Abstract:
To control the oscillation frequency of a local oscillator, a digital broadcast receiver demodulates a phase-reference symbol contained in an orthogonal frequency-division multiplexed broadcast signal. The resulting frequency-domain data are modified by multiplication with complex conjugates of the known data encoded in the phase-reference signal, under different assumed frequency offsets between the frequency-domain data and known data. The results are converted to time-domain data, yielding one time series for each assumed frequency offset. One value is taken from each time series, these values are compared, and the oscillation frequency is adjusted according to the comparison results. 
     A digital broadcast receiver for receiving a PSK-OFDM signal, having a local oscillator with a controllable oscillation frequency, a mixer for down-converting said PSK-OFDM signal to an intermediate-frequency signal by mixing said PSK-OFDM signal with a signal generated by said local oscillator, and demodulating circuits for obtaining an array of frequency-domain data from said intermediate-frequency signal, said array of frequency-domain data representing subcarrier phase information of said PSK-OFDM signal. The digital broadcast receiver further including a phase modifying means, an inverse-fast-Fourier-transform means, a peak detecting means, and a frequency-deviation detector. The digital broadcast receiver can also include a data selecting means in addition to the elements previously described.

Description:
BACKGROUND OF THE INVENTION 
     The present invention relates to a method of tuning a local oscillator to receive digital broadcasts that employ phase-shift keying (hereinafter, PSK) and orthogonal frequency-division multiplexing (hereinafter, OFDM), and to a digital broadcast receiver using this method. 
     OFDM broadcasts have multiple subcarrier signals, on which data are transmitted in parallel. In PSK-OFDM broadcasting, each subcarrier signal is modulated by phase-shift keying. The modulated subcarriers are combined and up-converted to the broadcast frequency to create the PSK-OFDM broadcast signal. 
     Reception of a PSK-OFDM signal requires that a local oscillator in the receiver generate a signal tuned in relation to the broadcast frequency. The local oscillator signal is used to down-convert the received signal to an intermediate-frequency signal, which is then demodulated to obtain the subcarrier phase-shift data. If the local-oscillator frequency is too high or too low, the demodulated phase shifts will be incorrect. 
     When quadrature phase-shift keying (QPSK) is employed, for example, the phase shifts have nominal radian values of zero, ρ/2, π, and -π/2. A conventional method of tuning control multiplies the demodulated phase data by four, modulo 2π, so that these nominal values all become zero. The sum of the results for all subcarriers is a phase error signal which can be used to control the local oscillator. Correct tuning is maintained by controlling the frequency of the local oscillator so as to reduce the phase error signal to zero. 
     The conventional method suffers, however, from inherent ambiguity. If the frequency error of the local oscillator causes a phase error of π/2, or any integer multiple of π/2, multiplication by four will convert the phase error to zero, and the frequency error will go uncorrected. The conventional method is thus able to correct only small frequency errors, such as frequency errors causing phase errors of less than π/4 radians. 
     SUMMARY OF THE INVENTION 
     It is accordingly an object of the present invention to control the tuning of a digital broadcast receiver unambiguously. 
     The invented method tunes the oscillation frequency of a local oscillator in a digital broadcast receiver by receiving and demodulating a phase-reference symbol in a PSK-OFDM broadcast signal to obtain an array of frequency-domain data, then multiplying this array of frequency-domain data element-wise by an array of complex conjugates of the known data encoded in the phase-reference signal. The demodulated frequency-domain data and the known data both comprise one value for each subearrier frequency in the PSK-OFDM signal. 
     The multiplication step is carried out once on the assumption of a frequency offset of zero between the demodulated frequency-domain data and the known data, thereby obtaining a first array of modified data, and at least once on the assumption of a non-zero frequency offset, thereby obtaining at least one additional array of modified data. All arrays of modified data thus obtained are transformed to the time domain by an inverse fast Fourier transform, thereby obtaining a first time series, representing the frequency offset of zero, and at least one additional time series, representing a non-zero frequency offset. 
     A peak value is detected in the first time series. An additional value is taken from each additional time series. The peak value and additional value or values are compared, and the oscillation frequency of the local oscillator is adjusted according to the comparison results. 
     According to one aspect of the invention, the additional values are peak values detected in the additional time series, and the oscillation frequency is adjusted according to the frequency offset represented by the time series in which the largest peak value is detected. Large frequency errors can be corrected unambiguously in this way. 
     According to another aspect of the invention, the additional values taken from the additional time series are the values of these time series at a time at which the peak value was attained in the first time series. Small frequency errors can be corrected accurately in this way. 
     According to yet another aspect of the invention, the Fourier transform of the phase-reference symbol is subtracted from the array of frequency-domain data before these data are multiplied under the assumption of a non-zero frequency offset. Small frequency errors can be corrected still more accurately in this way. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     In the attached drawings: 
     The present invention will become more fully understood from the detailed description given hereinbelow and the accompanying drawings which are given by way of illustration only, and thus are not limitative of the present invention, and wherein: 
     FIG. 1 is a block diagram of a first embodiment of the invented digital broadcast receiver; 
     FIG. 2 is a block diagram of a second embodiment of the invented digital broadcast receiver; 
     FIG. 3 is a block diagram of a third embodiment of the invented digital broadcast receiver; 
     FIG. 4 is a graph of the Fourier transform of a phase-reference sub-symbol; and 
     FIG. 5 is a similar graph, illustrating the effect of frequency deviation. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Further scope of applicability of the present invention will become apparent from the detailed description given hereinafter. However, it should be understood that the detailed description and specific examples, while indicating preferred embodiments of the invention, are given by way of illustration only, since various changes and modifications within the spirit and scope of the invention will become apparent to those skilled in the art from this detailed description. 
     Embodiments of the invention will be described with reference to the attached illustrative drawings, following a brief description of the PSK-OFDM digital broadcasting system. 
     The number K of subcarrier signals employed in OFDM digital broadcasting is typically large: one system employs one thousand five hundred thirty-six subcarrier signals (K=1536), for example. The K subcarrier signals have a constant frequency spacing F s . The OFDM signal is broadcast as a continuous series of frames, each consisting of a certain number M of OFDM symbols. Each OFDM symbol comprises K sub-symbols, one sub-symbol being encoded per subcarrier. In QPSK-OFDM, the sub-symbols represent the dibits `00,` `01,` `10,` and `11,` which are mapped onto the complex numbers 1, j, -1, and -j (where j is a square root of minus one), and are encoded as subcarrier phase shifts of zero, π/2, π, and -π/2 radians. 
     The subcarrier signals are combined by complex addition. One frame of the resulting signal s(t) can be described by equation (1) below, in which t is a time variable, T s  is the duration of one symbol, Z m ,k is the complex value (1, j, -1, or -j) of the m-th sub-symbol transmitted on the k-th subcarrier, and k ranges over the integers from -K/2 to K/2, inclusive. ##EQU1## 
     The symbol exp denotes the exponential function. The letter b denotes a function equal to unity on the interval between zero and T s , and equal to zero elsewhere, as defined by equation (2) below. ##EQU2## 
     The first symbol (m=0) in each frame is a null symbol, in which the signal level is reduced to zero to indicate the beginning of the frame, as described in equation (3). 
     
         z.sub.0,k =0 (k=-K/2, . . . , K/2)                         (3) 
    
     The next symbol (m=1) is a phase-reference symbol containing known data z k  for each subcarrier. The known data z k  vary according to the value of k in a pattern that may be regular, but must not repeat cyclically. These known data become the values of z 1 ,k in each frame, as indicated by equation (4). 
     
         z.sub.1,k =z.sub.k (k=-K/2, . . . , K/2)                   (4) 
    
     The known data z k  combine to give the reference-symbol waveform x(t) described by equation (5) below. This is the waveform produced in the transmitter, before up-conversion to the broadcast frequency. ##EQU3## First Embodiment 
     A first embodiment of the invented method of tuning control, and a first embodiment or the invented digital broadcast receiver, will be described with reference to FIG. 1, which is a block diagram of the digital broadcast receiver. 
     The conventional part of this digital broadcast receiver comprises an antenna 1 that receives a PSK-OFDM broadcast signal, a radio-frequency amplifier (RF AMP) 2 that amplifies the received broadcast signal, a mixer 3 that down-converts the amplified signal to an intermediate-frequency (IF) signal, an IF demodulator (DEMOD) 4 that demodulates the IF signal orthogonally to produce in-phase (I) and quadrature (Q) baseband signals, an analog-to-digital converter (ADC) 5 that converts the in-phase and quadrature baseband signals to digital signals, a fast-Fourier-transform processor 6 that executes a fast Fourier transform (FFT) on these digital signals to obtain the sub-symbol data for each subcarrier, an error corrector 7 that perform error correction, an output terminal 8 to which the sub-symbol data are supplied, and a voltage-controlled oscillator (VCO) 9. The voltage-controlled oscillator 9 is used as a local oscillator that supplies the mixer 3 with a signal tuned to a frequency differing from the PSK-OFDM broadcast frequency by a fixed amount. 
     The novel part of this digital broadcast receiver comprises a plurality of phase modifiers 12A, 12B, . . . , a like plurality of inverse-fast-Fourier-transform (IFFT) processors 13A, 13B, . . . , a like plurality of peak detectors 14A, 14B, . . . , and a frequency-deviation detector (FREQ DEV DET) 15. In each frame, these elements operate on the array of frequency-domain data which the fast-Fourier-transform processor 6 produces from the demodulated and digitized phase-reference symbol. This array of frequency-domain data comprises one complex value X&#39;(ω k ) for each subcarrier (k=-K/2, . . . , K/2). 
     The frequency-domain data X&#39;(ω k ) (k=-K/2, . . . , K/2) are supplied simultaneously from the FFT processor 6 to all of the phase modifiers 12A, 12B, . . . . These phase modifiers multiply the array of frequency-domain data by an array of the complex conjugates Z k  * of the known values of the phase-reference data, under the assumption of various frequency offsets between the two arrays. Each frequency offset is equal to the subcarrier frequency spacing F s  multiplied by an integer i, and can be expressed as an offset of i between the array subscript values. The phase modifiers thus perform multiplication operations of the following form, for various integers i. 
     
         Y&#39;.sub.i (ω.sub.k)=X&#39;(ω.sub.k)z.sub.k-i *      (6) 
    
     Phase modifier 12A assumes a frequency offset of zero (i=0), and produces modified data Y&#39; 0  (ω k ) equal to X&#39;(ω k )z k  *. Phase modifier 12B assumes a positive frequency offset equal to F s  (i=1), and produces modified data Y&#39; 1  (ω k ) equal to X&#39;(ω k )z k-1  * . Phase modifier 12C (not visible) assumes a negative frequency offset equal to F s  (i=-1), and produces modified data Y&#39; -1  (ω k ) equal to X&#39;(ω k )z k+1  *. Modified data are produced for at least these three assumed frequency offsets (i=0, 1, and -1). 
     The phase modifiers 12A, 12B, . . . supply the modified data Y&#39; i  (ω k ) to respective IFFT processors 13A, 13B, . . . , which execute the inverse fast. Fourier transform, transforming the modified data to the time domain. For each integer i, a time series . . . , y i  (t), . . . is obtained, in which t is a discrete time variable (t=t -K/2 , . . . , t K/2 ). Each time series represents a digitized, complex-valued waveform, and is associated with a frequency offset represented by the above integer i. 
     The time-series data are passed to respective peak detectors 14A, 14B, . . . . Each peak detector detects the data value having the largest absolute value in the received time series, and supplies this as a peak value to the frequency-deviation detector 15. 
     The frequency-deviation detector 15 compares the peak values received from the peak detectors 14A, 14B, . . . , finds the largest peak value, and controls the oscillation frequency of the voltage-controlled oscillator 9 according to the frequency offset (value of i) associated with the time series in which the largest peak value was detected. The oscillation frequency is altered in one direction if the frequency offset is positive, and in the opposite direction if the frequency offset is negative. Specifically, the oscillation frequency is decreased if i is positive, increased if i is negative, and left unchanged if i is equal to zero. If more frequency offsets than the three noted above (i=0, 1, and -1) are employed, the amount of increase or decrease in the oscillation frequency can be made to depend on the magnitude of i. 
     The above operation tunes the voltage-controlled oscillator 9 in such a way as to move the oscillation frequency toward the correct frequency, even if the original frequency error exceeds the subcarrier frequency spacing F s . The reason for this will be explained next. 
     The phase-reference symbol shown in equation (5) is the sum of phase-reference sub-symbols x k  (t) of the form given by equation (7). 
     
         x.sub.k (t)=z.sub.k b(t-T.sub.s)exp [2jπkF.sub.s (t-T.sub.s)](7) 
    
     A Fourier transform converts x k  (t) to the following frequency-domain function X k  (ω), in which ω is a frequency variable, ω k  is equal to 2πkF s  T s , and θ is a constant. ##EQU4## 
     The absolute value |X k  (ω)| of this function is illustrated in FIG. 4. 
     Equation (5), describing the waveform of the phase-reference symbol, is equivalent to the following equation (9). ##EQU5## 
     Similarly, the Fourier transform X(ω) of x(t) can be written as in equation (10). ##EQU6## 
     The values of X(ω -K/2 ), . . . X(ω K/2 ) can be calculated efficiently by means of the fast Fourier transform. As implied by the above equations (7), (8), and (9) and illustrated in FIG. 4, X i  (ω k ) is zero when i≠k, so equation (10) yields the following equation (11). 
     
         X(ω.sub.k)=X.sub.k (ω.sub.k)                   (11) 
    
     If the voltage-controlled oscillator 9 is accurately tuned to the broadcast frequency, the received phase-reference data X&#39;(ω k ) will be identical to the above X(ω k ) for all k from -K/2 to K/2, and the modified data produced by phase modifier 12A will be the data Y(ω k ) equal to X(ω k )z k  *. From equation (8), since z k  z k  * is always equal to unity, Y(ω k ) is the same for all values of k, having the value given by the following equation (12). 
     
         Y(ω.sub.k)=exp(jθ/2)                           (12) 
    
     Equation (12) describes the Fourier transform of an infinite impulse function, the location of the impulse being determined by the value of θ. The inverse Fourier transform performed by IFFT processor 13A therefore produces a time series similar to an impulse function, with a single large peak value. 
     The other IFFT processors 13B, . . . do not produce impulse-like time series, because when the integer i is not zero, z k  z k-i  * takes on various different values, depending on k. The peak values detected in these other time series will accordingly be comparatively small. The frequency-detector will receive the largest peak value from peak detector 14A (corresponding to i=0), and will leave the oscillation frequency of the voltage-controlled oscillator 9 unchanged, as desired. 
     If the voltage-controlled oscillator 9 is inaccurately tuned, and the phase-reference signal x&#39;(t) output by the analog-to-digital converter 9 deviates by a frequency ω n  from the transmitted phase-reference signal x(t) given by equation (5) or (8), the modified data Y&#39; i  (ω -k/2 ), . . . , Y&#39; i  (ω K/2 ) produced by the phase modifiers 12A, 12B, . . . will have the form given by equations (13) and (14). 
     
         Y&#39;.sub.i (ω.sub.k)=X&#39;(ω.sub.k)z.sub.k-i *      (13) 
    
     
         Y&#39;.sub.i (ω.sub.k)-X(ω.sub.k -ω.sub.n)z.sub.k-i *tm (14) 
    
     If ω n  is equal to n times the frequency spacing F s , where n is a positive or negative integer, then after the inverse Fourier transform performed by the IFFT processors 13A, 13B, . . . , an impulse-like time series will appear when i=n. When i≠n, the time series will not be impulse-like. If n is equal to one (ω n  =F s ), for example, then a large peak value will be detected in the output of IFFT processor 13B, and smaller peak values will be detected in the output of the other IFFT processors. The frequency-deviation detector 15 will receive the largest peak value from peak detector 14B (corresponding to i=1), and will alter the oscillation frequency of the voltage-controlled oscillator 9 in the appropriate direction. 
     If n lies outside the range of frequency offsets (i) assumed by the phase modifiers 12A, 12B, . . . , the largest peak value will still tend to be round in the direction of n, so if n is positive, the largest peak value will correspond to a positive value of i, and if n is negative, the largest peak value will correspond to a negative value of i. Thus the frequency-deviation detector 15 will still alter the oscillation frequency of the voltage-controlled oscillator 9 in the right direction. The same is true when the frequency deviation is not an integer multiple of F s . 
     The first embodiment is accordingly able to correct large frequency deviations without the ambiguity present in the prior art. Although the frequency-deviation detector 15 detects frequency deviations in multiples of F s , the corrections applied to the voltage-controlled oscillator 9 need not be equal to the detected deviation; corrections can be applied in smaller increments, enabling the oscillation frequency to be kept close to the correct frequency once approximately correct tuning is achieved. 
     Second Embodiment 
     A second embodiment of the invented method of tuning control, and a second embodiment of the invented digital broadcast receiver, will be described with reference to the block diagram in FIG. 2. The conventional elements with reference numerals 1 to 9 are the same as in the first embodiment; descriptions of these elements will be omitted. 
     The novel elements comprise three phase modifiers 12A, 12B, and 12C, three IFFT processors 13A, 13B, and 13C, and a peak detector 14A, all of which are the same as in the first embodiment. The frequency-deviation detector 15 operates somewhat differently from in the first embodiment. Two data detectors 16B and 16C are coupled between the frequency-deviation detector 15 and IFFT processors 13B and 13C, replacing peak detectors 14B and 14C in the first embodiment. 
     The operations performed by phase modifiers 12A, 12B, and 12C are as described in the first embodiment, with the same values of the integer i (0, 1, and -1). The IFFT processors 13A, 13B, and 13C produce respective time series y 0  (t), y 1  (t), and y -1  (t) (t=t -K/2 , . . . , t K/2 ). 
     The peak detector 14A outputs both the peak value y 0  (t p ) in the time series y 0  (t) representing a frequency offset of zero, and the value t p  of the time variable t at which the peak value occurs. The peak value y 0  (t p ) is output to the frequency-deviation detector 15. The time value t p  is output to data detectors 16B and 16C. 
     Data detector 16B takes the value y 1  (t p ) of time series y 1  (t) at the peak time t p  in time series y 0  (t), and supplies this value to the frequency-deviation detector 15. Similarly, data detector 16C takes the value y -1  (t p ) from time series y -1  (t), and supplies this value to the frequency-deviation detector 15. 
     The frequency-deviation detector 15 compares the values received from the peak detector 14A and data detectors 16B and 16C, and adjusts the oscillation frequency of the voltage-controlled oscillator 9 as follows. If y 1  (t p ) and y -1  (t p ) both differ from y 0  (t p ) by less than a certain amount D, and if y 1  (t p ) is greater than y -1  (t p ), the oscillation frequency is increased. Similarly, if y 1  (t p ) and y -1  (t p ) both differ from y 0  (t p ) by less than D, and y 1  (t p ) is less than y -1  (t p ), the oscillation frequency is decreased. In other cases, the oscillation frequency is left unchanged. 
     The increase or decrease can be a fixed amount, or the magnitude of the increase or decrease can be made to depend on the difference between t 1  (t p ) and t -1  (t p ), or on the relative values of t 0  (t p ), t 1  (t p ), and t -1  (t p ). 
     Next, the theory of operation of the second embodiment will be described. 
     If inaccurate tuning of the voltage-controlled oscillator 9 cause a frequency deviation Δω when the received signal is down-converted, the received phase-reference data x&#39;(t) output by the analog-to-digital converter 5 can be expressed as in equations (15) and (16). ##EQU7## The component x&#39; k  (t) of x&#39;(t) corresponding to the k-th subcarrier is given by equation (17). 
     
         x&#39;.sub.k (t)=x.sub.k (t)exp(jΔωt)              (17) 
    
     The Fourier transform X&#39; k  (ω) of x&#39; k  (t) is given by equation (18). 
     
         X&#39;.sub.k (ω)=X.sub.k (ω-Δω)        (18) 
    
     The absolute value |X&#39; k  (ω)| of this Fourier transform is shown in FIG. 5 for a case in which Δω of is less than the subcarrier frequency spacing F s . 
     In FIG. 5, since X&#39; i  (ω k )=0 does not hold true for unequal integers i and k (i≠k), the value of the Fourier transform X&#39;(ω) of x&#39;(t) when ω=ω k  is given by equation (19). ##EQU8## 
     The modified data Y 0  (ω k ), Y 1  (ω k ) and Y -1  (ω k ) obtained by phase modifiers 12A, 12B, and 12C are accordingly given by equations (20) to (23). ##EQU9## 
     When the inverse Fourier transform is applied to the modified data Y 0  (ω -K/2 ), . . . , Y 0  (ω K/2 ) output by phase modifier 12A, the first term in equation (21), which is comparatively close to the value given by equation (12), produces a large peak value y 0  (t p ) at a particular time value t p . The energy of the other terms in equation (21) is smaller, and is broadly distributed over the time-series values y 0  (t -K/2 ), . . . , y 0  (t K/2 ), so these terms do not contribute greatly to y 0  (t p ), or produce other large peaks. 
     When the inverse Fourier transform is applied to the modified data Y 1  (ω -K/2 ), . . . , Y -1  (ω K/2 ) output by phase modifier 12B, since the phases of the terms in equation (22) are aligned with the phases in equation (21), the energy of the first term of equation (22) is concentrated at y 1  (t p ), and the energy of the other terms is broadly distributed over y 1  (t -K/2 ), . . . , y 1  (t K/2 ), without contributing greatly to y 1  (t p ). 
     Similarly, when the inverse Fourier transform is applied to the modified data Y -1  (ω -K/2 ). Y 1  (ω K/2 ) output by phase modifier 12C, the energy of the first term in equation (23) is concentrated at y -1  (t p ), and the energy of the other terms is distributed over y -1  (t -K/2 ), . . . , y -1  (t K/2 ), without contributing greatly to y -1  (t p ). 
     Inspection of the first terms of equations (22) and (23) shows that y 1  (t p ) and y -1  (t p ) vary according to the frequency deviation Δω, and provide a sensitive indication of frequency deviations less than the subcarrier spacing F s . By controlling the oscillation frequency of the voltage-controlled oscillator 9 according to the difference between these values y 1  (t p ) and y -1  (t p ), the frequency-deviation detector 15 is able to detect and correct small frequency errors. In particular, frequency errors less than the subcarrier spacing F s  can be corrected. 
     Instead of using both y 1  (t p ) and y -1  (t p ), the frequency-deviation detector 15 can compare just one of these two values with y 0  (t p ) to decide how to alter the oscillation. This method is less accurate, but requires less computation. 
     Third Embodiment 
     A third embodiment of the invented method of tuning control, and a third embodiment of the invented digital broadcast receiver, will be described with reference to the block diagram in FIG. 3. The conventional elements with reference numerals 1 to 9 are the same as in the first embodiment; descriptions will again be omitted. 
     The novel elements comprise a phase modifier 12A, IFFT processors 13A, 13B, and 13C, a peak detector 14A, data detectors 16B and 16C, and a frequency-deviation detector 15 as in the second embodiment. The data input to IFFT processors 13B and 13C are provided by respective data modifiers 17B and 17C, which modify the output of the FFT processor 6. 
     Phase modifier 12A produces modified data V 0  (ω k ) equal to X&#39;(ω k )z k  *, thus identical to the modified data Y 0  (ω k ) in the preceding embodiments. Data modifiers 17B and 17C, however, subtract the Fourier transform X(ω k ) of the reference signal x(t) from the array of frequency-domain data X&#39;(ω k ), and multiply the resulting difference array element-wise by the array of complex conjugates of x k-1  or x k+1 . Specifically, data modifier 17B produces modified data V 1  (ω k ) equal to [X&#39;(ω k )-X(ω k )]z k-1  *. Data modifier 17C produces modified data V -1  (ω k ) equal to [X&#39;(ω k )-X(ω k )]z k+1  *. The Fourier-transform values X(ω k ) are readily available, because they are equal to the known data z k  multiplied by a constant value equal to exp(-jθ/2). The values of X(ω k ) are preferably computed in advance and stored in the digital broadcast receiver. 
     Subsequent processing is similar to the second embodiment. Inverse Fourier transforms are applied to the modified data V 0  (ω k ), V 1  (ω k ), and V -1  (ω k ) to produce time-series data v 0  (t), v 1  (t), and v -1  (t), respectively (t=t -K/2 , . . . , t K/2 ). Peak detector 14A detects the peak value of time series v 0  (t), outputs this peak value v 0  (t p ) to the frequency-deviation detector 15, and outputs the peak time value t p  to data detectors 16B and 16C. Data detectors 16B and 16C supply the corresponding values v 1  (t p ) and v -1  (t p ) of times series v 1  (t) and v -1  (t) at time t p  to the frequency-deviation detector 15. 
     The frequency-deviation detector 15 compares the data received from the peak detector 14A and data detectors 16B and 16C and takes action as in the second embodiment. If v 1  (t p ) and v -1  (t p ) differ from v 0  (t p ) by less than a certain value D, and v 1  (t p ) is greater than v -1  (t p ), the oscillation frequency of the voltage-controlled oscillator 9 is increased. If v 1  (t p ) and v -1  (t p ) differ from v 0  (t p ) by less than D, and v 1  (t p ) is less than v -1  (t p ), the oscillation frequency is decreased. 
     The values of V 0  (ω k ) V 1  (ω k ), and V -1  (ω k ) are given by equations (24), (25), and (26) below. ##EQU10## 
     The time-series data v 0  (t -K/2 ), . . . , v 0  (t K/2 ) produced from the modified data V 0  (ω -K/2 ), . . . , V 0  (ω K/2 ) are identical to the time-series data y 0  (t -K/2 ), . . . , y 0  (t K/2 ) in the second embodiment. The first term in equation (24) gives rise to a large peak value v 0  (t p ) at a particular time value t p , as in the second embodiment. 
     When the inverse Fourier transform is applied to the modified data V 1  (ω -K/2 ), . . . , V 1  (ω K/2 ) output by data modifier 12B, if Δω is comparatively small, the first term in equation (25) will make only a small contribution to the resulting time-series data, and this contribution will be broadly distributed over V 1  (t -K/2 ), . . . , v 1  (t K/2 ). The contribution of the second term in equation (25) will be larger, and will be concentrated at v 1  (t p ), since the phases are aligned as in equation (24). The energy of the other terms in equation (25) will be broadly distributed over v 1  (t -K/2 ), . . . , V 1  (t K/2 ), not contributing greatly to v 1  (t p ). 
     Similarly, when the inverse Fourier transform is applied to the modified data V -1  (ω -K/2 ), . . . , V -1  (ω K/2 ), the second term of equation (26) will make a comparatively large contribution at v -1  (t p ), while the contributions of the other terms will be distributed over v -1  (t -K/2 ), . . . , v -1  (t K/2 ). 
     The third embodiment accordingly operates in the same way as the second embodiment, but small frequency deviations Δω are detected more accurately by v 1  (t p ) and v -1  (t p ) in the third embodiment than by y 1  (t p ) and y -1  (t p ) in the second embodiment, because the first terms of equations (25) and (26) are substantially canceled out in the data modifiers 17B and 17C. 
     The frequency-deviation detector 15 in the third embodiment need not compare v 1  (t p ) and v -1  (t p ); generally similar results can be obtained by comparing one of these two values with v 0  (t p ). 
     As shown by the embodiments described above, the present invention provides accurate, automatic tuning control over a wide range of frequency deviations, from large to small. 
     The invention is not limited to the above embodiments. The phase modifiers 12A, 12B, 12C, . . . , IFFT processors 13A, 13B, 13C, . . . , peak detectors 14A, 14B, 14C, . . . , data detectors 16B and 16C, and data modifiers 17B and 17C, which were embodied as separate functional blocks above, can be combined in various ways. For example, a single IFFT processor can be made to carry out all of the computations performed by the plurality of IFFT processors 13A, 13B, 13C, . . . . Alternatively, all of the processing carried out by the novel elements can be executed by a suitably programmed digital signal processor (DSP) or other general-purpose processor. 
     The method of the first embodiment can be combined with the method of the second or third embodiment, the first embodiment being used for coarse tuning and the second or third embodiment for fine tuning. Alternatively, all three embodiments can be combined, the first embodiment being used for coarse tuning, the second embodiment for fine tuning, and the third embodiment for very fine tuning. 
     The frequency-deviation detector may operate in various ways not described above. Depending on how the subcarriers are numbered, for example, the actions of increasing and decreasing the oscillation frequency of the voltage-controlled oscillator may be reversed from the above description. 
     The invention is not limited to QPSK-OFDM, but is applicable to other types of PSK-OFDM as well. 
     The invention being thus described, it will be obvious that the same may be varied in many ways. Such variations are not to be regarded as departure from the spirit and scope of the invention, and all such modifications as would be obvious to one skilled in the art are intended to be included within the scope of the following claims.