1、240 STD-ITU-R RECMN SM-II27L-ENGL 1997 m q855212 05343Z8 333 Rec. ITU-R SM.1271 RECOMMENDATION ITU-R SM. 127 1 EFFICIENT SPECTRUM UTILIZATION USING PROBABILISTIC METHODS (Question ITU-R 4Y1) (1997) The ITU Radiocommunication Assembly, considering that communications technology has advanced rapidly d
2、uring the past decade and the use of radiocommuni- a cation services by administrations has multiplied and placed new demands on the radio spectrum; b) c) d) through the application of probabilistic methods; e) spectrum sharing situations and spectrum utilization against performance standards; that
3、frequency sharing is one of the important aspects of efficient frequency spectrum utilization; that many guidelines and sharing criteria are based on the most unfavourable interference assumptions; that more efficient spectrum utilization may depend on the acceptance of performance criteria develope
4、d that the statistical characteristics of both the desired and interference signals would be necessary to evaluate recommends 1 probability of interference and its impact on system performance. 2. that in order to assess fully the interference potential of introducing a new system into the environme
5、nt, the probability of interference due to multiple interference sources should be considered using techniques such as those shown in Annex 1 and for calculation a probability of interference for base to mobile and mobile to base interference modes in a land mobile duplex system a methodology given
6、in Annex 2 should be used. NOTE 1 - Future examples will be included to explain how probabilistic methods be used to estimate characteristics of desired and interfering signals with the objective of increasing spectrum utilization. that in order to achieve more efficient spectrum utilization, admini
7、strations should consider the use of the ANNEX 1 (Example i) The calculation of the received voltage due to the radiation from multiple Co-frequency sources 1 Introduction There are many frequency sharing situations where interference may occur. In some situations the number and location of possible
8、 interfering sources are not known (e.g. when the interference is from land-mobile radio transmitters). In these situations, interference can be estimated using probabilistic methods. This example describes a method that clearly demonstrates the concept of calculating interference levels due to mult
9、iple sources using probabilistic methods. Consider, for the sake of simplicity, the case of an airborne receiver flying over an urban area. In this particular case the effects of the earth curvature can be neglected. The airborne antenna will be assumed to be a half-wave dipole with a cosine pattern
10、. The N interfering sources are assumed to be uniformly distributed over the area which is assumed to be circular of radius R as shown in Fig. 1. STDoITU-R RECMN SM*L27l-ENGL 1777 W 4855232 0539327 27T W 241 Rec. ITU-R SM.1271 FIGURE 1 Airborne receiver over an urban area with uniformly distributed
11、interference sources The objective will be to derive a simple expression for the probability density function of the received r.m.s. voltage at the receiving antenna terminals. This example is based on several simplifying assumptions as follows: - The number of the interfering transmitters, N, is la
12、rge. - The interfering transmitters are uniformly distributed, in geographical terms, over a circular area of radius R. - All interfering transmitters have equal amount of radiated power. - The receiver, which is subjected to interference from all the mobiles, is airborne at an altitude h, directly
13、above the centre of the circular area that contains all the interfering sources. - The propagation law from any interferer to the airborne receiver is approximated by the free-space propagation rule. 2 The method Considering the airborne receiver now flying over the urban area, the voltage at the re
14、ceiving antenna terminals can be written as follows: STD-ITU-R RECMN SM.1271-ENGL 1797 II 98552L2 0534330 TL m 242 Rec. ITU-R SM.1271 CA is the relationship between the field strength at an antenna and the voltage across its terminals when matched to a 50 L2 load: A(dJ is the complex antenna factor
15、which is related to the interferer-to-antenna distance di as follows: A(di) = a(di) (3) Ki and p; are the amplitude and phase of the field at the receiving antenna due to interferer i and are defined as follows: Ki = EL %) K, (4) whereEL is the specified field strength limit (MV/m) at a distance d (
16、m) from a single interfering source. K, is the interferer radiation pattern factor, accounting for the reduction of the mean level compared to the maximum level. di is the interferer-to-antenna distance in (m). where h is the wavelength and p(0) is the initial phase of the signal as it leaves source
17、 i. Equation (1) can therefore be rewritten as follows: where: where It can be easily shown that I v I follows a Rayleigh distribution such that: is uniformly distributed between O and 2.n. 2 2 where c2 = (N/2). E(vi ) is the expected value of vi. The r.m.s. voltage is v. = . From the variables alre
18、ady stated, the r.m.s. voltage can be calculated as follows: STD*ITU-R RECMN SMm1271-ENGL 1777 W Li855212 0534331 928 W Rec. ITU-R SM.1271 243 The antennddistance factor: is due to the combined effect of the receiving antenna pattern and the spread of the interfering sources over a given area and ma
19、y be calculated by considering the probability distribution of the interfering sources. Assuming a uniform distribution for purposes of simplicity, refemng to Fig. 1, the probability density function of the locationr of the interfering sources is given by: Since the earth curvature is negligible, th
20、e interferer-to-receiving antenna distance is given by: di = dr2 + h2 Also since we assumed a cosine law for the antenna: a(di) - hidi Thus the antenna factor is given by: a(di)ldi - hid? = hi r + h (2 “1 of which the expected value is: 1 R2 + h2 The above expression is suitable for computing the co
21、mbined radiation from many sources over a relatively small area, such as small towns where earth curvature can be neglected. For large cities where the earth curvature cannot be neglected, a relatively more complex formula can be obtained. 3 Conclusion In this example, we can see that in order to es
22、timate the effect of multiple sources of interference which have unknown locations, it is necessary to use probabilistic methods under the assumptions given in the Introduction. The two random variables, namely the received voltage and the antenna factor, have to be considered in their expected valu
23、e form. Equations (10) and (15) are example formulae for computing the interference voltage from the summation of a relatively large number of interfering sources. STD-ITU-R RECMFI SM-1271-ENGL 1597 Hl 4855232 0514332 bli m 244 Rec. ITU-R SM.1271 ANNEX 2 (Example 2) A methodology to calculate a prob
24、ability of interference for base station to mobile station and mobile station to base station interference modes in a land mobile duplex system 1 Introduction In land mobile systems, the reuse distance between Co-channel base stations is traditionally determined according to acceptable level of inte
25、rference at the victim mobile station. This is a “deterministic” methodology in which probability of interference is not considered. Hence, the reuse distance calculation is based on worst case scenarios. Clearly, such systems do not frequently operate in such scenarios, hence leading to inefficient
26、 use of spectrum. The methodology presented herein is based on a “probabilistic” approach. It defines a probability of interference that is dependent on distance between Co-channel base stations. Reuse distance can hence be determined according to an acceptable level of interference probability, whi
27、ch is a function of specific system parameters, and also to the off-channel rejection (OCR) which is a measure of the capability of a receiver to reject interference. This parameter was defined in Recommen- dation IT-R SM. 337. The probability of interference is defined as the ratio of the area with
28、in the coverage area that would suffer interference to the total coverage area. In this example, the distribution of mobiles inside both the victim and the interfering coverage areas is assumed to be uniform. One would think that this probability would decrease as the distance of separation between
29、base stations increases. The analysis in this paper shows that this is not always the case. For certain values of OCR, the probability of interference will actually increase and then decrease as distance increases. Using the probability curves, it is possible to select a smaller distance of separati
30、on at an acceptable probability of interference, hence increasing the utilization of the spectrum. This method of calculating the probability of interference is independent of the modulation technique used. It can also be applied to both analog and digital radio systems of different channel widths.
31、2 Interference criteria calculation This example provides a methodology to determine the probability of interference in a land mobile duplex system. The base to mobile interference and the mobile to base interference are dealt with separately. First, it is necessary to define a criterion to determin
32、e if there is harmful interference or not. In the interference criterion, interference is assumed to occur if the interference power level Pi is higher than the desired power level P,. by a certain protection ratio, E (dB) (i.e. if Pi - P, E). By using the 4th power law, it is possible to express th
33、e power levels in terms of distances so that the interference critenon becomes d2 1. The interference areas for the three values of k are shown in Figs 2a), 2b) and 2c). Note that the shaded area corresponds to the area where interference exists and OCR = 1 corresponds to an OCR value of 18 dB. Anal
34、ysis results in 0 6 show that small values of OCR correspond to high probability of interference and large values of OCR correspond to low probability of interference for the same distance of separation. . FIGURE 2 Interference areas for the three values of k b) k= 1 c) k 1 127 1-02 STD-ITU-R RECMN
35、SM-LZ7L-ENGL 11777 Lia55212 353q33LJ b37 = 246 Rec. ITU-R SM.1271 3 Probabilistic model Figure 3 shows the coverage areas - or cells - of two base stations separated some S km from each other. FIGURE 3 Desired and interfering base stations Interferer cell I BI 1 I t 1-271-03 Within both the desired
36、and interferer cells are mobile stations. Here the desired base station is referred to as BD, the interfering base station as BI and in the same way, the mobiles station as MD and MI. The constant R defines the radius of the coverage areas. The base station BD is at the origin and the base station B
37、I is some S km away dong the i-axis. In both models dl is defined to be the distance between the desired Rx and the desired Tx. Similarly, d2 is defined to be the distance between the desired Rx and the interfering Tx. All distance parameters are in kilometres. 4 Base to mobile interference This typ
38、e of interference occurs when a desired mobile MD is interfered with by an interfering base station BI. To find the probability of interference, it is necessary to determine the overlapping area between the coverage and the interfering area. This interfering area is delimited by the boundary of the
39、coverage area on one side and the curve defined by d2 = k dl on the other. Depending on the value of k, this curve can be a circle enclosing the interference region (k 1). The interference circles, which are different from the coverage areas, have a centre and radius that vary with k and S. Once the
40、se areas are determined, the probability of interference can be obtained by dividing the interference area by the coverage area. STD-ITU-R RECMN SM-327L-ENGL 3777 4855232 0534335 573 6 247 Rec. ITU-R SM.1271 FIGURE 4 Base to mobile interference X s i - Podon of BD 1271-& 5 Mobile to base interferenc
41、e This type of interference occurs when a desired base station BD is interfered with by an interfering mobile MI. FIGURE 5 Mobile to base interference 248 Rec. ITU-R SM.1271 For mobile to base interference to occur, the desired mobile must be Y km from BD and the interfering mobile must be less than
42、 k I km from BD. The probability of interference at the base station receiver is the product of the probabilities of these two events. 6 Results Based on this methodology, the base to mobile and mobile to base interference is calculated for various values of OCR and S. The different values of OCR ta
43、ke into consideration that different land mobile systems (both analog and digital with different channel widths) may interfere with each other. The probability curves for base to mobile and mobile to base interference are plotted in Figs. 6 and 7. As an example, the values: RD = RI = 32 km, E = 18 d
44、B have been assumed. Also, the significance of the OCR is described in Table 1. 1 0.9 0.8 O .7 .- 2 0.6 - 3 0.5 D 3 0.4 0.3 0.2 o. 1 O O 10 20 30 40 50 60 70 80 90 i00 110 120 130 140 Distance between base stations, S (km) FIGURE 6 Probability of interference from base to mobile Curves 17.8 26.4 29.
45、0 42.9 1271-06 With these curves it is possible to determine the distance of separation between two land mobile duplex systems when the OCR and an acceptable probability of interference are known. For example, given an OCR value of 8.5 dB and an acceptable probability of interference of 0.05, the cu
46、rves give us a distance between transmitters of 73 km for the base to mobile interference and 68 km for the mobile to base interference. Hence, 73 km should be chosen, as it will guarantee minimum requirements for both types of interference. STD-ITU-R RECMN SM-1271-ENGL 1997 R Li855212 0534337 34b I
47、 Rec. ITU-R SM.1271 249 FIGURE 7 Probability of interference from mobile to base 1 0.9 0.8 0.7 h 2 0.6 5 0.5 e 0.4 .- 0.3 0.2 o. 1 O O 10 20 30 40 50 60 70 80 90 100 110 120 130 140 Distance between base stations, S (km) Curves 17.8 26.4 29 .O 42.9 1271-07 TABLE 1 Significance I A I 0.0 I 0.00 I ne
48、system typeinterfering with asimiiarsystem 1 I B I 8.5 I 6.25 I Two 12SkHzsystemsinterferingeachother 1 I C I 17.8 I 12.50 1 Two25kHzsystemsinterferingeachother 1 I D I 26.4 I 12.50 I A 25 kHz system interfering into a 12.5 kHz one 1 I E I 29.0 I 12.50 I A 12.5 kHz system interfering into a 25 kHz o
49、ne 1 I F I 42.9 I 12.50 I Two 12.5 kHzsystems interfering each other 1 7 Conclusion This example has presented a methodology to calculate the probability of interference for land mobile duplex systems. By selecting an acceptable level of probability of interference, the distance of separation between two such systems can be determined. In this way, the minimum distance of separation required can be determined, hence increasing spectrum utilization.
