Multi-Channel Multiplex Data Transmission System

The present invention relates to an improved data transmission system, and in particular, relates to a digital type multi-channel modulation and/or demodulation system which transmits digital data through a band-limited analog type transmission line.

A multi-channel orthogonal VSB (Vestigial SideBand) transmission system has been known as one of the data transmission systems using a band-limited analog type line. The prior modulation and/or demodulation system for the above orthogonal VSB system comprises a plurality of the transmission filters for each channel in a modulator and a correlation detector in a demodulator, and is disclosed in R. W. Chang;

"Synthesis of Band-Limited Orthogonal Signals for Multi-channel Data Transmission," B.S.T.J., 45, 10, p. 1775 (Dec. 1966). The present applicant has already filed some patent applications which improve Chang's device.

In the prior system proposed by Chang, a data transmission system with a theoretical transmission speed could be realized without suffering from a inter-symbol interference and/or a inter-channel interference, if an ideal line equalization and a modem were obtained. However, said theoretical speed could not be practically obtained due to some interferences by the various error factors.

It is an object, therefore, of the present invention to overcome the disadvantages and limitations of a prior data transmission system by providing a new and improved data transmission system.

According to the present invention, the sum and the difference signals of a pair of data channels are applied to a pair of roll-off filters, respectively. The outputs of said roll-off filters are modulated by a pair of carrier signals which have the phase difference (.pi./2) to each other. The modulated signals are added to each other in an adder and a single output signal is provided from the output of said adder. Said output signal and another output signal relating to another pair of data channels, and some pilot signals are applied to an adder, the output of which is transmitted to a receiving station in the form of a multichannel multiplex data signal. At the receiving station, the received signal is demodulated with the inverse process of the above modulation steps and the demodulated data signals are applied to an automatic equalizer. The present invention described above provides high speed data transmission through a narrow-band-line which has only almost the Nyquist band width.

The foregoing and other objects, features, and attendant advantages of the invention will be appreciated as the same become better understood by means of the following description and accompanying drawings wherein:

FIG. 1 shows a frequency spectrum of a data signal according to the present invention;

FIG. 2 is a brief block-diagram of the present data transmission system;

FIG. 3 is a block-diagram of the modulator according to the present invention;

FIG. 4 is a frequency spectrum of a transmitted signal;

FIG. 5 is a characteristics curve of a roll-off filter;

FIG. 6 is a block-diagram of a demodulator according to the present invention;

FIG. 7 is a phase error detector utilized with the demodulator of FIG. 6;

FIG. 8 is a sampling circuit utilized with the demodulator of FIG. 6;

FIG. 9 is a clock pulse generator utilized with the sampling circuit of FIG. 8;

FIG. 10 is a block-diagram of the automatic equalizer according to the present invention;

FIG. 11 is a block-diagram of a transversal filter (TFS) in the automatic filter of FIG. 10;

FIG. 12 is a block-diagram of the other automatic equalizer;

FIG. 13 is a block-diagram of the phase error detector (PED) in the automatic equalizer of FIG. 12;

FIG. 14 is a block-diagram of the timing error detector (TED) in the automatic equalizer of FIG. 12;

FIG. 15 is a block-diagram of the other timing error detector utilized at the end channels in the automatic equalizer of FIG. 12.

The embodiments of a four channel data transmission system will be explained hereinafter, however, the invention is not of course limited to a four channel system and any number channel system is possible with the invention.

A well-known theory teaches us that the band width required for transmitting a pulse train of a repetition period T is (1/2T) and said band width is called a Nyquist band. However, in a transmission system having the band width of exactly (1/2T), the demodulation of a signal is very difficult since only a small deviation of a sampling pulse results in a large error due to a narrow eye pattern. Therefore, in an actual system, a VSB (Vestigial Side-Band) system is utilized. However, a VSB system requires a wider band width than a Nyquist band (1/2T). In order to solve that problem, the present invention overlaps the roll-off portions in each VSB channel with each other, as shown in FIG. 1. In FIG. 1, it should be appreciated that the roll-off portion (a) of the channel 1 overlaps with the roll-off portion (b) of the channel 2.

According to the frequency allocation of FIG. 1, the entire band-width required for the transmission of four channels is almost equal to 2/T(=[1/2T].times.4), which is the Nyquist band-width of four channels.

FIG. 2 shows a brief block-diagram of a data transmission system according to the present invention. In FIG. 2, the modulator (MOD) receives the signals from channels 1, 2, 3 and 4, and modulates them. The modulated signal having the frequency spectrum of FIG. 1 is transmitted to the demodulator (DEM) at a receiving side through a line (LINE). The demodulator (DEM) demodulates the signal and provides the original four channel signals, which appear at the output terminals of each channel through an equalizer (EQU). Each of the members MOD, DEM, and EQU in FIG. 2 will be explained in detail hereinafter.

FIG. 3 shows an embodiment of modulator according to the present invention, in which 1.sub.1, . . . , 1.sub.4 are input terminals of channels 1, . . . , 4; 2.sub.1 and 2.sub.3 are adders; 2.sub.2 and 2.sub.4 are substracting units (to be referred to as "subtracters", hereinafter); 3.sub.1 and 3.sub.3 are roll-off filters with a transfer function R.sub.c (f) to be explained later; 3.sub.2 and 3.sub.4 are roll-off filters with a transfer function R.sub.s (f) to be explained later; 4.sub.1, . . . , 4.sub.4 are multipliers; 5.sub.1, 5.sub.2, and 6 are adders; 7 is an output terminal; 8.sub.1 and 8.sub.2 are 90.degree.-phase shifters; 9.sub.1 and 9.sub.2 are variable phase shifters; 10 is a clock frequency generator; 11 is a frequency doubler; 12 is a factor 4 frequency devider; 13 is a factor 11 frequency multiplier; 14 is a local oscillator; and 15.sub.1, . . . , 15.sub.4 are frequency converters. In the modulator, the input signals for each channel are applied to the input terminals 1.sub.1, . . . , 1.sub.4 in the form of multi-amplitude PAM signals, and the adders 2.sub.1, 2.sub.3 and subtracters 2.sub.2 and 2.sub.4 produce sums and differences of the input signals of a pair of the channel 1 and the channel 2 and another pair of the channel 3 and the channel 4. The output signals from the adders and the subtracters are shaped by the roll-off filters 3.sub.1, . . . , 3.sub.4, and act to amplitude-modulate carrier waves C.sub.1 and C.sub.2 by the multipliers 4.sub.1, . . . , 4.sub.4, which carrier waves are output signals from the frequency converters 15.sub.1 and 15.sub.2. The adders 5.sub.1, 5.sub.2, and 6 add the thus modulated signals and pilot signals f.sub.1 and f.sub.2 which are output signals from the frequency converters 15.sub.3 and 15.sub.4, so as to deliver the added signal to the output terminal 7. The clock frequency generator 10 generates a sinusoidal wave whose frequency is identical with the repetition frequency f.sub.c of the input signal of each channel. The frequency doubler 11 generates a sinusoidal wave with its double frequency 2f.sub.c, and the factor 4 frequency divider 12 generates a sinusoidal wave with its quarter frequency (1/4)f.sub.c, and the factor 11 frequency multiplier 13 generates a sinusoidal wave with its elevenquarters frequency (11/4)f.sub.c. The frequency converters 15.sub.1, . . . , 15.sub.4 mix the signals generated by the aforesaid generators 10, 11, 12, and 13 with a sinusoidal wave with a frequency f.sub.L generated by the local oscillator 14, so as to produce sinusoidal waves C.sub.1, C.sub.2, f.sub.1, and f.sub.2 whose frequencies are the sums or differences of the aforesaid frequencies. FIG. 4 illustrates the relations among the frequencies of the aforesaid sinusoidal waves and the spectra of the signals (shown in solid lines) at the output terminals 7, wherein f.sub.1 and f.sub.2 are pilot signals, C.sub.1 and C.sub.2 are carrier waves (suppressed), f.sub.L is the local oscillator signal (suppressed, and CH.sub.1, . . . , CH.sub.4 are spectra of transmitting signals of the channels 1, . . . , 4.

The transfer functions R.sub.c (f) and R.sub.s (f) of the roll-off filters 3.sub.1, . . . , 3.sub.4 of FIG. 3 are band-restricted to band widths of .vertline.f.vertline.<(3/4)f.sub.c, and the amplitude characteristics of both of the transfer functions have a 50% roll-off characteristic A(f) satisfying the Nyquist criterion, and the phase characteristics of the transfer function R.sub.c (f) is .theta..sub.c (f), except for a certain delay, and the phase characteristics of the transfer function R.sub.s (f) is -.theta..sub.c (f), except for a certain delay. Here, .theta..sub.c (f) is a function which has a constant value of .pi./4 in the band of .vertline.f-f.sub.c /2.vertline.<f.sub.c /4, and arbitrary values at other frequencies. FIG. 5 illustrates an example of the amplitude characteristic A(f) of the transfer function R.sub.c (f) and the phase characteristic .theta..sub.c (f) of the transfer function R.sub.c (f), except for the certain delay. The variable phase shifters 9.sub.1 and 9.sub.2 give certain phase delays to the carrier waves C.sub.1 and C.sub.2 for compensating for the certain delays of the roll-off filters 3.sub.1 and 3.sub.2 and the like, so as to ensure the orthogonality relation between the channel 2 and the channel 3 having different carrier waves.

It is noted here that the roll-off filters 3.sub.1 and 3.sub.2 and the like can have an arbitrary roll-off factor of not greater than 50%, and the band width in which the phase characteristics .theta..sub.c (f) is constant at .pi./4 can be .vertline.f-f.sub.c /2.vertline.<b.f.sub.c /2, where b is a roll-off factor having a value of 0<b.ltoreq.0.5.

FIG. 6 shows an embodiment of a demodulator to be used in the present invention, in which 21 is an input terminal; 22.sub.1, . . . , 22.sub.4 and 30.sub.1, 30.sub.2 are multipliers; 23.sub.1, 23.sub.3 and 23.sub.2, 23.sub.4 are roll-off filters whose characteristics are the same as those of the roll-off filters 3.sub.2, 3.sub.4 and 3.sub.1, 3.sub.3 of FIG. 3, respectively; 24.sub.1 and 24.sub.3 are substracters; 24.sub.2 and 24.sub.4 are adders; 25.sub.1, . . . , 25.sub.4 are output terminals of the channels 2, . . . , 4, respectively; 26.sub.1 and 26.sub.2 are 90.degree.-phase shifters; 27.sub.1 and 27.sub.2 are variable phase shifters which vary phase delays in proportion to carrier wave phase control signals applied to their control terminals 28.sub.1 and 28.sub.2, respectively; 29.sub.1, 29.sub.2, 29.sub.3, and 29.sub.4 are narrow-band-pass filters whose central frequencies are f.sub.2, f.sub.1, f.sub.2 -f.sub.1, and f.sub.L, respectively; 31 is a factor 5 frequency divider; 32 is a factor 2 frequency divider; 33 and 34 are frequency doublers; 35 is a clock signal output terminal; and 36.sub.1 and 36.sub.2 are frequency converters. In the demodulator, the pilot signals f.sub.2 and f.sub.1 are extracted from the received signals by the narror-band-pass filters 29.sub.1 and 29.sub.2, respectively, at the input terminal 21 and a sinusoidal wave with the differential frequency of the pilot signals, i.e., f.sub.2 -f.sub.1 =(5/2)f.sub.c is produced by passing the pilot signals through a frequency converter consisting of the multiplier 30.sub.1 and the narrow-band-pass filter 29.sub.3, and the output from the frequency converter is passed through the factor 5 frequency divider 31 for producing a sinusoidal wave with a frequency of f.sub.c /2. Then, the factor 2 frequency divider 32 generates a sinusoidal wave of frequency f.sub.c /4 from the wave at the output of the factor 5 frequency divider 31, and the multiplier 30.sub.2 mixes the wave from the divider 32 with the pilot signal f.sub.1, so as to reproduce the local oscillator signal f.sub.L by passing the signal from the multiplier 30.sub.2 through the narrow-band-pass filter 29.sub.4. On the other hand, the f.sub.c /2 signal is applied to the frequency doubler 33 for regenerating the clock signal f.sub.c, which clock signal is delivered to the clock signal output terminal 35 and directly to the frequency converter 36.sub.1 for generating the carrier wave C.sub.1 with a frequency equivalent to the sum (or difference) with the local oscillator signal f.sub.L and also to the other frequency converter 36.sub.2 through the frequency doubler 34 for generating the other carrier wave C.sub.2. The thus reproduced carrier waves C.sub.1 and C.sub.2 are used for demodulating the PAM signals of each channel which are orthogonal-VSB modulated. At first, the phase of the carrier wave C.sub.1 is delayed by a suitable amount by the variable phase shifter 27.sub.1, and the output from the phase shifter 27.sub.1 is directly applied to the multiplier 22.sub.2 and also to the other multiplier 22.sub.1 through the phase shifter 26.sub.1 delaying the phase by 90.degree.. The outputs from the multipliers 22.sub.1 and 22.sub.2 are applied to the roll-off filters 23.sub.1 and 23.sub.2, respectively, so as to demodulate those signals which are modulated by the inphase component and quadrature component of the carrier wave C.sub.1 in the modulator of FIG. 3, and the subtractor 24.sub.1 and the adder 24.sub.2 produce the difference and the sum of the outputs from the roll-off filters 23.sub.1 and 23.sub.2 for delivering the output signals of the channels 1 and 2 at the output terminals 25.sub.1 and 25.sub.2. Similarly, the output signals of the channels 3 and 4 are obtained at the output terminals 25.sub.3 and 25.sub.4 , by using the carrier wave C.sub.2.

With the aforesaid modulation and demodulation, it is possible to perform data transmission which is free from the interference between signals of individual channels (to be referred to as "inter-symbol interference", hereinafter) and free from the interference between channels (to be referred to as "inter-channel interference", hereinafter), as will be described hereinafter. If it is assumed that the transmission line is ideally equalized in the bands for passing the signal spectra of FIG. 4, the impulse response of the channel 1 path from the modulator input terminal 1.sub.1 to the demodulator output terminal 25.sub.1 is given by

here, r.sub.c (t) and r.sub.s (t) are inverse Fourier transforms of the transfer functions R.sub.c (f) and R.sub.s (f), f.sub.cl is the frequency of the carrier wave C.sub.1, .phi..sub.t and .phi..sub.r are phase angles of the carrier waves in modulation and demodulation, and represents convolution operation.

Upon Fourier transformation of the both sides of the equation (1) while considering the conditions of the roll-off filter band restrictions, the transfer function of the channel 1 is given by

If the transfer functions R.sub.c (f) and R.sub.s (f) are given by the following equation (3), as pointed out above, and if the condition of .phi..sub.t =.phi..sub.r is satisfied by successfully synchronizing the phase angles of the carrier wave, then the equation (2) can be rewritten as the following equation (4).

here, d is the delay of the roll-off filters.

Since the amplitude characteristic A(f) is assumed to satisfy the Nyquist criterion, the channel which has the transfer function of the equation (4) can transmit data without any inter-symbol interference therein. The same applies to other channels, too. The transfer function H.sub.12 (f) from the input of the channel 1 to the output of the channel 2 and the transfer function H.sub.21 (f) from the input of the channel 2 to the output of the channel 1 are given by

H.sub.21 (f)= -H.sub.12 (f) (5)

Thus, if the condition of .phi..sub.t = .phi..sub.r is satisfied, as in the foregoing assumption, both transfer function H.sub.12 (f) and H.sub.21 (f) become zero, and the inter-channel interference between the channels 1 and 2 disappears. Similarly, the inter-channel interference between the channels 3 and 4 can be eliminated.

The interference between channels having different carrier waves will now be described. If the transfer function of a path from the input of a channel j to the output of a channel k is represented by H.sub.jk (f) (j,k=1,2,3,4), then such transfer functions can be given by the following equations, as in the case of the equations (5).

here, .phi..sub.tl and .phi..sub.rl are the transmitting end phase angle and the receiving end phase angle of the carrier wave C.sub.1, and .phi..sub.t2 and .phi..sub.r2 are the transmitting end phase angle and the receiving end phase angle of the carrier wave C.sub.2.

Thus, there is no interference at all, except the interference between the channels 2 and 3. As regards the interference between the channels 2 and 3, if the carrier phase angles are suitably controlled in the modulation and demodulation so as to satisfy the conditions of

then, the Nyquist criterion is satisfied, and the transfer functions become zero at sampling points with intervals of T=1/f.sub.c and there is no interference for the data transmission. In order to provide the phase differences to the carrier waves C.sub.1 and C.sub.2 for satisfying the conditions of the equations (7), the modulator of FIG. 3 uses the variable phase shifters 9.sub.1 and 9.sub.2.

To ensure satisfactory operation of the demodulator of FIG. 6, it is necessary to synchronize the phase angle of the carrier wave, and suitable phase angle of the carrier wave, and suitable phase control signals must be applied to the control terminals 28.sub.1 and 28.sub.2 of the variable phase shifters 27.sub.1 and 27.sub.2.

FIG. 7 illustrates an example of a phase error detector which generates the phase control signals, wherein 25.sub.1, 25.sub.2 are input terminals connected to the output terminals 25.sub.1 and 25.sub.2 of FIG. 6. In FIG. 7, 37.sub.1 and 37.sub.2 are clippers; 38.sub.1 and 38.sub.2 are multipliers; 39 is a subtracter; 40 is a low-pass filter; 41 is an accumulator; and 28.sub.1 is an output terminal to be connected to the control terminal 28.sub.1 of FIG. 6. Here, a phase error signal sin (.phi..sub.tl - .phi..sub.rl) of the carrier wave C.sub.1 is produced at the output of the low-pass filter 40, and the accurate phase synchronization can be achieved, as will be explained hereinafter. If the inverse Fourier transform of the transfer function H.sub.jk (f) is represented by h.sub.jk (t), and if the transmission signal series of the channel j is represented by [x.sub.jn ], then the output signals of the channels 1 and 2 are given by the following equations (8), provided that noise and interference from other channels are negligible. ##EQU1## Since h.sub.11 (t) and h.sub.22 (t) have prominent peaks at t=2d, the following relations are satisfied.

here, sgn () represents a sign function.

Thus, the clipper 37.sub.1 of FIG. 7 derives sgn (y.sub.1 (t)), and the multiplier 38.sub.1 produces the product of the output from the clipper 37.sub.1 and y.sub.2 (t), and the subtracter 39 and the low-pass filter 40 produce a time average thereof, so as to provide the following output signal at the output thereof. ##EQU2##

Similarly, the circuit consisting of the clipper 37.sub.2, the multiplier 38.sub.2, and the low-pass filter 40 produces the following signal. ##EQU3##

Accordingly, the output of the filter 40 is a signal equivalent to the difference between the equations (10) and (11). Judging from the equation (5), h.sub.12 (2d) is proportional to sin (.phi..sub.t -.phi..sub.r) and h.sub.21 (2d) is proportional to its negative signal, so that the phase error signal sin (.phi..sub.t -.phi..sub.r) can be achieved at the output of the filter 40. Similarly, in order to ensure the phase synchronization of the carrier wave C.sub.2, an identical circuit to that of FIG. 7 is used.

To reproduce the transmitted signal from the output signal of the demodulator of FIG. 6, sampling is necessary at intervals T=1/f.sub.c. Since clock signals of frequency f.sub.c are available at the clock signal output terminal 35 of FIG. 6, sampling signals can be produced by changing the phase of this signal.

FIG. 8 illustrates an example of sampling circuit, wherein 25.sub.1 is an input terminal; 42 is a sampling gate; 43 is a variable phase shifter; 44.sub.1 is an output terminal; 45.sub.1, . . . , 45.sub.4 are 1-sample delay elements; 46.sub.1, . . . , 46.sub.4 are attenuators; 47 is an adder; 48 is a multiplier; 49 is a low-pass filter; 50 is an accumulator; and 35 is a clock signal input terminal. The input terminal 25.sub.1 of FIG. 8 is connected to the output terminal 25.sub.1 of channel 1 of FIG. 6, and the phase of the sampling signal is so controlled as to minimize the dispersion of the intersymbol interference within the channel and to sample the output from the demodulator for delivering the sampled information at the output terminal 44.sub.1. Similar sampling circuits are connected to other channel outputs, too. The aforesaid control of the phase angle of the sampling signal can be explained as follows.

The dispersion of the inter-symbol interference in the channel 1 is given by the following equation, provided that the timing error of the sampling signal is .tau.. ##EQU4## here, < > represents an ensemble average.

To control .tau. so as to minimize the Q(.tau.), it is sufficient to find the gradient of Q(.tau.) with respect to .tau., and apply it to the accumulator 50 of FIG. 8. The gradient of Q(.tau.) with respect to .tau. is given by ##EQU5## Thus, if the gains of the attenuators 46.sub.1, . . . , 46.sub.4 are set at ##EQU6## and if the product of the following output signal from the adder 47 ##EQU7## and the output signal y.sub.1 (2d + .tau.) from the delay element 45.sub.2 is formed by the multiplier 48 and its time average is made by the low-pass filter 49, then an approximate value of the gradient of the equation (13) in the proximity of .tau.=0 can be achieved.

In the foregoing description, two pilot signals are superposed to two ends of one signal spectrum, and the demodulator produces the necessary carrier waves and clock signals from such pilot signals, but if the frequencies of the carrier waves have a simple relation with the clock frequency, e.g., its integral multiples, only one pilot signal may be sufficient. Furthermore, it is possible to extract the carrier waves and the clock signal from the modulated signals, without using any pilot signals. As regards the extraction of the carrier waves, the method equivalent to that which was disclosed in the Japanese patent application 29413/1973 "Multi-channel Multiplex Demodulator" can be used; namely, the accumulator 41 of FIG. 7 and the variable phase shifter 27.sub.1 or 27.sub.2 of FIG. 6 can be replaced with voltage-controlled oscillators having central frequencies approximately equal to those of the carrier waves. Then, as regards the extraction of the clock signal, it is possible to use a method of detecting the beat of two carrier waves having adjacent frequencies (with a frequency difference of f.sub.c) or to use a method as illustrated in FIG. 9 in the case of two channel transmission (with only one carrier wave) which method is used in a conventional VSB transmission.

In FIG. 9, 25.sub.1 is an input terminal, which is connected to the output terminal 25.sub.1 of FIG. 6; 35 is a clock signal output terminal, which is, for instance, connected to the clock signal input terminal 35 of FIG. 8; 51 and 53 are band-pass filters having central frequencies of f.sub.c /2 and f.sub.c, respectively; 52 is a squaring equipment, and 54 is a phase-controlled oscillator having a frequency f.sub.c which generates the clock signal at its output terminal 35 by well-known operating principles.

As explained above, the interferences between channels and between symbols can be minimized by using the control through an automatic phase control loop for the purpose of controlling the phase synchronization of the carrier waves and the timing of the sampling. If the modulator-demodulator is ideal and the transmission line is ideally equalized, the inter-symbol interference and the inter-channel interference can be supressed to a sufficiently low level, but a considerable amount of interference remains in actual transmission lines and the data transmission is disturbed thereby. The present invention uses an automatic-equalizer of transversal filter type for compensating for such interferences, so as to realize a highly efficient data transmission.

FIG. 10 illustrates an automatic equalizer to be used in an embodiment of the present invention, in which 44.sub.1, . . . , 44.sub.4 are input terminals of channels 1, . . . , 4, respectively; 61.sub.1, . . . , 61.sub.10 are transversal filter portions; 62.sub.1, . . . , 62.sub.4 are adders; 63.sub.1, . . . , 63.sub.4 are decision circuits; 64.sub.1, . . . , 64.sub.4 are subtracters; 65.sub.1, . . . , 65.sub.4 are multipliers; 66.sub.1, . . . , 66.sub.4 are step generators; and 67.sub.1, . . . , 67.sub.4 are output terminals of the channels 1, . . . , 4, respectively.

FIG. 11 shows the details of one of the transversal filter portions (TFS) 61.sub.1 through 61.sub.10 of FIG. 10, in which 44 is an input terminal; 68.sub.1, . . . , 68.sub.M-l are onesample delay elements; 69.sub.1, . . . , 69.sub.M are multipliers; 70.sub.1, . . . , 70.sub.M are accumulators; 71.sub.1, . . . , 71.sub.M are multipliers; 72 is an adder; 73 is an output terminal; and 74 is an error signal input terminal. Of all the TFS's 61.sub.1 through 61.sub.10, the TFS's 61.sub.1, 61.sub.4, 61.sub.7, and 61.sub.10 are for compensating for the inter-symbol interferences within the channels 1, 2, 3, and 4, respectively, and the remainders are for compensating for the inter-channel interferences caused by adjacent channels. For instance, in the case of the channel 2, the input signal applied to the input terminal 44.sub.2 passes through the inter-symbol interference compensating TFS 61.sub.4 of that channel, and the output from the TFS's 61.sub.3 and 61.sub.5 compensating for the inter-channel interferences from the channels 1 and 3 are added by the adder 62.sub.2, and the transmitted multi-amplitude PAM signal is demodulated by the decision circuit 63.sub.2 consisting of a quantizing circuit and delivered to the output terminal 67.sub.2. On the other hand, the subtracter 64.sub.2 produces the difference between the input signal to the decision circuit 63.sub.2 and the output signal, i.e., an error signal, and the multiplier 65.sub.2 multiplies the error signal with an adapting step generated by the step generator 66.sub.2, so as to modify the amplitude thereof and to send the thus adapted signal to the error signal input terminal 74 of the TFS's 61.sub.3, 61.sub.4, and 61.sub.5. In each of the TFS's, the multipliers 71.sub.1, . . . , 71.sub.M produce the products of such error signal and tapped output signals from a delay line consisting of the delay elements 68.sub.1, . . . , 68.sub.M-l, and the products are applied to the accumulators 70.sub.1 through 70.sub.M, respectively, so as to modify the weight coefficient of the transversal filter (i.e., the output signal from the accumulators) in such a manner that the sum of the inter-symbol interference and the inter-channel interference is minimized at the input to the decision circuit 63.sub.2. Thus, it is possible to effectively reduce the intersymbol interference and the inter-channel interference, by repeating the process of the adapting control a plurality of times and converging the weight coefficients of the filters of the TFS's to the proximity of the optimal values. The adapting steps are to decide the time constants of the adapting control loops, and they are generally large in the initial stages and gradually reduced, and their values may be fixed at constant values under normal conditions. As far as an automatic equalizer for one channel transmission is concerned, for instance, detailed description is provided in chapter 6 of the "Principles of Data Communication", by R.W. Lucky et al, McGraw-Hill (1968), but the automatic equalizer according to the present invention is formed by extending it for application to multi-channel transmission. As for the algorism of the adapting control, the MS method (means square method) has been described in the foregoing, but other algorisms, e.g., ZF method (zero-forcing method), can be also used.

As described above, since the inter-symbol intereference and the inter-channel interference can be effectively suppressed by using automatic equalizers having the adapting control loops, even if the equalization of the transmission line and the synchronization of the carrier waves and the timing synchronization are not perfect, it is possible to provide an efficient data transmission free from such interferences.

The aforesaid method, however, has a shortcoming in that the three transversal filters are necessary per channel, resulting in complicated and expensive devices. The following method mitigates such shortcoming, by suppressing the inter-channel interference by carrier synchronization and timing synchronization while only the intersymbol interference in each channel is compensated for by the transversal filters.

FIG. 12 illustrates another embodiment of the automatic equalizer according to the present invention, in which 61.sub.1, 61.sub.4, 61.sub.7 and 61.sub.10 are transversal filter portions (to be referred to as TFS's, hereinafter); 63.sub.1, . . . , 63.sub.4 are decision circuits; 64.sub.1, . . . , 64.sub.4 are substracters; 65.sub.1, . . . , 65.sub.4 are multipliers; 66.sub.1, . . . , 66.sub.4 are step generators; and 67.sub.1, . . . , 67.sub.4 are output terminals; and such components fulfills the same functions as the functions of the corresponding components in the automatic equalizer of FIG. 10. In FIG. 12, 25.sub.1, . . . , 25.sub.4 are input terminals; 42.sub.1, . . . , 42.sub.4 are sampling gates; 43.sub.1, . . . , 43.sub.4 are variable phase shifters; and 35 is a clock signal input terminal; and such components function in the same manner as the input terminal 25.sub.1, the sampling gate 42, the variable phase shifter 43, and the clock signal input terminal 35 in the sampling circuit of FIG. 8. Furthermore, in FIG. 12, 75.sub.1 and 75.sub.2 are phase error detectors having output terminals 28.sub.1 and 28.sub.2, respectively; 76.sub.1 and 76.sub.2 are timing error detectors; and 77.sub.1 and 77.sub.2 are timing control terminals. The input terminals 25.sub.1, . . . , 25.sub.4 are connected to the output terminals 25.sub.1, . . . , 25.sub.4 of the demodulator of FIG. 6, and the demodulated outputs are sampled at the sampling gates 42.sub.1, . . . , 42.sub.4, equalized by the TFS's 61.sub.1, 61.sub.4, 61.sub.7, and 61.sub.10, and then quantized by the decision circuits 63.sub.1, . . . , 63.sub.4, so as to be delivered to the output terminals 67.sub.1 , . . . , 67.sub.4. Here, the TFS's 61.sub.1, 61.sub.4, 61.sub.7, and 61.sub.10 compensate for the inter-symbol interferences within the respective channels in the same manner as those of FIG. 10, but the interchannel interferences cannot be compensated for. However, the output terminals 28.sub.1 and 28.sub.2 of the phase error detectors 75.sub.1 and 75.sub.2 are connected to the phase control terminals 28.sub.1 and 28.sub.2 of the demodulator of FIG. 6 for controlling the phase angles of the carrier waves C.sub.1 and C.sub.2, so that the interference between the two channels having the same carrier waves, i.e., the interference between the channel 1 and the channel 2 and the interference between the channel 3 and the channel 4, can be eliminated. Besides, the output signals from the timing error detectors 76.sub.1 and 76.sub.2 are applied to the control terminals of the variable phase shifters 43.sub.2 and 43.sub.3 for controlling the timing phases of the channel 2 and the channel 3, so that the interference between the adjacent channels using different carrier waves, i.e., the interference between the channel 2 and the channel 3, can be eliminated.

FIG. 13 shows the details of the phase error detector 75.sub.1 or 75.sub.2 of FIG. 12, and FIG. 14 shows the details of the timing error detector 76.sub.1 or 76.sub.2 of FIG. 12. In FIG. 13, 67.sub.1 and 67.sub.2 are signal input terminals; 80.sub.1 and 80.sub.2 are error input terminals; 81.sub.1, . . . , 81.sub.6 are one sample delay elements; 82.sub.1, . . . , 82.sub.6 are attenuators; 83.sub.1 and 83.sub.2 are adders; 84.sub.1 and 84.sub.2 are multipliers; 85 is a subtracter; 86 is a low-pass filter; 87 is an accumulator; and 28.sub.1 is an output terminal. The weighted sum .SIGMA.x.sub.ln-m .multidot.h.sub.m of the demodulated signals x.sub.ln of the channel 1 delivered from the signal input terminal 67.sub.1 is obtained at the output from the transversal filter consisting of the delay elements 81.sub.1, 81.sub.2, the attenuators 82.sub.1, 82.sub.2, 82.sub.3, and the adder 83.sub.1. Here, h.sub.m (m = -1,0,1) is the gain of the attenuators 82.sub.1, 82.sub.2,82.sub.3, and the gain h.sub.m in the illustrated example is selected to be

here, h(t) is the inverse Fourier transform of the following quantity.

This output signal is multiplied with the error signal (whose amplitude is modified by the adapting step) e.sub.2n of the channel 2 at the output of the delay element 81.sub.3, and the product is applied to the low-pass filter 86 through the substracter 85 for smoothing, and then applied to the accumulator 87, so as to form the phase control signal. The delay elements 81.sub.5, 81.sub.6, the attenuators 82.sub.4, 82.sub.5, 82.sub.6, and the adder 83.sub.2 constitute another transversal filter, which has the same characteristics as the aforesaid transversal filter, and the demodulated signal x.sub.2n of the channel 2 is applied to the input terminal 67.sub.2 of the aforesaid other transversal filter while applying the error signal e.sub.ln of the channel 1 at the error input terminal 80.sub.1, so as to produce a weighted means -e.sub.ln .multidot..SIGMA.h.sub.m .multidot.x.sub.2n-m at the output terminal 28.sub.1 in the same manner as described above, which is superposed to said output. This output signal controls the phase angle of the carrier wave C.sub.1, so that the interference between the channel 1 and the channel 2 can be removed, as will be explained hereinafter.

The interferences from the channels 2 and 1 included in the demodulated output signals of the channels 1 and 2, respectively, can be given by the following equations, based on the foregoing equation (8). ##EQU8## here, h.sub.12 (t) and h.sub.21 (t) can be given by the following expression, based on the foregoing equation (5).

Since it is sufficient to minimize the means square value of the inter-channel interference, as given by the following equation (18), by modifying the phase angle .phi..sub.r of the received carrier wave,

the gradient of the object function Q(.phi..sub.r), as given by the following equation (19), may be derived and used as the control signal. ##EQU9##

It is apparent from the foregoing description that the phase error detector of FIG. 13 derives the approximate value of the aforesaid gradient. In FIG. 13, even when the signal input terminal 67.sub.1 and the error input terminal 80.sub.2 are interchanged, the same operation can be achieved. The phase error detector 75.sub.2 for the phase control of the carrier wave C.sub.2 is similarly constructed.

In FIG. 14, 67.sub.3 is a signal input terminal; 80.sub.2 is an error input terminal; 90.sub.1, . . . , 90.sub.3 are one sample delay elements; 91.sub.1, . . . , 91.sub.3 are attenuators; 92 is an adder; 93 is a multiplier; 94 is a low-pass filter; 95 is an accumulator; and 96 is an output terminal. The gains of the attenuators 91.sub.1, 91.sub.2, and 91.sub.3 are set as follows, respectively.

here h'.sub.32 (t) is the derivative of the inverse Fourier transform of the following quantity.

In FIG. 14, the demodulated signal x.sub.3n of the channel 3 is applied to the signal input terminal 67.sub.3, while the error signal e.sub.2n of the channel 2 is applied to the error input terminal 80.sub.2, so that a transversal filter consisting of the delay elements 90.sub.1, 90.sub.2, the attenuators 91.sub.1, 91.sub.2, 91.sub.3, and the adder 92 coacts with the delay element 90.sub.3 and the multiplier 93 for producing the following value in the same manner as that of FIG. 13. ##EQU10##

The output from the multiplier 93 is smoothed by the low-pass filter 94 and delivered to the output terminal 96 through the accumulator 95. This output signal controls the phase shifter 43.sub.2 for controlling the phase angle of the sampling timing of the channel 2, so as to eliminate the interference from the channel 3 to the channel 2 in the manner to be explained hereinafter.

The interference from the channel 3 to the channel 2 is given by ##EQU11## here, h.sub.32 (t) is the inverse Fourier transform of H.sub.32 (f) of the equation (21) which assumes zero value at t=nT+2d (n = . . . , -1, 0, 1).

Thus, in order to eliminate this interference, it is sufficient to modify the sampling timing phase .tau. of the channel 2, so as to minimize the following mean square value of the inter-channel interference.

Thus, the gradient of this object function Q(.tau.) may be derived, as shown in the following equation (25), for using it as the control signal in a feedback loop. ##EQU12##

It is apparent that the value of the equation (22), as derived in the circuit of FIG. 14, is an estimated value of the gradient of the equation (25). It should be noted here that, even if the signal input terminal 67.sub.3 and the error input terminal 80.sub.2 are interchanged, the same result can be achieved, provided that the sequential order of the attenuators 91.sub.1, 91.sub.2, and 91.sub.3 is reversed. For the timing control of the channel 3, a timing error detector 76.sub.2 with similar construction is used.

Since the timing control of the channel 1 and the channel 4 at the edges of the transmission band is irrelvant to the inter-channel interference, such timing control can be set so as to minimize the inter-symbol interference in the individual channel, and the method of FIG. 8 may be used for this purpose. More particularly, the system to the right of the output terminal of the sampling gate 42 of FIG. 8 may be connected to the output terminal of the sampling gate 42.sub.1 of FIG. 12, while connecting the output from the accumulator 50 of FIG. 8 to the timing control terminal 77.sub.1 of FIG. 12. As a more effective method, the timing may be so controlled as to minimize the intersymbol interference at the output of the transversal filter portion of the automatic equalizer.

FIG. 15 shows an example of timing error detectors based on this method, in which 67.sub.1 is a signal input terminal; 80.sub.1 is an error input terminal; 97.sub.1, 97.sub.2, and 97.sub.3 are one-sample delay elements; 98.sub.1 and 98.sub.2 are attenuators; 99 is an adder; 100 is a multiplier; 101 is a low-pass filter; 102 is an accummulator; and 77.sub.1 is an output terminal. The demodulated signal x.sub.1n of the channel 1 is applied to the signal input terminal 67.sub.1, while the error signal e.sub.1n of the channel 1 is applied to the error input terminal 80.sub.1, and the gains of the attenuators 98.sub.1 and 98.sub.2 are set at h'.sub.m (m=-1, 1), as defined by the foregoing euqation (13)', respectively. As in the case of the system of FIG. 14, the system of FIG. 15 derives the mean value of the following quantity. ##EQU13##

This output signal is applied to the control terminal 77.sub.1 of the phase shifter 43.sub.1 of FIG. 12 for controlling the timing phase of the channel 1, so as to minimize the inter-symbol interference at the channel 1, as will be explained hereinafter.

Since the inter-signal interference of the channel is given by ##EQU14## the object function becomes the mean square value thereof, as given by

and the gradient with respect to its timing error .tau. becomes ##EQU15## here, h'.sub.11 (t) is the derivative of h.sub.11 (t).

Since the means value of the equation (26), as determined by the system of FIG. 15, is an estimated value of the gradient of the equation (29), it is apparent that the inter-symbol interference can be minimized by the feedback control using the means value of the equation (26) as its control signal.

As described in the foregoing, the inter-channel interference can be eliminated by controlling the phase of the received carrier waves and the timing of the sampling signal with the error signal obtained from the automatic equalizer, so that the TFS's in the automatic equalizer of FIG. 10 for compensating for the inter-channel interference can be dispensed with. As a result, the size of the automatic equalizer can be reduced 1/2 to 1/3 which greatly improves its economy.

When the aforesaid modulators, demodulators, and automatic equalizers are used, even if the transmission line is not perfectly equalized, a highly efficient and stable data transmission, which is substantially free from the inter-channel interference and the inter-symbol interference, can be realized. As a result the characteristics of the multi-channel orthogonal multiplex VSB transmission can be fully utilized.

Although an embodiment using four channel transmission has been described, the present invention can be similarly applied to the transmission using an arbitrary number of channels.