United States Patent 19
`Jasper et al.
`
`US005381449A
`Patent Number:
`11
`(45) Date of Patent:
`
`5,381,449
`Jan. 10, 1995
`
`
`
`(56)
`
`References Cited
`U.S. PATENT DOCUMENTS
`3,955,141 5/1976 Lyon et al. ............................. 375/8
`4,464,767 8/1984 Bremer .................................. 375/67
`4,646,305 2/1987 Tretter et al. ......................... 375/39
`4,680,775 7/1987. Exarque et al........................ 375/39
`Primary Examiner-Stephen Chin
`Attorney, Agent, or Firm-Joseph P. Krause
`57
`ABSTRACT
`The ratio of peak power level to average power level in
`a power amplifier used in a QAM communication sys
`tem transmitter can be reduced by preselecting magni
`tudes and phase angles of complex-valued pilot symbols
`used in multi-channel, N-level QAM.
`
`20 Claims, 3 Drawing Sheets
`
`wn
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`uns
`
`no my ,
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`is m rw
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`it alwa
`
`100
`
`(75
`
`(54) PEAK TO AVERAGE POWER RATIO
`REDUCTION METHODOLOGY FOR QAM
`COMMUNICATIONS SYSTEMS
`Inventors:
`Steven C. Jasper, Hoffman Estates;
`Mark A. Birchler, Roselle, both of
`1.
`73 Assignee: Motorola, Inc., Schaumburg, Ill.
`(21) Appl. No.: 786,681
`22 Filed:
`Nov. 1, 1991
`Related U.S. Application Data
`Continuation-in-part of Ser. No. 536,825, Jun. 12, 1990.
`63
`5ll Int. Cl. ............................................. H04L27/04
`52 U.S. C. ....................................... 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
`
`
`
`
`
`
`
`INFORMATION
`SOURCE
`B BITS/SEC.
`
`SERIAL BITS
`O
`M-PARALE
`COPEX
`SYNBOLS
`
`8
`PILOT SYBOL
`INSERTION
`
`Qualcomm Incorporated
`Exhibit 1010
`Page 1 of 135
`
`

`

`U.S. Patent
`
`Jan. 10, 1995
`
`Sheet 1 of 3
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`5,381,449
`
`IMAGINARY
`
`3
`
`O
`
`(0,0,0,1)
`
`
`
`
`
`(0,1,0,0)
`
`(0,0,0,0)
`FIG.1
`2
`- PRIOR ART
`
`ENERGY
`
`FIG.2
`
`A
`
`B
`
`C
`
`D
`
`
`
`IMAGINARY.
`
`-
`
`-PRIOR ART
`
`REAL
`
`Page 2 of 135
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`US. Patent
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`Jan. 10, 1995
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`Sheet 2 of 3
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`5,381,449
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`U.S. Patent
`US. Patent
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`Jan. 10, 1995
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`Sheet 3 of 3
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`5,381,449
`5,381,449
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`Page 4 of 135
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`

`1.
`
`PEAKTO AVERAGE POWERRATO REDUCTION
`METHODOLOGY FOR QAM COMMUNICATIONS
`SYSTEMS
`
`5
`
`10
`
`15
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`5,381,449
`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
`fiers for QAM communications systems must be capable
`of handling a significant peak to average power level
`ratio and, accordingly, any reduction in the peak to
`average power ratio eases the requirements of a QAM
`power amplifier.
`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 amplifier,
`thereby further aggravating the requirements of such an
`amplifier.
`Any methodology by which the ratio of peak power
`amplitude to average power amplitude is reduced
`would therefore simplify and reduce the amplifier 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
`
`This is a continuation-in-part of Ser. No. 07/536,825,
`filed 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.
`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
`first 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
`25
`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
`30
`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)
`35
`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
`plification 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
`fication prior to broadcasting them on an antenna. In
`45
`QAM systems, non-linear amplification of QAM sym
`bols in a QAM signal, (which QAM signal is typically
`considered to be a pulse-shape filtered and frequency
`up-converted stream of QAM symbols), in a radio trans
`mitter can make coherent demodulation impossible.
`50
`Another more common problem with using non-linear
`amplifiers with QAM modulation is the frequency splat
`ter caused by non-linear amplification of a signal. For
`this reason, linear power amplifiers are required in
`QAM radio transmitters, which power amplifiers in
`55
`crease in cost, size, and complexity as their output
`power level and/or linearity increase.
`A problem in the design of a linear power amplifier is
`providing the ability of an amplifier to accommodate
`widely fluctuating input power levels while producing
`at its output a faithful reproduction of the input signal.
`While an amplifier can be readily designed to have a
`linear power amplification of a relatively constant
`amplitude input signal, designing an amplifier that can
`accommodate a peak power level that might, at any
`65
`given time, exceed the average power level by several
`decibels (db) can significantly increase the cost and size
`of the amplifier.
`
`Page 5 of 135
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`

`10
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`15
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`5,381,449
`3
`4.
`QAM symbol stream, will not lie on the constellation of
`symbols are transmitted with amplitudes and phase
`the QAM symbol. Such a non-constellation-based pilot
`angles that correspond to the magnitudes and phase
`symbol is considered to be any complex-valued symbol
`angles of the vectors used to represent the various pat
`that does not have a phase angle and/or amplitude
`terns, such as those shown for the vectors 10 and 14
`within pre-determined limits, or ranges, circumscribing
`depicted in FIG. 1.
`the mathematical points on the rectilinear complex
`FIG. 5A shows a simplified block diagram of a four
`plane upon which QAM symbols are identified.
`channel 16 level QAM (16-QAM) transmitter (100).
`Though depicted in block diagram format for the con
`BRIEF DESCRIPTION OF THE DRAWINGS
`venience of explanation and understanding it should be
`FIG. 1 shows a 16 QAM constellation map;
`understood that the invention shown in FIG.5A, can be
`FIG. 2 shows a plot of energy versus frequency for a
`practiced in a variety of embodiments; but in particular
`four subchannel QAM system;
`most of the functions (300) of the preferred embodiment
`FIG. 3 shows a plot of a prior art QAM pilot symbol;
`are performed in a digital signal processor such as the
`FIG. 4 shows a graphical representation of the place
`Motorola DSP56000 or DSP96000 families. Further
`ment of pilot symbols and QAM information symbols in
`more, although the embodiment described below is in
`various symbol times, in various time frames in a four
`the context of a 16QAM amplification it should also be
`subchannel QAM system;
`understood that the teachings herein are also applicable
`FIG. 5A shows a simplified block diagram of an
`to other, multi-subchannel, n-QAM systems.
`improved four channel, 16 QAM communications
`Referring to FIG. 5A, a processing unit (102) re
`transmitter that provides for improved peak power
`ceives an original information signal (101) from an in
`20
`ratio to average power ratio in a composite S(t)
`formation source. In this particular embodiment, this
`achieved by non-constellation-based pilot symbols;
`information signal constitutes a serial bit stream having
`FIG. 5B shows a simplified representation of the
`an effective baud rate of 53.2 kilobits per second. This
`improved pilot and its insertion into the QAM symbol
`bit stream can represent, for example, true data, digi
`tized voice, or other appropriate signals.
`Steam.
`25
`FIG. 6 shows a graphical representation of a 16-point
`The processing unit (102) functions to convert groups
`constellation for a 16QAM system, and shows examples
`of 16 serial bits of the original information signal into
`of both, non-constellation-based pilot symbols and con
`four 16 QAM complex signal points (symbols). For
`stellation-based pilot symbols.
`example, FIG. 1 depicts a 16 QAM complex signal
`symbol constellation (2). Each symbol from the pro
`DETAILED DESCRIPTION OF THE
`cessing unit is a complex quantity, substantially within
`PREFERRED EMBODIMENT
`the constellation and represents a different combination
`FIG. 1 shows a constellation for a 16QAM communi
`of four serial bits from the information signal (101). For
`cation system that is a map of 16 points on the complex
`example, a first one of these symbols (201) represents
`plane defined by a horizontal axis representing the real
`the bits "0001.” A second symbol (202), on the other
`portions, and a vertical axis representing imaginary
`hand, represents the bits "0100,' all in accordance with
`portions, of a complex number. Transmitted QAM in
`well understood prior art methodology.
`formation symbols on a communications channel, (and
`For each serially received 16 original information
`the pilot symbols as well) are discrete, packets of a
`bits, the processing unit (102) outputs, in parallel, on
`carrier signal modulated to convey information using
`each of 4 signal paths (103 cc 106), an appropriate repre
`40
`both the amplitude and phase-angle displacement of the
`sentative multibit symbol as described above. A pilot
`carrier from some reference. QAM information symbols
`insertion unit (107-110), located in each signal path
`are represented on the constellation of FIG. 1 as com
`(103-106), inserts a predetermined symbol following
`plex quantities represented as vectors having both mag
`receipt of 7 serially received information symbols from
`nitude (represented as length) and phase angles (which
`the processing unit (102) pursuant to one embodiment of
`45
`angles are measured with respect to one of the axes). In
`a communication methodology in accordance with the
`a 16QAM system, having 16 different magnitude and
`invention. Other embodiments of the invention would
`phase angle combinations that correspond to 16 differ
`of course include pilot insertion more or less frequently
`ent possible bit patterns of four bindery digits, (which
`than once every 7 information symbols.) For each seri
`bits are from a serial stream of bits from an information
`ally received 16 original information bits, (from the
`source), each of the 16 points on the constellation is
`information signal 101) the processing unit (102) out
`identified as representing one combination of four bits.
`puts, in parallel on each of the four signal paths
`A vector (10) (expressed in rectangular coordinates
`(103-106), an appropriate representative multibit sym
`as 3-3j and having a length=(32-32) 178 and a phase
`bol as described above.
`angle (12) equal to the arctan of 3/3 or forty five de
`A reduction in the ratio of peak output power level to
`55
`grees with respect to the real axis), points to the point
`average power level in the composite output signal s(t)
`{3,3} on the constellation, which point is shown in
`(500) can be achieved by pre-selecting, in advance, at
`FIG. 1 as representing the series of four binary digits,
`least the magnitude of, phase angle of, or both, for each
`(0,0,0,0). A second QAM symbol (14) points to yet
`of a plurality of the pilot symbols inserted by the pilot
`another point (1, -1j) in this constellation and repre
`insertion units (107, 108, 109, and 110). When these
`60
`sents four other digital symbols.
`preselected pilots are added to form QAM subchannel
`From the foregoing, it can be seen that eight bits of
`symbols streams, (111, 112, 114, and 116) and they are
`information can be represented by two, 16-QAM sym
`combined by the adder (400), (after they are pulse-shape
`bols. When a digital information stream is converted to
`filtered 120, 122, 124, and 126 and mixed 128, 130, 132,
`16 QAM, four-bit blocks of the data are mapped to the
`and 134, with an appropriate injection signal 136, 138,
`65
`various vectors that correspond to the bit pattern em
`140, and 142 of the form e2"?ofk), wherein j is the
`bodied in the four bits. When the QAM symbols that
`square root of negative one, tis time, and fifkcomprises
`represent the digital information are transmitted, the
`an offset frequency corresponding to the kth composite
`
`30
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`6
`signal) the composite signal (500) has a reduced peak to
`the subchannel signals will have a single, or first value
`average power ratio.
`and these might be considered fixed-pilot subchannel
`The form of the pilot in the embodiment shown in
`signals. In at least one other channel, channel B for
`FIG. 5A is substantially represented by the quantity
`example, using the method taught herein, during this
`Pijspieij, where 6ijis the phase of the i'th subchan
`finite time period (which period might be as short as one
`nel pilot at symbol timejand in the preferred embodi
`symbol time), will have a second value.
`ment is empirically determined using a computer pro
`In many instances, (depending for example on the
`gram, the source code of which is appended below. The
`number of symbol times in a frame and/or other factors)
`determination of the optimum value for the pilot sym
`during a finite length of time, the pilot symbols to be
`bols in the preferred embodiment contemplated a fixed
`added to a first subchannel at the pilot symbol times
`10
`QAM symbols frame, which frame is graphically de
`therefor, (subchannel. A for example) can be selected
`picted in FIG. 4 as the time period of seven consecutive
`from a first set of pilot values, and the pilots for a second
`QAM symbol times (including the pilot symbol time 1)
`subchannel signal be selected from a second set of pilot
`at a nominal carrier frequency (foin FIG. 1
`symbol values. The pilots from such a first and second
`In the preferred embodiment, for a given magnitude
`set of values might change in either their order of inser
`of pilot, the optimum phase of the injected pilot symbols
`tion, their values, or both, to optimally reduce the peak
`are calculated. (In a sense, both the magnitude and
`to average ratio for the system. A key feature of the
`phase angle are "calculated' by the program. An initial,
`method herein is that in any subchannel, during some
`desired magnitude is supplied to the program by the
`finite period of time, pilot symbol values might vary
`user and, using this user-supplied quantity, the program
`during successive pilot symbol times, in order to reduce
`calculates optimum phase-angle values, assuming that
`the peak to average ratio, of the system, during such
`all other symbols transmitted are zero. Accordingly, in
`length of time.
`the embodiment of the program below, to select differ
`Referring to FIG. 5A, since the QAM information
`ent phase angles and magnitudes, a user must select a
`symbols onlines 103-106 are complex valued quantities,
`different starting magnitude and re-calculate an opti
`and which represent data, (which data is substantially
`25
`mum phase angle value for the new magnitude). Alter
`random over time) the combination of these complex
`nate embodiments of the program contemplate includ
`valued quantities by the summation circuit (400) (ignor
`ing in the calculation of the phase angles and/or magni
`ing momentarily the effect of the inserted pilot symbols)
`tudes of the pilots, the effects of the random nature of
`will have a varying peak power level to average power
`the QAM information streams (103,104,105,106) upon
`level. This might be appreciated by referring to the
`30
`the peak to average power ratio in the composite signal
`constellation map again depicted on FIG. 1. At any
`s(t) (500).
`particular instant, the output or any one of the QAM
`Referring to FIG.4, there is graphically depicted, the
`information streams might have a QAM symbol that is
`placement and spacing of complex valued pilot symbols
`either identical with or differs from other QAM sym
`that are combined with the complex valued QAM infor
`bols on the other channels. Upon their combination at
`35
`mation symbols (103-106 in FIG. 5A) at predetermined
`the summing circuit (400), over time they will have
`symbol times, (A symbol time is typically the time dura
`randomly varying peak power level.
`tion of one QAM symbol.) to produce a QAM subchan
`In this invention by appropriate manipulation of the
`nel signal that is comprised of the complex valued QAM
`complex valued pilot symbols inserted by the pilot in
`information symbols (103-106) and the complex valued
`sertion units (107 and 110), the peak power level to
`pilots added by the pilot insertion units (107, 108, 109,
`average power level ratio in the composite signal s(t),
`and 110).
`(500) can be substantially reduced, when various proba
`In the embedded pilot sequence shown in FIG. 4,
`bilistic factors of the data with which they are com
`pilot symbols are shown being added in subchannels A
`bined with are considered. Improvements in the peak to
`and D, in frame 1, at symbol time 1. Pilot symbols are
`average power ratio of 1.5 dB have been realized in at
`45
`added to the subchannels B and C at symbol time 3 in
`least one embodiment of the invention.
`frame number 1. (Pilots inserted into subchannels dur
`Referring to FIG. 5B a simplified graphical represen
`ing the same symbol time are considered to be time
`tation of the pilot insertion unit (107-110 in FIG. 5A
`coincident.) In time frame number 2, which depicts an
`and which is implemented in a digital signal processor).
`alternate implementation of the pilot symbol insertion,
`The improved pilot insertion unit produces pilot sym
`50
`time coincident pilot symbols might just as well be
`bols that are added to the QAM symbol stream and
`inserted during a single symbol time 1 wherein insertion
`which can vary substantially anywhere on or off the 16
`of the pilots are all time coincident with respect to each
`QAM constellation map shown in FIG.1. In addition to
`other. Frame 3 shows yet another QAM frame, having
`having the time-coincident pilots of multiple subchan
`more than seven symbol times and having time coinci
`nels being different, the magnitude and/or phase of the
`55
`dent pilots added to at least two channels, every seven
`pilot symbols in each subchannel (A-D for example),
`symbol times. For purposes of this invention it is prefer
`can vary from pilot symbol time to pilot symbol time in
`able that at least two subchannels have so called time
`that subchannel.)
`coincident pilots and it is yet even more preferable that
`In this invention, while legitimate QAM information
`all subchannels have time coincident pilots but alternate
`symbols will of necessity have to be mapped to one of
`embodiments would contemplate using time coincident
`the 16 constellation points, it is expected using the meth
`pilots in two or more subchannels to further manipulate
`odology of this invention that at least one of the pilot
`the peak to average power ratio.
`symbols that are combined with the QAM information
`During a finite time period, which period might even
`streams (103-106) will not fall on a valid constellation
`be considered the sum of the frame times for frames 1,
`point. Instead, the invention, (which includes the imple
`65
`2, and 3, at least one pilot symbol, in at least one sub
`mentation of the apparatus shown in FIG.5A) contem
`channel, will have a value different from the values of
`plates pilots such as those shown in FIG. 6 identified
`the other pilots. It should be expected that a plurality of
`and depicted by reference numerals 84, 86 and 88 which
`
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`8
`pilots do not fall on valid constellation points, but
`and 110) does not lie on the permissible constellation
`points depicted in either FIGS. 1 or 5.
`which when combined with the QAM information
`streams (103-106) to form piloted QAM subchannel
`An exemplary selection process to select these prede
`symbol streams (123,125, 127, and 129), can when com
`termined pilot symbols is described below. The embodi
`ment of program below assumes:
`bined with the other complex values on the other sub
`channels to form a composite signal (500) substantially
`1) a four-subchannel QAM system, having 4, time
`reduce the peak to average power ratio of the compos
`coincident pilot symbols (220), such as those shown
`ite signal (500). (in addition to using the non-constella
`in frame 2 of FIG. 4.
`2) that the DSP, in which the apparatus (300) shown
`tion-based pilots 84, 86, and 88, constellation based
`pilots, such as pilot 90, when appropriately identified,
`in FIG. 5A is embodied, has a simulation sampling
`rate, Fs, (i.e. samples the composite signal s(t)) at 36
`can at appropriate times, also be used to reduce peak to
`times the composite symbol rate.
`average power ratio.) Both the constellation-based pilot
`symbols and the non-constellation based pilot symbols
`3) that the subchannel center frequencies are
`are considered to be pre-selected and pre-determined
`o1=27t(-3Fs/64);
`o2=27t(-1F/64);
`a)3=27T(1F/64); c)4=27T(3F/64).
`symbols. By virtue of the fact that the pilots occur at
`The user supplies the program: a slot format file con
`discrete instants of time, i.e. one or more QAM symbol
`sistent with assumption 1 above; a finite impulse re
`times they are considered time domain pilots. In so far
`sponse filter file, which defines the coefficients of the
`as the pilots are spread across the frequencies of the
`subchannel pulse shape filters 120, 122, 124, 126; the
`different subchannels, each subchannel of which is cen
`20
`symbol time position of the pilot in a slot for which to
`tered about a different frequency, the pilots are also
`carry out the pilot-phase set search; the desired magni
`considered to have a frequency domain characteristics.
`tude (squared) of the pilot symbol, (referred to in the
`In this sense, the pilots can be considered to be both
`program as sync symbols); the number of steps around
`time and frequency domain, and both non-constellation
`the unit circle at which to calculate s(t) for each of the
`and constellation based, predetermined, complex
`25
`four time coincident pilots for which the search is being
`valued pilots.
`carried out.
`In the preferred embodiment, the phase angle selec
`The programs' output is a set of phase angles for (i.e.
`tion for the pilots is accomplished by means of a com
`puter program which is depicted in the attached appen
`the e's shown in FIG. 5B) at which the peak transmitter
`output power is smallest, after calculating peak trans
`dix. It should be appreciated that in other embodiments,
`30
`mitter output power levels for all the possible combina
`a plurality of the pilots might have either their ampli
`tions of 6, in the step sizes specified by the user.
`tudes and/or their phase angles selected such that when
`combined with a probablistic determination of permissi
`While this embodiment of the invention contemplates
`ble QAM information symbols minimizes the peak to
`a particular pilot configuration, i.e. as shown in time
`average power ratio of the composite signal over some
`frame 2 of FIG. 4, other embodiments contemplate
`35
`finite length of time. In the embodiment of the appara
`other slot/pilot configurations, such as that shown in
`tus shown in FIG. 5A, at least one of the complex val
`frame 1 of FIG. 4 for example. A similar program could
`ued pilot symbols that are added to the QAM informa
`well be written by those skilled in the art for any other
`slot/pilot configuration.
`tion symbols by the pilot insertion units (107, 108, 109,
`
`define
`
`EXTERN
`
`# include <stdio.h>
`#include <math.h>
`
`#include "readlib.h"
`include "deficmath. h"
`# include "defdsp.h."
`
`main ()
`
`* Transmitter variables and pointers
`x/
`
`A
`
`Page 8 of 135
`
`

`

`tyrs'
`double
`*/.
`(sps)
`tSymb;
`double
`(sec per symb) */
`double
`ftx;
`sampling
`sk/
`
`5,381,449
`/* QAM sub-channel symbol N.
`
`/* QAM sub-channel symbol period
`
`/* sub-channel TX pulse shape filter
`
`rate (ksps)
`/k
`/k zero stuff ratio in sub-channel
`/* l/ftx (seconds per sample)
`
`*/
`
`ttX;
`
`*/
`
`/* number of QAM sub-channels in system
`
`/* sub-channel frequency spacing (Hz)
`
`/* sub-channel center frequencies
`
`nzst;
`int
`double
`'k/
`insub;
`'k/
`double
`
`int
`
`double
`(nautral)
`double
`for sub-c. .
`double
`
`COMPLEX
`
`COMPLEX
`*/
`COMPLEX
`
`fisc;
`k/
`woent 4 ;
`sk/
`tx philst (4);
`. /
`tx phase (4;
`k/
`ps pow;
`double
`impulse resp.
`k/
`double
`txpow;
`Output
`k/
`COMPLEX
`tx out;
`k/
`qam symb;
`k/
`sub ch (4);
`
`/* phase step in one sample period
`
`/* phase of sub-channel
`
`/* power in pulse shape filter
`
`/* average power at transmitter
`
`/k transmitter output
`
`/* complex QAM symbol variable
`
`/* sub-channel data vector
`
`ps out (4) (144);
`*/
`
`/* sub-channel data vector
`
`k/
`/* number of filter outputs ..
`outs;
`int
`IDFIR *tx pulse (4),
`/* pointer to pulse shaping TX filter
`
`Strcts
`k/
`int
`numb taps;
`
`double
`
`tx avg;
`
`.
`
`.
`
`.
`
`Page 9 of 135
`
`

`

`double
`double
`
`11
`tx scale;
`max pow;
`
`5,381,449
`
`12
`
`int
`
`int
`
`slot len;
`k/
`FILE *slot def; /* slot definition file pointer
`k/
`slot symb(100);
`f
`k/
`
`/* slot length in sub-channel symbols
`
`/* slot symbol definition array
`
`amp pdf (600);
`double
`pdf Cnt;
`double
`int pdf index;
`
`/* number of samples simulated per sync
`
`/* number of phase steps for each
`
`t
`
`sk/
`
`long CInt;
`long sync length;
`pattern
`k/
`long steps;
`variable
`k/
`int
`s symb cnt; /* sync symbol counter
`double
`phase step; /* 2pi/steps
`x/
`double
`double
`double
`double
`double
`double
`COMPEX
`COMPLEX
`COMPLEX
`COMPLEX
`COMPLEX
`COMPLEX
`COMPLEX
`
`phill;
`phi2.
`thetal;
`theta2;
`s magi
`invns;
`exppl;
`expp2;
`expti;
`expt2;
`mc expt1;
`Inc expt2;
`s symb4;
`
`double
`
`best iO 0. 6;
`
`Page 10 of 135
`
`

`

`5,381,449
`
`14
`
`13
`
`numb pilot;
`int
`numb data;
`int
`numb dump;
`int
`numb duit di
`int
`slot Cnt;
`int
`double
`inv_np;
`
`sync (1001);
`COMPLEX
`kmf (100);
`FILTER
`int
`mf_len;
`COMPLEX
`mf out;
`double
`max (2);
`double
`buf 3;
`int
`pilot (100);
`int
`pil loci
`
`/k
`* general purpose variables and pointers
`k/
`-
`
`x /
`/* general purpose string buffer
`*/
`/k general purpose string buffer
`*/
`f* general purpose string buffer s'
`/* general purpose temporary variable
`
`char stri (60);
`char, str2 (60);
`chair str3 (60);
`double
`temp;
`k/
`temp2,
`double
`- temp3;
`double
`pi2;
`double
`pit.
`double
`long i, j, k, l, In, n :
`*/
`COMPLEX
`variable
`COMPLEX
`COMPLEX
`COMPLEX
`
`c temp;
`k/
`c templ;
`c temp2;
`c temp3;
`
`/* 2. O*pi
`
`:k/
`
`/* general purpose counters
`
`/* complex general purpose temporary
`
`Page 11 of 135
`
`

`

`5,381,449
`A * 1 + j 0 (complex one)
`
`16
`
`/* 0 + j 0 (complex zero)
`
`COMPLEX
`
`COMPLEX
`
`15
`cone;
`k/
`c zero;
`is/
`FILE *fr, k fr1, .k fr2, *fw, *fw1, *fw2;
`cone. real = 1.0;
`cone.imag = 0 ... O
`czero. real = 0.0;
`czero. imag = 0.0;
`pi2 = 8.0%atan (1.0);
`pi = 4.0 katan (1.0);
`
`insub = 4;
`
`fsymb = 4000.0;
`tsymb = 1.0/fsymb;
`ftx = 144. 0;
`tit.x = i. O/ (ftxiki 000.0);
`nizst = 36;
`
`fisc = ftx*OOO. 0/32. 0;
`temp = - (insub - 1) * (fsc/2.0);
`for ( i = 0; i < insub; i---- )
`
`wcent (i) = pi2*temp;
`tx ph st(i) = woent (il *ttx;
`
`temp += fisc;
`
`again22:
`printf("VnEnter the slot definition filename. Vin");
`scanif ("%s", str3) ;
`slot def = fopen (str3, "r");
`if ( slot def == NULL )
`
`printf("\n"ILE ACCESS ERROR, TRY AGAIN. \n");
`goto again22;
`
`Page 12 of 135
`
`

`

`17
`
`5,381,449
`
`18
`
`fscanf (slot def, " $d", & slot len);
`if ( slot len > 90 )
`
`printf("\nMAXIMUM SLOT LENGTH OF 90 SYMBOLS EXCEEDED, TRY
`AGAIN. /n");
`goto again22;
`
`A.
`
`numb pilot = 0;
`numb data = 0;
`numb dump = 0;
`numb dum d = 0;
`slot cnt = 0;
`i = 0;
`while ( fscanif (slot def, "d", & slot symbslot cnt)) = EOF )
`{
`
`w
`
`if ( slot symb(slot cnt) == 0 )
`
`numb pilotte;
`pilot (i)
`slot ent;
`
`i++;
`
`;
`
`:
`
`}
`else if (slot symbslot cnt P
`numb data++;
`else if ( slot symb slot cnt)
`{
`
`R R
`
`1. )
`
`2 )
`
`numb dum pht;
`pilot (i)
`slot cnt;
`i++;
`
`}
`else if ( slot symb slot cnt) == 3 )
`numb dum dth;
`slot cnt++;
`
`if ( (slot.cnt = slot len)
`( (numb pilottnumb data+numb dumph numb durn d) = slot len) )
`
`printf("\niNVALID SLOT DEFINITION FILE, TRY AGAIN./n");
`
`Page 13 of 135
`
`

`

`19
`goto 3 gain22;
`
`}
`follose (slot def);
`
`5,381,449
`
`2O
`
`for ( i = 0; j < i; j++ )
`printf ("WinPILOT NUMBER $2d AT SLOT SYMBOL NUMBER $2d. \n", jr
`pilot (j));
`
`printf("\nenter the slot symbol number of the pilot to
`minimize. Wn");
`scanif ("d", &pilloc);
`
`again2:
`printf("\nenter the name of the TX pulse shaping filter