A frequencysharing weather radar network system using pulse compression and sidelobe suppression
 HwangKi Min^{1, 2},
 MyungSun Song^{1},
 Iickho Song^{2} and
 JaeHan Lim^{1}Email author
https://doi.org/10.1186/s1363801605953
© Min et al. 2016
Received: 2 October 2015
Accepted: 26 March 2016
Published: 12 April 2016
Abstract
To mitigate damages due to natural disasters and abruptly changing weather, the importance of a weather radar network system (WRNS) is growing. Because radars in the current form of a WRNS operate in distinct frequency bands, operating a WRNS consisting of a large number of radars is very costly in terms of frequency resource. In this paper, we propose a novel WRNS in which multisite weather radars share the same frequency band. By employing pulse compression with nearly orthogonal polyphase codes and sidelobe removal processing, a weather radar of the proposed frequencysharing WRNS addresses intersite and intrasite interferences simultaneously. Through computer simulations, we show the feasibility of the proposed system taking the performance requirement of a typical single weather radar into account.
Keywords
Weather radar network Frequency sharing Pulse compression Sidelobe suppression1 Introduction
The number of natural disasters has been increasing sharply since 1970 [1]. According to the statistics report in [2], over 330 natural disasters occurred in 2013 and took lives of a significant number of people (21,610) and caused serious economic damages ($156.7 billion). In an attempt to prevent damages from natural disasters, several research institutes (e.g., Oklahoma University) and governmental agencies (e.g., National Oceanic and Atmosphere Administration (NOAA)) have been collaborating with each other to develop a weather radar network system (WRNS) that enables forecasting unusual weather phenomena effectively.
A WRNS is composed of multiple weather radars, which are deployed in different geographical positions for monitoring the weather phenomena nearby. More specifically, each radar transmits radio pulse signal periodically, captures the signal that has been backscattered from weather targets, and extracts important parameters from the signal (e.g., reflectivity and radial velocity) for characterizing the current weather status. Although the current form of a WRNS works adequately, it has a significant limitation in terms of the frequency efficiency.
Frequency spectrum is a fundamental resource for wireless communication and remote sensing, but we lack the resource due to explosive demands for mobile communications. Despite the problem of frequency scarcity, the goal of the current deployment of a WRNS is not aligned with the frequency efficiency. To be specific, radars in the current WRNSs operate in distinct frequency bands; thus, the total bandwidth that is required for a WRNS increases linearly with the number of radar deployments. For example, in the US WRNS, 160 radars are deployed throughout the USA, each of which requires 5 MHz bandwidth [3]. Although a frequency reuse scheme can be employed in the deployment, we must allocate a significantly wide frequency band to the WRNS, which is extremely costly.
A simple solution is to make multiple radars share the same frequency band. Frequency sharing can be realized by operating radars separately in other domains than the frequency domain: as in wireless communications area, we can consider the time domain and code domain. In the approach of frequency sharing by separating radars in the time domain, only one radar operates for a certain period of time and, after the period, one of the other radars starts to operate in a given order. The main problem in this approach is that the time interval from a radar’s pulse emission to the next pulse emission grows linearly with the number of radars that share the spectrum. Due to the limitation of observation time, the increase in the pulsetopulse time interval reduces the amount of sensing data averaged over the whole observation time, which degrades estimation and forecasting accuracies.
In this paper, we consider frequency sharing by separating radars in the code domain, in which each radar is distinguished by exploiting its own code “orthogonal” to those of the other radars. (In a WRNS, the word “orthogonal” is used in a different sense, which will be defined in Section 3). By separating the radars of a WRNS in the code domain, we can avoid the problem of the decrease in estimation accuracy in the time domain approach. In the code domain approach, we need to employ the technique of pulse compression [4]. Pulse compression is a technique employed in a single radar (which is not necessarily a weather radar) system in order to improve the performances of range resolution and sensitivity together under the limited peak power. Meanwhile, in this paper, the technique of pulse compression is adopted for achieving the objective of frequency sharing in a WRNS in combination with orthogonal codes. Specifically, a radar transmits a pulse modulated with its own (pulse compression) code in waveform generation; on the reception mode, the radar can extract its own signal by canceling out the signals from other radars via the matched filter (MF).
Translating the idea of frequency sharing by using orthogonal codes into a feasible WRNS is an extremely difficult problem in itself. The difficulty is mainly attributed to the extremely significant signal interferences, which hinder accurate estimation of weather parameters. The interferences in a WRNS can be categorized into (1) intersite interference and (2) intrasite interference.
Intersite interference occurs when multiple radars share the same frequency band. Specifically, a signal associated with one radar can interfere with those associated with other radars. The interference inevitably distorts the received signals of the radars, thereby leading to inaccurate estimations of weather parameters. On the other hand, intrasite interference happens even when there is only one radar operating in the frequency band. It can be regarded as a kind of selfinterference due to partial overlap of the multiple backscattered signals that occur when the radar signal is backscattered by closely located multiple targets. This intrasite interference becomes highly serious in a radar system that employs a long pulse (e.g., pulse compression radar) and that deals with volumetype targets (e.g., weather radar).
There have been several studies to mitigate intersite interferences by proposing nearly orthogonal codes. In [5], an algorithm was proposed for deriving nearly orthogonal codes that can be exploited in multistatic radar network systems. In [6, 7], a design framework was proposed for generating polyphase codes that can be adopted for orthogonal netted radar systems. On the other hand, several studies have focused on mitigating intrasite interferences. For example, in [8], an algorithm was proposed to use an inverse filter in order to reconstruct real peaks from the received signal. In [9], effective sidelobe suppression algorithms were introduced for discrete point targets and contiguous scattering targets, which we refer to as the CLEAN algorithm in this paper. In [10], a combination of the phase distortion and spectrum modification techniques was proposed for sidelobe suppression in a single weather radar with pulse compression. Unfortunately, none of the previous approaches in [5–10] is appropriate to successfully address the two challenges (intrasite and intersite interferences) simultaneously.
In this paper, we propose a novel WRNS in which multisite weather radars operate in the same frequency band, with the key issue of overcoming the two challenges described above simultaneously. The proposed system suppresses the intersite interference by adopting pulse compression with nearly orthogonal codes, and at the same time, removes the intrasite interference based on a wellknown sidelobe suppression mechanism. Through computer simulations, the proposed frequencysharing WRNS is shown to be feasible even when the performance requirement of conventional single weather radar systems is applied.

The novelty of this paper mainly lies in the design of an architecture of a novel WRNS that enables the constituent radars to share the same frequency band. In Fig. 1, we have presented the architecture of the proposed frequencysharing WRNS. In the transmission mode, each radar transmits a pulse modulated with a distinct code from nearly orthogonal pulse compression codes. Then, in the reception mode, each radar captures signals backscattered by weather targets, which contain the signals originated from other radars also. The received signal first goes through the MF, which results in suppression of the intersite interference. Subsequently, by applying an additional process of sidelobe suppression, the intrasite interference is mitigated effectively.

We have conducted an elaborate study on feasibility of the WRNS. Specifically, the estimation accuracies on two weather parameters, reflectivity and velocity, satisfied the performance requirements of a typical single weather radar, WSR88D, under the expected SIR condition. To the best of our knowledge, this study is the first to validate the feasibility of frequencysharing weather radar systems.
The rest of this paper is organized as follows. We will first present the system model of a WRNS in Section 2. In Section 3, the key techniques for frequency sharing in the WRNS are described. Next, the performance of the proposed system is evaluated through computer simulations in Section 4. Finally, our work will be concluded in Section 5.
2 System model
Nomenclature
c  Speed of light 
Δ τ  Subpulse duration time 
g _{ n,1} (n≠1)  Reflection channel for interference from Radarn to Radar1 
\(\boldsymbol h_{1}^{(k)}\)  Reflection channel for backscattering of kth pulse of 
Radar1  
K  Number of emissions of pulses for observation of one 
direction  
λ  Wave length of radar signal 
L  Length of pulse compression code 
L _{ T }  Length corresponding to pulse repetition time T, L _{ T } = T / Δ τ 
N  Number of radars in radar network 
P  Number of possible phases in pulse compression code 
\(\boldsymbol R_{n_{1},n_{2}}\)  Normalized correlation of \(\boldsymbol s_{n_{1}}\) and \(\boldsymbol s_{n_{2}}\) 
(autocorrelation if n _{1}=n _{2}; otherwise, crosscorrelation)  
s _{ n }  Pulse compression code for Radarn 
τ  Pulse duration time, τ=L Δ τ 
T  Pulse repetition time 
v _{1}  Radial velocity of weather target in \(\boldsymbol h_{1}^{(k)}\) 
Z _{1}  Reflectivity of weather target in \(\boldsymbol h_{1}^{(k)}\) 
Assume a WRNS consisting of N monostatic weather radars with pulse compression, where the nth radar is denoted by Radarn. To understand how each radar can extract weather parameters in the presence of other radar signals, we focus on the operations of removing interferences and reconstructing target information in a specific radar (we call this radar the main radar) and regard the other radars as interferers (we call these radars interfering radars). Without loss of generality, we consider Radar1 as the main radar and Radars 2,3,⋯,N as interfering radars throughout this paper.
Each radar periodically switches its antenna mode between the transmission and reception modes. Specifically, in the transmission mode, the radar transmits its pulse in the current direction of the antenna; it switches the mode to the reception mode and captures radar signals in the air for a while. Then, it switches back to the transmission mode for transmitting the next pulse. Here, the interval between two adjacent transmissions is called the pulse repetition time (PRT), and is denoted by T. Note that, in order to improve observation performance for a specific direction, a radar stays in the direction during a number of repetitions of the two modes: we denote this number of repetitions by K.
2.1 Pulse transmission
We assume that all the radars in the WRNS considered in this study employ pulse compression. The purpose of employing pulse compression in our system is entirely different from that in conventional single radar systems. In conventional single radars, pulse compression is employed in order to improve both performances of range resolution and sensitivity (i.e., target detection capability) under the limitation of peak power [12]. On the other hand, in the WRNS of this study, pulse compression is for removing interferences from other radars by employing mutually uncorrelated codes, which will be addressed in detail in Section 3.
where L is the code length and corresponds to the pulse duration time τ=L Δ τ. Here, Δ τ denotes the subpulse duration time.
2.2 Reflection of pulse by weather targets
based on the weather radar equation [13]. Here, Z _{1}[ i] is the reflectivity of the ith target in the current direction of Radar1, \(d_{1}[\!i] = \frac {1}{2}ci \Delta \tau \) is the distance between the target and radar with c denoting the speed of light, G _{ t } and G _{ r } are the antenna gains for transmission and reception, respectively, and the constant k _{ R } depends on the radar parameters such as 3dB beamwidth, pulse duration time, and wavelength. Note that G _{ t } and G _{ r } rely on the path of the radar signal, which will be addressed in detail later in Section 4.1.3.
is the average phase change for the PRT due to the (average) radial velocity v _{1}[ i] of the ith target and λ is the wavelength of the radar signal. The term Δ φ _{1}[ i] indicates the variance of the phase change, which is associated with the variation of the velocity of the target. In this feasibility study, we assume Δ φ _{1}[ i]=0 for simplicity.
2.3 Reception of reflected pulses
Here, for n=2,3,⋯,N, g _{ n,1} is the impulse response of the reflection channel between the interfering Radarn and the main Radar1.
In (7), the term \(\boldsymbol s_{1} * \boldsymbol h_{1}^{(k)}\) contains the intrasite interference mentioned in Section 1: specifically, the difference between \(\boldsymbol s_{1} * \boldsymbol h_{1}^{(k)}\) and \(\boldsymbol h_{1}^{(k)}\) can be considered as the intrasite interference. On the other hand, the term \(\sum \limits _{n=2}^{N} \boldsymbol s_{n} * \boldsymbol g_{n,1}\) corresponds to the intersite interference.
2.4 Problem definition
To introduce a WRNS that shares the same frequency band, the main challenge lies in overcoming signal distortion that results from the intrasite and intersite interferences. Such distortion hinders accurate estimation of weather parameters such as the reflectivity and velocity. We can formulate this problem as follows:
Problem: Given the received signals \(\left \{\boldsymbol r^{(k)}\right \}_{k=1}^{K}\) at Radar1, which have been contaminated by both of the intrasite and intersite interferences, estimate the reflectivity Z _{1} and velocity v _{1} of the weather targets.
Our problem is, roughly speaking, to estimate the reflection channel \(\boldsymbol h_{1}^{(k)}\), sometimes called the main reflection channel, because the reflectivity and velocity are directly related with the amplitude and phase of \(\boldsymbol h_{1}^{(k)}\) as shown in (3)–(6).
3 Key techniques for frequency sharing
In order to solve the problem of this study, we employ two key techniques: (1) pulse compression with a nearly orthogonal code set and (2) signal processing for sidelobe suppression that further refines the output of the MF.
Let us now describe the details.
3.1 Pulse compression with (nearly) orthogonal code set
3.1.1 Matched filtering
for i=−L+1,−L+2,⋯,L−1 and n _{1},n _{2}=1,2,⋯,N: it is the autocorrelation if n _{1}=n _{2}; otherwise, it is the crosscorrelation.
3.1.2 Orthogonal code set
for n _{1}≠n _{2}. In this paper, we will refer to such a code set as an orthogonal code set.
3.1.3 Design of nearly orthogonal code set
It is impossible to design an orthogonal code set that perfectly satisfies both (12) and (13). Hence, an alternative is to design a code set that satisfies the conditions as closely as possible. In this paper, we call such a code set a nearly orthogonal code set.
There have been many studies on designing nearly orthogonal code sets [5–7, 15]. For example, in the design method proposed in [5], a simple full search algorithm was employed based on Hadamard and Fourier matrices that have the property \(R_{n_{1},n_{2}}[\!0] = 0\) for n _{1}≠n _{2}: it is noteworthy that the cost function of this method is defined in terms of the peak values of correlations, not energies. In [6], a hybrid optimization method combining simulated annealing (SA) with a traditional iterative code selection was proposed to design a nearly orthogonal polyphase code set. In [7], another optimization method based on cross entropy technique was proposed, where a structural constraint to maintain Doppler tolerance was considered together with the orthogonality conditions.
Procedure for the design of a nearly orthogonal polyphase code set
Step 1: SA  
1a.  Given N (number of radars), L (code length), and P (number of possible phases), initialize the code set matrix S with \(s_{n}[i] \in \left \{\exp \left (j\frac {p}{P}2\pi \right) p=0,1,\cdots,P1\right \}\). 
1b.  Set the current temperature t as a predefined initial temperature t _{0}. 
1c.  Randomly select an element from S and replace its phase with a phase randomly selected from the remaining P−1 phases. 
1d.  Evaluate the change Δ E of the cost value in (19) after the replacement. Accept the new phase value if Δ E<0; otherwise, accept it with probability \(\exp \left (\frac {\Delta E}{t}\right)\). 
1e.  Determine if the equilibrium state is reached based on a predefined criterion. If the state is reached, go to 1f; otherwise, go back to 1c. 
1f.  If the cost value is changed during the last three consecutive temperature reductions, update (reduce) the temperature t based on a predefined cooling schedule and then go back to 1c. Otherwise, stop the procedure. 
Step 2: iterative code selection for fine tuning  
2a.  Start with the design result S from Step 1. 
2b.  For every element of S, tentatively replace the phase with any of the other P−1 phases possible. If the evaluated cost value is reduced as a result of a phase replacement, accept the phase replacement; otherwise, keep the original phase value. 
2c.  If any of phase in S was changed, that is, any phase replacement was accepted, go back to 2b. Otherwise, stop the procedure. 
of the n _{1}th and n _{2}th codes (n _{1}≠n _{2}) in dB. Considering conditions (12) and (13) of an orthogonal code set, it is clear that the smaller the values of ASPs and CPs of a nearly orthogonal code set are, the closer the code set is to an orthogonal code set.
3.2 Iterative sidelobe removal
Unlike the MF output (14) where an orthogonal code set is employed, there exist two additional terms \(\boldsymbol h_{1}^{(k)}* \bar {\boldsymbol R}_{1,1}\) and \(\sum \limits _{n=2}^{N} \boldsymbol g_{n,1}*\boldsymbol R_{n,1}\) in (22), which makes it difficult to directly estimate \(\boldsymbol h_{1}^{(k)}\) from the MF output. The first term is caused by the nonzero autocorrelation sidelobe, i.e., \(\bar {\boldsymbol R}_{1,1} \neq \boldsymbol 0\), and therefore, can be regarded as distortion from autocorrelation sidelobe. In contrast, the second one comes from the nonzero crosscorrelation, i.e., R _{ n,1}≠0, and can be regarded as residual interferences from other radars after matched filtering.
The degree of performance degradation due to the distortion from autocorrelation sidelobe is much more serious than that due to the residual interferences. The reasons can be explained as follows. (A) the amplitude of the main reflection channel \(\boldsymbol h_{1}^{(k)}\) is usually much larger than that of the interfering channel g _{ n,1} because the antenna reception gain G _{ r } in \(\boldsymbol h_{1}^{(k)}\) is likely to be much higher than that in g _{ n,1}: we will elaborate the first reason later in Section 4.1.3. (B) Contiguous deployment of weather targets leads to an overlap between autocorrelation sidelobes of adjacent targets, which vastly distorts the MF output even with the code of low autocorrelation sidelobe. For this reason, a pulse compression radar system dealing with weather targets [16] has focused on addressing the distortion from autocorrelation sidelobe.
Procedure for the iterative sidelobe removal
3a.  Start with the MF output \(\boldsymbol y_{MF}^{(k)}\) in (22) as the input. 
Set the processing output y ^{(k)} to 0 initially.  
3b.  Set the sequence a for the innerloop processing as \(\boldsymbol a=\boldsymbol y_{MF}^{(k)}\). 
3c.  Find the peak of a: specifically, \(i_{M}=\arg \max \limits _{i} \left  a[\!i] \right \) and M=a[i _{ M }]. 
Let a _{0} denote the subsequence of a with length 2L−1, which is centered at i _{ M }: specifically, a _{0}[ i]=a[i _{ M }+i] for i=−L+1,−L+2,⋯,L−1. Then, evaluate the sidelobe level \(Q\left (\boldsymbol a_{0}\right)=\sum \limits _{i \neq 0} \left a_{0}[\!i]\right \) of a _{0}.  
Set the weight β for sidelobe subtraction to the initial value β _{0}∈(0,1).  
3d.  Tentatively subtract a portion of the sidelobe component corresponding the detected peak from a _{0}, and denote the result by a _{1}: specifically, a _{1}=a _{0}−β M R _{1}. Then, evaluate the the sidelobe level Q(a _{1}) of a _{1}. 
3e.  If Q(a _{0})−Q(a _{1})<γ β M Q(R _{1}) for the threshold coefficient γ∈(0,1], go to 3f1. Otherwise, go to 3f2. 
3f1.  Replace β with β/2. If β=β _{0}/32, stop the trial of sidelobe subtraction for this peak and go to 3g. Otherwise, go back to 3d. 
3f2.  Accept the sidelobe subtraction as follows: a[ i _{ M }+i]=a[ i _{ M }+i]−β M R _{1}[ i], \(y_{MF}^{(k)}[\!i_{M}+i]=y_{MF}^{(k)}[\!i_{M}+i]\beta M R_{1}[\!i]\), and y ^{(k)}[ i _{ M }+i]=y ^{(k)}[ i _{ M }+i]+β M R _{1}[ i]. 
3g.  Make this peak unavailable as a peak again in any subsequent innerloop by setting a[i _{ M }]=0. 
3h.  If the average amplitude \(\frac {1}{L_{T}} \sum \limits _{i} \left a[\!i]\right \) of a is smaller than the preset value, quit the inner loop and go to 3i. Otherwise, go back to 3c. 
3i.  If the standard deviation of \(\boldsymbol y_{MF}^{(k)}\) is close to the expected noise level, stop the procedure and output y ^{(k)}. Otherwise, go back to 3b. 
respectively.
4 Simulation results
In this section, we examine the feasibility of the proposed frequency sharing scheme for a WRNS through computer simulations. All programs for the simulations have been implemented in MATLAB and are available in [17].
4.1 Simulation conditions
4.1.1 Configuration of the radar network
We first assume a simple radar network consisting of N = 3 weather radars with pulse compression. In the radar network, as described in Section 2, Radar1 operates as the main radar while Radar2 and Radar3 operate as interfering ones against the main radar. Next, we artificially construct three reflection channels: \(\boldsymbol h_{1}^{(k)}\) (from Radar1 to Radar1), g _{2,1} (from Radar2 to Radar1), and g _{3,1} (from Radar3 to Radar1). Specifically, we design a set of three functions, which are then adopted as the amplitudes of the impulse responses of the three reflection channels. For the phase components of the impulse responses, each of which is associated with the velocities of the weather targets in the corresponding reflection channel as (5) and (6), we simply set all the velocities of the weather targets in each reflection channel to a constant: specifically, v _{1}[ i]=15, v _{2,1}[ i]=5, and v _{3,1}[ i]=−5.
4.1.2 Design of pulse compression codes
By using the design method described in Section 3.1.3, we have designed a nearly orthogonal polyphase code set with length L=128 and P=4 phases for N=3 radars: specifically, we have obtained the 3×128 code set matrix S=[s _{ n }[ i] ] for n=1,2,3 and i=1,2,⋯,128 with \(s_{n}[\!i] \in \left \{1,\exp \left (j\frac {\pi }{2}\right),\exp \left (j\pi \right),\exp \left (j\frac {3\pi }{2}\right)\right \}\).
4.1.3 Expected SIR
in dB, where ∥·∥ is the Euclidean norm.
Because a radar amplifies the received signals with its antenna gain G _{ r }, the gain should be included in calculating the SIR. In this paper, G _{ r } has already been considered as a factor of the channel amplitude as shown in (4). Here, we should note that a weather radar employs a directional antenna, of which the gain is maximum in the antenna direction (mainlobe direction) and the maximum gain is much larger than the gains of other directions (sidelobe direction): for example, in a typical single weather radar WSR88D [18], the gain difference between the mainlobe and sidelobe directions is at least 29 dB.
For simplicity, in our simulation, we exploit two different gain values when Radar1 amplifies the received signals: the mainlobe gain along the mainlobe direction, and the sidelobe gain along the sidelobe directions. Based on the discussions above, the sidelobe gain is set to the value less than the mainlobe gain by 29 dB. In the WRNS we consider, the backscattered signal \(\boldsymbol s_{1} * \boldsymbol h_{1}^{(k)}\) originated by the Radar1 is assumed to be amplified with the mainlobe gain, whereas the signals s _{ n }∗g _{ n,1} (n≠1) from interfering radars are assumed to be amplified with the sidelobe gain. This is because when a WRNS operates actually, most energy in \(\boldsymbol s_{1} * \boldsymbol h_{1}^{(k)}\) is concentrated on the mainlobe direction in most cases; in contrast, only a small fraction of energy in s _{ n }∗g _{ n,1} (n≠1) is concentrated on the direction.
From this simplification, the SIR of the WRNS can be expected to be around 29 dB if we assume that other factors (antenna H/W, weather conditions, etc.) are the same or similar over the weather radars in the network.
4.1.4 Performance requirements
from (15) and (24). Here, recall that y ^{(k)} is the output of the iterative sidelobe removal algorithm. For convenience, we define a new symbol y _{ av }^{2} of which ith (i=1,2,⋯,L _{ T }) element is \(\frac {1}{K}\sum \limits _{k=1}^{K} \left y^{(k)}[\!i]\right ^{2}\): this can be regarded as an estimate of the squared amplitude \(\left  \boldsymbol h_{1}^{(k)}\right ^{2}\) of the main reflection channel. In simulations, we set the value of K to 10.
The performance requirements of the WSR88D on reflectivity and velocity estimations are as follows [19]: (A) when the signaltonoise ratio (SNR) is higher than 10 dB, the reflectivity error should be less than 1 dB, and (B) when the SNR is higher than 8 dB, the velocity error should be less than 1 m/s. Although the WSR88D is a single radar (not radar network) and a simple pulse radar (not pulse compression radar), we refer to the criteria of the WSR88D in the evaluation of the proposed WRNS. Taking the worst case in the requirements into account, we set the SNR of the WRNS to 8 dB in simulations.
4.2 Result from Set A
4.2.1 When the SIR is 29 dB
Let us first see the performance of the proposed scheme when Set A is employed for the reflection channels and the SIR is set to its expected value of 29 dB. Figure 5 shows the outputs obtained in each step for processing the received signals. The results are generally in accordance with the expectation from the discussions depicted in Section 3. In short, it is clearly observed that the main radar operates successfully satisfying the performance requirement for the conventional weather radars under the influence of interferences from other radars in the same frequency band. Specifically, we can make the following observations. (A) Compared with the received signal shown in the subfigure (b), the MF output in the subfigure (c) is much closer to the main reflection channel in the subfigure (a), especially in terms of the magnitude. (B) Nonetheless, it is not reasonable to consider the MF output as a good approximation to the main reflection channel. As discussed in Section 3.2, the difference between the main reflection channel and MF output comes from three factors: the distortion from autocorrelation sidelobe, residual interferences from other radars, and noise. Among these factors, the effect of the residual interferences from other radars is negligible compared with that of the distortion from autocorrelation sidelobe in this case because the SIR is as high as around 30 dB. (C) Through the iterative sidelobe removal algorithm, we can effectively mitigate the distortion from autocorrelation as shown in the subfigure (d). Finally, the distortion from the remaining highfrequency noise is removed by averaging the outputs of the sidelobe removal process as shown in the subfigure (e). (D) In the subfigures (f) and (g), it is observed that the performances on the reflectivity and velocity estimations practically satisfy the requirements from the WSR88D. Specifically, the errors are around zero in the high reflectivity region. (E) Based on a comparison of the variance of the reflectivity errors with that of the velocity errors, it can be inferred that the phase estimation is more sensitive to noise than the amplitude estimation.
4.2.2 When the SIR is 8 dB
We next consider a case where the SIR condition is worse than 29 dB. From a similar reason of determining the SNR, we can set the SIR to 8 dB for the worst case to see the feasibility of the proposed WRNS. Note that, however, the SIR is generally expected to be around 29 dB in an actually operating WRNS and the possibility of this worst case is not high.
4.2.3 Performance versus SIR
Let us now investigate the average performance of the proposed WRNS with respect to the SIR. For every value of the SIR from 10 to 40 dB at the interval of 5 dB, we have first obtained the reflectivity error Z _{ err }[ i] and velocity error v _{ err }[i] through a simulation as in the subfigures (f) and () of Figs. 5 and 6, and then calculated the averages and standard deviations of the two absolute errors over the whole range (all i’s): we denote these measures by mean(Z _{ err }), std(Z _{ err }), mean(v _{ err }), and std(v _{ err }).
From the results, it is observed that the operation performance of the main radar on reflectivity estimation satisfies the requirement of the WSR88D when the SIR is higher than around 18 dB in terms of the mean. Even if we take the standard variation into account in addition to the mean, the main radar still operates successfully satisfying the requirement when the SIR is around its expected value (29 dB). Similarly, the performance on velocity estimation also satisfies the requirement when the SIR is around its expected value.
4.3 Result from Set B
5 Conclusions
In this paper, we have proposed a novel weather radar network system (WRNS) in which multisite weather radars share the same frequency band. In the proposed frequencysharing WRNS, the intersite interference and intrasite interference are removed simultaneously by adopting pulse compression with nearly orthogonal polyphase codes and an iterative sidelobe removal algorithm.
Through computer simulations, we have validated the feasibility of the proposed frequencysharing WRNS. Specifically, the estimation accuracies on two weather parameters, reflectivity and velocity, satisfied the performance requirements of a typical single weather radar, WSR88D, under the expected SIR condition. We have also observed that the estimation accuracies are not satisfactory when the SIR is lower than the expected level. These results pave the ground for possible improvements of the proposed system, which will be the theme of our future work.
In addition to the fact that (to the best of our knowledge) this study is the first to validate the feasibility of frequencysharing weather radar systems, the beauty of this work is that we can apply the proposed architecture to other radar applications in which the scarcity of frequency resource is serious. For example, the proposed architecture with minor modifications (e.g., selection of codes) can be employed in vehicular radar systems in which radars share the same frequency band.
Declarations
Acknowledgements
The authors wish to thank the Associate Editor and anonymous reviewers for their constructive suggestions and helpful comments. This work was supported by the ICT R &D program of MSIP/IITP [B010116222, Development of Core Technologies to Improve Spectral Efficiency for Mobile BigBang] and by the National Research Foundation of Korea, with funding from MSIP, under Grant NRF2015R1A2A1A01005868.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License(http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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