1、 Rep. ITU-R M.2136 1 REPORT ITU-R M.2136*Theoretical analysis and testing results pertaining to the determination of relevant interference protection criteria of ground-based meteorological radars (2008) The present Report provides theoretical analysis and testing results pertaining to the determina
2、tion of relevant interference protection criteria of ground based meteorological radars with the key objective to establish the maximum interference level that meteorological radar systems can withstand before their forecasting capability is compromised. The analysis and related test results as in A
3、nnex 1 are related to meteorological radars operating in the frequency band 2 700-2 900 MHz and support the requirement for a protection value that could be as low as 9 dB I/N for the base reflectivity data. Calculations show that the I/N value at which the spectrum width performance is degraded bey
4、ond the system requirements (bias 1 m/s) is even lower (14.4 dB) but measurements only support an I/N of 10 dB for spectrum width. The test results performed with a meteorological radar operating in the frequency band 5 600-5 650 MHz as in Annex 2 confirm the analysis described in Annex 1 for meteor
5、ological radar operating in the frequency band 2 700-2 900 MHz and support the requirement for a protection value that could be as low as 12.75 dB I/N for the base reflectivity, i.e. for products that are related to signal power. For meteorological products not related to signal power (such as Doppl
6、er of differential phase modes) lower sensitivity thresholds would likely be necessary. As an overall conclusion, this Report provides elements that confirm that, in order that most meteorological radars and their corresponding products be protected, a minimum I/N = 10 dB should be used. *This Repor
7、t should be brought to the attention of the World Meteorological Organization (WMO). 2 Rep. ITU-R M.2136 Annex 1 Results of tests with a meteorological radar operating in the frequency band 2 700-2 900 MHz Executive summary The key objective of the work contained in this Annex 1 was to establish the
8、 maximum interference level that meteorological radar systems can withstand before their forecasting capability is compromised. Based upon the radars technical specifications, mathematical models have been derived for key products (base reflectivity, mean radial velocity and spectrum width) that ind
9、icate what these expected levels should be. In order to physically validate this analysis, a test and data analysis methodology has been defined through which data were collected and analysed. The analysis of the data supports the calculated value required for protection of the reflectivity measurem
10、ents. Current limitations in the radar calibration and noise removal process performed by the low-level data processor limit the measurement of the necessary protection criteria for the spectrum width measurements. However, correction of the data for the limitations of this processing results in val
11、ues that support the calculated protection values. 1 Introduction Tests were run on a modern meteorological radar (noted as radar 1 in Annex 2 of Recommendation ITU-R M.1849) to determine the appropriate criteria necessary for protection from continuous wave (CW) and interference signals in the 2 70
12、0-2 900 MHz band. The tests were comprised of injecting a CW signal and six different digital modulation schemes into the radar receiver while it was scanning the atmosphere. Low-level or base meteorological products (base reflectivity, mean radial velocity and spectrum width) were recorded while co
13、nducting a series of antenna rotations at a single antenna elevation. Interference signals were injected with I/N ratios ranging from +6 dB to 15 dB. 2 Theoretical calculation of necessary protection criteria The radar generates three base products that are used by the signal processing system to de
14、rive the meteorological products that are used by the meteorologist. These base products are: volume reflectivity, Z (mm6/m3) which for rain is a measure of total water in the radar sample volume; mean radial velocity, V (m/s) which is the power weighted mean radial motion of the targets in the samp
15、le volume; spectrum width, W (m/s) which is a measure of the radial velocity dispersion of the targets in the sample volume. 2.1 Minimum signal level Signal processing removes the radar system noise effects from the reflectivity and spectrum width products so that the system can provide these produc
16、ts when the signal level is below the receiver noise level. The S/N threshold, i.e. the lowest level for which the return signal is processed, is selectable by the radar operator between the limits of 12 dB S/N and +6 dB S/N. With the present Rep. ITU-R M.2136 3 signal processing, the lower values a
17、re generally not used due to limitations with noise removal but the system provides useful products down to 3 dB S/N. The interference level that compromises the system is related to the minimum signal level of 3 dB S/N and the product characteristics themselves, as described below. Excessive interf
18、erence will impact data quality, degrade the meteorological products, and compromise the systems ability to accomplish its mission of providing data necessary for public weather forecasting, severe weather warning, and rainfall measurement for flash flood prediction and water management. 2.2 Reflect
19、ivity maximum I/N Reflectivity is used in multiple applications; the most important of which is rainfall rate estimation. Reflectivity is calculated from a linear average of return power and is subject to contamination by interference as an unknown increase in the measured reflectivity. Reflectivity
20、 is seriously contaminated if the bias exceeds the system specifications1. Given the radar systems dB bias and S/N, the following equations can be used to calculate the I/N that is required in order to protect the integrity of the reflectivity product. Bias in terms of I/S is given by: SIS += log10b
21、iasdB Solving for I/S yields: 110bias dB10/ =SI I/N is then equal to: NSSINI /)/(log10/ += Example calculation for a 1 dB bias and an S/N of 3 dB: 110110/ =SI I/S = 0.26 10 log I/S = 5.8 dB Therefore, reflectivity is biased 1 dB at an interference level 5.8 dB below the signal. Since the minimum sig
22、nal level has an S/N of 3 dB and the maximum I/S level for the reflectivity product is 5.8 dB, the maximum I/N is: (3 dB) + (5.8 dB) = 8.8 dB I/N 1The dB bias is a function of the radars calibration accuracy and equal to the standard deviation of the reflectivity estimate as specified in the radar t
23、echnical requirements. 4 Rep. ITU-R M.2136 2.3 Mean radial velocity maximum I/N Mean radial velocity is calculated from the argument of the single lag complex covariance. The complex covariance argument provides an estimate of the Doppler signal vector angular displacement from radar pulse to radar
24、pulse. The displacement divided by the time interval between the pulses is the Doppler vector angular velocity. As a broadband noise, the interference signal vector has uniform probability over the complex plane and thus does not introduce a systematic rotation of the Doppler vector and does not int
25、roduce a bias in the estimate. However, the “randomness” of the composite signals plus interference vector due to the interference increases the variance of the Doppler signal estimate. The Doppler frequency variance, retaining all terms except those inversely proportional to the number of samples s
26、quared can be calculated as: 22222222/3)(8)2(12)(82)var(TTMTSNSNTTMWTf+=where: f: frequency estimate (Hz) W: standard deviation of frequency spectrum (Hz) = 80 Hz with 4 m/s for N/T benchmark at fc= 2 995 MHz T: sampling interval (s) = 103s for N/T benchmark M: number of samples in estimate N: noise
27、 power S: signal power : signal correlation at lag T = exp (22W2T 2) for the assumed Gaussian spectra. The first term is the variance contribution due to the signal characteristics and the second term is the variance contribution due to the noise. The frequency variances are severely compromised if
28、the interference increases the variance by more than 50%. The uncertainty in the data degrades all velocity-based products and the velocity shear measurements in particular (velocity shear is a velocity difference over some distance). A 50% increase in variance increases the reliably detected shear
29、value approximately 25% above the severe weather event formative stage value. An expression for I/N as a function of a percentage variance increase of a given radars benchmark parameters and S/N is given by: )(2122/22/3TSINSINWTNI += Rep. ITU-R M.2136 5 where2: W: standard deviation of frequency spe
30、ctrum (Hz) T: sampling interval (s) M: number of samples in estimate N: noise power S: signal power : signal correlation at lag T. Example calculation for a 50% variance increase of the technical requirements benchmark parameters and an S/N = 3 dB is given by: )2(1)2(2/32/3)2(2/3)(212222/322/3TSNSNW
31、TTSINSINWT +=+where: W = 80 Hz T = 103 s 23/2WT = 0.89 1 (2T) = 0.4 S = 0.5 N. Substituting and solving for I/N yields the quadratic expression: 021.1)/(2)/(2=+ NINI 49.0/ =NI dB3/log10 =NI Therefore, the interference can be no greater than the minimum signal value. 2.4 Spectrum width maximum I/N Th
32、e spectrum width is calculated from the single lag correlation assuming a Gaussian spectral density. The algorithm is expressed as: 2/122n1SRVaW = 2The standard deviation of frequency spectrum (Hz), the sampling interval (s) the number of samples in the estimate and the S/N are governed by the radar
33、s technical specifications and performance benchmarks. 6 Rep. ITU-R M.2136 where: W: spectrum width (standard deviation) Va: Nyquist velocity, 25 m/s from the radar technical requirements R: single lag covariance power S: signal power. The interference signal causes both a bias and a variance increa
34、se in spectrum width estimation but the bias is more detrimental. Spectrum width is compromised when the interference induced bias exceeds the radar technical requirement width accuracy. The I/N at which this bias level occurs can be calculated by solving for the covariance that is defined by the ra
35、dars performance metric and signal power of N/2, then solving for the S + I level that produces a spectrum width that is equal to spectrum width base value as defined in the radars technical specifications plus value of the spectrum width accuracy requirement. An example calculation follows for rada
36、r with a width accuracy requirement of less than 1 m/s at a spectrum width of 4 m/s follows. To calculate I/N, the equation above is solved for the 4 m/s and 5 m/s cases (S/N = 3 dB). :m/s4For =W :m/s5For =W 4)/(n1/252/122= SR 5)(n1/252/122=+ IR 25.0)/(In22=SR 39.0)(/In22=+ ISR 88.0/ =SR 82.0)(/ =+
37、ISR SR 88.0= )2/(88.0 NR = :2/),2/(88.0:Substitute NSNR = 82.0)2/(/)2/(88.0 =+ INN )2/(88.0)2/(82.0 NIN =+ 0366.0/ =NI dB4.14)/(log10 =NI Table 1 shows the results of several I/N calculations that were based upon varying SNR and spectrum width accuracies. The results show that the theoretical I/N re
38、quirements of meteorological radars varies as a function of the radars technical specifications and base data accuracy requirements. Rep. ITU-R M.2136 7 TABLE 1 Comparison of I/N for several hypothetical meteorological radars Radar A SNR = 3 dB Radar B SNR = 0 dB Radar C SNR = 0 dB Base data accurac
39、y requirement TheoreticalI/N Base data accuracy requirementTheoreticalI/N Base data accuracy requirement TheoreticalI/N Reflectivity 1 dB 9 dB 1 dB 6 dB 1 dB 6 dB Radial velocity 1 m/s 3 dB 1 m/s 0 dB 1 m/s 0 dB Spectrum width 1 m/s 14.4 dB 1 m/s 14.4 dB 2 m/s 10.6 dB From this observation one can c
40、onclude that the defining of an “average” I/N for meteorological radars would provide some degree of overall meteorological radar protection but could not be applicable to all meteorological radars. As a result, I/N would have to be computed for various meteorological radars based upon their specifi
41、cations and base data accuracy requirements. In the absence of test data to determine protection criteria for specific radar, the formulas may be used to derive the protection criteria for studies where more detail is required. 3 System operation, output products and interference sensitivity 3.1 Sys
42、tem operation mode for testing The radar has multiple modes of operation that utilize different antenna rotation rates, antenna elevations and PRF. The operation mode selected for the tests is one of the more commonly used modes, and is optimized for system sensitivity leading to high susceptibility
43、 of interference. Table 2 provides the characteristics of the mode used in testing. TABLE 2 Characteristics of the meteorological radar system used in testing Radar characteristics Frequency 2 995 MHz Pulse power 750 kW Pulse width 4.7 s PRF 322 Hz (first cut) 446 Hz (second cut) Maximum coverage ra
44、nge 290 miles (approximately 467 km) RF bandwidth (at 3 dB points) 13 MHz IF bandwidth 630 kHz System noise figure 4.9 dB Antenna pattern type Pencil Antenna scan rate 0.84 r.p.m. Antenna scan time 71.4 s Antenna height 30 m Antenna beamwidth 0.90 Polarization Linear horizontal 8 Rep. ITU-R M.2136 I
45、n the mode used, the antenna rotation starts at an elevation of 0.5, the radar transmits a 4.7 s pulse every 3.1 ms for the first rotation, then transmits a pulse every 2.24 ms for the second rotation. These correspond to PRFs of 322 Hz and 446 Hz respectively. Each revolution covers 360 in azimuth.
46、 Under normal operation, the radar also performs antenna rotations at several higher elevation angles before returning to 0.5. For the purposes of this test, the two elevation cuts at the single antenna elevation provided sufficient data for analysis and the cuts at higher elevations were not perfor
47、med. The first antenna rotation is used to measure reflectivity and the second rotation is used to measure mean radial velocity and spectrum width (see further). For each location in the atmosphere, multiple pulses are transmitted and received. Due to the duration of the transmit pulses compared to
48、the time between pulses, the system is in receive mode more than 99.5% of the time. Magnitude of the received pulses are approximately 200 dB lower than the transmitted pulses because the pulses are scattered by small airborne objects (on the order of millimetres in diameter or smaller) at distances
49、 up to hundreds of kilometres from the radar. The received signal is down-converted from 2 995 MHz to the IF frequency of 57 MHz where it is then applied to the synchronous detector. The detected I and Q baseband signals are digitized to a 16-bit level for use in the processing subsystems. 3.2 Output products The returned pulses from each location are used by the processing subsystems to derive the three meteorologi
