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PleadingHeader for numbered pleading paperP@n   $] X X` hp x (#%'0*,.8135@8: 6uC;,;/Xu&_ x$&7XXx/c81,'c P7PH{>q*"xxxxWWxxxWWkkxxxA.SSxSSJJSJSSSSSS8888JSSSSSSSSS.xJxJxJxJxJorJiJiJiJiJ8.8.8.8.{SxSxSxSxS{S{S{S{SxSxJ{xSxSxS{S`SxSxSxSrSrSrS{SiSiSiSiSxSxSxSxSxS{SS.SSSSz]SSuSiSiSi.i.{c{S{SxSxSxoSoSZAZSZSiSiS{S{S{S{S{SxxSlJ8SSS88/NxxxSSS8JDDSSSSSS;SSSS;8SVVS++SSffSSxSc]]8V;"xxSxWxxS唔S88xfxxxxxxxxxxd8SxS]SxoS8SxJS`xrxxxxxxxxxxPxxxxxxdofxGcxxxxxxxSxxxxxxxJxxxxJxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx8xxx8xxx8xxx8xxxxxxxxxxxxxxfi]f]oJiAlJ{JxJ8.uJo]]{JoSxJxf`SfSSiJxJofx]fffxi{8SxxxfJffffd88SSSSx{SSSxxxf8fSJ8d Y  S a   #4L  p# !#March 1993`PT$5DOC: IEEE P802.1193/42Ѓ    Y ԟ  #Xw P7[AXP#  Submission'page #Xw P7[AXP#1 PREDICTION OF COVERAGE FOR DS MODULATION IN A > FREQUENCY SELECTIVE CHANNEL 1"Robert J. Achatz U.S. Department of Commerce  National Telecommunications and Information Administration F Institute for Telecommunication Sciences $325 Broadway Boulder, Colorado 80303 USA eTelephone: (303) 4973498 x#(Rev. 03/01/93   PERFORMANCE PREDICTION  The performance of a wireless modulation technique can be evaluated by its ability to transmit data at a specified rate and quality of service (QOS) over a given percentage of a coverage area.  Y Quality of service in this context refers to bit error rate (BER) or probability of a bit error (Pe). For  Y example, wireless data can be transmitted at 2 Mbps with a maximum 1x106 Pe over 60 % of a room. A summary of this performance prediction for a specified data rate can be displayed by a cumulative  Y distribution function (CDF) of Pe versus percent of locations in the coverage area with that Pe or less. A method for performing this prediction with measured impulse responses will now be described. COVERAGE PREDICTION METHOD  If the data symbol period is less than the delay spread of the channel, the receiver sampling  Y window will have more than one data symbol within its limits. The received signal strength and Pe are  Y dependent on the values of the data symbols within the sampling window. Thus the Pe must be averaged over all possible data sequences within the sampling window. All data sequences are assumed to be equally likely since each symbol's value occurs with equal probability. #0*$$Ԍ The maximum and minimum indexes of the data symbols within the sampling window are first determined. The maximum and minimum data indexes are computed by d(min) = floor((tstds)/T) d(max) = ceil(ts/T) where ts is the sampling time in seconds tds is the delay spread in seconds T is the symbol period in seconds ceil function rounds to higher integer floor function rounds to lower integer An array of all possible data sequences within these limits is then built. Data symbols can be either +1 or 1.  Ys  The Pe for a BPSK modulator in Additive White Gaussian Noise (AWGN) without Intersymbol Interference (ISI) is  Y- !# dddddddN :XP_e~=~Q sqrt {(2Eb/No)}x6X@87X@x6X@87X@x6X@87X@_P+e _Q_EbI_No:_[99O_(i_2_/9_):߷$T$T$-T$T$!!S$$  where Eb is the signal energy per bit No is the noise energy per Hertz  This expression can also be used for BPSK DS provided no wideband or narrowband jammers are present. 0s#0*$$S$!!0Ԍ  Y]  To determine the Pe with ISI and AWGN given the data sequence and impulse response measurement, h(t), we must determine the demodulator's response to the "direct path" and the remaining "multiple paths". The direct path component (DPC) is assumed to have zero delay and the same phase as the sampling clock. A# ]dddddddN X&stack {)_o ~=~0#_o~=~_s} x6X@87X@x6X@87X@x6X@87X@39)__o~+ob+sH9&_90ߖ$T$T$T$T$!AS$$The remaining multiple path component's (MPC) delays and phases are referenced to the DPC's delay and phase. Using the demodulators response, ro, from the appendix a# dddddNddN :X%r_o~=~r~left ( )_s~+~mT~ right )~=x6X@87X@x6X@87X@x6X@87X@_r+o _rq+s_mT:___e1l_):߷$T$T$T$T$!aS$$1# (ddddd>`ddN XSQRT E~Left( d_o_o~+ ~sum from {1=`inf} to inf~sum from{K=1} to inf~d_1~~beta_k~cos (3_o ( )_K``)_s~)right ).`.`. x6X@87X@x6X@87X@x6X@87X@OQNhQjQiHNoHqHpI IEdoo+Kdm k o K(sa 3Z ))]+1++7+ff+ 1-+1 cos} ( ().%..1$T$T$GT$T$!S$$# wddddd^ ddN ,XBLeft (_s~~_K~)~{R'}_{cc'}~(t_ ,`n`) right )~+~{n'}`(+)x6X@87X@x6X@87X@x6X@87X@el<_ _+ +s+K_R+ccb_t_n _nP_ddqY@ _ [ _4_)_(_,6_) _( _),ߩ$T$T$T$T$!S$$ Further simplifying (# !dddddd ddN X1r_o~=~SQRT E~ left ( DPC~+~MPC right )~+~{n'}~(t)x6X@87X@x6X@87X@x6X@87X@_r+oy_Ew_DPC_MPC_na _t:_7__e y9 9OI9do9k _( _)($T$T$`T$T$!S$$ where # ;a'dddddPsddN X[{n'} (t)~=~ int from {tT} to t~n (t) SQRT {2 over T}~cos~({3'} t~+~{'}) {c'} (t) dtx6X@87X@x6X@87X@x6X@87X@nGtt_+t+TntTx t(c]tMdtI+L IH  II()()d2wcos7 ( )()LH9TNSaR2W0 3 ߘ$T$T$T$T$!S$$y#0*$$a]S$WAS$8aS$^wS$!S$6$a'S$*Ԍ For BPSK demodulation, an error occurs if a 1 is sent but a voltage less than 0 is detected or a 1 is sent and a voltage greater than or equal to 0 is detected. Since the data sequence and h(t) are known in r(t), n(t) is the only random variable. Thus # s ddddd>ddN ,XLPe~=~1 over 2~Pr~Left ( SQRT E~ (`DPC~+~MPC` )~+`N~<~0~line~1~\sent` right )x6X@87X@x6X@87X@x6X@87X@!PewPrXEDPCF MPC" N sentiv  2WelXO182(( ) < 0:1,ߩ$T$T$tT$T$!S$$!# sdddddddN CXQ+~~~1 over 2~Pr~ left ( ` SQRT E~ (DPC~+~MPC`)~+~N~ >= ~0~line~1~\sent` right )x6X@87X@x6X@87X@x6X@87X@!QVt   \2'elNO182( ) 01PrNEDPC& MPCD NsentC$T$T$ T$T$!!S$$where N is a noise voltage chosen from the noise probability density function (PDF). If we assume n(t) to be zero mean AWGN we need only compute the variance of the demodulated noise to determine its PDF. JA# wdddddddN Xt%_{nn}^2~=~ ~left (~int from {sT} to S~n(s)~sqrt {2 over T}~cos ({3'} s~+~{-'})~c(s)~ds~.~.~. right ) x6X@87X@x6X@87X@x6X@87X@% 3 -b2(y)Ad29 cos (+)s(c){.K..nnS+si+TnsAT scs3dsY+ I  I1h1Nj1j1ioNqqpLHITINSIaR20J$T$T$0T$T$!AS$$a# wIdddddddN 5X`~~Left (~~~~Int from {tT} to t~n (t)~sqrt {2 over T}~cos ({3'} t~+~{-'})~c (t)~dt right )x6X@87X@x6X@87X@x6X@87X@hNjjioNqqpLHTNSaR20tb+t+TntT{ t ctdt+O IK  I"()d2cos: ( ) () 3 -5߲$T$T$T$T$!aS$$# ;"dddddIsddN MXt%_{nn}^2~=~2 over T~~int from {sT} to s~~int from {tT} to t~~  ~left (`n(s)~n`(t) right)~c (s) c (t) . . . x6X@87X@x6X@87X@x6X@87X@!%b2d2( ) ( ) ()u(e).U..nnTNs+s+Tt+t>+TZnJ s n t c sctN++>207LLd kM$T$T$JT$T$!S$$j# z&dddddddN X?cos~( {3'}` s~+~{-'})~cos ( {3'}~ t~ +~ {-'})~dt~dsx6X@87X@x6X@87X@x6X@87X@8cos8(r8)B8cos8( 8)J838-"83 8-z8Fzz 8` z)8sC 8t\ 8dt 8dsj$T$T$T$T$!S$$ #0*$$a S$S$z!S$AIS$#"a"S$t&z&S$(Ԍbut # sdddddddN !XS ~ left (~ n(s)~n~(t)~right )~=~~~~~stack {No/ 2} over 0~~{t=s} over \otherwisex6X@87X@x6X@87X@x6X@87X@0?dVk9 7 n~snta No ts_ 8 otherwise()()Q / 2 80!ߞ$T$T$]T$T$!S$$=#  dddddEddN X\and~ at~t~=~sx6X@87X@x6X@87X@x6X@87X@8and8at8t8s8=$T$T$T$T$!S$$ # sdddddddN X`cos`({3'}_s~+~{,'})~cos~({3'}~t~+~{,'})~=~1 over 2~(`cos~(2{3'}~+~2{,'})~+~1`)x6X@87X@x6X@87X@x6X@87X@!cos(H)cos( ) 1 82(Lcos (224)1b)3y,P3 ,3e,A   sq t2 ߓ$T$T$ T$T$!S$$!# Iddddd ddN Xc`(s)~c`(t)~=~1 x6X@87X@x6X@87X@x6X@87X@8c8s`8cf8t8(8)8(8)~818ߌ$T$T$ T$T$!!S$$therefore iA# sadddddddN X%_{nn}^2~=~{No} over 2x6X@87X@x6X@87X@x6X@87X@!%282nnNo i$T$T$T$T$!AS$$Knowing the mean and variance of the AWGN we can write the noise PDF as a# bddddd>4ddN XGf_n`()~=~{e ^{^{2}/2 (No/2)} over sqrt {2!`({No} over 2`)}}x6X@87X@x6X@87X@x6X@87X@ fnfeYNo]No ( )dd-2i/2 (/I2)2(82)p ! 2NNTSR 5$T$T$T$T$!aS$$# !ddddd8 ddN WX0~~~~~~~~~~=~{e^{^2/No} over sqrt {! No}}x6X@87X@x6X@87X@x6X@87X@)p GO?e]No8NoyG8!dd2 /W$T$T$cT$T$!S$$if # &dddddddN )XHP_e~=~Pr~ left ( sqrt E~(DPC~+~MPC )~+`N~ >= ~0~line~1~\sent~ right )x6X@87X@x6X@87X@x6X@87X@_P+e _Prc_E_DPC;_MPC _Na_sent:_|_k_s _ _q _ _R9e9lc99O3_( _) _0_1)ߦ$T$T$dT$T$!S$$j# )ddddd<ddN X>P_e~=~Pr~left (`N~>=~sqrt E~(DPC~+~MPC`)~line~1~\sent~right )x6X@87X@x6X@87X@x6X@87X@_P+e _Pr_N_E_DPCy _MPC _sent:_b__ _ o _R9e9l929Oq_( _) _1j$T$T$"T$T$!S$$0*$$ S$  S$S${IS$B!aS$7AbS$!a!S$'%&S$:))S$+Ԓ # Vdddddu ddN hXXP_e~=~int from {{sqrt E`(DPC ~+~MPC )}} to inf~e ^{}^{2/No} /`sqrt{ ! No}~dx6X@87X@x6X@87X@x6X@87X@"Pey+E'+DPC+MPCs"edd$No "Nof "d:"Q+dLry N * O+(+)dd2dd/"/Td "! "h$T$T$]T$T$!S$$t# v ddddd,ddN Xu~=~`/`sqrt {N_o}x6X@87X@x6X@87X@x6X@87X@_uI_N+o__L_/)IOt$T$T$T$T$!S$$u!# 1dddddddN Xdu~sqrt {N_o}~=~dx6X@87X@x6X@87X@x6X@87X@_du_NI+o_d)ZO_9_u$T$T$T$T$!!S$$then A# IdddddI ;ddN uXdP_e~=~~1 over sqrt !~~int from {{sqrt {E over N_o}~left ( DPC~+~MPC right )}} to inf~~e^{u^2} dux6X@87X@x6X@87X@x6X@87X@!PeRE/GNdd%oLDPCMPC e uU duIvi &OZLYPG~d~k,1dd ?2&%!u$T$T$ T$T$!AS$$a# (dddddr `ddN CX?P_e~=~1 over 2~erfc~ left (sqrt {E over No}~(DPC~+~MPC) right )x6X@87X@x6X@87X@x6X@87X@!PeWerfcE8NoDPC? MPCIo 27Nhji No q pNNTSR _1_827( )C$T$T$JT$T$!aS$$# (zddddd `ddN (X9P_e~=~Q~left ( sqrt {{2E} over {N_o}}~(DPC~+~MPC) right )x6X@87X@x6X@87X@x6X@87X@Pe Q<E"_N+oDPCMPC:Nhjij Noj qj pNNTSR <2( )(ߥ$T$T$T$T$!S$$ In the event that excessive ISI causes a symbol error, an N which causes the voltage to cross zero again  Y corrects the ISI error. In this case the Pe is # (%dddddr `ddN qXAP_e~=~1.0 ~Q left (~sqrt {{2E} over {N_o}}~(DPC~+~MPC`)~right )x6X@87X@x6X@87X@x6X@87X@PeBQ<EZ_N+o2DPC MPC:r  1.0J<2(@ )Nhji No q pNRNTRSRR "q$T$T$T$T$!S$$ #0*$$qS$ v S$1S${!IS$AS$aazS$ %S$)Ԍ  Y] When the Pe is computed for all possible data sequences for a given impulse response measurement the  Y ensemble of Pe are averaged and stored. OTHER METHODS OF PERFORMANCE PREDICTION  Y.  Chen [Chen, 1992] computed the average Pe for a DS transceiver in a frequency selective channel.  Y The Pe was averaged over all likely multipath component amplitudes, phases, and delays. Chen made the assumption that delay spread did not exceed 2 symbol periods which reduced the number of possible data sequences to 8 since only the current and two previous data symbols could appear in the sampling window. Probability densities for the multipath component amplitudes, phases and delays were taken from Saleh's [Saleh,1987] indoor model.  Y  Chuang [Chuang,1987] generated Pe as a function of normalized rms delay spread using Devasirvathem's [Devasirvathem, 1987] indoor power delay profile measurements. The study was  Ys inspired by Bello's GWSSUS channel research [Bello,1963] which predicted Pe as a function of the power delay profile's rms delay spread to symbol period ratio, d. A large number of impulse responses were stochastically generated from one of Devasirvatham's averaged power delay profiles. The generated impulse responses are reasonable estimates of impulse responses that may exist in the neighborhood of Devasirvatham's 4 foot measurement square. For each simulated impulse response,  YD Pe was calculated. This Pe was then averaged over other impulse responses having the same d. A graph  Y of average Pe versus d was constructed and compared with Bello's prediction methods. The results compared favorably for d < .2. Winter [Winter,1985] predicted the outage of a receiver with maximal ratio combining antenna diversity as a function of rms delay spread to symbol period, d. Computation of the BER and r#0*$$Ԍ probability of an outage was derived in terms of the squared sum of the antenna weighting function. Outage was defined as the probability that a communication link cannot meet a specified BER requirement. Thoma [Thoma,1992] predicted the performance of pi/4 DQPSK modulation while moving. Rappaport's [Rappaport,1990] channel model was used to simulate 1,125 complex impulse responses over 1 meter. The error distribution was then calculated for a given data rate and velocity. At a highway speed of 60 mph and a data rate of 1 Mbps the detection of 37,313 symbols can be simulated. At a walking speed of 3.75 mph and a data rate of 1 Mbps the detection of 597,014 symbols can be simulated. Performance was measured by outage probability where outage probability is defined as the probability that the number of errors in a code block exceeds a threshold. The number of errors in a code block below this threshold are assumed to be correctable with forward error correction and therefore unimportant. l%REFERENCES  [Bello, 1963], Bello, P.A., Nelin, B.D., "The Effect of Frequency Selective Fading on the Binary Error  Y  Probabilities of Incoherent and Differentially Coherent Matched Filter Receivers",#Xu&_ x$&7/XX# IEEE Trans  Y  on Communications Systems#Xw P7[AXP#, June 1963 [Chen, 1992], K.C. Chen, "Performance Comparison Between Direct Sequence and Slow Frequency  Y  Hopped Spread Sprectrum Transmission in Indoor Multipath Fading Channels",#Xu&_ x$&7/XX# doc: !!HIEEE T$T$M W P802.1192/80, July 1992#Xw P7[AXP# [Chuang, 1987], J.C.I. Chuang, "The Effects of Time Delay Spread on Portable Radio Communications  Y6!  Channels with Digital Modulation",#Xu&_ x$&7/XX# IEEE Journal on Selected Areas in Communications,#Xw P7[AXP# Vol  SAC5, No. 5, June 1987  #0*$$Ԍ [Papazian, 1992a], Papazian, P.B., Achatz, R.J., "Wideband Propagation Measurements for Wireless  Y  Indoor Communication", IEE 802 Submission,#Xu&_ x$&7/XX# IEE P802.1192/83,#Xw P7[AXP# pp. 128 [Papazian, 1992b], Papazian, P.B., ety al., "Wideband Propagation Measurements for Wireless Infdoor  Ya  Communication", #Xu&_ x$&7/XX#NTIA Report 93292,#Xw P7[AXP# January 1993 [Rappaport, 1990], Rappaport, T.S., Seidel, S.Y., Takamizawa, K., "Statistical Channel Impulse T$T$MResponse Model for Factory and Open Plan Building Radio Communication System Design", T$T$M Y #Xu&_ x$&7/XX#IEEE Trans. on Communications, Vol 39, No. 5#Xw P7[AXP#, May 1991  Y [Saleh, 1987], Saleh, A.A.M., "A Statistical Model for Indoor Multipath Propagation",#Xu&_ x$&7/XX# IEEE Journal  Y  on Selected Areas in Communications, Vol SAC5, No. 2,#Xw P7[AXP# February 1987  [Thoma, 1992], Thoma, B., "Simulation of Bit Error Performance and Outage Probability of pi/4 T$T$MDQPSK in Frequency Selective Indoor Radio Channels Using A Measurement Based Channel T$T$M Yl Model",#Xu&_ x$&7/XX# IEEE Trans. Globecomm 1992,#Xw P7[AXP# Dec 1992 [Winters, 1985], Winters, J.H., Yeh, Y.S., "On the Performance of Wideband Digital Radio T$T$M Y) Transmission Within Buildings Using Diversity", #Xu&_ x$&7/XX#IEEE Globecom 1985 Proceedings,#Xw P7[AXP# 1985   !  xP #^4L  P: P# Submission'Page #Xq4L  P: [AXP# # 0*$$Ԍ &APPENDIX This expression for the response of the demodulator assumes that delay spread is larger than symbol period. No limit on delay spread to symbol period ratio is imposed. The sampling clock can have any value between zero and the maximum delay spread. WHERE  144 Transmitted Symbol Index  m44 Received Symbol Index  Y  d144 1TH transmitted symbol  Y  k, k, )K Amplitude, phase, and delay of kth. multipath component  Y  )S, s44 Delay and phase of sample clock  Yy  3o44 Carrier frequency  Yb  R'cc'(t) Partial cross correlation function  YK  t 44 Sub chip offset  Y4  nTc44 Integral chip offset  '(n)44 Code correlation  Y  Tc44 Chip period  Y  Nc44 Number of chips in PW word  c (t)44 PN code waveform  T44 PN word period  Y  NA, ND Number of chips that agree/disagree # 0*$$Ԍ &APPENDIX #  dddddddN Xr~()~+~mT~)~=~r_o~=x6X@87X@x6X@87X@x6X@87X@_r_mT_rW+o_(7_)Z_)___ߖ$T$T$_T$T$!S$$ L# xddddd9#ddN Xsqrt E~~sum from {1=inf} to inf~d_1~sum from K~ left ( `_K~cos`(3_o` ()_{k}~~)_s)~+`_s~~_k~)~{R'} _{cc'}~(t_e,~n `right )x6X@87X@x6X@87X@x6X@87X@OIPIelETd+KK o k ssk`Rcct>e^n+1+%+u+1  !dd 3 )} )|'cos( (: ))F(,L$T$T$ T$T$!S$$ S# ;dddddusddN XW+~int from {tT} to t~n(t)~~sqrt {2 over T}~~cos~({3_o'}~ t~+~{'}`)~{c'}~(t)~ dtx6X@87X@x6X@87X@x6X@87X@2+ bO  I.ILHlTNSaR202t+t+T*ntT o t c*trdt()d2cos( )(): 3 S$T$T$bT$T$!S$$where |!# ddddddddN X{R'}_{CC'}~(t_ ,`)~=~left \{~(1~~{t_ } OVER {Tc})~{'}(n)~+~{t_ } over {Tc}~{'}~(n+1)~\if~~T~<= )_s~~()_K~~(m1)T)~