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2011 Seventh International Conference on Natural Computation

Comparison of SZ Phase Coding and Batch Mode to Mitigate Range Ambiguity of Doppler Weather Radar

Xu Wang Key Laboratory of Atmospheric Soundings

Chengdu University of Information Technology Chengdu, China

Chenghua Xie Hardware Development

Chengdu Yuanwang Science and Technology CO., LTD Chengdu, China

Abstract—Range ambiguity is an inherent problem of Doppler weather radar, particularly serious for X-band Radar because its wavelength is short. Firstly, this paper presents the principle of using SZ phase coding and Batch mode to mitigate range ambiguity. Secondly, compares Batch mode and SZ phase coding algorithm from capabilities of clutter suppression, suitable elevation, scan time, complexity of computation, and uses echoes acquired from X-band Doppler weather radar compared their performance of range ambiguity mitigation. This paper first applies SZ phase coding to X-band dual polarization Doppler weather radar in China, and gets the following conclusions: compared to Batch mode, SZ phase coding produces a significantly smaller amount of range ambiguity, this algorithm also satisfies the request of real-time processing and can be used at any elevation.

Keywords-Doppler weather radar; Maximum unambiguous range; Range ambiguity; Batch mode; SZ phase coding

I. INTRODUCTION For pulse-Doppler weather radars transmit a series of

equally spaced pulses (pulse repetition time is PRT), which produce a return signal from the scatters of interest that have their electromagnetic frequency phase-shifted in proportion to the relative velocity between the radar antenna and target. The maximum radial velocity that a pulse Doppler radar can detect unambiguously is given by the velocity, which just produces a phase shift of ±180°. This velocity is termed the Nyquist velocity (Vmax) and is expressed as (Battan 1973):

Vmax=±λ/(4·PRT). (1)

And the unambiguous range (Rmax) is expressed as:

Rmax=c·PRT/2. (2)

From (1) and (2), Vmax and Rmax are interrelated by (Doviak and Zrnic, 1993):

Rmax·Vmax=λ·c/8. (3)

Where c is the speed of light and λ is the wavelength. From (3), we know that for fixed λ, large Rmax results in small Vmax, and vice versa. From the viewpoint of Doppler ambiguities, it is

best to have the product Rmax·Vmax as large as possible, which requires large λ. But beam width and/or antenna size place limits on λ which prevent both a large Rmax and a large Vmax.

When the velocity along the radar radial of target is greater than Vmax, radar will give a velocity of less than Vmax to this target, this is called "velocity ambiguity". When the distance between target and radar is greater than Rmax is k·Rmax+Rs (where k represents any positive integer, Rs represents positive number that is less than Rmax), the target will appear on the distance of Rs at radar echoes image, this is called "range ambiguity". Echo within the distance Rmax is called "the first trip echo", between Rmax and 2·Rmax is called "the second trip echo", and so on, maybe even have "the third trip (k=2) echo" or more times (k>2) echo. When range ambiguity appears, the second or higher trip echo will be folded into the first trip, then will result in our misjudgment to the echo location and will impact of the quality of products. If echoes are overlaid the velocity estimate will be erroneous even if the actual velocity is less than Vmax. So, the overlaid signals must be separated prior to estimating the velocities of two overlaid signals. The process of return the folded echo to the actual location and estimate the corresponding velocity of folded echo is called "range de-aliasing" or "ruin range ambiguity". When using Doppler weather radar to observe severe convective weather of large and medium-scale (requires higher Rmax and Vmax), in order to reduce the ambiguity of velocity, choose small PRT, then Rmax is small, maybe appear range ambiguity.

So far, there is no method can completely remove the fold. Usually there are two types of approach: processing in time domain or frequency domain. Most of the existing Doppler weather radar using Batch mode or split cut method to ruin range ambiguity, they are both time domain method [1]. In 1999, Sachidananda and Zrnic proposed SZ phase coding to ruin range ambiguity in frequency domain. In 2002, Frush used experimental data proved this algorithm. In 2003, Hubbert used experimental data evaluated of the algorithm statistically [2]. Since the spring of 2007, SZ phase coding algorithm has been realized on the weather surveillance radar in the United States [3]. In China, the study on using SZ phase coding algorithm to ruin range ambiguity starts late. At present, only Sichuang Company applied SZ phase coding algorithm to C band (5cm) Doppler weather radar [4]. Since the wavelength of X-band (3cm) radar is shorter than S-band (10cm) and C-band radar, according to (1), (2) and (3), we know that the possibility of X-

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band radar appears range ambiguity is much larger than S-band and C-band radar, so this paper first applies SZ phase coding to X-band dual polarization Doppler weather radar to analyze and compare the performance of Batch mode and SZ phase coding to ruin range ambiguity.

This paper describes the theory of Batch mode and SZ phase coding to ruin range ambiguity firstly, then on the basis of theory analyzes and compares the clutter suppression capability, suitable elevation, scan time, computation time, complexity of the algorithm and the performance of ruin range ambiguity. The results show that: Batch mode can not do clutter suppression, can not recover the velocity of overlaid weak echo, and when the echo power ratio of overlaid echoes is less than threshold TOVER, the velocity of overlaid strong and weak echo can not be recovered. Although SZ phase coding requires longer scan time, computation is more complicated, but it can do clutter suppression, the performance of ruin range ambiguity is significantly better than Batch mode.

II. BATCH MODE TO RUIN RANGE AMBIGUITY Batch mode ruins range ambiguity in time domain, which

works as follows.

Batch mode uses two interlaced PRTs shown in Fig. 1: at first, transmits a set of pulses with long PRT (PRT1) to estimate the echo’s intensity (namely, power or reflectivity) and position, here corresponding to large Rmax and small Vmax, so get the unfolded echo, but not use to estimate velocity. Then transmits a set of pulses with short PRT (PRT2) to estimate the echo’s velocity, here corresponding to small Rmax and large Vmax, maybe appears range ambiguity. Therefore, we must use the power and location information getting from PRT1 to determine the position of velocity getting from PRT2, then put the velocity estimate to the right position. Using Batch mode ruins range ambiguity has two cases [1]: have overlaid and no overlaid, overlaid represents that have echoes folded into the same range bin.

A. No overlaid This case has no echo folded into the same range bin, can

follow next steps to ruin range ambiguity. Firstly, compute all possible positions Rk (k=0, 1, 2…, Rk is the position corresponding to PRT1) corresponding to Rs (Rs is the position corresponding to PRT2): Rk=k·Rmax2+Rs (Rmax2 represents the maximum unambiguous range of PRT2). For this case has no echo overlaid, one velocity estimate in PRT2 corresponds to one power estimate in PRT1, it means that k is unique. According to the position of power acquired by PRT1, determine the value of k, then assign the velocity to the position of k·Rmax2 + Rs.

Figure 1. Pulse transmit mode of Batch mode

B. Have overlaid This case has two or more echoes folded into the same

range bin, can follow next steps to ruin range ambiguity. The first step is the same as the case no overlaid, that is compute all possible positions Rk corresponding to Rs. Then, compare all possible positions Rk with powers obtained with PRT1, due to this case have multi-echo folded into the same range bin, so one velocity estimate corresponding to multi-power estimations, it means that k is not unique. Because the weight of velocity estimate is power, so compare powers that folded into the same range bin, only when a target’s power is significantly greater than the other objectives’, the velocity estimate is assigned to the target that produce larger power. As shown in Fig. 2, two targets A and B overlaid, B’s power is significantly greater than A, then the velocity estimate is closer to B, the velocity is assigned to B.

When comparing the power that folded into the same range bin, need to calculate the power ratio of two echoes in dB is:

Ratio=10·log[Phigh/Plow]. (4)

Where, Phigh and Plow represents respectively strong and weak echo’s power that folded into the same range bin.

If the Ratio of a range bin satisfies Ratio>TOVER (TOVER is a threshold), then the velocity will be assigned to the target with strong power, and the other folded echo’s position will be assigned to purple in velocity Plan Position Indicator (PPI), it means that can not make sure these echo’s velocity estimates. If Ratio<TOVER, then all folded echoes will be assigned to purple in velocity PPI, that means the algorithm of ruin range ambiguity is failure, can not make certain the targets’ velocity. So, the choice of TOVER will affect the performance of ruin range ambiguity of Batch mode. Higher TOVER can improve the precision of velocity, but will produce larger purple area in velocity PPI. Lower TOVER can reduce the purple area in velocity PPI but will reduce the precision of velocity. In this article we choose TOVER equal to 5dB.

Figure 2. Velocity estimation assignment when two targets folded into the same range bin

III. SZ PHASE CODING TO RUIN RANGE AMBIGUITY Use variation phase can extend the unambiguous range and

eliminate the estimation deviation of spectral moments caused by overlaid echoes. Variation phases are divided into two types: random phase and coding phase. When using random phase to recover expected echo un-expected echo behaves as white noise, decreases the equivalent signal to noise ratio, further will impact the estimate accuracy of spectral moments, so limits the use of this method. Phase coding methods code

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phase of transmit pulse according to a certain cyclical change and decode phase according to the law at the receiving end. In order to reduce the impact of echo overlaid on the spectral moments estimate of the desired signal the un-expected echo spectrums are dispersed, make weak echo to be copied in frequency domain, there will have one or more spectrum copies distant from strong echo spectrum, then after filter strong echo, use two remaining weak echo spectrum copies can recover weak echo and can estimate the parameters of weak echo [5, 6]. Basic principles are as follows.

Pulse pair processing (PPP) uses phase of autocorrelation R(PRT) with the time delay PRT to estimate velocity. When there is echo overlaid, signal samples are the sum of the first trip echo and the second trip echo, Since in most cases, the first trip echo and the second trip echo is not related or related small, so R(PRT) can be expressed as the sum of the first trip echo’s autocorrelation function R1(PRT) and the second trip echo’s autocorrelation function R2(PRT) [4]:

R(PRT)=R1(PRT)+R2(PRT) . (5)

Then average velocity of the first trip echo Vr1 is:

Vr1=λ·arg[R(PRT)]/(4·π·PRT)

=λ·arg[R1(PRT)+R2(PRT)]/(4·π·PRT) . (6)

At this time, R2 (PRT) will introduce bias to estimation of Vr1, if R2(PRT) is equal to zero can eliminate the impact of the second trip echo caused to Vr1.

The purpose of using variation phase is to change the phase of the second trip echo, so that R2(PRT)=0, then the second trip echo will no longer impact the velocity estimate of the first trip echo. On the other hand, changing the phase of the first trip echo, so that R1(PRT)=0, then the first trip echo will no longer impact the velocity estimate of the second trip echo.

Phase coding approach is as follows. Uses the sequence ak=exp(j·Ψk) to modulate transmit pulse, namely, the phase of transmit pulse sequence increase Ψk, the received echo signal samplings multiply by ak* to recover the phase, that is the phase of received sampling sequence minus the phase of Ψk. In this way, the first trip echo is synchronized and the second trip echo is modulated by ck=ak-1·ak*, then R2(PRT)=0. We also can use the received echo signal samplings multiply by ak-

1* to synchronize the second trip echo and modulate the first

trip echo by ck*=ak-1*·ak, then R1(PRT)=0. Many domestic and foreign scholars simulated a variety of phase coding sequences, the widely used is SZ (8/64) (referred to as SZ) phase coding, spectrum of this code has eight nonzero spectral weight evenly distributed, distance between the spectral components is eight.

SZ phase coding does twice 360-degree azimuth scan at the same elevation. At first, uses a long PRT scan without phase coding to get powers of unfolded echoes. Then, uses a short PRT scan with phase coding to get velocities of folded echoes. How to acquire the overlaid echo’s velocity is

described simply as follows [7]: in frequency domain, firstly uses PPP to estimate the spectral moments of strong echo and finds the spectrum center; then uses a notch filter with specific width and take the spectrum center as the filter’s center to filter the spectrum of strong echo and retain two spectrum copies of modulated weak echo signal, when overlaid is resulted by the first trip echo and the second trip echo (in most cases this is true), the modulated weak echo has eight replicate spectrums, choose a notch filter whose notch width is 3/4 [8]; Finally, reconstruct the spectrum and recover the velocity of weak echo. Detailed description of the algorithm refers to [9].

Because range overlaid occurs at the lower elevation, the presence of ground clutter is inevitable, in order to reduce the impact of ground clutter, need to do ground clutter suppression. Use frequency domain filter can suppress ground clutter and anomalous propagation ground clutter of all trips and have no use for pre-set clutter map (Siggia and Passarelli, 2004) [10].

IV. COMPARISON OF BATCH MODE AND SZ PHASE CODING

A. Capability of clutter suppression For Batch mode uses alternate PRT rather than uniform

spacing PRT, how to do ground clutter suppress is a difficulty, current Batch mode has no ground clutter suppression, so the impact caused by ground clutter has not been eliminated in Batch mode. SZ phase coding uses uniform spacing PRT, does clutter suppression in frequency domain, can effectively suppress ground clutter of propagation normal, but also can suppress ground clutter of propagation anomalous.

B. Suitable elevation Because Batch mode do not suppress ground clutter, so it is

not suitable for the elevation contaminated by ground clutter, generally only used at moderate elevation. But SZ phase coding uses advanced frequency-domain clutter suppression processing so it is suitable for all required elevation which need to ruin range ambiguity.

C. Scan time If Batch mode and SZ phase coding use the same PRF

(PRF is short for pulse repetition frequency, PRF=1/PRT) and number of sampling, Batch mode just do once 360-degree azimuth scan, but SZ phase coding needs to do twice 360-degree azimuth scans at the same elevation, and in this process, needs to switch the scanning process, so requires more time than Batch mode.

D. Computation time and complexity Batch mode ruins range ambiguity in time domain, the

algorithm is simpler and requires less processing time. SZ phase coding ruins range ambiguity in frequency domain, needs to do Fourier transformation and inverse Fourier transform, requires longer computation time than Batch mode.

E. Performance of ruin range ambiguity Here, we will compare the performance of Batch and SZ

phase coding to ruin range ambiguity through an example. The experience data were collected with X-band D-Pol Doppler

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weather radar in Chengdu University of Information Technology at 0.5° elevation on 24 September 2008. An experimental VCP (Volume Cover Pattern) was designed to compare Batch mode with SZ phase coding. This VCP consists of four scan modes, uses the parameters shown in Table 1 (where, Batch mode and SZ phase coding use the same PRF).

Fig. 3 through Fig. 6 show the results of reflectivity and velocity acquired with the parameters in table 1. In all figures each range circle represents 50km (kilometer). Fig. 3 shows the reflectivity obtained by Surveillance mode (long PRT) without ground clutter filter (GCF), Clutters spike to the north-east and south-west of radar are caused by the mountains (shown with Elliptical region). Fig. 4 shows the Doppler velocity obtained by Doppler mode (short PRT) without ground clutter filter. Fig. 5 shows the Doppler velocity obtained by Batch mode (short PRT). Fig. 5 shows the Doppler velocity obtained by SZ phase coding mode (short PRT).

Compared Fig. 4 with Fig. 3, can see that: in Fig. 3, the second trip echoes outside 100km (outside the circle) are folded into 100km result range overlaid. Velocities outside of 100km can not be estimated, and because there are multiple echoes folded into the same range bin, if use the overlaid echo to estimate the velocity of the first trip echo (inside of 100km) is not accurate.

Compared Fig. 5 with Fig. 4 can see that: the second trip echoes outside of 100km folded into 100km overlaid with the first trip echoes (namely, the second case of Batch mode)，and most of the power ratios of the first trip echoes and the second trip echoes are larger than TOVER, so the velocities of the first trip echoes are recovered, but the velocities of the second trip echoes can only be expressed in the corresponding position in purple, means that the algorithm is failure, can not recover the velocity of this position.

Fig.5 also shows that: there are some purple areas in the first trip echoes, mean that the overlaid echoes of the first trip and the second trip are considerable (the power ratio is less than TOVER), the velocities of the first trip and the second trip can not be recovered. And because Batch mode has no ground clutter filter, clutter echoes in the elliptical region will affect our judge to the weather echoes.

TABLE I. PARAMETERS USING TO COLLECT DATA

Scan Mode Scan Parameters

PRF(Hz) Rmax(km) Vmax (m/s) Sampling points Surveillance

mode 375 400 3 32 Doppler mode 1500 100 12 64

SZ phase coding mode

375 (uncoded) 400 3 32

1500 (coded) 100 12 64

Batch mode 375 400 3 321500 100 12 64

Figure 3. Reflectivity (Surveillance mode without GCF)

Figure 4. Velocity (Doppler mode without GCF, echoes outside of 100km in

Fig.3 folded into 100km)

Figure 5. Velocity (Batch mode without GCF, have no range overlaid but

purple area)

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Figure 6. Velocity (SZ phase coding mode with GCF, have no range

overlaid and purple area)

Compared Fig. 6 with Fig. 3 can see that: SZ phase coding used ground clutter filter and eliminated the impact of ground clutter. Compared Fig. 6 with Fig. 5 can see that: the purple areas appear in velocity PPI acquired by Batch mode no longer exists in the velocity PPI acquired by SZ phase coding mode, SZ phase coding mode gets more continuous velocity PPI. This means that using SZ phase coding can not only recover the overlaid velocity of the first trip echo but also can recover the velocity of the second trip echo. The performance of SZ phase coding is significant better than Batch mode.

V. CONCLUSIONS This paper focused on algorithms of Batch mode and SZ

phase coding to ruin range ambiguity, analyzed and compared these two algorithms from the clutter suppression capability, suitable elevation, scan time, computation time, complexity and performance of ruin range ambiguity. After experimented these two algorithms on X-band dual polarization Doppler weather radar got the following results: although SZ phase coding required slightly longer scan time, and the computation is more complicated, but it can do clutter suppression, the performance of ruin range ambiguity is significantly better than Batch mode, and can recover the velocity of overlaid strong and weak echo, greatly improved the detection performance of X-band Doppler weather Radar. And the experiment showed that: by reasonable software programming, can meet the need of real-time processing. But SZ phase coding algorithm requires for high precision of phase shifter, so demands higher hardware design of radar

signal processor. In order to obtain the best results still need a large number of experiments and research in future. And we expect SZ phase coding will be a significant improvement of the national network of weather surveillance radars. This can improve the detection capability of medium and large scale weather systems, thereby increasing the accuracy of forecast.

ACKNOWLEDGMENT This work was supported by Research Foundation of

Chengdu University of Information Technology (CRF201012) and partially supported by the National Science Foundation of China (41075010).

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