44
`
`man rmnsacrroxs on vsnrcrrsn rr;on>:oLoor, voL. v'r—18, N0. 1, MAY 1969
`
`in a sequential
`[19}C. H. Hammer, “Tirnelines and accurae
`es. Ofiice, Wash-
`decision making task,” Army Personnel
`ington, D. C., Rept. AD 625 223, October 1965.
`[20] W. C. Howell, “Some princilfsles for the design of decision
`systems: a review of six years 0 research on a. oommand—control
`system simulation,” Human Performance Center Ohio State
`Iniversity, Columbus, Rept. AD 665 469, September 1967.
`[21} D. R. Israel, “System design and engineering for real-time
`military data
`rocessing systems,” MITRE Corp, Bedford,
`Mass., Rept. .
`610 392, January 1965.
`[22] C. L. Meserve, “An approach to data processing in operations
`command centers,” U. S. Naval Postgraduate School, Mon-
`terey, Calif., Rept. AD 481 264, 1964.
`[23] G. A. Miller, “Human memory and the storage of information,”
`IEEE Trans.
`Information Theory, vol.
`IT-2, pp. 129437,
`September 1956.
`[24] H. M. Parsons and W. E. Perry, “Concepts for command and
`control systems," System Development Corp., Falls Church,
`Va., Rept. AD 479 368, December 1965.
`
`[252 E. H. Porter, “A paradigm for system analysis of command
`and control functions,” System Development Corp., Santa
`Monica, Calif., Rept. AD 608 588, October 1964.
`[261 S. Ringel and F. L. Vicino, “Information assimilation from
`symbolic disp1ays—amount of
`information presented and
`removed,” U. S. Army Personnel Res. Office, Washington,
`D. C., Re t. AD 600 036, March 1964:.
`[27] S. Ringo, “Command information processing systems—a.
`human factors research program,” U. S. Army Personnel Res.
`Office, Washington. D. C., Rept. AD 637 814, June 1966.
`[28} A. I. Siege! and M. A. Fischl, “Dimensions of visual informa-
`tion displays,” Applied Psychological Services, Wayne, Pa.,
`Rept. AD 661 346, September 1967.
`[29] C. A. Silver et al., “Development of criteria for evaluation of
`large-screen displays,” Franklin Inst. Res. Labs, Philadelphia,
`Pa., Rept. AD 621 231, August 1965.
`[30] Dept. of Defense, “Logistics research conference,” vol. H-6,
`Airlie Conf. Center, Warrenton, Va., Rept. AD 623 230,
`May 1965.
`
`Effects of Multipath Transmission on the
`Measured Propagation Delay of an
`FM Signal
`
`JOEL S. ENGEL, snmon MEMBER, IEEE
`
`Abstract—Position location techniques based on propagation
`delay have been proposed previously. A narrow-band version of
`this technique involves the transmission of RF carrier, modulated
`by a single audio frequency. At a receiver, the audio phase is a
`measure of distance provided the propagation delay is less than
`one quarter cycle. The transmission medium introduces multipath
`distortion and the received signal consists of a set of signals, each
`an attenuated and delayed replica of the transmitted signal, having
`traversed a difierent path. When FM is employed, the phase of the
`demodulated composite is a nonlinear function of the parameters
`of the multipath structure of the channel. In this paper,
`this
`functional relationship is derived.
`
`1.
`
`INTRODUCTION
`
`EVERAL techniques which have been proposed for the
`automatic location of mobile units are based on the
`
`measurement of propagation delay.‘ When the locating
`process is performed by the mobile party, signals are trans-
`mitted simultaneously by several land stations and the
`
`Manuscript received May 23. 1968. This paper was presented
`at the IEEE 2nd Symposium on Vehicular Communications Systems,
`Los Angeles, Calif., Mav 23. 1968.
`NT)he author is with Bell Telephone Laboratories, Inc., Holmdel,
`1 A very recent proposal was described by C. A.
`'Rypinski in “A
`system for generating location information in police vehicles,”
`presented at the 18th Annual Conference of the IEEE Vehicular
`Group, December 1967.
`
`mobile receiver measures the differences among their times
`of arrival. When the location is performed centrally, the
`mobile unit transmits a signal to several land stations each
`of which reports its time of arrival to a central processor.
`The differences in propagation delay are then used to
`locate the mobile unit.
`
`In general, the transmission medium introduces multi-
`path distortion. The received signal consists of a set of
`signals, each an attenuated and delayed replica of the
`transmitted signal, having traversed a different path. The
`receiver must attempt to measure a time of arrival for this
`composite signal. If the transmitted signal is a pulse (or
`step) of an RF carrier and the receiver can detect the
`leading edge of the received envelope, the multipath dis-
`tortion does not impair the measurement since the direct
`signal always arrives before the multipath signal. In some
`cases, the direct pulse may be attenuated with respect to
`the multipath pulses, but it is still detectable and later
`arriving pulses may be ignored. However, a signal with a
`sufliciently short rise time has an extremely wide-band
`spectrum. In many situations, the RF bandwidth which
`may be allocated to the location system is limited. A
`narrow-band technique must be used which involves the
`transmission of an RF carrier, modulated by a single audio
`frequency. At each receiver, the signal is demodulated and
`
`PETITIONERS 1009-0001
`
`

`
`ENGEL1 EFFECTS OF MCLTIPATH TRANSMISSION
`
`45
`
`the phase of the audio signal is measured. If the audio fre-
`quency is sulficiently low so that the propagation delay is
`less than one quarter cycle, the phase lag is an unam-
`biguous measure of time of arrival.
`With such a technique, the measured time of arrival is
`not the occurrence of the leading edge, but is different
`from that by an error term which is a function of the
`multipath spread. In this paper, the functional relationship
`between this error and the parameters of the multipath
`structure is derived. When frequency modulation is
`employed, the nonlinearity of the detection process intro-
`duces some interesting and unexpected results. The meas-
`ured value of propagation delay is found to depend not
`only on the relative amplitudes and delays of the multipath
`signals, but strongly on the carrier phase relationships
`among these signals as well. Thus very small variations in
`multipath structure can result
`in large fluctuations in
`measured time of arrival. It is also found that occasional
`
`in negative
`combinations of carrier phase can result
`errors; the measured value of propagation delay is oc-
`casionally less than the line-of-sight propagation delay.
`This results from the fact that the system is measuring
`the principal value of a steady-state phase shift and cannot
`distinguish between a phase lead of less than 1r/:2 radians
`and a phase lag of more than 31r/2 radians.
`Data from a channel sounding experiment are available,
`and these show some typical multipath structures. They
`have been analyzed, and the distributions for the corre-
`sponding measurement error have been computed, using
`the results of the derivation. These illustrate the range of
`errors which can occur and their relative frequencies.
`
`II. ENVIRONMENTAL DATA AND Srsrnlu IMPLEMENTATION
`
`Some time ago, experiments were conducted to deter-
`mine the wide-band transmission characteristics of the
`
`environment.“ A single pulse of an RF carrier was trans-
`mitted and the envelope of the received signal was dis-
`played on an oscilloscope and photographed. The received
`signal was seen to consist of a sequence of attenuated and
`delayed replicas of the transmitted pulse, each apparently
`arriving over one of a multitude of paths. The variation in
`length among these multiple paths was usually such that
`the pulses overlapped, but their individual peaks could be
`distinguished. The impulse response of the channel was
`seen to be given by
`
`IN) = Z a,.6(l ~ — -—- n.)
`
`‘V
`
`n==-1
`
`cl
`
`C
`
`(1)
`
`pagation delay over the nth path. 5( s) is the Dirac delta
`function and M 13) is the response of the channel to such a
`signal. The oscilloscope sweep was triggered by the first
`received pulse; hence the ditierences among the delays
`may be determined from the photographs, but no measure
`of absolute delay is available. It seems reasonable, how-
`ever, to assume that the first received pulse traveled over
`the direct line-of-sight path or one that was very close to it
`in length. In terms of (1), it is assumed that 1-, is very
`small, much smaller than the subsequent 1-,., and that it
`may be considered equal to zero. The derivation to be
`presented is general and does not rely on this assumption.
`It is only when the results of the derivation are to be
`applied to the measured data to obtain the desired distri-
`bution for the measured phase that the assumption is
`invoked.
`
`Under this assumption, a location teclmique involving
`the transmission of a pulse { or step) of an RF carrier and
`the detection at each receiver of the leading edge of the
`envelope of the received signal would result in a negligible
`incidence of location error. However, any signal with a
`sufficiently short rise time has a spectrum which is con-
`siderably wider than that of a modulated speech signal.
`In most situations, the RF bandwidth available for the
`location system precludes the transmission of such a
`Wide-band signal.
`A narrow-band version of the propagation delay tech-
`nique involves the transmission of an RF carrier frequency
`modulated by a single audio frequency. At a receiver, the
`signal is demodulated and the phase of the audio signal is
`measured.
`If the audio frequency, denoted by we,
`is
`sufficiently low so that
`
`d
`
`“’0(2 "i" 7:2) < g
`
`in all circumstances, then the phase lag is an unambiguous
`measure of propagation delay. With such a technique, the
`measured time of reception is no longer the occurence of
`the leading edge, but is somewhat different from that by
`an error term which is a function of the multipath spread.
`At a receiver, the measured propagation delay, equal to
`the measured phase lag divided by we, is equal to
`
`TM = {(3/6) + To
`
`(3)
`
`where the error 7;; is some function of the values of an and
`
`-r,,. In the following section, this functional relationship is
`derived.
`
`where an is the attenuation over the nth path, cl is the
`line-of-sight distance between transmitter and receiver, c
`is the speed of light, d/c is the propagation delay over the
`direct
`line-of—sight path, and 1-,.
`is the additional pro-
`
`’ W. R. Young, Jr., and L. Y. Lacy, “Echoes in transmission at
`450 megacycles from land-to-car radio units,” P2-oc. IRE, vol. 38,
`pp. 255-258, March 1950.
`
`III. Rnsronsn or AN FM DETECTOR TO A
`MULTIPATH Drsronrnn SIGNAL
`
`In the narrow-band location system, the transmitted
`signal, denoted by r(t), consists of a carrier at (tic; frequency
`modulated by a single sinusoid at «:9. This signal may be
`Written as
`
`r(£} = cos (we: —- 1: cos coat)
`
`(3)
`
`PETITIONERS 1009-0002
`
`

`
`46
`
`IEEE TRANSACTIONS ox VEHICCLAR TECHNOLOGY, MAY 1969
`
`Where, for a typical system, the parameters would he on
`the order of
`
`103 S we/21r S 109 Hz
`
`a uniformly distributed random variable independent of
`the associated r,,.
`Each signal v,.(t) may be written as
`
`5Xl03$coo/2:-_<§3>(10‘Hz
`
`(4)
`
`v,.(t) = a,, cos [acct - 99,, —- A: cos was —- r,.)]
`
`(10)
`
`IS In
`
`‘.23.
`
`and this is equal to
`
`Note that the instantaneous deviation in frequency about
`w, is equal to
`
`v,,(t) = a,.{cos wct cos [k cos wo(t - n.) + on]
`
`w¢(t) = keno sin ant
`
`+ sin wctsin [Io cos wo(t — -r,,_) + o,,]}.
`
`and equals zero at t = 0. As a result of the multipath
`transmission, the received signal s(t) consists of a finite
`set of signals s,.(t),
`
`N
`
`The total signal M!) is thus equal to
`
`221:) = p(t) cos on: + q(l) sin w,.t
`
`80!) = 2 Salt)
`:1-1
`
`(5)
`
`where
`
`where, by (1), each signal s,,{t) is an attenuated and de-
`layed replica of r(:.'),
`
`s..(t) = Gm cos [c)¢(t — E: — 13,) -- :1: cos w.;(i — i — r..)] .
`
`For ease of notation, let cm and v..(t) denote the signals
`am and s,,(t), respectively, each advanced by the line—of-
`sight propagation delay d/c,
`
`(6)
`
`v(t) ésll + (cl/cl]
`
`v,,(t) ésnft + (d/c)].
`
`(7)
`
`The measured phase lag of the modulation on s(t) is equal
`to wo[(d/c) + 7'3]. The measured phase lag of the modula-
`tion on v(t‘) is equal to the error worg, and it is this latter
`variable which is of interest. By (7),
`
`= [p3(ft) + q2(i)]"’ cos [acct -— tan*1
`
`v
`
`r(!)..
`
`(11)
`
`N
`
`p{t) = Z :1... cos Us cos wg(t -— 1-,.) + an]
`R-=1
`
`A’
`
`go} = Z as sin [a cos waft — an + a,,].
`and
`
`(12)
`
`Let co.-(2') denote the instantaneous frequency deviation
`of c(t) about the carrier frequency on. The output of the
`detector is equal to the instantaneous frequency deviation
`of 80.‘) and, by (7), to cu,-[i — (d/c) ]. The phase lag of the
`detector output
`is, by the definition of 1-3, equal
`to
`[(d/c) + rgjwo. The variable of interest more is thus equal
`to the phase lag of o.~,(t), and that signal is equal to
`
`_£ _
`
`“M ‘ml ta” ‘ml’
`
`_ _qfi_)_ _q<t)zi(t) -77(i)q'(t‘)
`
`7)2(t)+q"<t)
`
`'
`
`(13)
`
`The numerator on the right-hand side of (13) is equal to
`N N
`
`9(3) = .§i:%’n(fl
`3-!
`
`(8)
`
`g(t);i(t) —- p(i)q'(t) = km. 2 Z M... sin welt — 7,)
`ma). n=1
`
`where
`
`93(2) = (1,. cos [m.,(£ - 13,) — is cos wg(£ - 73)].
`
`(9)
`
`The measurement data show the delays 2-,. to be on the
`7 order of microseconds, corresponding to many hundreds of
`cycles of the carrier. Let the principal value of wen be
`denoted by g;,.. In theory, on is a deterministic function of
`r,.. However, a. small variation in 1-,, results in a variation
`of on over many multiples of 21;-. In practice, therefore, if
`r,. is known nith only reasonable precision, $0.. is not known
`at all. With specific reference to the data at hand, each
`photograph shows the envelope of the received signal when
`a single pulse of an RF carrier has been transmitted. It
`thus provides a single sample of the an and 1-,,, but the
`precision with which the 7., may be measured is such that
`each of the on could have any value uithout afiecting the
`photograph to any distinguishable extent. Each photo-
`graph could represent any set of values on with equal
`likelihood, and each sequence of photographs probably
`does include such a range of values. Therefore, for the
`purposes of this analysis, each phase on is considered to be
`
`X cos {k[cos waft — rm)
`
`- cos wo(f - val] -l- ea... - 9991i
`
`(14)
`
`and the denominator is equal to
`xv
`N
`
`p*(t) + q2(f) = Z Z emu. cos {I:[cos wg{t — 7...)
`ms-l n=1
`
`— cos wg(i — r,,):] + gr... — (psi.
`
`(15)
`
`Before substituting (14) and (15) in (13), they can be
`simplified by some extremely close approximations. The
`delays 7,. are on the order of microseconds, almost always
`less than ten microseconds, while coo
`is approximately
`21r X 103 radians per second. Thus the angle O)|)Tn is almost
`always less than 3.5 degrees and the angle kwm-,. is almost
`always less than 10 degrees. In this range of values, to a
`good approximation,
`
`sinx=:::
`
`cosx = 1.
`
`PETITIONERS 1009-0003
`
`

`
`ENGELZ EFFECTS OF MULTIPATH TRANSMISSION
`
`By virtue of this set of approximations
`
`01‘
`
`sin wo(t — 1-,.) = sin wot — won. cos cool
`
`(16)
`
`w.-(t) = kwo{[l + <%)2:'1/2 sin [wot — tan‘1
`
`and
`
`cos {k[cos wo(t — -r,,.) — cos wo(t — -r,.)] + go... — goo}
`
`= cos (so... — §9n) — kwo(rm -
`
`1-,.) sin («pm — go.) sin wot.
`
`(BC — AD)
`
` Q sin wot COS wot} .
`
`(27)
`
`(17)
`
`The first term in (27) is a sinusoid at the frequency wo;
`the second term is harmonic distortion and consists of
`
`sinusoids at integer multiples of the frequency wo. The
`multipath transmission is thus seen to have two effects:
`it shifts the phase of the fundamental tone and introduces
`harmonic distortion.
`
`It is seen that the shift in phase of the fundamental is by
`far the dominant effect. The component of 1-3 introduced
`by the harmonic distortion is seen to be negligible. Two
`receiver implementations are possible. In one case, the
`times of the zero crossings of w,-(t) may be measured
`directly, yielding the value of TE. As an alternative, the
`signal may be filtered after detection and before measure-
`ment to remove the harmonic distortion, resulting in a
`signal w,«( t) which is equal to
`
`w;(t) = kwo[l + <%)2J1/2 sin [wot — tan‘1
`
`— 0] .
`
`(28)
`
`The filter introduces an additional phase shift 0, but this is
`a known constant which is identical at every receiver and
`thus has no effect. The times of the zero crossings of w,(t)
`may be measured, yielding a value denoted by 1-5; to
`indicate filtering, which is equal to
`
`__1‘_t —1(£>
`TE/—wo an
`O .
`
`(29)
`
`The value of no corresponding to a single set of values of
`a,,, 1-,, and (0,. is not as readily obtained. The signal w,-(t) is
`given by (20). The delay T15‘ is equal to the time of the
`zero crossing of w.~(t) , so that the phase COOTE is equal to the
`principal value which satisfies
`
`Sl.I1C0o7'E — )\('rg) COS won; = 0.
`
`(30)
`
`Substituting (21) into (30) and rearranging terms yields
`
`Substituting (16) and (17) into (14) and (15) yields
`
`9(t)I5(t) - P(t)d(t)
`
`N N
`
`kwo Z Z a,,.a,.[sin wot — wov-,. cos wot]
`rrnl n-1
`
`X l:c0s (Wt: ’ (Pu) - k‘~‘D(7'm — 7'»)
`
`(18)
`
`X Sin (so... — so.) Sin wot]
`
`NZ
`
`:V_: amantcos (‘Pm ” ‘Pn)
`m=1 n=1
`
`— kwo(r,,. — 1,.) Sin (99,. - <p,.) sin wot].
`
`(19)
`
`P’(1) + 92(1)
`
`Substituting (18) and (19) into (13) yields the result that
`the instantaneous frequency deviation is equal to
`
`w,-(t) = kwo[sin wot — ).(t) cos wot]
`
`(20)
`
`where
`
`and
`
`A + B sin wot
`W) ' 0 + Dsin wot
`
`(21)
`
`N N
`
`A = wo Z Z a,..a,.-r,. cos (¢p,,_ ._ op”)
`m=l n—1
`
`(22)
`
`N N
`
`B = W2 2.‘ aw-an7'n25i11(<Pm — <pn)
`m=l n=1
`
`<23)
`
`N N
`
`C = Z Z a...a,. cos (son. — to.)
`nv-1 n=l
`
`<24)
`
`N N
`
`D = 219030 2 Z armanTn sin (‘Pm — ¢n)-
`m—1 n==l
`
`Equation (21) may be rewritten in the form
`
`'
`
`cos won;
`
`Sm “W [1 + — (Dsin to-E — B cos woTE)] = — (31)
`
`1
`
`C
`
`A
`
`C
`
`(BC — AD) sin wot
`A
`= — ———-z
`c+0w+Dmww
`
`“”
`
`or
`
`26
`()
`
`tan wo7'E(C + D sin coo-rg) — B Sin won; = A.
`
`(32)
`
`and substituting (26) into (20) yields
`
`For values of wow-E up to 0.175 radian
`
`w,(t) = kwo[Sin wot — 6 cos wot
`
`(BC — AD)
`
`+
`
`sin wot COS cool]
`
`tan won; = sin wary = (.0075
`
`(33)
`
`With less than a one-percent error in the tangent and less
`than two-thirds of one-percent error in the sine. It is pos-
`sible for wow-E to have a magnitude of up to 1r/2 radians, but
`it is extremely unlikely. In almost all cases, the approxima-
`
`PETITIONERS 1009-0004
`
`

`
`48
`
`IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, MAY 1969
`
`tion is an extremely good one. Substituting (33) into (31)
`and rearranging terms yields
`
`D(wo1-E)? + (C -— B)woTE -— A = 0.
`
`(34)
`
`Equation (34) is quadratic and has two solutions, but one
`of these is not a principal value and may be discarded. In
`almost all cases, to an extremely good approximation,
`
`_ ;[—<C — B) + no — Br + 4AD.]“2
`
`7” ‘
`
`0-30
`
`21)
`
`J.
`
`(35)
`
`Furthermore, the approximation has a built-in accuracy
`test. If the value of 7-1.; given by (35) is found to be such
`that wary is less than 0.175 radian, it is accepted as suffi-
`ciently accurate. If worg is greater than 0.175 radian, the
`following procedure is employed to obtain a more accurate
`value.
`
`Equation (31) may be rewritten in the form
`
`where
`
`(I +
`
`tan (.0073 =
`
`E = gigwf sin <woTE — tan-1 :3)
`
`(37)
`
`may be considered as a percent error term. Experience
`with the data indicates that those combinations of the
`
`values of (0,. which result in large values of TE also result in
`extremely low values of B and D, so that E is quite small.
`As a first step, (36) is approximated by
`
`_ 1%-. ($1.)
`
`0
`
`TE _ we
`
`(38)
`
`which, it should be noted, is equal to the corresponding
`value of 7-5,. The resulting value of T12; is used to compute
`E by (37). If E is found to be less than 0.01, the value of
`TE is accepted as accurate. If E is found to be greater than
`0.01, the transcendental equation (36) is solved numeri-
`cally using a trial-and-error technique, with the value
`obtained from (38) used as the first trial and the value of
`E determining the second trial. Representative samples of
`the data have been processed, and the resulting distribu-
`tions for -rE and TE, have been derived. It is seen that for
`each sample there is no significant difference between the
`distributions for the filtered and unfiltered signals.
`
`the set of N pairs of values of an and 1-,. are measured. The
`N phases on are each stepped through the range from zero
`to 360 degrees in small steps and at each step the corre-
`sponding values of TE and ‘l'E_r are computed. A histogram
`of each is formed, showing the distribution of the values
`represented by that photograph.
`Some representative samples of the data have been
`selected and processed. These are shown in Figs. 1, 4, and
`7. Sample I is typical of most of the data; Samples II and
`III are atypical and have been selected to see if their
`special properties yield unusual
`results. Sample II is
`atypical in that the received pulses are disjoint.
`(This
`does not mean that the received signals are disjoint when
`the narrow-band technique is used. In the system being
`analyzed, the transmitted signal is much longer in duration
`than the multipath spread.) Sample III is atypical in that
`the first pulse is not the largest, indicating that the direct
`line-of-sight path introduces more attenuation than some
`longer paths.
`For purposes of this example, a modulation index k
`equal to 3 and an audio frequency of we/27r equal to 1 kHz
`have been assumed. The distributions are seen to be ex-
`
`tremely insensitive to the values of these parameters.
`The resulting distributions for 1-3 are shown in Figs.
`2(a), 5(a), and 8(a), respectively. Figs. 2(b), 5(b), and
`8(b) show the same distributions with the scale of the
`ordinate expanded by a factor of 100 to show the occur-
`rence of the low probability extreme values. The ragged
`nature of the distributions results from the use of a finite
`
`set of samples of gen.
`The corresponding distributions for TE/‘ are shown in
`Figs. 3(a), 6(a), and 9(a), respectively. Figs. 3(b), 6(b),
`and 9(b) show the same distributions with an expanded
`ordinate scale. These distributions are each seen to be
`
`essentially the same as those for the corresponding 1E.
`The distributions are seen to be quite sharply peaked
`with small variance. In all cases, the mode of the distri-
`bution occurs at the center of gravity of the received set
`of pulses. However, while the variance is small, it should
`not be neglected. The pertinent measure of performance
`for a location technique is the frequency of occurrence of
`significant errors, and these will be introduced substan-
`tially by the occurrences of measurements which deviate
`from the mode.
`
`IV. REPRESENTATIVE DISTRIBUTIONS or ERROR
`IN PROPAGATION DELAY
`
`V. CoNcLUsroNs
`
`As described previously, the propagation data consist
`of photographs of the envelope of the received signal when
`a single pulse of an RF carrier has been transmitted. Each
`photograph thus yields a sample of the random variables
`a,. and -r,,, but the variables go, are not known. Therefore,
`each photograph does not yield a single value of measured
`delay, but represents the entire continuum of values lying
`in the range (—1r/Qwo, 1r/2wo). The relative frequency of
`occurrence, or probability distribution,
`represented by
`each photograph is to be found. From each photograph
`
`A procedure has been developed for processing the
`environmental data and deriving the distribution for the
`error in the measured value of propagation delay at a
`receiver. This procedure has been used on a representative
`sample of the data and the results have been presented. In
`the near future, a statistically sufiicient sample will be
`selected and processed and the results will be analyzed.
`The distribution for the measurement error will be derived
`
`in a form suitable for the prediction of the performances of
`various candidate systems. An item of immediate interest
`
`PETITIONERS 1009-0005
`
`

`
`ENGELZ EFFECTS or MYLTIPATI! TRANSMISSION
`
`49
`
`Ill
`.l....L
`
`Fig. 1. Sample l——typical response.
`
`0.50
`
`E
`Lu
`8
`g
`“
`g
`:
`<
`d
`I
`
`°
`-100.0
`
`.005
`
`g
`u
`2
`o
`W
`E
`
`E‘
`Z
`-1
`Lu
`4!
`
`0
`-1000
`
`0
`MEASUREMENT ERROR - (;4SEC0NDS)
`(‘ll
`
`I00.0
`
`.
`
`O
`MEASUREMENT ERROR - Unsecouos)
`(b)
`
`|O0.0
`
`0.50
`
`S2
`2:
`0
`E
`u.
`Lu
`2
`'3
`_|
`u
`K
`
`0
`400.0
`
`_oo5
`
`5
`E
`3
`o
`u.|
`E
`
`2
`:
`.1
`m
`n‘:
`
`o
`_|Qo_o
`
`0
`MEASUREMENT ERROR _ (FSECONDS)
`(a)
`
`moo
`
`2!
`
`0
`musunzmeur snnoa - (pseconos)
`(b)
`
`|oo_o
`
`Fig. 2. Histogram of -r,,~ (unfiltered). Sample I—typical response
`
`Fig. 3. Histogram of TE] (filtered). Sample I——typical response.
`
`PETITIONERS 1009-0006
`
`

`
`50
`
`IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, MAY 1969
`
`J... L.
`
`Fig. 4. Sample II—disjoint response.
`
`0.50
`
`0.50
`
`>-
`
`U2|
`
`J.l
`
`3ON2I
`
`L
`Lu
`2I-
`<.1W
`K
`
`>-
`
`U2L
`
`u30I
`
`nIL
`
`I.
`LU
`2D-
`<.1
`Lu
`K
`
`9
`-|oo.o
`
`.oo5
`
`o
`MEASUREMENT arenon - (pseconos)
`(a)
`
`|O0.0
`
`o
`-|O0.0
`
`.005
`
`o
`unsunzuzm em-«on - (yszcouos)
`(a)
`
`|oo.o
`
`>-0
`
`2I
`
`d30H
`
`al
`KII.
`MI
`2l-
`<.J
`
`WI
`
`>-O
`2lal
`
`DOUKU
`
`.
`H]
`2P-
`<_I
`In
`K
`
`o
`-|O0.0
`
`o
`MEASUREMENT canon - ( pseconos)
`(b)
`
`|oo.o
`
`o
`-I00.0
`
`0
`MEASUREMENT ERROR - (f£5EC°NDS)
`(b)
`
`100.0
`
`Fig. 5. Histogram of -rg (unfiltered). Sample II—disjoint response.
`
`Fig. 6. Histogram of 1-,; (filtered). Sample II—disjoin’c response.
`
`PETITIONERS 1009-0007
`
`

`
`ENGEL2 EFFECTS OF MULTIPATH TRANSMISSION
`
`I
`-41»
`
`I
`L-
`
`Fig. 7. Sample III—-attenuated direct path.
`
`0.50
`
`5
`2
`‘”
`3
`'3
`E‘
`|-
`W
`2
`'5
`-1
`W
`'3
`
`°
`-|O0.0
`
`.005
`
`3
`2
`W
`3
`°
`”
`"5
`“'
`
`3
`,_
`5
`""
`"5
`
`0
`- |00.0
`
`0
`MEASUREMENT ERROR - ( pSECOND5)
`(a)
`
`|O0.0
`
`0
`MEASUREMENT ERROR - ULSECONDS)
`(b)
`
`I00-0
`
`0,50
`
`S
`z
`ua
`3
`c
`Lu
`E
`In
`Z
`'5
`.1
`m
`u:
`
`0
`—|O0.0
`
`‘Q05
`
`S
`z
`Lu
`:
`0
`Lu
`n:
`u.
`
`2
`_
`E
`Lu
`tz
`
`o
`-:oo.o
`
`O
`MEASUREMENT ERROR - ULSECONDS)
`(3)
`
`|O0.0
`
`o
`MEASUREMENT ERROR - (;a.SECONDS)
`(b)
`
`lO0.0
`
`Fig. 8. Histogram of T3 (unfiltered). Sample III—attenuated
`direct path.
`
`Fig. 9. Histogram of 15,- (filtered). Sample III—attenuated
`direct path.
`
`PETITIONERS 1009-0008
`
`

`
`52
`
`man TRAXSACTIONS on‘ VEBICCLAR rncnxonoer, MAY 1969
`
`is the correlation between distance and error. The multi-
`
`It is also found that occasional unfortunate combina-
`
`path spread, and hence 1-E, may depend on the distance
`between transmitter and receiver or it may be stationary
`with respect to that parameter, and this must be deter-
`mined.
`
`Some interesting and unexpected results have been
`obtained. The measured value of propagation delay is
`found to depend, not only on the relative amplitudes and
`delays of the set of receiver signals, but strongly on the
`carrier phase relationships among these signals as well.
`Thus a very wide variation in measured propagation delay
`can occur for very small variations in multipath structure.
`Since the multipath signals must always traverse a path
`which is longer than the direct lineoilsight path, they
`must always arrive later than the direct signal. Intuitively,
`then, it would be expected that the presence of the multi—
`path signals should always introduce positive errors; the
`measured value of propagation delay should be always
`sornewhat greater than the line—of-sight propagation delay.
`One interesting result of this analysis is to show that this
`is not always the case. In most instances the errors are
`positive, but some combinations of carrier phase result in
`negative errors; the measured value of propagation delay
`is occasionally less than the line-of-sight propagation delay.
`This is because the system is measuring the principal value
`of a steady-state phase shift and cannot distinguish be
`tween 21. phase lead of less than 1r,/2 radians and a phase lag
`of greater than 31r/2 radians.
`
`tions of carrier phase result in errors that are quite large.
`Intuitively, it would be expected that the error would lie
`between zero and the total multipath spread, and the
`majority of values do fall in this range. However, with
`small but nonzero probability, the magntiude of the error
`can be many times the multipath spread.
`The effect of postdetection filtering has also been ex-
`amined. When the modulating signal is a single sinusoid,
`the Inultipath transmission introduces harmonic distortion
`in addition to the shift in the phase of the fundamental
`signal, and this distortion may be eliminated by a low-pass
`filter following the detector. However, it has been found
`that the harmonic distortion is almost always quite small
`and that the post-detection filter has negfigible effect on
`the distribution of measurement error.
`
`ACKNOWMJDGMENT
`
`The narrow-band technique for measuring propagation
`delay by the phase of the audio modulation on an RF
`carrier was proposed to the author by A. Daskalakis,
`R. H. Frenkiel, and P. T. Porter of Bell Telephone Labor-
`atories, Inc. The author is also indebted to J. G. Schweins-
`berg of Bell Telephone Laboratories, Inc., for developing
`all the computer programs necessary to read and normalize
`each pulse return, compute the 1-,; and my, and generate
`the automatically plotted histograms.
`
`PETITIONERS 1009-0009