无线信号服从瑞利分布的验证方法

无线信号服从瑞利分布的验证方法 2009 ???? 05 ?????? 42 ???? ?? ?? ??Vol.42??No.05,2009 *??? 209 ??Communications TechnologyNo.209,Totally ????????E???????E?????????E?E? ???????? ???? ???/???????????????????? ???? 610039?? !??? ??!?????????????????????????????????????????????E???????E?????????????E??????????????????????????? ??????????!???????????????????????????????????????????*????? k ?*????????,?????? k ?*??????????????*????? k ?*?? ??????;????????????????????????????????????????????????????????E?E???????????????????E???????E???!? !???????!?????E?????????E????????????????????????????????? !?????E?????!?TN919.72!????*??????!?A!?????????!?1002-0802(2009)05-0051-03 Verification of Wireless Signal in Submission to Rayleigh Distribution LI Cheng-jie?? PEI Zheng (School of Mathematics and Computer Emg., Xihua University, Chengdu Sichuan 610039, China) !?Abstract!?In signal transmission system, it is well known that the envelope of the signal transmitted from the air always submits to the Rayleigh distribution or the Rice distribution. However, how to distinguish them is rarely mentioned. From the view point of the statistical theory, based on: ??when the whole k-order moment exists in parameter estimation, the k-order moment of the sample converges in probability to the whole one; ?? the inflection point of probability density function; Accompany with the application of fuzzy estimation, this paper describes two methods to prove that the envelope of the signal transmitted from the air submits to the Rayleigh distribution. !?Key words!?Rayleigh distribution??Rice distribution??envelope??channel??probability density function?? moment ???? a ?? a >0???????????? X E????????? a ??????E??????? ???????????????????????? 1 ????!?0 ???? ????????????????????????????????????E???????E??? ??????????E????????????????????????????????????????? ??????????????????????????????????E???????E????????? ??????!????????????????????????????????????????????? ???????????????????????????????????????????????????? ??E???????E???????????!? f(x) 1 ???????? 1.1 ????????f/Hz[1]???? 1 ????E???!????????????????? X ?????????? ?????????? 1 ????E??????????????????? [2]???? 2 ????????!???U ?????????? U ?????????? ?????? A ??U ????????????????2x?( ??) x ? : U ? [0,1],2 A a2?ex !? 0,,2f ( x) ? ?a?x ? 0,0,u ? ? (u) ?A ??????????2008-09-29!? ???????????????!????????????-??????????????E?????????????2008GZ0118????????*???????????*?????????60872089??!? */????????????????1979-?????????????????????/??????E????????????????????? ????1968-???????????????? ???????/??????E?????????????????!? 44.0306 ? 43.300483.58583.69583.715? ? 1 ?? 0.9916 !?83.52583.565A44.0306 ? 43.300483.78584.78584.84583.71583.785 85.88585.88585.89584.87584.885 85.92585.935??????????????????????????E???????E?????E???????E? ???????????????????!?? 77.621 ?? ?? ??311 ?? ?? ??[7]????????????????????????*??????? 99.16% ??????E????? ??E???!? 311/401 ? 77.556%???????????????????? a ?? a ??????????2 12.2 ????????????E??????? ????????E??????????????????????????????????????? 77.687 ? 77.556[6]????????E???*????????????????????? (1)????????????????????????E????????? ? ? 1 ?? 0.99916 ???????? *??????? A77.687 ? 77.556 99.916% ??????E???????E???!? 2t ?? x t 2 2a?x !? 0,dt, e?2 F(x)= 0 ?a?x ? 0!?0,?2x???2 2 ax !? 0,3 ????1 ? e ,(9)? ?0,x ? 0!?????????????????????????????????????/?????????? ????????????????????????????????E?????????E??????? ??????E??????????????????????????????????????????? E?????????????????E???????E??????????????????????? ??????E???????E???????????????????????????????????? ???????!!?(2)?????? 2x( ??) x 2 a2f ( x) ? e??10??,2a22xx( ??)( ??)1221 x a2 a2' f ( x) ? e?e? (?) ? 2x ?2222aaa???????*2x 2( ? )x 1 2[1] Lin Jin-guan.Parameter Estimations of Rayleigh Distribu-2 a( ? )e,(11)2 4aation[J].Chinese Quarterly Journalof Mathematics2000,15(4)??22x x 2( ? )( ? )x2 x x 1 222 a2 a'' 49-54.=f ( x) ?? e? ( ? )e44 22aaaa[2] ??????.??????.??????.??????????????????[M].????:????????2x 3( ? )3x x22 a? )e,(12)( ????2005:175-182.6 4aa2[3] ????,??????.????.???????????/??E???[J].????????????????:*? x 3( ? ) x 21 x 32 a3a???? ???? ()e? =0???? x ?F(x)=????????,2005,13(2):49-52.6 42aa2t [4] ????,???/??.?????????E????Okumura-Hata??????????????????1t ? 3a 2 2 a? 0.77687=77.687%!?edt =1 ??2??[J].??????????2008,41(5):67-68,78.0 aee [5] ??????,????. ????????????????MIMO??????????????E???[J]. ????E?E?1?? a =44.0306?????? x ? 3a ? 76.261 ?????? ????????2007,40(12):40-42.?????? E??? ?????? E??? ?????? ???? ??E??? ??*? 3a[6] ????,??????.??????.????????????????[M]. ????:????????????F(x)= f (t)dt =77.687%???????????????!?? 76.261 ?????0??,2008: 276-281. ????????????E??? 77.687%????!?[7] ??E???.??????????*???????????????[J].??????????, 2006(10): (3)?? 401 ???????????????????!?? 76.261 ?????????? ??????E??? 77.687%????!?36-41. [8] ??????,????.??????????????[M]. ????:??????????????,2004:41.345 41.36542.28542.30542.325162-173.43.15542.32543.13543.155 ?? ????????!???????????????????!E???? ??E???????62-208 ????????!?????????!E???? ??E???????62-304