , 2003: Parameteric spectral moments estimation for wind profiling radar. IEEE Trans. Geosci. Remote Sens., 41 , 1859–1868.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Bringi, V. N., and Chandrasekar V. , 2001: Polarimetric Doppler Weather Radar: Principles and Applications. Cambridge University Press, 636 pp.

    • Search Google Scholar
    • Export Citation

  • Brunkow, D., Bringi V. N. , Kennedy P. C. , Rutledge S. A. , Chandrasekar V. , Mueller E. A. , and Bowie R. K. , 2000: A description of the CSU–CHILL national radar facility. J. Atmos. Oceanic Technol., 17 , 1596–1608.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Caylor, I., and Chandrasekar V. , 1996: Time-varying ice crystal orientation in thunderstorms observed with multiparameter radar. IEEE Trans. Geosci. Remote Sens., 34 , 847–858.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Chandrasekar, V., and Keeler R. J. , 1993: Antenna pattern analysis and measurements for multiparameter radars. J. Atmos. Oceanic Technol., 10 , 674–683.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Chandrasekar, V., Bringi V. N. , and Brockwell P. J. , 1986: Statistical properties of dual-polarized radar signals. Proc. 23rd Conf. on Radar Meteorology, Snowmass, CO, Amer. Meteor. Soc., 193–196.

    • Search Google Scholar
    • Export Citation

  • Chandrasekar, V., Bringi V. N. , Balakrishnan N. , and Zrnić D. S. , 1990: Error structure of multiparameter radar and surface measurements of rainfall. Part III: Specific differential phase. J. Atmos. Oceanic Technol., 7 , 621–629.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Doviak, R. J., and Zrnić D. S. , 1993: Doppler Radar and Weather Observations. Academic Press, 562 pp.

  • Doviak, R. J., Bringi V. N. , Ryzhkov A. , Zahrai A. , and Zrnić D. S. , 2000: Polarimetric upgrades to operational WSR-88D radars. J. Atmos. Oceanic Technol., 17 , 257–278.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Fang, M., Doviak R. J. , and Melnikov V. , 2004: Spectrum width measured by WSR-88D: Error sources and statistics of various weather phenomena. J. Atmos. Oceanic Technol., 21 , 888–904.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • George, J., Brunkow D. , and Chandrasekar V. , 2006: Networking CSU-CHILL and CSU-Pawnee to form a bistatic radar system. Proc. IGARSS, Denver, CO, IEEE, 656–659.

    • Search Google Scholar
    • Export Citation

  • Giuli, D., Fossi M. , and Facheris L. , 1993: Radar target scattering matrix measurement through orthogonal signals. IEE Proc., 140 , 233–242.

    • Search Google Scholar
    • Export Citation

  • Lim, S., Chandrasekar V. , and Bringi V. , 2005: Hydrometeor classification system using dual-polarization radar measurements: Model improvements and in situ verification. IEEE Trans. Geosci. Remote Sens., 43 , 792–801.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Liu, H., Chandrasekar V. , and Bringi V. N. , 2000: Classification of hydrometeors based on polarimetric radar measurements: Development of fuzzy logic and neuro-fuzzy systems and in situ verification. J. Atmos. Oceanic Technol., 17 , 140–164.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Moisseev, D. N., and Chandrasekar V. , 2007: Nonparametric estimation of raindrop size distributions from dual-polarization radar spectral observations. J. Atmos. Oceanic Technol., 24 , 1008–1018.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Moisseev, D. N., Unal C. M. H. , Russchenberg H. W. J. , and Ligthart L. P. , 2002: Improved polarimetric calibration for atmospheric radars. J. Atmos. Oceanic Technol., 19 , 1968–1977.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Moisseev, D. N., Chandrasekar V. , Unal C. M. H. , and Russchenberg H. W. J. , 2006: Dual-polarization spectral analysis for retrieval of effective raindrop shapes. J. Atmos. Oceanic Technol., 23 , 1682–1695.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Mudukutore, A. S., Chandrasekar V. , and Keeler R. J. , 1998: Pulse compression for weather radars. IEEE Trans. Geosci. Remote Sens., 36 , 125–142.

  • Nguyen, C. M., Moisseev D. N. , and Chandrasekar V. , 2008: A parametric time domain method for spectral moment estimation and clutter mitigation for weather radars. J. Atmos. Oceanic Technol., 25 , 83–92.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Proakis, J. G., 2001: Digital Communications. 4th ed. McGraw-Hill, 1002 pp.

  • Ryzhkov, A. V., 2001: Interpretation of polarimetric radar covariance matrix for meteorological scatterers: Theoretical analysis. J. Atmos. Oceanic Technol., 18 , 315–328.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Sachidananda, M., and Zrnić D. , 1999: Systematic phase codes for resolving range overlaid signals in a Doppler weather radar. J. Atmos. Oceanic Technol., 16 , 1351–1363.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Seminario, M., Gojara K. , and Chandrasekar V. , 2001: Noise correction of polarimetric radar measurements. Preprints, 30th Conf. on Radar Meteorology, Munich, Germany, Amer. Meteor. Soc., 38–40.

    • Search Google Scholar
    • Export Citation

  • Siggia, A., 1983: Processing phase coded radar signals with adaptive digital filters. Preprints, 21st Conf. on Radar Meteorology, Edmonton, AB, Canada, Amer. Meteor. Soc., 513–518.

    • Search Google Scholar
    • Export Citation

  • Skolnik, M. I., 1990: Radar Handbook. 2nd ed. McGraw-Hill, 1200 pp.

  • Stagliano, J. J., Helvin R. J. , Alford L. J. , and Nelson D. , 2006: Measuring the linear depolarization ratio simultaneously with the other polarimetric variables. Proc. Fourth European Conf. on Radar in Meteorology and Hydrology, Barcelona, Spain, Servei Meteorològic de Catalunya, 80–83.

    • Search Google Scholar
    • Export Citation

  • Straka, J. M., Zrnić D. S. , and Ryzhkov A. V. , 2000: Bulk hydrometeor classification and quantification using polarimetric radar data: Synthesis of relations. J. Appl. Meteor., 39 , 1341–1372.

    • Crossref
    • Search Google Scholar
    • Export Citation

  • Tragl, K., 1990: Polarimetric radar backscattering from reciprocal random targets. IEEE Trans. Geosci. Remote Sens., 8 , 856–864.

  • Wang, Y., and Chandrasekar V. , 2006: Polarization isolation requirements for linear dual-polarization weather radar in simultaneous transmission mode of operation. IEEE Trans. Geosci. Remote Sens., 44 , 2019–2028.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • <sc>Fig</sc>. 1.
    View in gallery
    Fig. 1.

    Simplified block diagram of a two-transmitter radar system with dual-channel waveform generator.

  • <sc>Fig</sc>. 2.
    View in gallery
    Fig. 2.

    Standard deviation of as a function of the number of samples for copolar Doppler spectral widths of 2 and 4 m s−1.

  • <sc>Fig</sc>. 3.
    View in gallery
    Fig. 3.

    Illustration of the effect of orthogonal coding on the copolar signal spectrum contaminated with the cross-polar signal. Spectrum of received signal without any coding (thick line) and spectrum of recohered Walsh–Hadamard coded signal (thin line) at S band. Code length N = 128.

  • <sc>Fig</sc>. 4.
    View in gallery
    Fig. 4.

    Bias in using phase coding as a function of true LDR with an rms phase error of 0.5° at λ = 11.01 cm.

  • <sc>Fig</sc>. 5.
    View in gallery
    Fig. 5.

    Standard deviation of using phase coding as a function of true LDR with an rms phase error of 0.5° at λ = 11.01 cm.

  • <sc>Fig</sc>. 6.
    View in gallery
    Fig. 6.

    Error in estimated copolar parameters with and without phase coded waveform for wco = 4 m s−1 and α = 1.2 at λ = 11 cm. (a) Differential reflectivity, (b) differential propagation phase shift, and (c) lag-0 copolar correlation coefficient.

  • <sc>Fig</sc>. 7.
    View in gallery
    Fig. 7.

    Histogram of phase error measured with the CSU–CHILL radar.

  • <sc>Fig</sc>. 8.
    View in gallery
    Fig. 8.

    Comparison of reflectivity and LDR measurements from alternate mode and simultaneous mode. Data collected from CSU–CHILL radar on 29 May 2007 with alternate mode (2034:00 UTC) and Walsh-coded simultaneous mode (2028:51 UTC) (a) reflectivity from alternate mode, (b) LDR from alternate mode, (c) reflectivity from simultaneous mode with Walsh–Hadamard code, and (d) LDR estimated from simultaneous mode with Walsh–Hadamard code.

  • <sc>Fig</sc>. 9.
    View in gallery
    Fig. 9.

    Illustration of Doppler spectrum of signal contaminated with clutter (solid line) and clutter filtered spectrum (dashed line). Data collected from CSU–CHILL radar on 29 May 2007 with Walsh–Hadamard code.

  • <sc>Fig</sc>. 10.
    View in gallery
    Fig. 10.

    Frequency response of ground clutter filter for Walsh–Hadamard coded waveform.

Fig. 1.

Simplified block diagram of a two-transmitter radar system with dual-channel waveform generator.
Fig. 2.

Standard deviation of as a function of the number of samples for copolar Doppler spectral widths of 2 and 4 m s−1.
Fig. 3.

Illustration of the effect of orthogonal coding on the copolar signal spectrum contaminated with the cross-polar signal. Spectrum of received signal without any coding (thick line) and spectrum of recohered Walsh–Hadamard coded signal (thin line) at S band. Code length N = 128.
Fig. 4.

Bias in using phase coding as a function of true LDR with an rms phase error of 0.5° at λ = 11.01 cm.
Fig. 5.

Standard deviation of using phase coding as a function of true LDR with an rms phase error of 0.5° at λ = 11.01 cm.
Fig. 6.

Error in estimated copolar parameters with and without phase coded waveform for wco = 4 m s−1 and α = 1.2 at λ = 11 cm. (a) Differential reflectivity, (b) differential propagation phase shift, and (c) lag-0 copolar correlation coefficient.
Fig. 7.

Histogram of phase error measured with the CSU–CHILL radar.
Fig. 8.

Comparison of reflectivity and LDR measurements from alternate mode and simultaneous mode. Data collected from CSU–CHILL radar on 29 May 2007 with alternate mode (2034:00 UTC) and Walsh-coded simultaneous mode (2028:51 UTC) (a) reflectivity from alternate mode, (b) LDR from alternate mode, (c) reflectivity from simultaneous mode with Walsh–Hadamard code, and (d) LDR estimated from simultaneous mode with Walsh–Hadamard code.
Fig. 9.

Illustration of Doppler spectrum of signal contaminated with clutter (solid line) and clutter filtered spectrum (dashed line). Data collected from CSU–CHILL radar on 29 May 2007 with Walsh–Hadamard code.
Fig. 10.

Frequency response of ground clutter filter for Walsh–Hadamard coded waveform.
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