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`ENSEMBLE MODEM STRUCTURE FOR
`IMPERFECT TRANSMISSION MEDIA
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`1.
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`BACKGROUND OF THE INVENTION
`Field of the Invention:
`The invention relates generally to the field
`of data communications and, more particularly, to a
`high speed modem.
`2. Description of the Prior Art:
`Recently, specially designed telephone lines.
`for the direct transmission of digital data have been
`introduced. However, the vast majority of telephone
`lines are designed to carry analog voice frequency (VF)
`signals. Modems are utilized to modulate VF carrier
`signals to encode digital information on the VF carrier
`signals and to demodulate the signals to decode the
`digital information carried by· the signal.
`Existing VF telephone lines have several
`limitations that degrade the performance of modems and
`limit the rate at which data can be transmitted below
`desired error rates. These limitations include the
`presence of frequency dependent noise on the VF tele(cid:173)
`phone lines, a frequency dependent phase delay induced
`by the VF telephone lines, and frequency dependent sig-
`nal loss.
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`Generally, the usable band of a VF telephone
`line is from slightly above zero to about four kHz.
`The power spectrum of the line noise is not uniformly
`distributed over frequency and is generally not deter-
`30 minative. Thus, there is no ~ priori method for deter(cid:173)
`mining the distribution of the noise spectrum over the
`usable bandwidth of the VF line.
`Additionally, a frequency-dependent propaga(cid:173)
`tion delay is induced by the VF telephone line. Thus,
`for a complex multi-frequency signal, a phase delay
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`between the various components of the signal will be
`induced by the VF telephone line. Again, this phase
`delay is not determinative and must be measured for an
`individual VF telephone line at the specific time that
`transmission takes place.
`Further, the signal loss over the VF
`telephone line varies with frequency. The equivalent
`noise is the noise spectrum component added to the
`signal loss component for each carrier frequency, where
`both components are measured in decibels (dB).
`Generally, prior art modems compensate for
`equivalent line noise and signal loss by gear-shifting·
`the data rate down to achieve a satisfactory error
`rate. For example, in U.S. patent 4,438,511, by Baran,
`a high speed modem designated SM9600 Super Modem
`In
`manufactured by Gandalf Data, Inc., is described.
`the presence of noise impairment, the SM9600 will 11gear
`shifttr or drop back its transmitted data rate to 4800
`bps or 2400 bps. The system described in the Baran
`patent transmits data over 64 orthogonally modulated
`carriers. The Baran system compensates for the frequency
`dependent nature of the noise on the VF line by termi(cid:173)
`nating transmission on carriers having the same frequency
`as the frequency of large noise components on the line.
`Thus, Baran gracefully degrades its throughput by ceas(cid:173)
`ing to transmit on carrier frequencies at the highest
`points of the VF line noise spectrum. The Baran system
`essentially makes a go/no go decision for each carrier
`signal, depending on the distribution of the VF line
`noise spectrum. This application reflects a continua(cid:173)
`tion of the effort initiated by Baran.
`Most prior art systems compensate for fre(cid:173)
`quency dependent phase delay induced by the VF line by
`an equalization system. The largest phase delay is
`induced in frequency components near the edges of the
`usable band. Accordingly, the frequency components
`near the center of the band are delayed to allow the
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`frequency components at the outside of the band to
`catch up. Equalization generally requires additional
`circuitry to accomplish the above-described delays.
`A further problem associated with two way
`transmission over the VF telephone line is that inter(cid:173)
`ference between the outgoing and incoming signals is
`possible. Generally, separation and isolation between
`the two signals is achieved in one of three ways:
`(a) Frequency multiplexing in which different
`frequencies are used for the different signals. This
`.method is common in modem-based telecommunication sys-
`terns.
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`(b) Time multiplexing, in which,different
`time segments are used for the different signals. This
`method is often used in half-duplex systems in which a
`transmitter relinquishes a charmel only after sending
`all the data it has. And,
`(c) Code multiplexing, in which the signals
`are sent using orthogonal codes.
`All of the above-described systems divide the
`space available according to constant proportions fixed
`during the initial system design. These constant
`proportions, however, may not be suitable to actual
`traffic load problem presented to each modem. For
`example, a clerk at a PC ~ork station cormected to a
`remote host computer may type ten or twenty characters
`and receive a full screen in return.
`In this case,
`constant proportions allocating the channel equally
`between the send and receive modems would greatly
`overallocate the channel to the PC work station clerk.
`Accordingly, a modem that allocates channel capacity
`according to the needs of the actual traffic load
`situation would greatly increase the efficient
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`SUMMARY OF TEE INVENTION
`The present invention is a high-speed modem
`for use with dial-up VF telephone lines. The modem
`5 utilizes a multicarrier modulation scheme and variably
`allocates data and power to the various carriers to
`maximize the overall data transmission rate. The
`allocation of power among the carriers is subject to
`the constraint that the total power allocated must not
`exceed a specified limit.
`In a pref erred embodiment, the modem further
`includes a variable allocation system for sharing con(cid:173)
`trol of a communication link between two modems (A and(cid:173)
`B) according to actual user requirements.
`Another aspect of the invention is a system
`for compensating for frequency dependent phase delay
`and preventing intersymbol interference that does not
`require an equalization network.
`According to one aspect of the invention,
`quadrature amplitude modulation (QAM) is utilized to
`encode data elements of varying complexity on each
`carrier. The equivalent noise component at each
`carrier frequency is measured over a communication link
`between two modems (A and B).
`As is known in the art, if the bit error rate
`(BER) is to be maintained below a specified level, then
`the power required to transmit a data element of a
`given complexity on a given carrier frequency must be
`increased if the equivalent noise component at that
`frequency increases. Equivalently, to increase data
`complexity, the signal to noise ratio, S/N, must be
`increased.
`In one embodiment of the present invention,
`data and power are allocated to maximize the overall
`data rate within external BER and total available power
`constraints. The power allocation system computes the
`marginal required power to increase the symbol rate on
`each carrier from n to n + 1 information units. The
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`system then allocates information units to the carrier
`that requires the least additional power to increase
`its symbol rate by one information unit. Because the
`5 marginal powers are dependent on the values of the
`equivalent noise spectrum of the particular established
`transmission link, the allocation of power and data is
`specifically tailored to compensate for noise over this
`particular link.
`According to another aspect of the invention,
`a first section of the symbol on each carrier is
`retransmitted to form a guard-time waveform of duration
`TE + TPH where TE is the duration of the symbol and TP~
`is the duration of the first section. The, magnitude of
`TPH is greater than or equal to the maximum estimated
`phase delay for any frequency component of the
`waveform. For example, if the symbol is represented by
`the time series, x 0 ••. xn-l' transmitted in time TE;
`then the guardtime waveform. is represented by the time
`xn-l' x 0 ••• xm-l' transmitted in time
`series, x 0
`TE + TPH" The ratio that m bears to n is equal to the
`ratio that TPH bears to TE.
`At the receiving modem, the.time of arrival,
`T0 , of the first frequency component of the guard-time
`25 waveform is determined. A sampling period, of dura(cid:173)
`tion TE' is initiated a time T0 + TPH"
`Accordingly, the entire symbol on each carrier
`frequency is sampled and intersymbol interference is
`eliminated.
`According to a still further aspect of the
`invention, allocation of control to the transmission
`link between modems A and B is accomplished by setting
`limits to the number of packets that each modem may
`transmit during one transmission cycle. A packet of
`information comprises the data encoded on the ensemble
`of carriers comprising one waveform. Each modem is also
`constrained to transmit a minimum number of packets to
`maintain the communication link between the modems.
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`Thus, even if one modem has no data to transmit, the
`minimum packets maintain timing and other parameters
`are transmitted. On the other hand, if the volume of
`data for a modem is large, it is constrained to transmit
`only the maximum limited ~umber of packets, N, before
`relinquishing control to the other modem.
`In practice, if modem A has a small volume of
`data and modem B has a large volume of data, modem B
`10 will have control of the transmission link most of the
`time.
`If control is first allocated to modem A it will
`only transmit the minimal number, I, of packets. Thus
`A has control for only a short time. Control is then
`allocated to B which transmits N packets, where N may
`be very large. Control is again allocated to modem A
`which transmits I packets before returning control to
`B.
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`Thus, allocation of control is proportional
`to the ratio of I to N.
`If the transmission of the
`volume of data on modem A requires L packets, where L
`is between I and N, then the allocation is proportional
`to the ratio of L to N. Accordingly, allocation of the
`transmission link varies according to the actual needs
`of the user.
`Additionally, the maximum number of packets,
`N, need not be the same for each modem, but may be
`varied to accommodate known disproportions in the data
`to be transmitted by A and B modems.
`According to another aspect of the invention,
`signal loss and frequency offset are measured prior to
`data determination. A tracking system determines
`variations from the measured values and compensates for
`these deviations.
`According to a further aspect of the inven-
`tion, a ~ystem for determining a precise value of T0
`is included. This system utilizes two timing signals,
`at f 1 and f 2 , incorporated in a waveform transmitted
`from modem A at time TA. The relative phase difference
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`between the first and second timing signals at time TA
`is zero.
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`The waveform is received at modem B and a
`rough estimate, TEST' of the time of reception is
`obtained by detecting energy at f 1 • The relative phase
`difference between the timing signals at time TEST is
`utilized to obtain a precise timing reference, T0 .
`
`BRIEF DESCRIPTION OF THE DRAWINGS
`Fig. 1 is a graph of the ensemble of carrier
`frequencies utilized in the present invention.
`Fig. 2 is a graph of the constellation illus(cid:173)
`trating the QAM of each carrier.
`Fig. 3 is a block diagram of an embodiment of
`the invention.
`Fig. 4 is a flow chart illustrating the syn(cid:173)
`chronization process of the present invention.
`Fig. 5 is a series of graphs depicting the
`constellations for 0, 2, 4, 5, 6 bit data elements and
`exemplary signal to noise ratios and power levels for
`each constellation.
`Fig. 6 is a graph illustrating the waterfill(cid:173)
`ing algorithm.
`Fig. 7 is a histogram illustrating the appli-
`cation of the waterfilling algorithm utilized in the
`present invention.
`Fig. 8 is a graph depicting the effects of
`phase dependent frequency delay on frequency components
`in the ensemble.
`Fig. 9 is a graph depicting the wave forms
`utilized in the present invention_to prevent inte~­
`symbol interference.
`Fig. 10 is a graph depicting the method of
`receiving the transmitted ensemble.
`Fig. 11 is a schematic diagram depicting the
`modulation template.
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`Fig. 12 is a schematic diagram depicting the
`quadrants of one square in the modulation template.
`Fig. 13 is a schematic diagram of a hardware
`embodiment .of the present invention.
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`DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
`The present invention is a modem that
`adaptively allocates power between various carrier
`frequencies in a frequency ensemble to compensate for
`frequency dependent line noise, eliminates the need for
`equalization circuitry to compensate for a frequency
`dependent phase delay, and provides a duplex mechanism
`that accounts for varying channel load conditions to
`allocate the channel between the send and receive
`15 modems. Additional features of the invention are de(cid:173)
`scribed below.
`A brief description of the frequency ensemble
`and modulation scheme utilized in the present invention
`is first presented with respect to Figs. l and 2 to
`facilitate the understanding of the invention. A
`specific embodiment of the invention is then described
`with reference to Fig. 3. Finally, the operation of
`various features of the invention are described with
`reference to Figs. 4 through 13.
`Modulation and Ertsemble Configuration
`Referring now to Fig. 1, a diagrammatic
`representation is shown of the transmit enselnble 10 of -
`the present invention. The ensemble includes 512 car(cid:173)
`rier frequencies 12 equally spaced across the available
`4 kHz VF band. The present invention utilizes
`quadrature amplitude modulation (QAM) wherein phase
`independent sine and cosine signals at each carrier
`frequency are transmitted. The digital information
`transmitted at a given carrier frequency is encoded by
`amplitude modulating the independent sine and cosine
`signals at that frequency.
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`The QAM system transmits data at an overall
`bit rate, Ra· However, the transmission rate on each
`carrier, denoted the symbol or baud rate, Rs, is only a
`fraction of RB. For example, if data were allocated
`equally between two carriers then Rs = R8/2.
`In the preferred embodiment O, 2, 4, 5 or 6
`bit data elements are encoded on each carrier and the
`modulation of each carrier is changed every 136 msec.
`10 A theoretical maximum, Rs' assuming a 6 bit Rs for each
`carrier, of 22,580 bit/sec (bps) results. A typical
`relizable Rs, assuming 4 bit R8 over 75% of the
`carriers, is equal to about 11,300 bps. This extremely
`high Rs is achieved with a bit error rate ?f less than
`1 error/100,000 bits transmitted.
`In Fig. 1, a plurality of vertical lines 14
`separates each ensemble into time increments known
`hereafter as "epochs." The epoch is of duration TE
`where the magnitude of TE is determined as set forth
`below.
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`The QAM system for encoding digital data onto
`the various carrier frequencies will now be described
`with reference to Fig. 2.
`In Fig. 2 a four bit 11con(cid:173)
`stellation11 20 for the nth carrier is depicted. A four
`25 bit number may assume sixteen discrete values. Each
`point in the constellatiort represents a vector {xn,yn)
`with xn being the amplitude of the sine signal and Yn
`being the amplitude of the cosine signal in-the above(cid:173)
`described QAM system. The subscript n indicates the
`carrier being modulated. Accordingly, the four bit
`constellation requires four discrete Yn and four dis(cid:173)
`crete xn values. As described more fully below,
`increased power is required to increase the number of
`bits transmitted at a given carrier frequency due to
`the equivalent noise component at that frequency. The
`receive modem, in the case of fotir bit transmission,
`must be able to discriminate between four possible
`values of the xn and Yn amplitude coefficients. This
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`ability to discriminate is dependent on the signal to
`noise ratio for a given carrier frequency.
`In a preferred embodiment, packet technology
`is utilized to reduce the error rate. A packet includes
`the modulated epoch of carriers and error detection data.
`Each packet in error is retransmitted until correct.
`Alternatively, in systems where retransmission of data
`is undesirable, epochs with forward error -correcting
`codes may be utilized.
`Block Diagram
`Fig. 3 is a block diagram of an embodiment of
`the present invention. The description that follows is
`of an originate modem 26 coupled to an originate end of
`a communication link formed over a public switched
`telephone line. It is understood that a communication
`system also includes an answer modem coupled to the
`answer end of the communication link.
`In the following
`discussion, parts in the answer modem corresponding to
`identical or similar parts in the originate modem will
`be designated by the reference number of the originate
`modem primed.
`Referring now to Fig. 3, an incoming data
`stream is received by a send system 28 of the modem 26
`at data input 30. The data is stored as a sequence of
`data bits in a buffer memory 32. The output of buffer
`memory 32 is coupled to the input of a modulation
`parameter generator 34. The output of the modulation -
`parameter generator 34 is coupled to a vector table
`30 buffer memory 36 with the vector table buffer memory 36
`also coupled to the input of a modulator 40. The out(cid:173)
`put of the modulator 40 is coupled to a time sequence
`buffer 42 with the time sequence buffer 42 also coupled
`to the input of a digital-to-analog converter 43 in-
`eluded in an analog I/O interface 44. The interface
`44 couples the output of the modem to the public
`switched telephone lines 48.
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`A receive system 50 includes an analog-to(cid:173)
`digital converter {ADC) 52 coupled to the public switched
`telephone line 48 and included in the interface 44. The
`output from the ADC 52 is coupled to a receive time
`series buffer 54 which is also coupled to the input of
`a demodulator 56. The output of the demodulator 56 is
`coupled to a receive vector table buffer 58 which is
`also coupled to the input of a digital data generator
`60. The digital data generator 60 has an output coupled
`to a receive data bit buffer 62 which is also coupled to
`an output terminal 64.
`A control and scheduling unit 66 is coupled
`with the modulation parameter generator 34,, the vector
`table buffer 36, the demodulator 56, and the receive
`vector table buffer 58.
`An overview of the functioning of the embodi(cid:173)
`ment d~picted in Fig. 3 will now be presented. Prior
`to the transmission of data, the originate modem 26, in
`cooperation with the answer modem 26 1 , measures the equi(cid:173)
`valent noise level at each carrier frequency, determines
`the number of bits per epoch to be transmitted on each
`carrier frequency, and allocates power to each carrier
`frequency as described more fully below.
`The incoming data is received at input port
`30 and formatted into a bit sequence stored in the
`input buffer 32.
`The modulator 34 encodes a given nUmber of
`bits into an (xn,yn} vector for each carrier frequency
`30 utilizing the QAM system described above. For example,
`if it were determined that four bits were to be trans(cid:173)
`mitted at frequency fn then four bits from the bit
`stream would be converted to one of the sixteen points
`in the four bit constellation of Fig. 2. Each of these
`constellation points corresponds to one of sixteen pos(cid:173)
`sible combinations of four bits. The amplitudes of the
`sine and cosine signals for frequency n then corresponds
`to the point in the constellation encoding the four bits
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`of the bit sequence. The (xn,yn) vectors are then
`stored in the vector buffer table 36. The modulator
`receives the table of (xn,yn) vectors for the carriers
`in the ensemble and generates a digitally encoded time
`series representing a wave form comprising the ensemble
`of QAM carrier frequencies.
`In a pref erred embodiment the modulator 40
`includes a fast Fourier transform (FFT) and performs an
`inverse FFT operation utilizing the (x,y) vectors as
`the FFT coefficients. The vector table includes 1,024
`independent points representing the 1,024 FFT points of
`the 512 frequency constellation. The inverse FFT
`operation generates 1,024 points in a time series
`representing the QAM ensemble. The 1,024 elements of
`this digitally encoded time series are stored in the
`digital time series buffer 42. The digital time
`sequence is converted to an analog wave form by the
`analog to digital converter 43 and the interface 46
`conditions the signal for transmission over the public
`switched telephone lines 48.
`Turning now to the receive system 501 the
`received analog waveform from the public switched tele(cid:173)
`phone lines 48 is conditioned by the interface 46 and
`directed to the analog to digital converter 52. The
`analog to digital converter 52 converts the analog
`waveform to a digital 1,024 entry time series table
`which is stored in the receive time series buffer 54. -
`The demodulator 56 converts the 1,024 entry time series
`table into a 512 entry (xn,Yn) vect~r table stored in
`the receive vector table buffer 58. This conversion is
`accomplished by performing an FFT on the time series.
`Note that information regarding the number of bits
`encoded onto each frequency carrier has been previously
`stored in the demodulator and digital data generator 60
`so that the (x,y) table stored in the receive vector
`table buffer 58 maybe transformed to an output data
`bit sequence by the digital data generator 60. For
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`example, if the (xn,yn) vector represents a four bit
`sequence then this vector would be converted to a four
`bit sequence and stored in the receive data bit buffer
`62 by the digital data generator 60. The receive data
`bit sequence is then directed to the output 64 as an out(cid:173)
`put data stream.
`A full description of the FFT techniques uti(cid:173)
`lized is described in a book by Rabiner et al., entitled
`10 Theory and Applications of Digital Signal Processing,
`Prentice-Hall, Inc., N.J., 1975. However, the FFT modu(cid:173)
`lation technique described above is not an integral part
`of the present invention. Alternatively, modulation -
`could be accomplished by direct multiplica~ion of the
`carrier tones as described in the above-referenced Baran
`patent, which is hereby incorporated by reference, at
`col. 10, lines 13-70, and col. 11, lines 1-30. Addition(cid:173)
`ally, the demodulation system described in Baran at col.
`12, lines 35-70, col. 13, lines 1-70, and col. 14, lines
`1-13 could be substituted.
`The control and scheduling unit 66 maintains
`overall supervision of the sequence of operations and
`controls input and output functions.
`Determination of Equivalent Noise
`As described above, the information content
`of the data element encoded on each frequency carrier
`and the power allocated to that frequency carrier
`depends on the magnitude of the channel noise component
`at that carrier frequency. The equivalent transmitted
`noise component at frequency fn' N(fn), is the measured
`(received) noise power at frequency fn multiplied by
`the measured signal loss at frequency fn. The equiva(cid:173)
`lent noise varies from line to line and also varies on
`a given line at different times. Accordingly, in the
`35 present system, N(f) is measured immediately prior to
`data transmission.
`The steps of a synchronization technique
`utilized in the present system to measure N(f) and
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`establish a transmission link between answer and ori(cid:173)
`ginate modems 26 and 26' are illustrated in Fig. 4.
`Referring now to Fig. 4, in step 1 the originate modem
`dials the number of the answer modem and the answer
`modem goes off hook.
`In step 2 the answer modem trans(cid:173)
`mits an epoch of two frequencies at the following power
`levels:
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`(a) 1437.5 Hz. at -3 dBR; and
`(b) 1687.5 Hz at -3 dBR.
`The power is measured relative to a reference, R, where,
`in a preferred embodiment, OdBR = -9dBm, m being a milli(cid:173)
`volt. These tones are used to determine timing and fre(cid:173)
`quency offset as detailed subsequently.
`The answer modem then transmits an answer comb
`containing all 512 frequencies at -27dBR. The originate
`modem receives the answer comb and performs an FFT on the
`comb. Since ~he power levels of the 512 frequencies were
`set at specified values, the control and scheduling unit
`66 answer modem 26 compares the (xn,yn) values for each
`frequency of the received code and compares those values
`to a table of (xn,yn) values representing the power lev(cid:173)
`els of the transmitted answer code. This comparison
`yields the signal loss at each frequency due to the
`transmission over the VF telephone lines.
`During step 3 both the originate and answer
`modems 26 and 26' accumulate noise data present on the
`line in the absence of any transmission by either
`modem. Both modems then perform an FFT on the accumu-
`lated noise signals to determine the measured
`(received) noise spectrum component values at each
`carrier frequency. Several epoch~ of noise may be aver(cid:173)
`aged to refine the measurement.
`In step 4 the originate modem transmits an
`epoch of two frequencies followed by an originate comb
`of 512 frequencies with the same power levels described
`above for step 2. The answer modem receives the epoch
`and the originate comb and calculates the timing, fre-
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`quency off set and signal loss values at each carrier
`frequency as described above for the originate modem in
`step 2. At this point the originate modem 26 has accum-
`5 ulated noise and signal loss data for transmission in
`the answer originate direction while the answer modem
`has accumulated the same data relating to transmission
`in the originate answer direction. Each modem requires
`data relating to transmission loss and receive noise in
`both the originate-answer and answer-originate direc(cid:173)
`tions. Therefore, this data is exchanged between the
`two modems according to the remaining steps of the syn(cid:173)
`chronization process.
`In step 5 the originate modem generates and
`transmits a first phase encoded signal indicating which
`carrier frequencies will support two bit transmission
`at standard power levels in the answer-originate direc(cid:173)
`tion. Each component that will support two bits in the
`answer-originate direction at a standard power level is
`generated as a -28 dBR signal with 180° relative phase.
`Each component that will not support two bit transmis(cid:173)
`sion in the answer-originate direction at the standard
`power level is coded as a -28 dBR,0° relative phase
`signal. The answer modem receives this signal and
`determines which frequency carriers will support two
`bit transmission in the answer-originate direction.
`In step 6 the answer modem generates and
`transmits a second phase encoded signal indicating
`which carrier frequencies will support two bit trans-
`30 mission in both the originate-answer and answer-origi(cid:173)
`nate directions. The generation of this signal is
`possible because the answer modem has accumulated noise
`and signal loss data in the originate-answer direction
`and has received the same data for the answer-originate
`direction in the signal generated by the originate
`modem in step 5.
`In the signal generated by the origi(cid:173)
`nate modem, each frequency component that will support
`two bits in both directions is coded with 180° relative
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`phase and all other components are coded with 0° rela(cid:173)
`tive phase.
`A transmission link now exists between the
`two modems.
`In general, 300 to 400 frequency compo(cid:173)
`nents will support two bit transmission at a standard
`power level, thereby establishing about a 600 bit/epoch
`rate between the two modems.
`In step 7 the originate
`modem sends data on the number of bits (0 to 15} and
`the power levels (O to 63dB) that can be supported on
`each frequency in the answer-originate direction in
`ensemble packets formed over this existing data link.
`Accordingly, both the originate and answer modem now
`have the data relating to transmission in the answer-
`15 originate direction. The steps for calculating the
`number of bits and power levels that can be supported
`on each frequency component will be described below.
`In step 8 the answer modem sends data on the
`number of bits and power levels that can be supported
`on each frequency in the originate-answer direction
`utilizing the existing data link. Thus, both modems
`are apprised of the number of bits and power levels to
`be supported on each frequency component in both the
`answer-originate and originate-answer directions.
`The above description of the determination of
`the equivalent noise level _component at each carrier(cid:173)
`frequency sets forth the required steps in a given
`sequence. However, the sequence of steps is-not criti(cid:173)
`cal and many of the steps may be done simultaneously or
`in different order, for example, the performance of the
`FFT on the originate code and the accumulation of noise
`!A- precise timing
`data may be done simultaneously.
`reference is also calculated during the synchronization
`process. The calculation of this timing reference will
`be described more fully below after the description of
`the method for calculating the number of bits and power
`levels allocated to each frequency component.
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`It is a common VF telephone line impairment
`that a frequency offset, of up to 7 Hz, exists between
`transmitted and received signals. This offset must be
`corrected for the FFT to function reliably.
`In a
`preferred embodiment, this correction is achieved by
`performing a single sideband modulation of the quadra(cid:173)
`ture tones at the offset frequency by the true and Hil(cid:173)
`bert images of received signal. Synchronization and
`tracking algorithms generate estimates of the frequency
`offset necessary.
`Power and Code Complexity Allocation
`The information encoded on each carrier fre-
`quency signal is decoded at the receiver CQannel by the
`demodulator 56. Channel noise distorts the transmitted
`signal and degrades the accuracy of the demodulation
`process. The transmission of a data element having a
`specified complexity, e.g., B0 bits at a specified fre(cid:173)
`quency, f 0 , over a VF telephone line characterized by
`an equivalent noise level component, N0 , will now be
`analyzed. Generally, external system requirements
`determine a maximum bit error rate (BER) that can be
`tolerated. For the transmission of b 0 bits at noise
`level N0 and frequency f 0 , the signal to noise ratio
`25 must exceed Eb/No where Eb is the signal power per bit
`to maintain the BER below~a given BER, (BER) 0 .
`Fig. 5 depicts the QAM constellations for
`signals of various complexities B. An exemplary signal
`to noise ratio, Eb/No, for each constellation and the
`power required to transmit the number of bits in the
`constellation without exceeding (BER) 0 is depicted
`alongside each constellation graph.
`A modem operates under the constraint that
`the total available power placed on the public switched
`telephone lines may not exceed a value, P0 , set by the
`telephone companies and government agencies. Thus,
`signal power may not be increased indefinitely to
`com