328
`
`PROCEEDINGS OF THE IEEE, VOL. 68, NO. 3, MARCH 1980
`
`{66] —, “Toward a unified theory of modulation,” Proc, [EEE,vol.
`54, pp. 340-353, Mar. 1966, and pp. 735-755, May 1966.
`—, “Generation of digital signalling waveforms,” IEEE Trans.
`Commun., vol. COM-16, pp. 81-93, Feb, 1968.
`—, “Method and apparatus for intepolation and conversion of
`signals specified by real and complex zeros,” U.S. Patent 3510640,
`May 1970.
`—., “Zero-crossing properties of angle-modulated signals,’ JEEE
`Trans. Commun., vol. COM-20, pp. 307-315, June 1972.
`H. B. Voelcker and A. A. G. Requicha, “Clipping and signal
`determinism: Two algorithms requiring validation,” JEEE Trans.
`Commun., vol. COM-21, pp. 738-744, June 1973.
`“Band-limited random-eal-zero signals,”
`Commun., vol. COM-21, pp. 933-936, Aug. 1973.
`
`[67]
`
`[68]
`
`[69]
`
`[70]
`
`[71]
`
`in optics,’’ Opt.
`
`[72] A. Walther, “The question of phase retrieval
`Acta, vol. 10, pp. 41-49, Jan. 1963.
`[73] N. Wiener, The Fourier Integral and Certain of its Applications,
`New York: Dover, 1958.
`[74] E. Wolf, “Is a complete determination of the energy spectrum of
`light possible from measurements of the degree of coherence?”
`Proc. Phys. Soc., vol. 80, part 6, pp. 1269-1272, 1962.
`[75] J. L. Yen, “On nonuniform sampling of bandwidth-limited sig-
`nals,” IRE Trans, Circuit Theory, vol. CT-3, pp. 251-257, Dec.
`1956.
`{76] M. Zakai, ““Band-limited functions and the sampling theorem,”
`Inform, Contr., vol. 8, pp. 143-158, 1965.
`[77] A. Zygmund, Trigonometric Interpolation. Chicago, IL: Univ.
`of Chicago Press, 1950.
`
`IEEE Trans.
`
`Introduction to Spread-Spectrum Antimultipath
`Techniques and Their Application to Urban
`Digital Radio
`
`GEORGEL. TURIN,FEL.ow, 1£EE
`
`Abstract—In a combination tutorial and research paper, spread-
`spectrum techniques for combating the effects of multipath on high-
`rate data transmissions via radio are explored. The tutorial aspect of
`the paper presents: 1) a heuristic outline of the theory of spread-
`spectrum antimultipath radio receivers and 2) a summary ofa statistical
`model of urban/suburban multipath. The research section of the paper
`presents results of analyses and simulations of various candidate re-
`ceivers indicated by the theory, as they perform through urban/sub-
`urban multipath. A major result shows that megabit-per-second rates
`through urban multipath (which typically lasts up to 5 us) are quite
`feasible,
`
`I. INTRODUCTION
`
`channels and the theory of multipath and other diversity
`receivers.
`
`In this paper, we first present a tutorial review of pertinent
`aspects of both underlying disciplines, particularly in the con-
`text of spread-spectrum? systems. We then carry out rough
`analyses of the performances of two promising binary spread-
`spectrum antimultipath systems. Finally, since the analyses
`contain a number of oversimplifications that make them
`heuristic rather than definitive, we present results of computer
`simulations of the two proposed configurations and others, as
`they operate through simulated urban/suburban multipath.
`The simulation results highlight the importance of usingrealis-
`tic simulations of complex channels rather than simplified
`analyses, or they show that the analytic results, although based
`on standard assumptions, are unduly optimistic.
`
`II. MODELING MULTIPATH PROPAGATION
`
`Ultimately, a reliable multipath model must be based on
`empirical data rather than on mathematical axioms. Two types
`
`7In a spread-spectrum system, the bandwidth W of the transmitted
`signals is much larger than 1/7, the reciprocal of the duration of the
`fundamental signalling interval,so TW >> 1. The transmitted spectrum
`is said to be “spread” since a signal lasting T seconds need not occupy
`more than the order of W= 1/T Hz of bandwidth, in which case TW = 1.
`See [6] for references on the spread-spectrum concept.
`
`OME DIGITAL radio systems must operate through an
`
`Gcxtenety harsh multipath environment,
`
`duration of the multipath may exceed the symbol length.!
`Two disciplines combine to shed light on receiver design for
`this environment: the modeling and simulation of multipath
`
`in which the
`
`Manuscript received February 8, 1979;revised October 9,1979. This
`work was supported by the National Science Foundation under Grant
`ENG 21512 and SRI International under Advanced Research Projects
`Agency Contract MDA 903-78-C-0216.
`The authoris with the Department of Electrical Engineering and Com-
`puter Sciences and the Electronics Research Laboratory, University of
`California, Berkeley, CA 94720.
`1 An example is the ARPA Packet Radio network [38).
`
`0018-9219/80/0300-0328$00.75 © 1980 IEEE
`
`Petitioner Sirius XM Radio Inc. - Ex. 1008, p. 1
`
`Petitioner Sirius XM Radio Inc. - Ex. 1008, p. 1
`
`

`

`329
`
`“bursty”? transmissions, measurement of sequences of ‘‘im-
`pulse responses”’ of the propagation medium suffices.
`The simulations of data reception that are presented in a
`later section are based on the “impulse response” approach,
`and it is to this type of model that we restrict ourselves.
`In
`order that the model and the simulations themselves be fully
`understood, we shall review here the experiments underlying
`the model. These were performed in urban/suburban areas
`[32], (333.
`
`A, The Underlying Experiments
`Pulse transmitters were placed at fixed, elevated sites in the
`San Francisco Bay Area. Once per second, these would simul-
`taneously send out 100-ns pulses of carrier at 488, 1280, and
`2920 MHz. The pulses were received in a mobile van that
`moved through typical urban/suburban areas, recording on a
`multitrace oscilloscope the logarithmically scaled output of
`the receiver’s envelope detectors (see Fig. 1).
`Since the
`oscilloscope was triggered by a rubidium frequency standard
`that was synchronized with a similar unit at the transmitters
`prior to each experimental run, absolute propagation delays
`could be measured within experimental accuracies of better
`than 20 ns.
`Four series of experiments were performed, in the following
`typical urban/suburban areas:
`
`A) dense high-rise—San Francisco financial district,
`B) sparse high-rise—downtown Oakland,
`C) low rise—downtown Berkeley,
`D) suburban—residential Berkeley.
`
`TURIN: SPREAD SPECTRUM ANTIMULTIPATH TECHNIQUES
`
`
`
`(280 MHz- DENSE HIGH RISE
`
`
`
`w 100
`
`su
`
`
`HALF-POWER
`80}
`w
`TRANSMITTED
`|
`2
`“60
`PULSE WIOTH
`(100 ns}
`a
`
`46
`NOISE
`
`
`THRESHOLD
`
`of data are available. The more commontypegive the results
`of narrow-band or CW measurements, in which only a single
`fluctuating variable, a resultant signal strength, is measured
`[11]. Although the fluctuation of this strength variable de-
`pends on reception via multiple paths, these paths are not re-
`solved by the measurements. We shall denote the results of
`such measurements as “fading” data rather than multipath
`data, because they determine a fading distribution of the
`single strength variable, e.g., Rayleigh, log-normal, Rice, etc.
`Wide-band experimental data that characterize individual
`paths are less common [5], [10], [19], [33], [37].
`In order
`to resolve two paths in such measurements, the soundingsig-
`nal’s bandwidth must be larger than the reciprocal of the dif-
`ference between the paths’ delays, Although bandwidths of
`100 MHz or more have been used in exceptional circumstances
`to resolve path delay differences of less than 10 ns [10], the
`bulk of available data derives from 10-MHz bandwidths orless
`[5],
`[19],
`[33], [37].
`In the latter measurements, paths
`separated by delays of more than 100 ns are resolved; multiple
`paths with smaller separations are seen as single paths.
`The natureof the multipath measurements depends somewhat
`on the use envisioned for them. If understanding of the effect
`of the multipath channel on CW transmissions is required,
`measurements that show Doppler effects may be important
`[5], and these are reasonably related to a scattering-medium
`model of the channel [1], [12]. For high-rate packetized-
`data transmission, for vehicle-location sensing, and for other
`
`B. A Fundamental Model
`
`The model upon which data reduction was based was one
`first posed in [27].
`In this model, it is assumed that a trans-
`mission of the form
`
`s(t) = Re [a(t) exp (jwot)]
`
`will be received as
`
`r(t) = Re [p(t) exp (jwot)] +n(t)
`
`where
`
`K-1
`P(t)= >> ay oft - ty) exp (jO,).
`k=0
`
`(1)
`
`(2)
`
`(3)
`
`In (1)-(3), o(t) is the complex envelope of the transmission, i.c.,
`|o(t)| is its amplitude modulation and tan™' [Im o(t)/Re o(1)]
`is its phase modulation. The transmission is received via K
`paths, where K is a random numberthat mayvary from trans-
`mission to transmission. The kth path is characterized by
`three variables: its strength a,, its modulation delay t,, and
`its carrier phase shift @,. The waveform n(r) is an additive
`noise component.
`In the context of the spread-spectrum systems on which we
`shall concentrate, it is desirable to assume that all paths are
`
`Petitioner Sirius XM Radio Inc. - Ex. 1008, p. 2
`
`
`
`5
`4
`IN MICROSECONDS
`
`6
`
`65
`
`= &
`
`3
`“
`
`
`°6
`1
`:
`3
`ies
`DELAY BEYOND LINE OF SIGHT [LOS)
`(b)
`Fig. 1. Example of measured multipath profiles for a dense high-rise
`regions of dimensions roughly 500-1000 ft
`In each area,
`topography.
`(a) Top to bottom: 2920, 1280, 488 MHz. Vertical
`(along the transmitter-receiver line of sight) by 2500-4000 ft
`scale: 35 dB/cm. Horizontal scale: 1 us/em. Different apparent LOS
`delays are due to difference in equipment delays. (b) Middle trace of
`(tangential to line of sight) were exhaustively canvassed, with
`(a) onalinear scale.
`care taken to include proper topographic cross sections: inter-
`sections, midblocks, points at which the transmitter site was
`visible or occluded, etc. About 1000 frames of data of the
`type shown in Fig. 1(a) were obtained in each area.
`
`Petitioner Sirius XM Radio Inc. - Ex. 1008, p. 2
`
`

`

`330
`
`PROCEEDINGS OF THE IEEE, VOL. 68, NO. 3, MARCH 1980
`
`BINS
`
`ror
`tn eo, ee een ee eee
`D123 456 ses
`10
`6162
`+++
`67686970
`MULTIPATH PROFILE
`tay ,8yoo)
`(a2,82)
`(d9,80)
`(0,8,
`(a, 83)
`i.
`
`|
`4ox-19«-1)
`fle ty
`'k-2 er
`'o
`1 ee
`7.0
`0
`0.5
`6.5
`Lo
`6.9
`(LOS)
`wS BEYOND LOS DELAY ———+
`
`PATH INDICATORS
`‘a "a Tio
`oes
`NeiTga > Tereatestr0
`ori Tats a8
`ioo1'ioroooo
`0100001000
`
`(a)
`
`(b)
`
`(c)
`
`(a) Division of excess delay axis into
`Fig. 2. Discrete-time model.
`seventy one 100-ns bins. (b) A typical multipath profile.
`(c) Discrete-
`time path-delay indicatorstring, {r1}}9o-
`
`resolvable, i.e., that
`
`|t, ~t)>-1/W,
`
`forallk #/
`
`(4)
`
`holds, where W is the transmission bandwidth. Distinct paths
`in the physical medium that violate this resolvability condition
`are not counted separately, since they cannot be distinguished
`by a measurement using bandwidth W.
`Instead, any two
`paths—call
`them k, and k,—for which |t,, - t,%,|<1/W are
`considered as a single path in (3), with a common delay t,; =
`te, = tr, and a strength/phase combination given by
`ay exp (JO) Sax, exp ({0x,) + ax, xP (iOx,)-
`It is the triplet {t,,a,, 0,} that is to be determined for each
`“resolvable” path. To be sure, if a continuum of paths existed,
`it would be difficult uniquely to cluster the “‘subpaths”’ into
`paths. But many media, including the urban/suburban one,
`have a natural clustering, e.g., groups of facades on buildings,
`that make the modelfeasible.
`
`C. A Discrete-Time Approximation to the Model
`In addition to the additive random noise n(t) in (2), the re-
`ceived signal r(t) is therefore characterized by the random
`variables {t,}<~-!, {a,}£-!, {6,}£7! and K. The purpose
`of data reduction from the “‘multipath profiles’’ exemplified
`by Fig.
`1 was to obtain statistics of these random variables
`upon which to base a simulation program. A number of gen-
`erations of statistical models—based both on the data and on
`physical reasoning when the data were insufficient or unde-
`cisive—ensued [8], [9], [25], [26], [32]. The following final
`version emerged.
`Each multipath profile starts with the line-of-sight (LOS)
`delay, which is chosen as the delay origin. Since the resolu-
`tion of the original experiment is 100 ns, the delay axis is
`made discrete by dividing it into 100-ns bins, numbered from
`0 to 70. Bin O is centered on LOS delay, subsequent bins
`being centered on multiples of 100 ns. The delay of any
`physical path lying in bin / is quantized to 100/ ns, the delay
`of the bin’s center. Fig. 2 shows the bin structure, a multi-
`path profile, and the resulting discrete-time path-delay struc-
`ture. Notice that only paths with delays less’ than 7.05 pus
`beyond LOS delay are encompassed in this model; experi-
`mental evidence shows that significant paths with larger de-
`lays are highly improbable.
`The path-delay sequence {t,}<~! is approximated by a
`string {7;}2° of 0’s and 1’s, as shown in Fig. 2(c).
`If a path
`
`
`
`ONTRACK
`
`2
`
`(a)
`
`PROFILE
`fein}? fal, a ee
`
`fa. en
`{riie {tal”,aye”
`
`(b)
`(a) A vehicle's track,
`Fig. 3. Spatial variation of the multipath profile.
`with spatial sample points.
`(b) The sequence of multipath profiles
`at the sample points on thetrack.
`
`In the sample string
`exists in bin /, t;= 1; otherwise 7;=0.
`in Fig. 2(c), only T9, 73, T4, T6, °° 5 762, T67 ATE NONZerO, cor-
`responding to the quantized path delays fp = 0, 7, = 300 ns,
`#2 = 400 ns, 73 = 600 ns,---, t~2 = 6200 ns, ix-, = 6700
`ns. (fy is the value of ty, as quantized to the nearest 100 ns.)
`Associated with each nonzero 7; is the corresponding(a;,, 0)
`pair. Thus the discrete-time model is completed by appending
`to the 7; string a set of strength-phase pairs {(a;, Ox)}eao
`where the index k refers to the kth nonzero entry in the 7;
`string. This is shown in Fig. 2(b).
`The discrete-time model of Fig. 2 pictures the multipath
`profile at a single point in space. A sequence of such profiles
`is needed to depict
`the progression of multipath responses
`that would be encountered bya vehicle following a track such
`as shown in Fig. 3(a). One imagines points 1,2,°°-,n,°"-,
`arbitrarily placed on the track, at each of which a multipath
`response is seen. The discrete-time versions of these responses
`are arrayed in Fig. 3(b), where an additional spatial index n
`has been superscribed onall variables.
`One begins to recognize the complexity of the model and of
`the required reduction of experimental data on realizing that
`in aeaincnae the need for first-orderstatistics of the random
`variables 7, af, 9), and K™(where 0<1<70;0<k<
`K®- 1; i <n ea) there are two dimensions along which
`at
`least second-order statistics are necessary:
`temporal and
`spatial. For each profile (fixed m), there are temporal cor-
`relations of the delays, strengths and phases of the several
`paths;
`in addition,
`there are spatial correlations of these
`variables at neighboring geographical points.
`[33] and
`The reduction of experimental data [9], [25],
`physical reasoning led to the following model, which was the
`basis for simulation.
`1) The {7{”} string of the nth profile is a modified Ber-
`noulli sequence, in which the probability of a 1 in the /th
`place depends on: a) the value of /; b) whether a 1 or a 0 oc-
`curred in the (/- 1)th place of the same profile; c) whether a
`1 or a O occurred in the /th place of the (mn - 1)th profile.
`
`Petitioner Sirius XM Radio Inc. - Ex. 1008, p. 3
`
`Petitioner Sirius XM Radio Inc. - Ex. 1008, p. 3
`
`

`

`
`
` =a0
`
`
`
`
`
`PROBABILITYPLELooasec
`
`PROGABILITY
`
`
`
`CUMULATIVEPROBABILITY
`
`as
`
`.
`
`oh
`
`TURIN: SPREAD SPECTRUM ANTIMULTIPATH TECHNIQUES
`
`2) The strength ai”) of the kth path of the nth profile is
`conditionally log-normally distributed,
`the conditions being
`the values of strengths of the (k - 1)th path of the nth profile
`and of the path with the closest delay in the (nm - 1)th profile;
`appropriate empirically determined correlation coefficients
`govern the influence these conditions exert on af”), The mean
`and variance of the distribution of a(”) are also random vari-
`ables, drawn from a spatial random process thatreflects large-
`scale inhomogeneities in the multipath profile as the vehicle
`moves over large areas.
`3) The phase af”) of the kth path of the nth profile is in-
`dependent of phases of other paths in the same profile, but
`has a distribution depending on the phase of a path with the
`same delay in profile (mn - 1), if there is such a path; if no
`such path exists gi”) is uniformly distributed over [0, 27).
`4) The spatial correlation distances of the variables just
`described vary considerably, ranging from less than a wave-
`length for the @,’s, through tens of wavelengths for the a;,’s
`and 7,’s, to hundreds of wavelengths for the means and vari-
`ances of the a,’s.
`These statistics are more fully explained in [8], [9].
`
`D. The Simulation Program
`
`Hashemi’s simulation program SURP, based onthestatistics
`just outlined, generates sequences of multipath profiles, as
`depicted in Fig. 3.
`If one were to examine a sequenceof such
`profiles, he would see paths appearing and disappearing at a
`rate depending on the spacing of points on the vehicle’s track
`(Fig. 3(a)).
`Profiles at only slightly separated geographical
`points would look very similar, with high correlations of path
`delays and strengths (and, for very close points, phases). Pro-
`files at greatly separated points would not only have grossly
`dissimilar {7}, {a,, 6,} strings, but the gross strength statis-
`tics of these strings (e.g., the average strength of the paths in a
`string) would be dissimilar, reflecting the spatial inhomogeneity
`incorporated into the model. The “motion picture” of simu-
`lated profiles just described is in fact very much like experi-
`mental data [37].
`The simulation program can be run, using empirically deter-
`mined parameters, for each of the three frequencies and four
`areas of the original experiment. Long sequences ofstrings
`were in fact generated for each of the twelve frequency/area
`combinations, assuming that the points on the vehicle track
`are uniformly spaced by distance d. An example of such se-
`quences is given later in Fig. 25. For various values of d, the
`statistics of the simulated sequences were then compared with
`the original empirical statistics. Excellent agreement was ob-
`tained [8], [9].
`(See Fig. 4 for examples.)
`It should be noted that initial simulation experiments on
`urban/suburban radio ranging and location systems, using a
`rudimentary propagation simulation program preceding SURP,
`gave results which compared extraordinarily accurately with
`actual hardware experiments
`[34].
`In particular,
`it was
`verified that although the data upon which the simulation
`program is based were taken in the San Francisco Bayarea,
`one can expect simulation results that are not correspondingly
`restricted geographically. For example, use of the Area-A
`parameters in the program led to results that are as applica-
`
`> Actually, Suzuki [25] showed that paths with small delays (beyond
`LOSdelay) were better modeled by Nakagami distributions, but Hashemi
`[9] was forced to approximate these log-normally because of the com-
`plexity of the simulation program.
`
`PROGASILITY-OF-GCCUPANCY (8-2)
`
`cereee
`dep .Gh
`
`fier
`
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`soon
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`EXCESS GELAY (nsec)
`SOLUS LIMES © ERPER Tee ag
`GOTTEn LIMCh= Sivw.aTee
`
`(a)
`PATH NUMBER DISTRIBUTIONS (8-2)
`
`|
`
`teaeae
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`i
`
`Wi
`
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`
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`
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`
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`SHLI0 LIES © CLPER inetAL
`WOTTON G1NESs SimeLaTeD
`
`Tt}
`
`if
`
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`
`(b)
`PATH STRENGTH GISTRIBUTIONS £8-2)
`
`Ve ssge Tnate
`Of Mee a ste
`Ol Te. Tee 1 mae
`Portree
`OS 037s0. etse1 aE
`
`“18
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`PATH STRENGTH ¢
`SEL10 LIMES © ERPEE me eTAL
`OOTTED LIMESe SIMBLATED
`
`=10
`
`-T8
`
`(c)
`Fig. 4. Comparison of empirical statistics with statistics of simulation
`tuns: sparse high-rise, 1280 MHz; 3000 simulation samples at 1-ft
`spacings.
`Solid curves: empirical; broken curves: simulation.
`(a)
`Ordinate is probability that a path occurs within +50 ns of abscissa
`value.
`(b) Ordinate is probability that there are the number of paths
`given by the abscissa within the first N bins.
`(c) Ordinate is the prob-
`ability that the strength of a path in the indicated delay interval is
`less than the abscissa value.
`
`ble to, say, downtown New York City or Chicago as to down-
`town San Francisco.
`This initial success encouraged the
`development of the more elaborate simulation capability just
`described.
`Thus the sequence generated by SURP, described above,
`provide a data base with which to perform accurate experi-
`ments with urban/suburban radio systems, and theresults of
`
`Petitioner Sirius XM Radio Inc. - Ex. 1008, p. 4
`
`Petitioner Sirius XM Radio Inc. - Ex. 1008, p. 4
`
`

`

`332
`
`PROCEEDINGSOF THE IEEE, VOL. 68, NO. 3, MARCH 1980
`
`
`
`
`TO Salt)
`
`ENVELOPE
`OETECTOR
`
`can be any of M possible waveforms
`
`5j(t) = Re [o,(t) exp (jwot)],
`
`i= 1," ee
`
`M.
`
`(5)
`
`We assume that the transmitter has chosen amongthe s, at
`random with equal probability and that the s; have equal
`energy:
`
`f sj(r)dr=&,
`
`0
`
`Lait.
`FILTER
`these experiments can be expected to have wide applicability
`
`to typical urban/suburban topographies.
`MATCHED
`[DECISION
`27
`+
`6
`ENVELOPE]
`
`TO Slt}]|OETECTOR CIRCUIT
`
`FILTER
`ENVELOPE [pata
`III. DESIGN OF MULTIPATH RECEIVERS
`SAMPLE
`
`
`AT
`t=T
`Multipath reception is one form of diversity reception, in
`
`
`AND
`which information flows from transmitter to receiver via the
`OUTPUT
`
`DIGITAL
`| RECEIVED
`
`natural diversity of multiple paths rather than via the planned
`[oure
`INDEX
`WAVEFORM
`
`
`
`r(t) WATER,|_|ENveLoPe of poet
`
`
`diversity of multiple frequency channels, multiple antennas,
`
`
`LARGEST
`TO $j(t)|
` |DETECTOR
`
`
`multiple time slots, etc. Thus instead of regarding the multi-
`SAMPLE
`
`
`
`
`path phenomenon as a nuisance disturbance whoseeffects are
`
`
`FILTER
`to be suppressed, it should be regarded as an opportunity to
`
`MATCHED
`
`
`
`improve system performance.
`TO Sylt)
`Two bodies of work in the literature are concerned with
`Fig. 5. Optimal noncoherent-phase receiver for single-path channel.
`multipath receiver design. The older(see, e.g., [1], [4], [22],
`(Equiprobable, equienergy signals, Gaussian noise.)
`{23], [27]) concentrates on the explicit diversity structure of
`resolvable paths; its thrust is to take advantage of this struc-
`ture by optimally combining the contributions of different
`paths.
`In its simplest form, this approach ignores the inter-
`symbol interference that can be caused when the multipath
`medium delays a response from a transmitted symbol into
`intervals occupied by subsequent symbols, an approach that
`is justified only when the duration of the transmitted symbol
`is large compared with the duration of the multipath profile.
`More recently [15]-[18], equalization techniques that were
`developed for data transmission over telephonelines [14] have
`been applied to the radio multipath problem. Here, receiver
`design concentrates on reduction of the effects of intersymbol
`interference, and the diversity-combining properties of the re-
`ceiver are only implicit. This approach appears most suitable
`when the paths are not resolvable and when the symbol dura-
`tion is much smaller than the multipath profile’s “spread.”
`A melding of the two approachesis currently being worked
`on by L-F. Wei of ERL, UC Berkeley. Since we are concerned
`here with the case in which resolvability condition (4) is satis-
`fied, we shall in this paper pursue only the former diversity-
`oriented approach, as modified to take into account
`the
`deleterious effects of intersymbol interference.
`Instead of
`indulging in general and complex derivations, however, we
`shall present results using a tutorial “building block” approach,
`employing intuitive arguments that are justified by references
`to more formal developmentsin the literature.
`
`Tr
`
`for alli.
`
`(6)
`
`The additive noise n(t) of (2) is for simplicity assumed to be
`white and Gaussian, although non-Gaussian noise is also com-
`mon in urban radio communication.
`(See [39]
`for a com-
`prehensive survey of urban noise.)
`It is well known that the optimal receiver—i.e., the receiver
`that decides which s; was sent with minimum probability of
`error—has the form depictedin Fig. 5 (see, e.g., [36]). Asshown
`there, r(t) is passed through a bank of M filters, “matched”
`respectively to s;(t), i=1,°°',M, i., having impulse re-
`sponses s;(T- t), OS¢t<T [29].
`Thefilter outputs are en-
`velope detected and the envelopes sampled at t= 7 and com-
`pared. The index i=1,'°*-,M of the largest sampie is the
`receiver's output.
`In Fig. 5, we have shown the outputs of the envelope de-
`tectors when sj(t) is the transmitted signal and when the re-
`ceived noise component n(t) is negligible, assuming that the
`s; have been “well chosen.” This latter assumption means
`that if we define complex correlation function
`
`T
`
`int) & { Oj*(r) 0,(7 - t) dr,
`
`0
`
`i,k=1,°°°,M,
`
`|thST (7)
`
`then [27]
`
`IYn(DI<<28,
`
`all #i,
`
`ly(O1<< 28,
`
`for It >=,
`
`all i
`
`all i
`
`(8a)
`
`(8b)
`
`where W is the bandwidth shared byall s;, and, optimally but
`not necessarily,
`
`%jx(0)=0,
`
`allk#i,
`
`alli.
`
`(8c)
`
`A. The Optimal Single-Path Receiver
`
`We start with the simple case in which the channel com-
`prises only one path: K=1 in (3). We assumeinitially that
`the path strength ag and delay tp are known (fg =0 for
`simplicity), but that the carrier phase 69 is unknown, being
`a random variable, uniformly distributed over [0, 2n)3
`Since the absence of multipath implies the absence ofinter-
`symbol interference (a point we discuss more fully later), we
`can concentrate on the reception of a single symbol, say over
`the interval O<¢<T. Knowledge of this interval of course
`implies. some sort of synchronization procedure at the re-
`ceiver, a question discussed below.
`Suppose the received signal r(t) is as in (2), withO <¢< T,
`and where, in (3), K =1, to =0, ao 1s known, and @o is ran-
`dom as described above. The transmitted signal s(t) of (1)
`
`*Random path phases are assumed throughout this paper, since these
`generally change too rapidly in the mobile environment to make use of
`coherent-receiver techniques.
`
`In sketching the envelope detector outputs, we have also as-
`sumed that TW >> 1,
`i.e.,
`the signals are of the so-called
`
`Petitioner Sirius XM Radio Inc. - Ex. 1008, p. 5
`
`Petitioner Sirius XM Radio Inc. - Ex. 1008, p. 5
`
`

`

`TURIN: SPREAD SPECTRUM ANTIMULTIPATH TECHNIQUES
`
`333
`
`0
`
`T
`
`2T
`
`3T 2T+A
`
`@
`
`iw
`
`oO
`
`T = S2t PP 3T ates
`ree eo
`2
`
`.
`
`B. The Optimal Multipath Receiver: Known Delays
`If we should attempt to use the receiver of Fig. 5 when
`many paths are present (K > 1 in (3)), we would expect from
`the linearity of the medium and of the matchedfilters that
`the envelope detector output waveforms will look something
`like those in Fig. 6. Here, we have shown a four-path situa-
`tion (K = 4).
`The /th response in Fig. 6 is the envelope of the superposi-
`tion of the several paths’ contributions, and, when noise is
`absent, can be shown from (3) and (7) to be of the form
`[27]
`
`K-1
`
`at 8 >; ay exp (jO,)
`
`k=0
`
`tT
`
`0
`
`of(r) o(r +T +t, - t) dr],
`
`1=1,-°-,M, O<t<2T+A.
`
`(10)
`
`|
`
`9
`
`T
`
`2T
`
`3T 2T+A
`
`Fig. 6. Envelope detector output waveforms (small-noise case) for the
`receiver of Fig, 5; four-path channel.
`
`spread-sspectrum type [6]. None of the foregoing assump-
`tions about the structure of the signal set {s;(0}M,
`is neces-
`sary for the optimality of the single-path receiver of Fig. 5
`to hold; but we shall invoke them when discussing multipath
`receivers later, as they become necessary or desirable.
`The noisefree waveforms sketched in Fig. 5 are in fact given
`by [27]
`ex(t) 2 3 lya(t - T),
`
`t= 13M, OF <2T.
`
`(9)
`
`Underresolvability condition (4), the mainlobe peaks in the
`jth output e;(t) are distinct, and occur as shown at fo = 0,
`ti, t2, and tj =A.° The heights of these peaks are propor-
`tional to the path strengths a,. The sidelobes, both ofe;(t)
`and of the other outputs (none of the latter having mainlobe
`peaks), are mixtures of sidelobes due to the several paths.
`We stress that Fig. 6 is drawn for the isolated transmission
`of a single waveform s;(t),O<t<T.
`The waveforms of Fig. 6 differ from those of Fig. 5 in
`several important respects.
`If
`1) Strong peaks are available in e;{t) at multiple times.
`the decision circuit of Fig. 5 knows the values of the path
`delays fp,°**,fx-, it can sample the contributions of all
`paths and combine them, affording the receiver the advantages
`of diversity reception, as discussed earlier. The ability to re-
`solve the paths in Fig. 6 is the essence of the spread-sspectrum
`approach.
`If we instead had TW=1,
`the peaks in Fig. 6
`would merge, and explicit diversity combination would no
`longer be available.
`Conditions (8a, b) and TW >>1assure that the jth output
`2) The sidelobe levels of all outputs is increased, since
`envelope e;(t) consists of a sharp ““mainlobe”’ peak surrounded
`(10) showsthe addition of multipath contributions.
`by low-level “‘sidelobes,” while all other outputs have only
`3) The responses to the symbol sent during 0 <¢< T now
`low-level sidelobes. By careful signal selection, (8a, b) can be
`extends beyond t= 2T, thus overlapping with the responses
`satisfied with the maximum sidelobe level in all these wave-
`to the next symbol, which is sent during TS ¢<27T. That
`forms at a factor of about 2/./TW down from the mainlobe.
`is, we now have intersymbol
`interference, caused by the
`Typically, for TW = 100, this means that the maximum side-
`multipath.
`lobe is about 17 dB or more down from the mainlobe.
`Effects 2) and 3) are deleterious, while 1) is favorable. As
`If condition (8c) is also satisfied, the values of e;(T) for
`we shall see, however, the benefits of 1) usually far outweigh
`1#j are zero at
`the sampling instant t= 7, so that—in the
`the deterioration caused by 2) and 3).
`absence of received noise—the receiver will not make an
`For the time being, we shall ignore the effects of intersym-
`error.
`If the received noise is nonzero, the probability that
`bol interference, and inquire into the structure of the op-
`the /th output exceeds the jth at t= 7 for some /#j is also
`timum receiver for
`reception of a single symbol
`through
`multipath, assuming first that the path delays {t,}<~! are
`nonzero, and it
`is this probability (of erroneous decision)
`known. However, we again assume random phases {6,}* at.
`that characterizes the receiver’s performance.
`A final feature of Fig. 5 is important. There, we have de-
`independently and uniformly distributed over [0, 27); we also
`assume that the path strengths {a,}<~! are random, perhaps
`picted the output waveforms whenasingle isolated symbol
`is sent during O<t< 7.
`If another symbol, say s,(t), were
`having different distributions.
`sent immediately afterward, in T<t< 2T,it is clear that the
`Intuitively, one might expect under these conditions that
`response to it would occur over the interval T<t<.3T. The
`the optimal receiver is still of the form of Fig. 5, but what
`mainlobe peak in the /th output would be centered exactly
`at t= 27, precisely when all responses from the first symbol
`have died out. Thus on sampling the outputs at f= 27, one
`would be able to make a decision based on the response to
`the second symbol alone, whence our previous statementthat
`no intersymbol interference occurs in this single-path case.
`
`5 The maximum excess delay anticipated in the channel-—i.e., MaXte4
`. minyy(tK=1 ~ to) & A—is called the multipath spread; it is by this
`amount that the waveforms of Fig. 6 can spread beyond those of Fig. 5.
`In the four-path example of Fig. 6, it is assumed that tz - fg achieves
`this maximum.
`
`Petitioner Sirius XM Radio Inc. - Ex. 1008, p. 6
`
`Petitioner Sirius XM Radio Inc. - Ex. 1008, p. 6
`
`

`

`334
`
`PROCEEDINGS OF THE IEEE, VOL. 68, NO. 3, MARCH 1980
`
`the decision circuit now samples each ofits inputs at multiple
`times T+t,, kK=0,°**,X- 1, combines these samples for
`each input, and compares the resulting combined values; the
`decision would be the index of the largest combined value.
`Indeed this is the case, at least when (4) and (8b) hold so that
`the pulses in output j of Fig. 6 are distinct [27]. However,
`the optimal combining law is sometimes complicated, and de-
`pends on thestatistics of the path strengths.
`Suppose that the sample of the /th output envelope at time
`T+t, is Xjz.
`(In the absence of noise x;, = e;(t,) as given
`by (10).) Then, if all path strengths a, are known, the op-
`timal® combining of the samplesis given by [27]
`
`Ww) = > log,Ip om
`
`2aXie
`0
`
`x-1
`k=0
`
`(11)
`
`where Jy is a Bessel function and where No is the channel
`noise power density.
`If, on the other hand, the kth path
`strength is Rayleigh distributed with mean-square strength
`w, 2£{a?], and all path strengths are independent,” the
`optimal combining law is [27], [30]
`K-i
`ne
`WaeXthe
`k=0 No + Vp&
`
`(12)
`
`2
`
`where & is the common energy ofthesignals s,, given by (6).
`More complicated combining laws for other strength dis-
`tributions are given elsewhere [3], [27], [30].
`In any case,
`a decision is made by comparing the w, and favoring the
`largest.
`Note that different combining laws accentuate the various
`samples in different ways.
`In (11), for example, the samples
`are approximately linea