IEEE COMMUNICATIONS LETTERS, VOL. 9, NO. 2, FEBRUARY 2005
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LMDS Diversity Systems: A New Performance Model Incorporating Stratified Rain Athanasios D. Panagopoulos, Member, IEEE, Pantelis-Daniel M. Arapoglou, Student Member, IEEE, George E. Chatzarakis, Member, IEEE, John D. Kanellopoulos, Senior Member, IEEE, and Panayotis G. Cottis
Abstract— Cell-site diversity may prove an efficient fade mitigation technique to increase the availability of Local Multipoint Distribution Service systems. In this Letter, a recently suggested physical model for the prediction of cell-site diversity performance is properly modified to include stratified rain. The model obtained is satisfactorily verified using radar derived data from UK and Canada. Simulated BEP results concerning LMDS diversity systems are also presented. Index Terms— LMDS systems, stratified rain, diversity reception, radio propagation. Fig. 1.
I. I NTRODUCTION
L
OCAL Multipoint Distribution Service (LMDS) systems provide a wireless local loop infrastructure employing line-of-sight (LOS) mm-wave radio links for broadband wireless access [1]. LMDS outage performance and cell coverage are predominantly influenced by rain attenuation [2], [3], [4], [5]. Cell-site diversity protection is an effective method to increase the carrier-to-noise power ratio at the subscriber terminal [6], [7], [8]. So far, due to possible lack of LOS to the terminal sites, cost and practical implementation reasons, the applicability of cell-site diversity is questionable. The use of this technique in LMDS systems requires suitable antenna equipment at the subscriber site to continuously monitor the alternative links from the two hub stations in order to implement the handover [7]. Since real life LMDS networks in urban regions are expected to become capacity limited rather than link length limited, there is a great need to minimize lost capacity by employing cell-site diversity. According to this protection scheme, every subscriber is linked to two or more Hubs. The alternative signals received by the subscriber at each moment are processed based on either the selection or the combining principle. Thus, the outage time of the hubsubscriber link due to rain attenuation is reduced. Recently, a statistical propagation model for the evaluation of the cellsite diversity outage performance has been proposed [8]. The model assumes the unconditional lognormal distribution for the point rainfall rate statistics as well as the convective raincell model for the spatial structure of rainfall. The objective of this Letter is to extend the previous propagation model to
Manuscript received May 17, 2004. The associate editor coordinating the review of this letter and approving it for publication was Dr. Philippe Ciblat. The National Research Program Pythagoras supported this work. A. D. Panagopoulos and G. E. Chatzarakis are with the School of Pedagogical and Technological Education, N. Heraklion, Greece (e-mail:
[email protected]). P.-D. M. Arapoglou, J. D. Kanellopoulos, and P. G. Cottis are with the School of Electrical and Computer Engineering, National Technical University of Athens, Greece. Digital Object Identifier 10.1109/LCOMM.2005.02015.
Configuration of an LMDS cell-site diversity system.
incorporate the stratiform type of rain, dominant in regions with low rainfall [9]. This is an important modification since the frequency bands allocated for LMDS are usually higher than 20GHz, where even low rainfall rates influence system outage significantly. The modified model is compared with radar derived results coming from Hampshire, UK at 42 GHz [10] and from Montreal, Canada at 30 GHz [7] with very good results. II. S TATISTICAL P REDICTION M ODEL A cell-site diversity system is shown in Fig.1, where a subscriber S is linked to hub stations H1 and H2 through different paths of lengths Li (i=1,2) (km) forming an angle θ (deg). The stratified description of rain is more realistic for rainfall rates up to 10-20mm/hr. Consequently, the lower values of rain induced attenuation are mainly due to stratified rain. To distinguish between stratified and convective rain, an attenuation threshold Athr (dB) is considered Athr = aRSb L
(1)
where a and b are constants depending on the frequency, the incident polarization and the assumed raindrop size distribution [8]. Furthermore, RS (mm/hr) is the rainfall rate transition threshold from stratified rain to convective rain depending on the geographic location. Because the microwave paths in LMDS cell-site diversity schemes are generally different, L is assumed to be L = 0.5(L1 + L2 ). The outage performance analysis of LMDS diversity systems is separated into two steps according to the rain attenuation value A (dB) considered. The two steps are: 1) For the joint exceedance probability P1,2 is determined assuming that the rain attenuations on the converging paths follow a joint lognormal distribution. After straightforward
c 2005 IEEE 1089-7798/05$20.00
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IEEE COMMUNICATIONS LETTERS, VOL. 9, NO. 2, FEBRUARY 2005
algebra one obtains [8]
=
1 2
∞
uD1
P1,2 = P AS1 ≥ xS1 , AS2 ≥ xS2 u2 uD2 − ρnst u1 1 1 √ exp − erf c √ du1 (2) 2 2π 2 1 − ρ2nst
ln ASi − ln Ami ln xSi − ln Ami , u Di = (i = 1, 2) Sαi Sαi (3) xSi (dB) are the corresponding fade margins of the two links and Ami ,Sαi are the lognormal statistical parameters of the rain induced attenuations concerning the two microwave paths SH1 and SH2 respectively. They can be expressed in terms of the point rainfall rate statistical parameters Rm , Sr , and of the path lengths Li [8]. Also, ρnst is the logarithmic correlation coefficient given in terms of and the path correlation coefficient ρst . In the present Letter, the calculation of ρst is proposed taking into account the stratified type of rain in a way similar to the one concerning Earth-space diversity systems [9]. As a result ρst is determined through ui =
H12st ρst = √ H1st H2st
Fig. 2.
Cell-site diversity gain vs. angular separation.
(7)
Fig. 3.
Cell-site diversity gain vs. angular separation.
(8)
exceedance probability of a certain BEP level is defined as [12] P r BEP1 ≥ BEP (Eb /n0 )thr1 ,
(4)
where the quantities H1st ,H2st and H12st are expressed in terms of the unconditional correlation coefficient ρst describing the stratified structure of the rainfall medium L1 L2 ρust (d = |x − y|)dxdy(i = 1, 2) (5) Hist = 0
0
H12st =
L1
0
d(x, y) =
0
L2
ρust (d(x, y))dxdy
x2 + y 2 − 2xy cos θ 2
ρust
(6)
2
P (1, 2; d) eb Sr 1 = − P (0) eb2 Sr2 − 1 eb2 Sr2 − 1
In (9), P (0) is the annual probability that rain will occur at a point, obtainable for every geographical region through [11], while the function P (1, 2; d) is the probability that rain will simultaneously occur at two points located at a distance d apart √ (9) P (1, 2; d) = P (0) − P (0)2 e−q d + P (0)2 More details for the derivation of ρust can be found in [9]. In addition, the parameter q km−1/2 is a parameter characterizing the spatial structure of the stratified rainfall medium. It can be obtained through experimental testing, as it will be shown in the Numerical Results Section. 2) For A > Athr the cell-site diversity performance analysis follows the steps presented in [8], where the convective raincell model for the spatial rainfall structure is adopted. III. C ALCULATION OF BEP The performance of wireless links suffering from rain fading is generally quantified in terms of the BEP achieved over one year. For a diversity LMDS system, the annual joint
BEP2 ≥ BEP (Eb /n0 )thr2
(Eb /n0 )thri = (Eb /n0 )csi − xSi (i = 1, 2)
(10) (11)
where (Eb /n0 )csi is the bit energy over noise spectral density value provided at the input of the correlation receiver of the subscriber under clear sky conditions. Details for the calculation of this probability can be found elsewhere [12]. The only difference in the whole analysis is the proposed rain attenuation model. IV. N UMERICAL R ESULTS A ND D ISCUSSION The proposed procedure is applied to simulated cell-site diversity gain data taken from radar in Hampshire [10]. The rainfall rate threshold RS up to which stratiform rain is dominant is assumed 10mm/hr. Employing further regressionfitting analysis on the ITU-R rainmaps [11] for Hampshire,
PANAGOPOULOS et al.: LMDS DIVERSITY SYSTEMS: A NEW PERFORMANCE MODEL INCORPORATING STRATIFIED RAIN
Fig. 4.
Cell-site diversity gain vs. angular separation.
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A validation of the value chosen for the parameter q for the Hampshire area has been made using experimental data from an LMDS diversity system located at Montreal, Canada (P (0) = 8.2471%, Rm = 0.10219 and Sr = 1.4714). A very good agreement of the results obtained applying the proposed model with the experimental data is observed (see Fig. 4). On the other hand, much more data of this kind around the world are required to establish a global value for the parameter q. In Fig. 5, the BEP performance of single and diversity LMDS systems is shown. More specifically, LMDS systems located at Montreal with the same geometrical and technical characteristics as in Fig. 4 are considered employing QPSK modulation. BEP versus the percentage of total outage time curves are drawn for a single link and two diversity schemes with separation angles 60o and 120o . The (Eb /n0 )csi values at the input of the subscriber receiver have been assumed 14dB. As expected, the improvement of the LMDS diversity system BEP becomes greater as the angular separation increases V. C ONCLUSION A prediction model for the evaluation of the outage performance of LMDS diversity systems incorporating the effect of stratified rain has been presented. The proposed model is recommended for systems operating at relatively low availabilities in regions where stratified rain is dominant. For LMDS diversity systems operating at high availability values in regions with heavy rainfall conditions, stratified rain has no considerable effect on the outage performance. R EFERENCES
Fig. 5.
BEP vs. percentage of total time.
the following values for the parameters employed have been obtained:( P (0) = 5.977% Rm = 0.03787, Sr = 1.7358). The appropriate value for q, so that it fits better to the simulated data, has been chosen to be q = 0.06km−1/2 . In Fig. 2, the cell-site diversity gain (CSDG) of an LMDS diversity system operating in Hampshire, UK, is examined. The CDSG is defined as the difference between the rain attenuation exceeded on a single link and the rain attenuation jointly exceeded on the two alternative links of the diversity scheme for a fixed percentage of time. The predicted values of CSDG obtained applying the proposed model, those obtained through the model that takes into account only convective rain [8], as well as the measured ones are drawn.A quite good agreement of the proposed model with the experimental data is observed particularly in comparison with the existing method. In Fig. 3, the simulated diversity data for another LMDS system located in Hampshire are also compared with results obtained from the two physical models. As expected, both prediction models give results very close to the simulated data, since at high availability requirements, systems are mainly influenced by higher rainfall rates, where the convective type of rain is dominant. All the other cases presented in [10] have been satisfactorily tested applying the proposed method.
[1] A. Nordbotten, “LMDS systems and their application,” IEEE Commun. Mag., vol. 38, pp. 150-154, June 2000. [2] A. Paraboni, G. Masini, and A. Elia, “The effect of precipitation on microwave LMDS networks: perfomance analysis using a physical raincell model,” IEEE J. Select. Areas Commun., vol. 20, pp. 615-619, Apr. 2002. [3] D. D. Falconer and J. P. DeCruyenaere, “Coverage enhancement methods for LMDS,” IEEE Commun. Mag., vol. 41, pp. 86-92, July 2003. [4] ITU-R Recommendation P.1410-2, “Propagation data and prediction methods required for the design of terrestrial broadband millimetric radio access operationg in frequency range of about 20-50GHz,” 2003. [5] A. D. Panagopoulos et al., “General coverage prediction algorithm for LMDS,” IEE Electron. Lett., vol. 39, pp. 684-686, Apr. 2003. [6] C. Shinka and J. Bito, “Site diversity against rain fading in LMDS systems,” IEEE Microwave and Wireless Components Lett., vol. 13, pp. 317-319, Aug. 2003. [7] G. Hendrantoro, R. J. C. Bultitude, and D. D. Falconer, “Use of cell-site diversity in millimeter wave fixed cellular systems to combat the effects of rain attenuation,” J. Select. Areas Commun., vol. 20, pp. 602-614, Apr. 2002. [8] A. D. Panagopoulos and J. D. Kanellopoulos, “Cell-site diversity performance of millimetric-wave fixed cellular systems operating at frequencies above 20GHz,” IEEE Antennas and Wireless Propagat. Lett., vol. 1, pp. 183-185, 2002. [9] J. D. Kanellopoulos and S. Ventouras, “A modification of the predictive analysis for the multiple site diversity performance taking into account the stratified rain,” European Trans. Telecommun., vol. 1, pp. 49-57, Jan./Feb. 1990. [10] I. S. Usman, M. J. Willis, and R. J. Watson, “Route diversity site diversity against rain fading in LMDS systems,” Cost Action 280, 1st International Workshop, paper PM2032, July 2002. [11] ITU-R Recommendation P.837-4, “Characteristics of precipitation for propagation modelling,” 2003. [12] S. N. Livieratos and P. G. Cottis, “Avalablity and performance of single/multiple site diversity satellite systems under rain fades,” European Trans. Telecommun., vol. 12. pp. 55-65, Jan./Feb. 2001.
