.
`
`Umted States Patent [19]
`Jasper et a1.
`
`USOO5381449A
`
`[11] Patent Number:
`[45] Date of Patent:
`
`5,381,449
`Jan. 10, 1995
`
`[54] PEAK TO AVERAGE POWER RATIO
`REDUCTION METHODOLOGY FOR QAM
`COMMUNICATIONS SYSTEMS
`
`[75] Inventors= Steven 0- Jasper, Hoffman Estates;
`Mark A. Birchler, Roselle, both of
`n1.
`_
`[73] Assignee: Motorola, Inc., Schaumburg, Ill.
`[21] APPL No; 786,681
`
`[56]
`
`References Cited
`
`U.S. PATENT DOCUMENTS
`3,955,141 5/1976 Lyon et a1. ........................... .. 375/8
`4,464,767 8/1984 Bremer ..... ..
`. 375/67
`4,646,305 2/1987 Tretter et a1. ..
`375/39
`4,680,775 7/1987‘Exarque m1. ................. .. 375/39
`Ian-man, Examiner_stephen Chin
`Attorney, Agent, or Firm-Joseph P. Krause
`
`[22] Filed: ‘
`
`Nov. 1, 1991
`
`[57]
`
`ABSTRACT
`
`_
`_
`Related U'S' Apphcahon Data
`Continuation-impart 0f Ser- NO- 536,825, Jun 12, 1990-
`[63]
`Int. Cl.6 ........................................... .. H04L 27/04
`51
`[52] US. Cl. .............................. .. 375/59; 332/103
`[58] Field of Search ..................... .. 375/38, 39, 42, 59,
`375/60; 370/9, 10, 12, 18, 19, 20; 332/103, 144
`
`The ratio of peak power level to average power level in
`a power ampli?er used in a QAM communication sys
`tem transmitter can be reduced by preselecting magni
`tudes,and phase angles of complex'valued Pilot symbols
`used 1“ mum-channel’ N'level QAM
`
`20 Claims, 3 Drawing Sheets
`
`'F' — _ _ _ — _ _ _ _ — _ — _ _ _ _ _ _ — _ ‘T “I
`
`g)
`
`102
`~ ‘
`
`I
`'-
`|
`,
`I
`
`‘
`
`103
`I
`
`107
`'
`PILOT SYIBOL
`INSERTION
`
`11401211111011
`SOURCE
`.
`a ans/3203
`
`~|
`I
`"I" ,
`
`.
`
`‘
`
`'
`
`_
`
`I
`
`-
`-
`
`I
`I
`|
`|
`
`'
`
`10s ,
`“i4 PILOT SYIBOL
`.
`SERIAL .ans '
`INSERTION
`To '*
`M-PARALLEL
`109
`COWLEX
`I
`105
`SYNBOLS
`, PILOT 3114301
`-‘,INSERTION
`
`110
`‘
`PILOT SYMBOL
`
`106
`1
`
`'
`
`_
`
`I —
`
`INSERTION ‘
`
`1
`
`126
`
`‘
`'
`142
`81W t)’.
`
`'
`I
`
`|
`|
`|
`|
`
`'
`
`Petitioner Samsung - SAM1020
`
`

`
`US. Patent
`
`Jan. 10, 1995
`
`Sheet 1 of 3 '
`
`5,381,449
`
`(0,0,Q,0)
`2
`
`F I c1
`
`’ — PRIOR ART —
`
`REAL
`
`O
`
`O
`
`—3--—
`
`O
`
`O
`
`ENERGY
`
`'_ FIG 2
`
`AV B
`/ I
`l
`fA
`fB-
`
`'
`
`0 V n
`I
`l \ FREQUENCY
`fc
`f1)
`
`.
`
`IMAGINARY- .
`
`'
`
`v
`
`v
`
`'
`
`'
`
`3____.I__
`
`'
`
`.
`
`.--
`
`l
`
`1y .
`i
`:
`1
`3
`
`}
`i
`-s -1
`.4..
`
`‘I
`
`..
`
`'
`
`~
`
`I
`
`f.
`
`--—‘PRIOR ART—.
`REAL-
`-
`~
`~
`
`_3__
`
`2
`
`

`
`U.S. Patent
`
`Jan. 10, 1995
`
`Sheet 2 of 3
`
`5,381,449
`
`.ms?._8..;mo.._zH25nD
`
`«Na3_$2:325-m-------m-=--w-=
`:e2:ua=e©m~om.A
`E:swimSEn§.\«,
`..n~_:.::_::
`.
`
`.
`
`
`=<_m.W_._H.o.._\.._§z.Y1_..§.u.<._
`.xHn_=8:2%3:_.
`§TSc\__.a_c.3n2n._
`n..rII._
`
`m~m1nu~n~W
`
`ngs:
`
`-----m-_--
`
`3
`
`
`
`
`

`
`U.S. Patent
`
`Jan. 10, 1995
`
`Sheet 3 of 3
`
`5,381,449
`
`.
`
`..
`
`3...m3.m_n_<=m“£2E..+mg
`uwg..C0..3m»..«A.L.¢~_
`L
`.
`
`.zoH_zumzH
`
`
`
`.om=>m»oaHm
`
`__
`
`L
`
`._
`
`%._
`
`m_Hm._<Hmmm
`
`op
`
`.;u..<z<¢.=
`
`m4om=»m
`
`xm4¢=oo.L
`
`____._.
`..oN
`
`
`
`..oum\m.Hmmjuom=om
`
`zoH_<=¢omzH
`
`4
`
`
`
`
`

`
`1
`
`5,381,449
`
`PEAK TO AVERAGE POWER RATIO REDUCTION
`METHODOLOGY FOR QAM COMMUNICATIONS
`SYSTEMS
`
`This is a continuation-in-part of Ser. No. 07/536,825,
`?led Jun. 12, 1990.
`
`FIELD OF THE INVENTION
`This invention relates to communications systems.
`More particularly this invention relates to methods for
`improving the peak power to average power ratio in a
`linear modulation communications system particularly
`a QAM communications system.
`
`15
`
`20
`
`BACKGROUND OF THE INVENTION
`Various communication systems are known in the art.
`Pursuant to many such systems, an information signal is
`modulated on to a carrier signal and transmitted from a
`?rst location to a second location. At the second loca
`tion, the information signal is demodulated and recov
`ered.
`Typically, the communication path used by such a
`system has various limitations, such as bandwidth. As a
`result, there are upper practical limitations that restrict
`the quantity of information that can be supported by the
`communication path over a given period of time. Vari
`ous modulation schemes have been proposed that effec
`tively increase the information handling capacity of the
`communication path as measured against other modula
`tion techniques. Sixteen-point quadrature amplitude
`modulation (QAM) provides a constellation of modula
`tion values (distinguished from one another by each
`having a different combination of phase and amplitude)
`wherein each constellation point represents a plurality
`of information bits.
`By virtue of their changing amplitude from QAM
`symbol time-to-QAM-symbol time, QAM symbols in a
`QAM communication system require linear power am
`pli?cation to be able to accurately distinguish one QAM
`symbol at one amplitude level and another QAM sym
`bol at some other power level. In a radio communica
`tions system, QAM symbols require a very linear ampli
`?cation prior to broadcasting them on an antenna. In
`QAM systems, non-linear ampli?cation of QAM sym
`bols in a QAM signal, (which QAM signal is typically
`considered to be a pulse-shape ?ltered and frequency
`up-converted stream of QAM symbols), in a radio trans
`mitter can make coherent demodulation impossible.
`Another more common problem with using non-linear
`ampli?ers with QAM modulation is the frequency splat
`ter caused by non-linear ampli?cation of a signal. For
`this reason, linear power ampli?ers are required in
`QAM radio transmitters, which power ampli?ers in
`crease in cost, size, and complexity as their output
`power level and/or linearity increase.
`A problem in the design of a linear power ampli?er is
`providing the ability of an ampli?er to accommodate
`widely ?uctuating input power levels while producing
`60
`at its output a faithful reproduction of the input signal.
`While an ampli?er can be readily designed to have a
`linear power ampli?cation of a relatively constant
`amplitude input signal, designing an ampli?er that can
`accommodate a peak power level that might, at any
`65
`given time, exceed the average power level by several
`decibels (db) can signi?cantly increase the cost and size
`of the ampli?er.
`
`2
`In QAM communications systems, the ratio of the
`peak power level to average power level of a QAM
`symbol stream will usually continuously vary by virtue
`of the fact that the data represented by the QAM sym
`bols itself varies randomly. Accordingly, power ampli
`?ers for QAM communications systems must be capable
`of handling a signi?cant peak to average power level
`ratio and, accordingly, any reduction in the peak to
`average power ratio eases the requirements of a QAM
`power ampli?er.
`Some prior art, single channel QAM systems are
`frequently transmitted on a communications channel,
`such as a radio frequency channel, in conjunction with
`a pilot component. Such pilot components, by construc
`tively or destructively adding with other QAM symbols
`can at times aggravate the the peak to average power
`level ratio requirements of a QAM power ampli?er,
`thereby further aggravating the requirements of such an
`ampli?er.
`Any methodology by which the ratio of peak power
`amplitude to average power amplitude is reduced
`would therefore simplify and reduce the ampli?er cost
`associated with a QAM system and would be an im
`provement over the prior art.
`
`SUMMARY OF THE INVENTION
`In a multi-subchannel, N-level QAM communication
`system using complex-valued pilot symbols, there is
`provided herein a method of reducing the ratio of peak
`to average power by pre-selecting amplitude and/or
`phase angles for the embedded, complex-valued, pilot
`symbols added to QAM information symbols, so as to
`minimize the peak to average power ratio of a compos
`ite QAM signal that is transmitted on a communications
`channel. Such pre-selected pilot symbols include com
`plex-valued symbols that are not part of the well-known
`constellation of values used in an N-level QAM system,
`such as the 16 constellation points used in a 16 QAM
`system. In fact, using the method herein, in a multi
`channel, N-level QAM system wherein, over some
`length of time during which several QAM symbol
`frames can occur, in addition to have different valued
`time-coincident pilots in several subchannels, the pilot
`values in one or more subchannel can also change over
`this length time. Stated alternatively, pilot values can
`change both over time and over subchannels to reduce
`the peak to average power ratio in the composite signal.
`Frequently at least one pilot symbol will be selected to
`be off the constellation of values in order to maximally
`reduce the peak to average power level in the compos
`ite signal of a QAM system, which composite signal is
`comprised of the combination or summation of a plural
`ity of N-level QAM subchannels, which subchannels
`are in-turn comprised of complex-valued QAM infor
`mation symbols combined with the complex-valued
`preselected pilot symbols. In a multi-channel, N-level
`QAM system, by proper selection of these preselected
`pilot signals, which are combined with the QAM infor
`mation symbols (which QAM information symbols in
`clude the information of interest to be transmitted) the
`combined QAM symbols and the preselected pilot can
`have a substantially lowered peak power level to aver
`age power level ratio, compared to prior art systems
`that use only one or more QAM constellation points for
`pilot symbols.
`In most application of the method herein, and in the
`embodiment of a QAM transmitter disclosed herein, at
`least one pilot symbol that is to be combined with a
`
`30
`
`35
`
`45
`
`55
`
`5
`
`

`
`5,381,449
`3
`QAM symbol stream, will not lie on the constellation of
`the QAM symbol. Such a non-constellation-based pilot
`symbol is considered to be any complex-valued symbol
`that does not have a phase angle and/or amplitude
`within pre-determined limits, or ranges, circumscribing
`the mathematical points on the rectilinear complex
`plane upon which QAM symbols are identi?ed.
`
`10
`
`30
`
`BRIEF DESCRIPTION OF THE DRAWINGS
`FIG. 1 shows a 16 QAM constellation map;
`FIG. 2 shows a plot of energy versus frequency for a
`four subchannel QAM system;
`FIG. 3 shows a plot of a prior art QAM pilot symbol;
`FIG. 4 shows a graphical representation of the place
`ment of pilot symbols and QAM information symbols in
`various symbol times, in various time frames in a four
`subchannel QAM system;
`FIG. 5A shows a simpli?ed block diagram of an
`improved four channel, 16 QAM communications
`transmitter that provides for improved peak power
`20
`ratio to average power ratio in a composite S(t)
`achieved by non-constellation-based pilot symbols;
`FIG. 5B shows a simpli?ed representation of the
`improved pilot and its insertion into the QAM symbol
`stream.
`FIG. 6 shows a graphical representation of a 16-point
`constellation for a 16 QAM system, and shows examples
`of both, non-constellation-based pilot symbols and con
`stellation-based pilot symbols.
`DETAILED DESCRIPTION OF THE
`PREFERRED EMBODIMENT
`FIG. 1 shows a constellation for a 16 QAM communi
`cation system that is a map of 16 points on the complex
`plane defined by a horizontal axis representing the real
`portions, and a vertical axis representing imaginary
`portions, of a complex number. Transmitted QAM in
`formation symbols on a communications channel, (and
`the pilot symbols as well) are discrete, packets of a
`carrier signal modulated to convey information using
`40
`both the amplitude and phase-angle displacement of the
`carrier from some reference. QAM information symbols
`are represented on the constellation of FIG. 1 as com
`plex quantities represented as vectors having both mag
`nitude (represented as length) and phase angles (which
`angles are measured with respect to one of the axes). In
`a 16 QAM system, having 16 different magnitude and
`phase angle combinations that correspond to 16 differ
`ent possible bit patterns of four bindery digits, (which
`bits are from a serial stream of bits from an information
`source), each of the 16 points on the constellation is
`identi?ed as representing one combination of four bits.
`A vector (10) (expressed in rectangular coordinates
`as 3+3j and having a length=(32+32)1"8 and a phase
`angle (12) equal to the arctan of 3/3 or forty ?ve de
`grees with respect to the real axis), points to the point
`{3,3j} on the constellation, which point is shown in
`FIG. 1 as representing the series of four binary digits,
`(0,0,0,0). A second QAM symbol (14) points to yet
`another point (1, - lj) in this constellation and repre
`sents four other digital symbols.
`From the foregoing, it can be seen that eight bits of
`information can be represented by two, l6-QAM sym
`bols. When a digital information stream is converted to
`16 QAM, four-bit blocks of the data are mapped to the
`various vectors that correspond to the bit pattern em
`bodied in the four bits. When the QAM symbols that
`represent the digital information are transmitted, the
`
`4
`symbols are transmitted with amplitudes and phase
`angles that correspond to the magnitudes and phase
`angles of the vectors used to represent the various pat
`terns, such as those shown for the vectors 10 and 14
`depicted in FIG. 1.
`FIG. 5A shows a simpli?ed block diagram of a four
`channel 16 level QAM (16-QAM) transmitter (100).
`Though depicted in block diagram format for the con
`venience of explanation and understanding it should be
`understood that the invention shown in FIG. 5A, can be
`practiced in a variety of embodiments; but in particular
`most of the functions (300) of the preferred embodiment
`are performed in a digital signal processor such as the
`Motorola DSP56000 or DSP96000 families. Further
`more, although the embodiment described below is in
`the context of a 16 QAM ampli?cation it should also be
`understood that the teachings herein are also applicable
`to other, multi-subchannel, n-QAM systems.
`Referring to FIG. 5A, a processing unit (102) re
`ceives an original information signal (101) from an in
`formation source. In this particular embodiment, this
`information signal constitutes a serial bit stream having
`an effective baud rate of 53.2 kilobits per second. This
`bit stream can represent, for example, true data, digi
`tized voice, or other appropriate signals.
`The processing unit (102) functions to convert groups
`of 16 serial bits of the original information signal into
`four 16 QAM complex signal points (symbols). For
`example, FIG. 1 depicts a 16 QAM complex signal
`symbol constellation (2). Each symbol from the pro
`cessing unit is a complex quantity, substantially within
`the constellation and represents a different combination
`of four serial bits from the information signal (101). For
`example, a ?rst one of these symbols (201) represents
`the bits “0001.” A second symbol (202), on the other
`hand, represents the bits “0100,” all in accordance with
`well understood prior art methodology.
`For each serially received 16 original information
`bits, the processing unit (102) outputs, in parallel, on
`each of 4 signal paths (103 c: 106), an appropriate repre
`sentative multibit symbol as described above. A pilot
`insertion unit (107-110), located in each signal path
`(103-106), inserts a predetermined symbol following
`receipt of 7 serially received information symbols from
`the processing unit (102) pursuant to one embodiment of
`a communication methodology in accordance with the
`invention. (Other embodiments of the invention would
`of course include pilot insertion more or less frequently
`than once every 7 information symbols.) For each seri
`ally received 16 original information bits, (from the
`information signal 101) the processing unit (102) out
`puts, in parallel on each of the four signal paths
`(103-106), an appropriate representative multibit sym
`bol as described above.
`A reduction in the ratio of peak output power level to
`average power level in the composite output signal S(t)
`(500) can be achieved by pre-selecting, in advance, at
`least the magnitude of, phase angle of, or both, for each
`of a plurality of the pilot symbols inserted by the pilot
`insertion units (107, 108, 109, and 110). When these
`preselected pilots are added to form QAM subchannel
`symbols streams, (111, 112, 114, and 116) and they are
`combined by the adder (400), (after they are pulse-shape
`fltered 120, 122, 124, and 126 and mixed 128, 130, 132,
`and 134, with an appropriate injection signal 136, 138,
`140, and 142 of the form ea?fo?m), wherein j is the
`square root of negative one, t is time, and fo?k comprises
`an offset frequency corresponding to the kth composite
`
`25
`
`35
`
`45
`
`55
`
`60
`
`65
`
`6
`
`

`
`0
`
`25
`
`35
`
`5,381,449
`5
`signal) the composite signal (500) has a reduced peak to
`average power‘ ratio.
`The form of the pilot in the embodiment shown in
`FIG. 5A is substantially represented by the quantity
`P,-J-=p,-Jei9i,j, where 9,;jis the phase of the i’th subchan
`nel pilot at symbol time j and in the preferred embodi
`ment is empirically determined using a computer pro
`gram, the source code of which is appended below. The
`determination of the optimum value for the pilot sym
`bols in the preferred embodiment contemplated a ?xed
`QAM symbols frame, which frame is graphically de
`picted in FIG. 4 as the time period of seven consecutive
`QAM symbol times (including the pilot symbol time 1)
`at a nominal carrier frequency (f0 in FIG. 1
`In the preferred embodiment, for a given magnitude
`of pilot, the optimum phase of the injected pilot symbols
`are calculated. (In a sense, both the magnitude and
`phase angle are “calculated” by the program. An initial,
`desired magnitude is supplied to the program by the
`user and, using this user-supplied quantity, the program
`20
`calculates optimum phase-angle values, assuming that
`all other symbols transmitted are zero. Accordingly, in
`the embodiment of the program below, to select differ
`ent phase angles and magnitudes, a user must select a
`different starting magnitude and re-calculate an opti
`mum phase angle value for the new magnitude). Alter
`nate embodiments of the program contemplate includ
`ing in the calculation of the phase angles and/or magni
`tudes of the pilots, the effects of the random nature of
`the QAM information streams (103, 104, 105, 106) upon
`the peak to average power ratio in the composite signal
`s(t) (500).
`Referring to FIG. 4, there is graphically depicted, the
`placement and spacing of complex valued pilot symbols
`that are combined with the complex valued QAM infor-'
`mation symbols (103-106 in FIG. 5A) at predetermined
`symbol times, (A symbol time is typically the time dura
`tion of one QAM symbol.) to produce a QAM subchan
`nel signal that is comprised of the complex valued QAM
`information symbols (103-106) and the complex valued
`40
`pilots added by the pilot insertion units (107, 108, 109,
`and 110).
`-
`In the embedded pilot sequence shown in FIG. 4,
`pilot symbols are shown being added in subchannels A
`and D, in frame 1, at symbol time 1. Pilot symbols are
`45
`added to the subchannels B and C at symbol time 3 in
`frame number 1. (Pilots inserted into subchannels dur
`ing the same symbol time are considered to be time
`coincident.) In time frame number 2, which depicts an
`alternate implementation of the pilot symbol insertion,
`time coincident pilot symbols might just as well be
`inserted during a single symbol time 1 wherein insertion
`of the pilots are all time coincident with respect to each
`other. Frame 3 shows yet another QAM frame, having
`more than seven symbol times and having time coinci
`dent pilots added to at least two channels, every seven
`symbol times. For purposes of this invention it is prefer
`able that at least two subchannels have so called time
`coincident pilots and it is yet even more preferable that
`all subchannels have time coincident pilots but alternate
`embodiments would contemplate using time coincident
`pilots in two or more subchannels to further manipulate
`the peak to average power ratio.
`During a ?nite time period, which period might even
`be considered the sum of the frame times for frames 1,
`65
`2, and 3, at least one pilot symbol, in at least one sub
`channel, will have a value different from the values of
`the other pilots. It should be expected that a plurality of
`
`6
`the subchannel signals will have a single, or ?rst value
`and these might be considered ?xed-pilot subchannel
`signals. In at least one other channel, channel B for
`example, using the method taught herein, during this
`?nite time period (which period might be as short as one
`symbol time), will have a second value.
`In many instances, (depending for example on the
`number of symbol times in a frame and/ or other factors)
`during a ?nite length of time, the pilot symbols to be
`added to a ?rst subchannel at the pilot symbol times
`therefor, (subchannel A for example) can be selected
`from a ?rst set of pilot values, and the pilots for a second
`subchannel signal be selected from a second set of pilot
`symbol values. The pilots from such a ?rst and second
`set of values might change in either their order of inser
`tion, their values, or both, to optimally reduce the peak
`to average ratio for the system. A key feature of the
`method herein is that in any subchannel, during some
`?nite period of time, pilot symbol values might vary
`during successive pilot symbol times, in order to reduce
`the peak to average ratio, of the system, during such
`length of time.
`Referring to FIG. 5A, since the QAM information
`symbols on lines 103-106 are complex valued quantities,
`and which represent data, (which data is substantially
`random over time) the combination of these complex
`valued quantities by the summation circuit (400) (ignor
`ing momentarily the effect of the inserted pilot symbols)
`will have a varying peak power level to average power
`level. This might be appreciated by referring to the
`constellation map again depicted on FIG. 1. At any
`particular instant, the output or any one of the QAM
`information streams might have a QAM symbol that is
`either identical with or differs from other QAM sym
`bols on the other channels. Upon their combination at
`the summing circuit (400), over time they will have
`randomly varying peak power level.
`In this invention by appropriate manipulation of the
`complex valued pilot symbols inserted by the pilot in
`sertion units (107 and 110), the peak power level to
`average power level ratio in the composite signal s(t),
`(500) can be substantially reduced, when various proba
`bilistic factors of the data with which they are com
`bined with are considered. Improvements in the peak to
`average power ratio of 1.5 dB have been realized in at
`least one embodiment of the invention.
`Referring to FIG. SE a simpli?ed graphical represen
`tation of the pilot insertion unit (107-110 in FIG. 5A
`and which is implemented in a digital signal processor).
`The improved pilot insertion unit produces pilot sym
`bols that are added to the QAM symbol stream and
`which can vary substantially anywhere on or off the 16
`QAM constellation map shown in FIG. 1. In addition to
`having the time-coincident pilots of multiple subchan
`nels being different, the magnitude and/or phase of the
`pilot symbols in each subchannel (A-D for example),
`can vary from pilot symbol time to pilot symbol time in
`that subchannel.)
`In this invention, while legitimate QAM information
`symbols will of necessity have to be mapped to one of
`the 16 constellation points, it is expected using the meth
`odology of this invention that at least one of the pilot
`symbols that are combined with the QAM information
`streams (103-106) will not fall on a valid constellation
`point. Instead, the invention, (which includes the imple- I
`mentation of the apparatus shown in FIG. 5A) contem
`plates pilots such as those shown in FIG. 6 identi?ed
`and depicted by reference numerals 84, 86 and 88 which
`
`50
`
`55
`
`60
`
`7
`
`

`
`5
`
`25
`
`5,381,449
`7
`pilots do not fall on valid constellation points, but
`which when combined with the QAM information
`streams (103-106) to form piloted QAM subchannel
`symbol streams (123, 125, 127, and 129), can when com
`bined with the other complex values on the other sub
`channels to form a composite signal (500) substantially
`reduce the peak to average power ratio of the compos
`ite signal (500). (in addition to using the non-constella
`tion-based pilots 84, 86, and 88, constellation based
`pilots, such as pilot 90, when appropriately identi?ed, 10
`can at appropriate times, also be used to reduce peak to
`average power ratio.) Both the constellation-based pilot
`symbols and the non-constellation based pilot symbols
`are considered to be pre-selected and pre-determined
`symbols. By virtue of the fact that the pilots occur at 15
`discrete instants of time, i.e. one or more QAM symbol
`times they are considered time domain pilots. In so far
`as the pilots are spread across the frequencies of the
`different subchannels, each subchannel of which is cen
`tered about a different frequency, the pilots are also
`considered to have a frequency domain characteristics.
`In this sense, the pilots can be considered to be both
`time and frequency domain, and both non-constellation
`and constellation based, predetermined, complex
`valued pilots.
`In the preferred embodiment, the phase angle selec
`tion for the pilots is accomplished by means of a com
`puter program which is depicted in the attached appen
`dix. It should be appreciated that in other embodiments,
`a plurality of the pilots might have either their ampli
`tudes and/or their phase angles selected such that when
`combined with a probablistic determination of permissi
`ble QAM information symbols
`the peak to
`average power ratio of the composite signal over some
`?nite length of time. In the embodiment of the appara
`tus shown in FIG. 5A, at least one of the complex val
`ued pilot symbols that are added to the QAM informa
`tion symbols by the pilot insertion units (107, 108, 109,
`
`8
`and 110) does not lie on the permissible constellation
`points depicted in either FIGS. 1 or 5.
`An exemplary selection process to select these prede
`termined pilot symbols is described below. The embodi
`ment of program below assumes:
`1) a four-subchannel QAM system, having 4, time
`coincident pilot symbols (220), such as those shown
`in frame 2 of FIG. 4.
`2) that the DSP, in which the apparatus (300) shown 7
`in FIG. 5A is embodied, has a simulation sampling
`rate, F8, (i.e. samples the composite signal s(t)) at 36
`times the composite symbol rate.
`3) that the subchannel center frequencies are
`c01=27r(—-3FS/64);
`w2=21r(— lFs/64);
`m3=2n'(1FS/64); m4=21r(3FS/64).
`The user supplies the program: a slot format ?le con
`sistent with assumption 1 above; a ?nite impulse re
`sponse ?lter ?le, which de?nes the coefficients of the
`subchannel pulse shape ?lters 120, 122, 124, 126; the
`symbol time position of the pilot in a slot for which to
`carry out the pilot-phase set search; the desired magni
`tude (squared) of the pilot symbol, (referred to in the
`program as sync symbols); the number of steps around
`the unit circle at which to calculate s(t) for each of the
`four time coincident pilots for which the search is being
`carried out.
`The programs’ output is a set of phase angles for (i.e.
`the 6’s shown in FIG. SE) at which the peak transmitter
`output power is smallest, after calculating peak trans
`mitter output power levels for all the possible combina
`tions of 9, in the step sizes speci?ed by the user.
`While this embodiment of the invention contemplates
`a particular pilot con?guration, i.e. as shown in time
`5 frame 2 of FIG. 4, other embodiments contemplate
`other slot/pilot con?gurations, such as that shown in
`frame 1 of FIG. 4 for example. A similar program could
`well be written by those skilled in the art for any other
`slot/pilot con?guration.
`
`#clefine
`
`EXTERN
`
`#include <stdio . h>
`
`#include <mat'h. h>
`
`#include
`
`" readlib . h"
`
`#include
`
`"defcmath . h"
`
`#include
`
`"defdsp. h"
`
`main ()
`
`I/a
`* Transmitter variables and pointers
`
`/ .
`
`8
`
`

`
`double
`(sps)
`double
`
`9
`fsymb;
`*/j_-
`tsymb;
`
`(sec per symb) */
`
`double
`sampling
`
`ftx;
`*/
`
`5,381,449
`
`10
`/* QAM sub—channel symbol rate
`
`/* QAM sub—channel symbol period
`
`/* sub-channel TX pulse shape filter
`
`/*
`
`rate (ksps)
`
`*/
`
`int
`
`nzs't,"
`
`l /* zero’ stuff ratio in sub—channel
`
`'
`
`*/
`
`double
`*/
`
`int
`
`nsub;
`*/
`
`ttx;
`
`/* l/ftx (seconds per sample) I
`
`/* number of QAM sub-channels in system
`
`double
`
`fsc;
`
`/* sub-channel frequency spacing (Hz)
`
`double
`
`wcent [4] ;
`
`/* sub-channel center frequencies
`
`(neutral)
`
`*/
`
`tx_ph_st[4]';
`double
`for sub-03:1 */
`
`double
`
`tx_phase[4] ;
`*/
`
`_
`
`/* phase step in one san'pl'e period
`
`/* phase of sub—channel
`
`double
`
`ps__pow;
`
`/* power in pulse shape filter
`
`impulse resp. -
`
`*/
`
`double
`output
`
`tXJJQW;
`*/
`
`/* average power at transmitter
`
`COMPLEX
`
`tx__out;
`
`/* transmitter . output
`
`COMPLEX
`
`*/
`
`qam_symb;
`*/
`
`'
`
`/* complex QAM symbol variable
`
`COMPLEX
`
`sub_ch[4] .'
`
`/* sub—channel data vector
`
`\ */
`
`COMPLEX
`
`ps__out[4] [144] ;
`*/
`
`~
`
`.
`
`/* sub—channel data vector
`
`int pouts;
`'
`. /* number of filter outputs ..
`'IDEIR *t:r_pulse[£1] ;
`strcts
`*/
`int
`numb_taps;
`
`/* pointer to pulse shaping TX filter
`
`I
`
`*/
`
`double
`
`tx_avg;
`
`9
`
`

`
`double
`double
`
`11
`tx__scale;
`max_pow;
`
`5,381,449
`
`12
`
`int
`
`slot_len;
`
`/* slot length in sub-channel symbols
`
`FILE *slot__def; /* slot definition file pointer
`*/
`
`int
`
`slot_symb[l00] ;
`
`/* slot symbol definition array
`
`I.
`
`*/'
`
`amp__pdf [600] ;
`double
`pdf_cnt;
`double
`int
`Pdf_index;
`
`long cnt;
`
`long sync_length;
`pattern
`*/
`
`long steps;
`variable
`*/
`
`/* number of samples simulated per sync
`
`/* number of phase steps for each
`
`int
`
`s_symb__cnt; /* sync symbol counter ~
`
`double
`
`phase_step; /* 2pi/steps
`
`‘
`
`*/
`
`’
`
`*/
`double
`double
`
`double
`double
`double
`double
`
`phil;
`phi2;
`
`thetal;
`theta2;
`s_mag;
`inv__ns;
`
`COMPLEX I
`
`exp_p1;
`
`COMPLEX -
`COMPLEX
`
`exp;p2l;
`. exp__trl;
`
`COMPLEX
`
`' exp_t2;
`
`COMPLEX
`
`mc__exp_tl;
`
`COMPLEX
`
`mc_"_exp_t2;'
`
`COMPLEX
`
`s__symb[4] ;
`
`double
`
`best [100] [6] ;
`
`10
`
`

`
`5,381,449
`
`14
`
`13
`
`int
`
`numb_pilot;
`
`int - Hnumb_;data;
`int
`numb_dum_p:
`
`numb_dum_d; ,
`int
`slot_cnt;
`int
`double
`inv__np;
`
`COMPLEX
`
`sync[100l] ;
`
`FILTER
`*mf [100];
`int
`mf_len;
`COMPLEX
`mf_out;
`double
`max[2] ,-_
`
`double
`
`bufi3] ;
`
`int
`int
`
`pilot [100] ;
`pil__loc;
`
`/*
`
`* general purpose variables and pointers
`
`*/
`
`‘
`
`char str1[60] ;
`
`/* general purpose string buffer
`
`*/
`
`char ‘ str2 [60] ;
`char str3 [60] ; I
`double
`ter‘np;
`
`_*/
`/* general‘ purpose ‘string buffer '
`*7
`/* general purpose string buffer
`/* general purpose temporary variable
`
`*/
`
`'
`
`'
`
`.
`
`.
`
`double
`
`temp2f;. ‘
`
`" double
`
`- temp3;
`
`double
`double
`
`pi2;
`pig-3.
`
`/* 2.0*pi
`
`*/ ‘
`
`long i, j,k, l,m,n;
`
`/* general purpose counters
`
`*/
`
`I
`
`COMPLEX _
`
`c_temp;
`
`/* complex general purpose temporary
`
`variable
`
`*/ '
`
`COMPLEX
`COMPLEX
`
`v c__templ;
`c__temp2}
`
`COMPLEX
`
`' c_temp3 ;
`
`11
`
`

`
`COMPLEX
`
`15
`
`q_one;
`.x/
`
`5,381,449
`
`_
`/* 1 + jO (complex one)
`
`16
`
`COMPLEX
`
`c_zero:
`
`/* 0 + j0 (complex zero)
`
`*A
`
`FILE *fr,'*fr1, *fr2, *fw, *fw1, *fw2;
`q_one.rea1 = 1.0;
`c;one.imag = 0.0;
`
`q_zero.real = 0.0:
`
`q_zero.imag = 0.0;
`
`pi2 = 8.0*atan(1.0);
`
`pi = 4.0*atan(1.0):
`
`nsub = 4;
`
`fsymb = 4000.0;
`
`tsymb = 1.0/fsymb;
`
`ftx = 144.07
`
`ttx = 1.0/(ftx*1000.0):
`
`nzst = 36;
`
`fsc = ftx*l000.0/32.0;
`
`temp = -(nsub —.1)*(fsc/2.0);
`
`for ( i = 0; i <5-isub;
`{
`
`i++)
`
`wcent[i] = pi2*temp;
`
`tx_ph_st[;J = wcent[i]*ttx;
`
`temp += fsc;
`
`agaih22:
`
`printf("\nEnter-the slot définition filename;\n");
`scanf("%s", str3);
`
`slot_§ef = fopen(str3, "r");
`if ( slot_def == NULL )
`(
`
`printf("\nFILB ACCESS ERROR, TRY AGAIN.\n");
`
`goto again22;
`
`
`
`12
`
`

`
`17
`
`5,38L449
`
`18
`
`} £
`
`scanf(slot_def,
`
`" %d", &slot_;en);
`
`if ( slot_}en > 90 )
`{
`
`printf(“\nMAXIMUM SLOT LENGTH OF 90 SYMBOLS EXCEEDED, TRY
`AGAIN./n");
`
`goto again22;
`
`}
`
`,
`
`numb_pilot = 0;
`
`numb__data = 0;
`
`numb_§um_p = 0;
`
`nunktfhuqid = 0;
`II
`
`0;
`
`slot_pnt
`
`i = 0;
`
`while( fscanf(slot_§ef,
`'
`{"
`.
`if ( slot_§ymb[slot_pnt] é= 0 )
`
`" %d", &s1ot_symb[slot_pnt])
`_.
`
`!= EOE )
`
`{.
`
`.
`numb_piIo£++;
`pilotfil ;.slot_pnt;
`i++;'
`'
`T
`
`ll
`
`1 )
`
`2 )
`
`} e
`
`lse if (Tslot_symb[slot_cnt] =
`
`nunmL§ata++;
`
`else if ( slot_symb[slot_pnt] =
`{
`
`numb_dunLp++;
`
`pi1ot[i] = s1ot_gnt:
`'i++;
`V
`
`} e
`
`lse if ( slot_§ymb[slop_cnt] == 3 )
`
`numb_dum_d++;
`
`slot_pnt++;
`
`2}
`
`if (
`
`(slot_pnt
`
`!= slot_1en) H
`
`((numb_pilot+numb_data+numb_dum_p+numb_dum_d)
`
`!= slot_len) )
`
`printf("\nINVALID SLOT DEFINITION FILE, TRY AGAIN./n");
`
`
`
`13
`
`

`
`5,381,449
`
`20
`
`19
`goto again22;'
`
`} f
`
`close(slot_def);
`
`for (
`
`j = 0;
`
`j < i; j++ )
`
`printf("\nPILOT NUMBER %2d AT SLOT SYMBOL NUMBER %2d.\n",
`P