CA2256562A1 - A method of and an apparatus for training tap coefficients of an adaptive equalizer - Google Patents

Abstract

For training tap coefficients of an adaptive equalizer of L taps to be used for equalizing an impulse response of a transmission channel (200) to be shorter than ~ taps, stably and speedily, a training circuit comprises: a transmitter (100) for transmitting a transmission signal (x(D)) produced by converting a frequency-domain transmission vector (X) encoded with a PRBS into a time-domain; a target-impulse-response update means (1300) for producing an updated target impulse response (B u) making use of frequency-domain division method referring to windowed tap coefficients (W W(D)), a reception signal (y(D)), and a training vector (X) encoded with a replica of the PRBS; a target-impulse-response windowing means (1400) for outputting a windowed target impulse response (B w) together with a normalization coefficient (S) by windowing and normalizing the updated target impulse response (B u) within L taps in a time-domain; a tap-coefficient update means (2500) for updating the windowed tap coefficients (W w(D)) making use of a frequency-domain LMS method referring to the normalization co-efficient (S), the windowed target impulse response (B w), the training vector (X') and the reception signal (y(D)); and a tap-coefficient windowing means (1600) for windowing the updated tap coefficients into v taps. By updating the windowed tap coefficients (W W(D)) repeatedly until a certain convergence condition is attained, the windowed tap co-efficients (W W(D)) are outputted as the tap coefficients of the adaptive equalizer.

Description

CA 022~6~62 1998-12-18 A METHOD OF AND AN APPARATUS FOR TRAINING
TAP COEFFICIENTS OF AN ADAPTIVE E~UALIZER
BACKGROUND OF THE INVENTION
The present invention relates to a method of and an apparatus for 5 training tap coefficients of an adaptive equalizer, and particularly to the method of and the apparatus for optimi7ing tap coefficients of a FIR (Finite Impulse Response) filter used as an adaptive equalizer to equalize a multicarrier data signal that has beell transmitted through a distorting channel.
In a multicarrier data transmission system, input digital data are grollped into blocks, called symbols, of a certain number of parallel bits. The parallel bits of a symbol are further divided into a plurality of bit sets, and each of the bit sets is used to modulate each one of the same rlumber of carrier signals of different frequencies. A preferred method of modulation/demodulation is a modulation to use an IFFT
(Inverse Fast Fourier Transformation) and a demodulation to use a FFT (Fast Fourier Transformation).
FIG. 12 is a block diagram illustrating a system configuration of the multicarrier data transmission system, having a transmitter 300 20 comprising an encoder 120, an IFFT circuit 130 and a D/A (Digital to Analog) converter 140, and a receiver 400 for receiving a multicarrier data signal transmitted frorn the transmitter 300 through a transmis-sion chanllel 200, comprisillg an A/D (Analog to Digital) converter 410, a FFT circuit 430, a FEQ (Frequency-domain EQualization) cir-25 cnit 440 and a decoder 450. As to all adaptive equalizer 420 and atraining circuit 500, they will be described afterwards.
When a symbol consists of binary data of 512 bits for modulating CA 022~6~62 1998-12-18 256 carrier signals, for example, the encoder 120 divides the binary data into 256 sets of 2 bits, and encodes each n-th (n = 1 to 256) component of a 256-dimensional frequency-domain vector representing the 256 carrier signals by n-th of the 256 sets of 2 bits, as follows.
When logic of n-th 2-bit set is {0, 0}, {0, 1}, {1, 0} or {1, 1}, the n-th component of the frequency-domain vector is encoded as 1 + j, 1--j, --1 +.i or--1--j, for example, j being an imaginary.
The frequency-domain vector thus encoded is transformed into a time-domain digital signal by the IFFT circuit 130 and converted by 0 tlle D/A converter 140 into an analog signal to be transmittecl through the transmission channel 200 as the multicarrier data signal.
The multicarrier data signal received by the receiver 400 is sam-pled and converted into a time-domain digital signal by the A/D con-verter 410 and further transformed into a frequency-domain vector by the FFT circuit 430. The FEQ circuit 440 performs frequency-domain equalization of the frequency-domain vector for compensat-ing distortion of the frequency-domain vector due to attenuation and delay caused through the transmission channel 200, and the decoder 450 reproduces the symbol data by decoding each component of the 20 frequency-domain vector.
However, when duration of the impulse response of the transmis-sion channel 200 is not negligible compared to symbol length, inter-symbol interference, that is, interference of a symbol with a preceding or a following symbol, or inter-channel interference, that is, interfer-25 ence of a signal of a carrier frequency with signals of neighboring car-rier frequencies due to transmission distortion becomes clominant and impossible to be compensated by the above frequency-domain equal-CA 022~6~62 1998-12-18 zatlon.
A method developed for dealing with this problem is to shorten duration of the impulse response by compensating and equalizing the time-domain digital signal sampled by the A/D converter 410, by per-5 formin~ convolution of the time-domain digital signal through a FIR
filter 420 provided between the A/D converter 410 and the FFT circuit 430, and the training circuit 500 for optimi7,ing tap coefficients of the FIR filter 420 so as to correctly equalize the tr~,n.~mi~.~ion characteristic of the tr~,n.~mi.~sion channel 200.
A usual method of optimizing the tap coefficients of the FIR filter 420 is to repeatedly generate and transmit a PRBS (Pseudo-Random Binary Sequence) from the transmitter 300, and to make each of the tap coefficients converge into an optimum value at the receiver 400 by comparing the signal received from the transmitter 300 with a corre-sponding signal obtained from the same PRBS generated at the re-ceiver side. The FIR filter 420 which has variable tap coefficients to be optimizecl for equalizing duration of the impulse response is here-inafter called the adaptive equalizer, and a process of and a means for optimizing the tap coefficients are called the training and the training 20 circuit.
The present invention pertains to the training method and the training circuit for stably and rapidly optimi7,ing tap coefficiellts of the adaptive equalizer.
As a prior art of the trainiIlg method, there is a technique disclosed 25 in a United States Patent No. 5,285,474.
FIG. 13 is a block diagram illustrating a training circuit according to the prior art. The training circuit of FIG. 13 consists of a transmitter CA 022~6~62 1998-12-18 100 and a receiver 1000 and performs training of tap coefficients of an adaptive equalizer (not depicted in FIG. 13) provided in the receiver 1000 for equalizing signal distortion due to transmission characteristic of a tr~,nsmi.~.sion channel 200 connecting the transmitter 100 and the 5 receiver 1000.
The transmitter 100 comprises a first PRBS generator 110 for generating a PRBS signal, a first encoder 120 for encodillg the PRBS
si~nal into a frequency-domain tr~ mi~ion signal vector X, an IFFT
circuit 130 for transforming the frequency-domain transmission sig-10 nal vector X into a time-domain transmission signal x(D). (Here-inafter, a frequency-domain vector is denoted by a capital letter and a time-domain signal obtained by processing the frequency-domain vec-tor with IFFT is expressed as a function of discrete delay variable D
denoted by a corresponding small letter.) The time-domain tr~,n.~mi.~.~ion signal x(D) is converted into ana-log si~nal, transmitted through the tr~,n.~mi.~ion channel 200, received by the receiver 1000 and converted again into a time-domain reception signal 1J(D). (Ordinary elements such as D/A and A/D converters are omitted to depict in FIG. 13.) Here, following equation stands;
~J(D) = x(D) * h(D) + n(D)~
wherein h(D) and n(D) represent the impulse response and the noise signal of the transmission channel 200, and the operator '*' denotes convolution operation.
The above equation is expressed as Y = XH + N in the frequency domain.
The receiver 1000 comprises a second PRBS generator 1200 for CA 022~6~62 1998-12-18 generatillg a replica of the PRBS signal generated by the first PRBS
~,enerator 110, a second encoder 1250 for generatil1g a frequency-domain training vector X' by encoding a frequemcy domain vector with the replica of the PRBS signal in the same way and in synchro-5 nization with the first encoder 120, a target-impulse-response update means 1300, a target-impulse-response windowing means 1400, a tap-coefficient update means 1500 and a tap-coefficient winclowing means 1600.
The target-impulse-response update means 1300, the target-10 impulse-respol1se winclowing means 1400, the tap-coefficient update means 1500 and the tap-coefficient winclowing means 1600 operate so as to make tap coefficients of the adaptive equalizer having L taps (L
being a fixed integer) converge into optimum values which enable the adaptive equalizer to equalize and shorten the duration of the impulse 15 response H, or h(D), of the transmission channel within v taps (v being another fixed integer), that is, within target duration of the equalized impulse response, by updating transitional values of the target impulse response and the tap coefficients alternately and repeatedly, referring to the reception signal ~(D) and the training vector X'.
In the following paragraphs, outlines of operation of the target-impulse-response update means 1300, the target-impulse-response Will-clowing means 1400, the tap-coefficient update means 1500 ancd the tap-coefficient windowing means 1600 will be described in the order.
The target-impulse-response update means 1300 outputs an up-25 dated target impulse response Bl, by updating a windowed target im-pulse response Bw outplltted from the target-impulse-response win-dowing means 1400 (as will be described afterwards), making use of CA 022~6~62 1998-12-18 the reception signal ~J(D), the trainil1g vector X' and winclowed tap co-efficients utlu(D) outputted from the tap-coefficient windowillg means 1600 (as will be describecl also afterwards), so that the upclated target impulse response BU better approximates the frequency-domain vector 5 HW of the equalizecl impulse response h(D) * w~u(D) of the transmis-SiOll channel 200 (Hereinafter, the subscript "u" refers to an upclated quantity and the subscript "w" refers to a windowed quantity.) In other words, the target-impulse-response update means 1300 asymptotically and recursively revises the windowed target impulse 10 response B,u towards a target, that is, a frequency-domain vector of all impulse response whereof duration can be equalized withill v taps by the adaptive equalizer.
First, initial values of the windowecl target impulse response BW
and the tap coefficients w~u(D) are set reasonably, then a loop of steps is repeated until a predetermined collvergence conditioll is reached.
The windowed target impulse response Bw is updated making use of either a frequency-domaill LMS (Least Meall Sqlrare) method or a frequency-domaill division method.
When the frequency-domain LMS method is employed, an error 20 value E is calculated according to following equation (1) as a differ-ence betweell the windowed target impulse response Bw multiplied by the training vector X/~ which corresponds to a target reception signal, and the frequency-domaill reception signal vector Y multiplied by a frequency-domain vector Wlu of the windowed tap coefficients ww(D)~
25 which corresponds to the equalized reception signal.
E = Bwxl--WIuY (1) Then, the updated target impulse response Bu is obtained accord-CA 022~6~62 1998-12-18 inbr to followiug equation (2) from the error value E.
BU = BW + 2~1EX*, (2) where 11 is the LMS stepsize ancl X* clenotes the complex conjugate of the training vector X'.
When the frequency-domain division method is ernployed, the up-dated target impulse response BU is calculated from above equation (1) as the windowed impulse response BW which gives the error value E = 0, as follows;
BU = WWY/X'. (3) The target-impulse-response windowing means 140() windows the updated target impulse response BU into the windowed target impulse response BlU having v taps in the time-domain, as follows.
The updated target impulse response B,, is transformecl into a time-domain signal bU(D) through the IFFT, whereof consecutive v taps (or samples), which give a maximum total power, are selected, zeroing other taps. The selected consecutive v taps are then normalized to have a fixed power for preventillg the training from converging into the all-zero, that is, Bw = ww(D) = 0. The normalized time-domain signal bW(D) of v taps is transformed again into a frequency-domain 20 vector through the FFT and outputted as the windowed target impulse response BlU, to be updated at the next step by the target-impulse-response update means 1300.
The tap-coefficiellt update mealls 1500 updates the willdowed tap coefficients ~UlU(D), in a similar way with the target-impulse-response 25 update means 1300, that is, produces an updated tap-coefficient vector Wu by upclating the windowed tap coefficients ww(D) outputted from the tap-coefficient windowing means 1600 after windowed into L taps, CA 022~6~62 1998-12-18 referring to the windowecl target impulse response Bw outputted from the target-impulse-response windowillg means 1400, the time-domain reception si~,nal ~J(D) and the training vector X', so as to recluce the error value E given by above equation (1), m~l~ing use of the freqllency-5 domain LMS method or the frequency-domain division method.
The upclated tap-coefficient vector Wu is calculated according to following equation (4) when the frequency-domain LMS method is ap-plied, or according to equation (5) when the frequency-domain division method is applied.
lo Wu = W~u + 2,uEY* (4) Wu = B,UY/X', (5) where ~l is the LMS stepsize, W~u is the frequency-domaill vector of the windowed tap coefficients ww(D)7 and X* denotes the complex conjugate of the training vector X'.
The tap-coefficient windowing means 1600 windows the updated tap-coefficient vector W~, with a time-window of L taps in a similar way with the target-implllse-response windowing means 14()0, as follows.
The updated tap-coefficiellt vector Wu is expandecl in the time-domain as the updated tap coefficients wu(D) through the IFFT, 20 whereof consecutive L taps (coefficients) which give a maximum to-tal power are selected, zeroing other taps. The selected consecutive L
tap coefficiellts are outputted as a first to an L-th component of the willdowed tap coefficients wlu(D), which are to be referred to by the target-implllse-response update mealls 1300 and to be upclated by the 25 tap-coefficient update means 1500 at the next step of the convergence loop.
In the prior art of FIG. 13, by generating the PRBS signals repeat-CA 022~6~62 1998-12-18 edly in synchronization with each other at the transmitter 100 and the receiver 1000, the trainillg steps at the target-implllse-respollse update means 1300, the target-impulse-respollse windowillg means 1400, the tap-coefficient update means 1500 and the tap-coefficient windowing 5 means 1600 are repeated until a predetermined convergence condition is reached, that is, until the error value E of equation (1) becomes within a threshold value, for example, and by applying convergence values of the winclowed tap coef~cients ww(D) thus obtained to the tap coefficients of the adaptive equalizer, the inter-symbol interference and 0 the inter-channel interference are eliminatecl from the reception signal transmitted through the severe transmission cannel, impulse response duration of the transmission channel being equalized and sufficiently shortened by the adaptive equalizer.
In the above prior art, either or both of the windowed target 15 impulse response B2U alld the windowed tap coefficients ww(D) may be updated either one of the frequellcy-domaill LMS method and the frequency-domain division method. Therefore, following four applica-tions call be considered:
1. To update both the windowed target impulse response BW and 20 the windowed tap coefficients ww(D) m~lcing use of the frequency-domain LMS method;

2. To update the windowed target impulse response B2U m~l~ing use of the frequency-domain LMS method, and the windowecl tap co-efflcients ww(D) m~l~ing use of the frequency-domain division method;

3. To update the winclowecl target impulse response B2U m~l~ing use of the frequellcy-domaill division method, and the windowed tap coefficients w2u(D) m~l~ing use of the frequency-domain LMS method;

CA 022~6~62 1998-12-18 and 4. To update both the winclowed target impulse response BW ancd the windowecl tap coefflcients ww(D) making use of the frequency-domain division method.
5However, the first and the fourth application wherein both the windowed target impulse response Bw and the windowed tap coeffi-cients wlv(D) are updated with the same methocl do not always give stable convergence. Therefore, when the tap number L of the adaptive equalizer is larger than the duration v of the target impulse response, 10 the seconcl application is usually employed, and the third application is employed usually when the tap number L is smaller than the target duration v.
When the third application is employed, that is, when the win-dowed tap coefflcients ww(D) is upclated by the frequency-domain LMS
15 method, however, following problems have been observed.
First, it takes certainly long time for the windowed target impulse response B,u or the windowed tap coefficients wlu(D) to converge. This is because the normalization, which is performed in the target-impulse-response windowing means 1400 for preventing the training from con-20 verging into Bw = ww(D) = 0, of the selected consecutive v taps of thetime-domain target impulse response bl,(D) affects the first term BlUX' of the rigllt side of ecluation (1) for giving the error value E to be used ill equation (4) to calculate the updated tap coefficient vector T~u, and makes the error value E at the tap-coefficient update means 1500 not 25 equivalent to the error value E at the tar~et-impulse-response update means l3no.
Second, the windowed target impulse response Bw or the windowed CA 022~6~62 1998-12-18 tap coefficients ~U~U(D) may rather diffuse than converge because of the same reason, when the noise signal n(D) of the tr~n.~mi.ssion channel is comparatively large.
SUMMARY OF THE INVENTION
Therefore, a primary object of the present invention is to provide a methocl of ancl apparatus for training tap coefficients of an adaptive equalizer stably in a short time by resolving above problems.
In order to achieve the object, in an embodiment according to the invention, a normalization coefficient S is outputted when normaliza-0 tion is performed for obtaining the windowed target impulse response B2", and referring to the normalization coefficient S, the revision of the windowed rap coefficients ww(D) is performed making use of the frequency-domain LMS method according to following equations;
Wu = SWW + 2,uE'Y*
E' = BWX'--SWu~Y
More concretely, in the method according to the embodiment of training tap coefficients of an adaptive equalizer havillg a first number of taps, for equalizing duration of an impulse response of a transmission channel to be shorter than a second number of taps with a sufficiently 20 small error, having a step of initializing windowed tap coefficients to some predetermined values, a step of repeating a training procedure until a certain convergence condition of the windowed tap coefficients is attained, alld a step of outputting the windowed tap coefficients as the tap coefficients of the adaptive equalizer after the certain convergence 25 condition is attained; the training procedure comprises:
a transmission step of trallsmitting a tr~.n.smi.~sion signal x(D) which is produced by transforming a frecluency-domain transmission CA 022~6~62 1998-12-18 vector X encoded with a PRBS (Pseudo-Random BinaIy Sequence) into a time-domain;
a target-impulse-response update step of producing an updated target impulse response Bu by dividing an equalized reception signal 5 vector Z with a trainillg vector ~'', the equalized reception signal vec-tor Z being produced by transforming an equalized reception signal z(D), which is obtained by processing the tr~n~mi.~.sion signal ~(D) received througll the transmission chamlel with an equalizer having the first mlmber of taps whereof coefficients are set to have values of 10 the willdowed tap coefficients wlu(D)~ into a frequency-domain, and the training vector X being produced by encoding a frequency-domain vector with a replica of the PRBS;
a target-impulse-response windowillg step of outputting a win-dowed target impulse response Bw together with a normalization co-efficient S, the windowed target impulse response Bl,, being produced by transforming the upclated target impulse response B.u illtO a time-domain upclatecl target impulse response signal bU(D), selectillg the second llumber of consecutive tap values giving a maximum total power from tap values of the time-domain updated target impulse response 20 bU(D), normalizing the selected consecutive tap values and transform-ing the normalized consecutive tap values into the frequency-domain, and the normalization coefficiellt S being obtained by dividing the nor-malized conseclltive tap values with the selected consecutive tap values before normalization;
a tap-coefficient update step of producing an updated tap coeffi-cient vector Wll by updating a frequency-domaill tap coefficient vec-tor Ww multiplied by the normalization coefficient S malring use of CA 022~6~62 1998-12-18 a frequency-domaill LMS (Least Mean Square) metllocl with an error value E' defined as a dif~erence of a product of the training vector X' and the windowed target impulse response B " to a product of the nor-malizatioll coefficient S, the frequency-domaill tap coefflcient vector 5 W~u and a reception sigllal vector Y, the frequency-domain tap coef-ficient vector Wlu being obtained by transforming the windowed tap coefficiellts ww(D) into the frequency-domain, and the reception sigllal vector Y being obtained by transforming the tr~1l.smi.ssion signal ~(D) received through the transmission channel into the frequency-domain;
10 and a tap-coefficient windowillg step of producing the windowed tap coefficiellts u)1l,(D) by transforming the updated tap coefficient vec-tor Wu into updatecl tap coefficients wu(D)~ selecting the first number of consecutive coefflcients giving a maximum total power from coeffi-cients of the updated tap coefficients wu(D) and shifting the selected consecutive coefficients to be assigned from a top of the windowed tap coefficients wl"(D).
Therefore, the windowecl tap coefficiellts ww(D) call be updatecl more effectively according to the embodiment than the prior art of 20 FIG. 13, by thus reflectillg the normalization coefficient S obtained at the target-impulse-respollse windowing step along with the window-ing process of the time-domain upclated target impulse response signal l)l.(D), on the frequency-clomaill LMS operatioll for producing the up-dated tap coefficient vector Wu, enabling to shorten the convergence 25 time ancl to improve robustness of the training operation against noises.
Ill allother embodimellt of the illvelltioll, the llormalization is per-formed whell windowing of the updated tap coefficients wu(D) is per-CA 022~6~62 1998-12-18 formed, and the revision of the windowed target impulse response BW
is performed referring to the windowed tap coefficients wtu(D) after the normalization.
For the purpose, the target-impulse-response windowing step, the 5 tap-coefficient update step and the tap-coefficient windowing step of the above embodimçnt are replaced with following respective steps, that is:
a target-impulse-response windowing step of producing the win-dowed target impulse response BW by transforming the updated target 0 impulse response BU into the time-domain updated target impulse re-sponse signal bU(D), selecting the second number of consecutive tap values giving a maximum total power from tap values of the time-domain updated tarbret impulse response bU(D) and transforming the selected consecutive tap values into the frequency-domain;
a tap-coefficient update step of producing the updated tap co-efficient vector Wu by updating the frequency-domain tap coefficient vector Wtu makillg use of the frequency-domain LMS method with an error value E defined as a difference of a product of the trailling vector X' and the windowed target impulse response BW to a product of the 20 frequency-domain tap coefficient vector Ww and the reception signal vector Y; and a tap-coefficient windowing step of producing the windowed tap coefficients ww(D) by transforming the updated tap coefficient vector Wu into updated tap coefficients wu(D), selecting the first number of 25 consecutive coefficients giving a maximum total power from coefficients of the updated tap coefficients wu(D), norm~li7.ing the selected cosecu-tive coefficients and shifting the normalized consecutive coefficients to CA 022~6~62 1998-12-18 be assigned from a top of the windowed tap coefficients ww(D).
Therefore, effective revision of the windowed tap coefficients ww(D) considering the normalization can be realized also in this em-bodiment in the same way with the previous embodiment, enabling to 5 shorten the convergence time and to improve robustness of the training operation against noises, without expressly retaining conformity of the normalization by way of the normalization coefficient S as required in the previous embodiment.
When the windowed target impulse response BW is to be updated 0 making use of the frequency-domain LMS method and the windowed tap coefficients wlu(D) are to be updated m~l~ing use of the frequency-domain division method, the target-impulse-response update step, the tap-coefficient update step and the tap-coefficient windowing step may be replaced with following respective steps, that is:
a target-impulse-response update step of producing the updated target impulse response BU by updating the windowed target impulse response BW multiplied by a normalization coefficient S m~l~ing use of the frequency-domain LMS method with an error value defined as a difference of a product of the normalization coefficient S, the training 20 vector X' and the windowed target impulse response BW to a product of the frequency-domain tap coefficient vector W,u and the reception signal vector Y;
a tap-coefficient update step of producing an updated tap coeffi-cient vector Wu by dividing a product of the windowed target response 25 BW and the reception signal vector Y with the training vector X'; and a tap-coefficient windowing step of outputting the windowed tap coefficients ww(D) together with the normalization coefficient S, the ... .. . .

CA 022~6~62 1998-12-18 windowed tap coefficients ww(D) being produced by transforming the updated tap coefficient vector Wu into updated tap coefficients wu(D), selecting the first number of consecutive coefficients giving a maximum total power from coefficients of the updated tap coefficients wu(D)~
5 normali7illg the selected consecutive coefficients and shifting the nor-malizecl consecutive coefficients to be assigned from a top of the win-dowed tap coefficients wlu(D)~ and the normalization coefficient S being obtainecl by dividing the normalizecl consecutive coefficients with the selected consecutive coefficients before normalization.
BRIEF DESCRIPTION OF THE DRAWINGS
The foregoing, filrther objects, features, and advantages of this invention will become apparent from a consideration of the follow-ing description, the appended claims, and the accompanyillg drawings wherein the same numerals indicate the same or the corresponding 15 parts.
In the drawings:
FIG. 1 is a blocl~ diagram illustrating a training circuit according to an embodiment of the invention;
FIG. 2 is a bloclc cliagram illustrating an internal configuratioll of 20 the target-impulse-respollse update means 1300 of FIG. l;
FIG. 3 is a block diagram illustrating an internal configuration of the target-impulse-response windowing means 1400 of FIG. 1;
FIG. 4 is a blocl~ diagram illustratillg an internal configuration of the tap-coefficient upclate means 250n of FIG. 1;
FIG. 5 is a blocl~ diagram illustrating an internal configuration of the tap-coefficient windowing means 1600 of FIG. 1;
FIG. 6 is a graphic chart schematically illustrating windowing of ... . ..

CA 022~6~62 1998-12-18 a time-domain tarbret impulse response bU(l~);
FIG. 7 is a graphic chart schematically illustrating windowil1g of updated tap coefflcients wu(D);
FIG. 8 is a block diagram illustrating a functiol1al configuratiol1 of 5 a training circuit according to another embodiment of the invention;
FIG. 9 is a blocl~ diagram illustrating an internal configuration of the target-impulse-response windowing means 3400 of FIG. 8;
~ FIG. 10 is a blocl~ diagram illllstrating an intell1al configuratio of the tap-coefflcient update rneans 350() of FIG. 8;
FIG. 11 is a block diagram illustrating an internal configuration of the tap-coefflcient windowing means 3600 of FIG. 8;
FIG. 12 is a block diagram illustrating a system configuration of a multicarrier data transmissiol1 system; and FIG. 13is a block diagrarn illustrating a training circuit accorcling 5 to a prior art.
DETAILED DESCRIPTION OF THE PREFERRED
EMBODIMENTS
Now, embodiments of the present inventiol1 will be described in connection with the drawil1gs.
FIG. 1 is a blocl~ diagram illustrating a training circuit according to an embocliment of the invention, comprising a transmitter 100 and a receiver 2000 for trai~ g tap coefficients of an adaptive equalizer (not clepictecl in the drawings) proviclecl in the receiver 2000 in accor-dance with transmissiol1 characteristics of a tr~ll.sn~i.ssion chal1nel 200 connectil1g the transmitter 100 ancl the receiver 2000.
The tral1smitter 100 comprises, in the same way with the trans-mitter 100 of FIG. 13, a first PRBS generator 110 for generating a CA 022~6~62 l998- l2- l8 PRBS signal, a first encoder 12n for encodillg the PRBS signal into a frequellcy-domaill transmissioll si~,nal vector X, an IFFT circuit 130 for transforming the frequency-domaill tr~l-.smi.~.sion signal vector X
into a time-domain transmission signal x(D).
The time-domain tr~n.smi.~.sion signal x(D) is converted into ana-log signal, trallsmittecl through the tr~n.~mi.~sion channel 200, received by the receiver 2000 ancl sampled and converted again into a time-domain reception signal v(D). (Ordinary elements such as D/A and A/D converters are omitted to depict also in FIG. 1.) lo Similarly to the receiver 1000 of FIG. 13, the receiver 2000 com-prises a second PRBS gellerator 1200 for generatillg a replica of the PRBS si~,nal generated by the first PRBS generator 110, a second encoder 1250 for generatillg a frequency-domaill traiIling vector X' by encoding the replica of the PRBS signal in the same way and in synchronization with the first encoder 120, a target-impulse-response update means 1300, a target-impulse-response windowing means 1400, a tap-coefficient update means 2500 and a tap-coefficient windowing means 1600.
A difference from the receiver 1000 of FIG. 13 is that the tap-20 coefficient update means 2500 is provided in place of the tap-coefficient update means 1500 which updates the winclowed tap coefficients wtu(D) referring to the windowecl target impulse response B~u outputted from the tcarget-impulse-response windowing means 1400, the time-domain receptioll sigllal ~(D) and the trainillg vector X'.
The tap coefficient update means 2500 of FIG. 1 updates the win-dowed tap coefficients wlu(D) further referring to a norrnalizatioll co-efficient S employecl in the normalization of the time-domain target CA 022~6~62 1998-12-18 impulse response bW(D) performed in the target-impulse-response Will-dowing means 1400, in additioll to the windowed target impulse re-sponse BlU, the time-domain reception signal ~J(D) and the training vector X'.
The target-impulse-response update means 1300, the target-impulse-respollse windowing means 1400, the tap-coefficient update mealls 2500 and the tap-coefficient windowing means 1600 operate, in the same way with the prior art apparatus of FIG. 13, so as to make tap coefficients of the adaptive equalizer having L taps (L being a fixed 0 integer) converge into optimum values which enable the adaptive equal-izer to equalize and shorten the duration of the impulse response H, or h(D), of the tr~n.~mi.~.~ion channel within v taps (v being another fixed integer), that is, within target cluration of the equalized impulse re-spollse, by updating transitional values of the target impulse response 15 and the tap coefficients alternately and repeatedly, referring to the time-domain reception signal ~J(D) and the training vector X'.
In the following paragraphs, detailecl configurations and operation of the target-impulse-respollse update means 1300, the target-impulse-response windowing means 1400, the tap-coefficient update means 2500 20 and the tap-coefficient windowing means 1600 will be described in the order.
FIG. 2 is a block diagram illustrating an internal configuration of the target-implllse-respollse update means 1300 of FIG. 1.
Referring to FIG. 2, the target-impulse-response update means 25 1300 comprises a convolution unit 1370, an FFT unit 1380, and a divider 1390, and upclates the windowed target impulse response B~u m~ ing use of the frequency-domain division method.

CA 022~6~62 1998-12-18 The convollltioIl unit 1370 consists of a FIR filter having L taps, which may be the adaptive equalizer itself, and tap coefficients thereof are set with values of the windowecl tap coefficiellts wlu(D) outputted from the tap-coefficient windowillg means 1600, or with reasonable 5 values at the beginning of the training. The convolution unit 1370 performs convolution operation onto the time-domain reception signal v(D) and OUtplltS an equalized reception signal z(D) = uJ~,(D) * ~J(D).
The FFT Ullit 1380 performs discrete Fourier transformation onto the equalized reception signal z(D) for producing a frequency-domain 0 equalized reception signal vector Z = T~UY.
The divider 1390 outputs the updatecl target impulse response BU by dividing each compouent of the frequency-domain equalized re-ception signal vector Z by a corresponding component of the training vector X'.
Thlls, the target-impulse-response update means 1300 procluces the updated target impulse response calculated as follows;
Bl, = WluY/X~ (3) m~l~ing use of the frequency-domain division method.
FIG. 3 is a blocl~ ~liagram illustratillg an internal con~,uratio 20 of the target-impulse-respollse windowing means 1400 of FIG. 1, com-prisin~ an IFFT Ullit 1410, a winclowin~ section 1420 and a FFT unit 1460. The windowing section 1420, comprising a selection unit 1430, a winclowing unit 1440 alld a normalization unit 1450, tal~es charge of cuttin~, out a time-domain signal with a time window of v taps de-25 fined by a window functioll as illustrated in a graphic chart of FIG. 6,wherein tlle time-clomaill discrete sigllal is depicted as a colltinuous signal.

~ . . ..

CA 022~6~62 l998- l2- l8 The IFFT unit 1410 performs an inverse discrete Fourier trans-formation of the updated target impulse response Bu outputted from the target-impulse-respollse update means 1300 for producing a time-domain target-impulse-response bU(D) to be processed by the window-5 ing section 1420.
In the windowill~, section 1420, the selection unit 1430 selects COll-secutive v taps ~ivillg a maximum total power from a tap sequence of the time-domain target-impulse-respollse bU(D), other taps of the tap sequence being suppressed to zero by the windowing unit 1440. The 0 selected consecutive v taps are then normalized by the normalization Ullit 1450, so that a stanclard deviation of the selected consecutive v taps becomes 1, for example. This normalizatioll is performed for pre-venting the training process from converging into bW(D)--ww(D) = 0.
Thus, the winclowed target impulse response bW(D) in the time-domain is outputtecl from the windowing section 1420. The FFT unit 1460 produces the windowed target impulse response BlU by trans-forming the windowed time-domain impulse response bU,(D) into the frequency-domain.
Here, in the embodiment, the normalization unit 1450 outputs a 20 normalization coefficient S, which is supplied to the tap-coefficient up-date means 2500 in parallel with the windowed target impulse response B~". In the above example, the normalization coefficient S is calculated as S = 1/(J, (J being the standard deviation of the selected consecutive v taps before the normalization.
FIG. 4 is a block dia~ram illustrating an internal configuration of the tap-coe~cient update means 2500 of FIG. 1, wherein the tap coefflcients lu~u(D) is updated m~killg use of the frequency-dornain LMS

CA 022~6~62 1998-12-18 method, in the embocIiment.
Referring to FIG. 4, the tap-coefficient update means 2500 com-prises;
a first FFT Ullit 151() for transformillg the reception signal ~(D), 5 which is the same with the reception signal ~(D) supplied to the target-impulse-response update means 1300, into a frequency-domain recep-tion signal vector Y, a second FFT unit 1520 for transforming the tap coefficient wtu(D), which is also the same with the tap coefficients ww(D) supplied 0 to the target-impulse-response update mealls 1300, into a frequency-domain tap coefficient vector Ww, a first multiplier 1525 which multiplies the normalization coef-ficient S supplied from the target-impulse-response windowing means 1400 onto each component of the frequency-domain tap coefficient vec-tor WIu,a second multiplier 1530 for multiplying each cornponent of the OUtpllt vector SWIu of the first multiplier 1525 onta a corresponding component of the frequellcy-domaill reception signal vector Y, a third multiplier 1540 for multiplying each component of the win-20 dowed target impulse response Bw supplied from the target-impulse-response windowing means 1400 onto a corresponding component of the training vector X', which is the same with the training vector X' suppliecI to the target-impulse-respollse update means 1300, a subtracter 1550 for producing the error value E' by subtracting 25 an output vector ST~uY of the second multiplier 1550 from an output vector BlUX' of the third mllltiplier 1540, and a frequency-clomain LMS Ullit 1560 for calculating ancl outputting .~, .

CA 022~6~62 1998-12-18 the updated tap-coefficient vector Wu from the error value E', the output vector SW~, of the first multiplier 1525, and the frequency-domain reception signal vector Y outputted from the first FFT unit 1510.
Having the above configllration, the tap-coefficient update means 2500 outputs the updated tap coefficient vector Wu which is defined by following equations;
Wu = SWw + 2,uE'Y* (6) E' = B",X'--SWwY (7) Therefore, the tap-coefficient update means 2500 according to the embodiment can upclate the windowed tap coefficient vector Ww more effectively than the prior art of FIG. 13, by thus reflecting the nor-malization performed in the target-impulse-response windowing means 1400 along with the windowing process of the time-domain target im-pulse response l~U(D) on the frequency-domain LMS operation for pro-ducing the updated tap coefficient vector Wu, enabling to shorten the convergence time and to improve robustness of the t~aining operation against noises.
FIG. 5 is a block diagram illustrating an internal configuration 20 of the tap-coefficient windowing means 1600 of FIG. 1, comprising an IFFT unit 161() and a windowing section 1620. The windowing section 1620, comprising a selection unit 1630, a windowing unit 1640 and a tap shift unit 1650, takes charge of cutting out L consecutive tap coefficients from a sequence of tap coefficients given as a time-domain 25 discrete signal with a time window of L taps defined by a window fullctioll as illustrated in a graphic chart of FIG. 7, wherein also the tap coefflcients consisting of discrete values are depicted as a continuous CA 022~6~62 1998-12-18 signal.
The IFFT unit 1610 performs an inverse discrete Fourier trans-formation of the updatecl tap coefficient vector Wu outputtecl from the tap-coefficient upclate means 2500 for producin~, upclatecl tap coeffi-5 cients wu(D) to be processed by the windowing section 1620.
In the windowing section 1620, the selection unit 1630 selects con-secutive L tap coefficients giving a maximum total power from a co-efficient sequence of the updated tap coefficients wu(D)~ other tap co-efficients of the coefficient sequellce bein~, suppressed to zero by the 0 winclowing unit 1640. The selected consecutive L tap coefficients are then shifted to the first to L-th coefficients by the tap shift unit 1650 for producing the windowed tap coefficients ww(D) to be outputted.
The tar~,et-impulse-response update means 1300 refers to the win-dowed tap coefficients ww(D) for producing the updated target impulse response Btl to be outputted to the target-impulse-response window-ing means 1400 at the next step, and the tap-coefficient update means 2500 llpdates again the winclowed tap coefficients ~ u(D) referring to the windowed target-impulse-respollse B~u outputted from the target-impulse-response windowing means 1400 at the next step.
Thus, the revision of the windowed target impulse response BW
and the windowed tap coefficients w~u(D) are performed repeateclly and alternately throu~ the target-impulse-response update rneans 1300, the tar~et-impulse-lespollse winclowing mealls 14()0, the tap-coefficient llpdate means 25()0 and the tap-coefflcient windowing means 1600, by 25 generatiIlg the same PRBS signals repeatedly iIl synchrol1ization by the first PRBS generatol 110 of the transmitter 100 and the second PRBS gellerator 1200 of the receiver 2000, until a certain predeter-~, .. .

CA 022~6~62 1998-12-18 mined conclitioll is reached, and through this repetition, the windowecl tap coefficients w",(D) are trained into coefficient values which enable the adaptive eqllalizer to equalize and shorten duration of impulse re-sponse of the reception signal ~J(D) transmitted through the trallsmis-5 sion channel 200 witllil1 v taps with an error sufficiently srnall.
The convergence condition applied in the embodiment is a condi-tion that the total power of the consecutive L tap coefficients, selected by the selection unit 1630 of the tap-coefficient windowing means 1600, of the updated tap coefficients w1"(D) becomes sufficiently large com-0 parecl to a total power of the other tap coefficients thereof. However,other appropriate conditions such as a condition that the error value E' obtained from equation (7) becomes within a threshold value, or a condition that the repetition times of the above convergence process attains to a predetermined number may be used indepelldently or in 15 combination.
FIG. 8 is a block diagram illustrating a functional configuration of a trainiIlg circuit according to another embodiment of the invention.
Instead of the receiver 2()00 of the embodiment of FIG. 1, the training circuit of FIG. 8 has a receiver 3000, wherein the target-20 impulse-respollse windowing means 1400, the tap-coefficient update means 25no and the tap-coefficient windowing means 1600 of FIG. 1 are replaced by a target-impulse-response windowing means 3400, a tap-coefficient update means 3500 al1d a tap-coefficient windowing means 3600, respectively. Other elements ancl their operation are the same 25 with correspondiIlg elements of FIG. 1, and the duplicatecl description is omitted.
FIG. 9 is a blocl~ diagram illustrating an interl1al configuration of . . . ~

CA 022~6~62 1998-12-18 the target-impulse-respollse windowillg means 3400 of FIG. 8, whereill the windowillg section 1420 of FIG. 3 is replaced with a windowing section 3420 not havillg the normalization unit 1450. As can be under-stood from FIG. 9, in the target-impulse-respollse windowing means 5 3400, the normalization of the consecutive v taps selected ancl win-dowed from the time-domain target impulse response bu (D) is not performed, and conseqllently, the normalization coefficient S is not olltputted.
Hence, the tap-coefficient update means 3500 has an internal con-10 figuration wherein the first multiplier 1525 is omitted from the tap-coefficient update means 2500 of FIG. 4, as illustrated iIl a block dia-gram of FIG. 10, and the frequency-domain tap coefficient vector T~,u r)roduced by the second FFT unit 1520 is supplied as it is to the second multiplier 1530 and the frequency-domain LMS unit 1560.
The frequellcy-domaill LMS unit 1560 produces the updated frequency-domain tap coefficient Wu accordillg to following equation (4) previously described in connectioll with the prior art training cir-cuit of FIG. 13;
Wu = WtU + 2,uEY*. (4) On the other hand, in a windowing section 3620 of the tap-coefficient windowing means 3600 whereof an internal configuration is illustrated in FIG. 11, a normalization unit 3660 is further com-prised iIl addition to the configuration of the windowillg sectioll 1620 of FIG. 5.
Being provided between the willdowing unit 1640 and the tap shift unit 1650, the normalizatioll ullit 3660 takes charge of llormali%ing consecutive L tap coefficients outplltted from the windowing unit 1640 CA 022~6~62 1998-12-1X

after windowed, so as to give a stalldard deviatioIl of 1. The tap sllift unit 1650 shifts the windowed L taps thus llormalized for assigllillg them from the first to the L-th tap coefficiellt composiIlg the wiIldowed tap coefficients ww(D) to be outputted.
5Referring to the willdowed tap coefficieIlts wlu(D) thus obtaiIled, the target-impulse-respollse update meallsl30() of FIG. 8 produces alld outputs the updated target impulse respollse Bu at the llext step to the target-imPU1Se-reSPO11Se Wi11dOWi11g meaI1S3400, alld the tap-coefficieIlt update means 3500 updates agaill the windowed tap coefficiellts ww(D) 0 referring to the windowed target-impulse-respollse BlU outputted frorn the target-impulse-response windowiIlg mealls 3d~00 at the Ilext step.
II1 the secolld embodirrleIlt of FIG. 8, by thus llor~ .li7il-~g the windowed tap coefficiellts ww in the tap-coefficieIlt willdowiIlg meaIls 3600, the traiIliIlg process can be as well preveIlted from mal-coIlvergiIlg into bU(D)--ww(D) = 0, as in the first embodirneIlt of FIG. 1 and the prior art of FIG. 13.
Ill the target-impulse-response update meaIls 1300, the updated target impulse response BU is produced makiIlg use of the fieclueIlcy-domaill division method accordiIlg to the ecluatioIl (3), that is, iIl pro-20 portioIl to the windowed and llormalized tap coefficiellts ww(D)~ alld based Oll the updated target impulse Bu thus obtailled, recursive revi-SiOll of the willdowed tap coefficiellts ww(D) is coIltiIlued.
Therefore, effective revisioll of the windowe(l t~Lp coefficients ww(D) consideriIlg the norrrlalizatioIl caIl be realized also iIl the em-25 bodimellt of FIG. 8 ill the same way with the ernbodirneIlt of FIG. 1,enablillg to shorten the collvergence time and to improve robustness of the trai~ lg operatioll agaiIlst noises, without expressly retaiIliIlg con-CA 022~6~62 1998-12-18 formity of the norn1alizatiol1 by way of the normalizatiol1 coefficient S
as requirecl in the embodiment of FIG. 1.
Heretofore, the presel1t invention is described iIl conl1ection with embocliments whereil1 the windowed target impulse response Bw is 5 updatecl m~lcing use of the frequency-domain clivision method ancl the windowecl tap coefficients ww(D) are updated making use of the frequel1cy-domail1 LMS method. However, the present invention can be also applied in a case where the windowed target impulse response Bw is upclated m~l~ing use of the frequency-domain LMS method and 10 the windowecl tap coefflcients ww(D) are updated makillg use of the frequel1cy-domain division method.
For example, by obtainil1g the normalization coefficient S from the normalization process performed in the normalization unit 3660 of FIG. 11, and upclating the wil1dowed target impulse response 15 B2U according following equations (7) and (8) with a target-impulse-response means having a similar configuration with the tap-coefficient llpclate means 25()0 of FIG. 4,' the updated target impulse response Bu conforming to the normalization can be obtained.
Bll = sBI,, + 2/1E"~*, (7) E" = sBIuX' - WWY (8) The updated target irnpulse response BU is wil1dowed with the target-implllse-response windowing meaIls 3400 of FIG. 9, and the up-datecl tap coefficieI~t vector Wu is produced accordil1g to followillg equa-tion (5) previously described, with a tap-coefficient update means, to 2s be winclowed again with the tap-coefficient wil1dowing means 3600;
WU = B",Y/X'. (5) As heretofore described, the winclowed tap coefficients ww(D) ancl ... .

CA 022~6~62 1998-12-18 the windowed target impulse response BlU can be recursively revised and normalized mailltailling conformity between them, according to the invention. Therefore, the convergence time of the training process can be remarkably reduced and the robustness against noises can be 5 improved as well.
Further, the present invention is described in connection with training of the adaptive equalizer employed in a multicarrier data trans-mission system employing IFFT/FFT modulation. However, it is eas-ily understood that the training method of the present invention can 10 be applied effectively for training or optinlizing tap coefficients of the adaptive equalizer to be employed in other systems.

~ ,~., .

Claims (15)

1. A method of training tap coefficients of an adaptive equalizer having a first number of taps, for equalizing duration of an impulse response of a transmission channel to be shorter than a second number of taps with a sufficiently small error, having a step of initializing windowed tap coefficients to some predetermined values, a step of repeating a training procedure until a certain convergence condition of the windowed tap coefficients is attained, and a step of outputting the windowed tap coefficients as the tap coefficients of the adaptive equalizer after the certain convergence condition is attained; said training procedure comprising:
a transmission step of transmitting a transmission signal which is produced by transforming a frequency-domain transmission vector encoded with a PRBS (Pseudo-Random Binary Sequence) into a time-domain;
a target-impulse-response update step of producing an updated target impulse response by dividing an equalized reception signal vector with a training vector, the equalized reception signal vector being produced by transforming an equalized reception signal, which is obtained by processing the transmission signal received through the transmission channel with an equalizer having the first number of taps whereof coefficients are set to have values of the windowed tap coefficients, into a frequency-domain, and the training vector being produced by encoding a frequency-domain vector with a replica of the ' a target-impulse-response windowing step of outputting a windowed target impulse response together with a normalization coefficient, the windowed target impulse response being produced by transforming the updated target impulse response into a time-domain updated target impulse response signal, selecting the second number of consecutive tap values giving a maximum total power from tap values of the time-domain up-dated target impulse response, normalizing the selected consecutive tap values and transforming the normalized consecutive tap values into the frequency-domain, and the normalization coefficient being obtained by dividing the normalized consecutive tap values with the selected consecutive tap values before normalization;
a tap-coefficient update step of producing an updated tap coefficient vector by updating a frequency-domain tap coefficient vector multiplied by the normalization coefficient making use of a frequency-domain LMS (Least Mean Square) method with an error value defined as a difference of a product of the training vector and the windowed target impulse response to a product of the normalization coefficient, the frequency-domain tap coefficient vector and a reception signal vector, the frequency-domain tap coefficient vector being obtained by transforming the windowed tap coefficients into the frequency-domain, and the reception signal vector being obtained by transforming the transmission signal received through the transmission channel into the frequency-domain; and a tap-coefficient windowing step of producing the windowed tap coefficients by transforming the updated tap coefficient vector into updated tap coefficients, selecting the first number of consecutive coefficients giving a maximum total power from coefficients of the updated tap coefficients and shifting the selected consecutive coefficients to be assigned from a top of the windowed tap coefficients.

2. A method of training tap coefficients of an adaptive equalizer having a first number of taps, for equalizing duration of an impulse response of a transmission channel to be shorter than a second number of taps with a sufficiently small error, having a step of initializing windowed tap coefficients to some predetermined values, a step of repeating a training procedure until a certain convergence condition of the windowed tap coefficients is attained, and a step of outputting the windowed tap coefficients as the tap coefficients of the adaptive equalizer after the certain convergence condition is attained; said training procedure comprising:
a transmission step of transmitting a transmission signal which is produced by transforming a frequency-domain transmission vector encoded with a PRBS into a time-domain;
a target-impulse-response update step of producing an updated target impulse response by dividing an equalized reception signal vector with a training vector, the equalized reception signal vector being produced by transforming an equalized reception signal, which is obtained by processing the transmission signal received through the transmission channel with an equalizer having the first member of taps whereof coefficients are set to have values of the windowed tap coefficients, into a frequency-domain, and the training vector being produced by encoding a frequency-domain vector with a replica of the PRBS;

a target-impulse-response windowing step of producing a windowed target impulse response by transforming the updated target impulse response into a time-domain updated target impulse response signal, selecting the second number of consecutive tap values giving a maximum total power from tap values of the time-domain updated target impulse response and transforming the selected consecutive tap values into the frequency-domain;
a tap-coefficient update step of producing an updated tap coefficient vector by updating a frequency-domain tap coefficient vector making use of a frequency-domain LMS method with an error value defined as a difference of a product of the training vector and the windowed target impulse response to a product of the frequency-domain tap coefficient vector and a reception signal vector, the frequency-domain tap coefficient vector being obtained by transforming the windowed tap coefficients into the frequency-domain, and the reception signal vector being obtained by transforming the transmission signal received through the transmission channel into the frequency-domain;
and a tap-coefficient windowing step of producing the windowed tap coefficients by transforming the updated tap coefficient vector into updated tap coefficients, selecting the first number of consecutive coefficients giving a maximum total power from coefficients of the updated tap coefficients, normalizing the selected consecutive coefficients and shifting the normalized consecutive coefficients to be assigned from a top of the windowed tap coefficients.

3. A method of training tap coefficients of an adaptive equalizer having a first number of taps, for equalizing duration of an impulse response of a transmission channel to be shorter than a second number of taps with a sufficiently small error, having a step of initializing a target impulse response and windowed tap coefficients to some predetermined values, a step of repeating a training procedure until a certain convergence condition of the windowed tap coefficients is attained, and a step of outputting the windowed tap coefficients as the tap coefficients of the adaptive equalizer after the certain convergence condition is attained; said training procedure comprising:
a transmission step of transmitting a transmission signal which is produced by transforming a frequency-domain transmission vector encoded with a PRBS into a time-domain;
a target-impulse-response update step of producing an updated target impulse response by updating the windowed target impulse response multiplied by a normalization coefficient making use of a frequency-domain LMS method with an error value defined as a difference of a product of the normalization coefficient, a training vector and the windowed target impulse response to a product of a frequency-domain tap coefficient vector and a reception signal vector, the training vector being produced by encoding a frequency-domain vector with a replica of the PRBS, the frequency-domain tap coefficient vector being obtained by transforming the windowed tap coefficients into a frequency-domain, and the reception signal vector being obtained by transforming the transmission signal received through the transmission channel into the frequency-domain;
a target-impulse-response windowing step of producing a windowed target impulse response by transforming the updated target impulse response into a time-domain updated target impulse response signal, selecting the second number of consecutive tap values giving a maximum total power from tap values of the time-domain updated target impulse response and transforming the selected consecutive tap values into the frequency-domain;
a tap-coefficient update step of producing an updated tap coefficient vector by dividing a product of the windowed target response and the reception signal vector with the training vector; and a tap-coefficient windowing step of outputting the windowed tap coefficients together with the normalization coefficient, the windowed tap coefficients being produced by transforming the updated tap coefficient vector into updated tap coefficients, selecting the first number of consecutive coefficients giving a maximum total power from coefficients of the updated tap coefficients, normalizing the selected consecutive coefficients and shifting the normalized consecutive coefficients to be assigned from a top of the windowed tap coefficients, and the normalization coefficient being obtained by dividing the normalized consecutive coefficients with the selected consecutive coefficients before normalization.

4. A training circuit for training tap coefficients of an adaptive equalizer having a first number of taps to be used for equalizing duration of an impulse response of a transmission channel to be shorter than a second number of taps with a sufficiently small error; the training circuit comprising:
a transmitter for transmitting a transmission signal which is produced by transforming a frequency-domain transmission vector encoded with a PRBS into a time-domain;
a target-impulse-response update means for producing an updated target impulse response by dividing an equalized reception signal vector with a training vector, the equalized reception signal vector being produced by transforming an equalized reception signal, which is obtained by processing the transmission signal received through the transmission channel with an equalizer having the first number of taps whereof coefficients are set to have values of the windowed tap coefficients, into a frequency-domain, and the training vector being produced by encoding a frequency-domain vector with a replica of the PRBS;
a target-impulse-response windowing means for outputting a windowed target impulse response together with a normalization coefficient, the windowed target impulse response being produced by transforming the updated target impulse response into a time-domain updated target impulse response signal, selecting the second number of consecutive tap values giving a maximum total power from tap values of the time-domain updated target impulse response, normalizing the selected consecutive tap values and transforming the normalized consecutive tap values into the frequency-domain, and the normalization coefficient being obtained by dividing the normalized consecutive tap values with the selected consecutive tap values before normalization;
a tap-coefficient update means for producing an updated tap coefficient vector by updating a frequency-domain tap coefficient vector multiplied by the normalization coefficient making use of a frequency-domain LMS method with an error value defined as a difference of a product of the training vector and the windowed target impulse response to a product of the normalization coefficient, the frequency-domain tap coefficient vector and a reception signal vector, the frequency-domain tap coefficient vector being obtained by transforming the windowed tap coefficients into the frequency-domain, and the reception signal vector being obtained by transforming the transmission signal received through the transmission channel into the frequency-domain;
a tap-coefficient windowing means for producing the windowed tap coefficients by transforming the updated tap coefficient vector into updated tap coefficients, selecting the first number of consecutive coefficients giving a maximum total power from coefficients of the updated tap coefficients and shifting the selected consecutive coefficients to be assigned from a top of the windowed tap coefficients; and a control means for initializing the windowed tap coefficients to some predetermined values, controlling the transmitter, the target-impulse-response update means, the target-impulse-response windowing means, the tap-coefficient update means and the tap-coefficient windowing means to update the windowed target impulse response and the windowed tap coefficients alternately and recursively by generating the PRBS and the replica of the PRBS repeatedly until a certain convergence condition of the windowed tap coefficients is attained, and outputting the windowed tap coefficients as the tap coefficients of the adaptive equalizer after the certain convergence condition is attained.

5. A training circuit as recited in claim 4; wherein the selected consecutive tap values are normalized by the target-impulse-response windowing means to give a standard deviation of a value of 1.

6. A training circuit as recited in claim 4; wherein a condition that a total power of the selected consecutive coefficients selected by the tap-coefficient windowing means becomes sufficiently large compared to a total power of other coefficients of the updated tap coefficients is included in the certain convergence condition of the windowed tap coefficients.

7. A training circuit as recited in claim 4; wherein a condition that a number of repetition times of updating the windowed target impulse response and the windowed tap coefficients reaches a predetermined number is included in the certain convergence condition of the windowed tap coefficients.

8. A training circuit for training tap coefficients of an adaptive equalizer having a first number of taps to be used for equalizing duration of an impulse response of a transmission channel to be shorter than a second number of taps with a sufficiently small error; the training circuit comprising:
a transmitter for transmitting a transmission signal which is produced by transforming a frequency-domain transmission vector encoded with a PRBS into a time-domain;
a target-impulse-response update means for producing an updated target impulse response by dividing an equalized reception signal vector with a training vector, the equalized reception signal vector being produced by transforming an equalized reception signal, which is obtained by processing the transmission signal received through the transmission channel with an equalizer having the first member of taps whereof coefficients are set to have values of the windowed tap coefficients, into a frequency-domain, and the training vector being produced by encoding a frequency-domain vector with a replica of the PRBS;
a target-impulse-response windowing means for producing a windowed target impulse response by transforming the updated target impulse response into a time-domain updated target impulse response signal, selecting the second number of consecutive tap values giving a maximum total power from tap values of the time-domain updated target impulse response and transforming the selected consecutive tap values into the frequency-domain;
a tap-coefficient update means for producing an updated tap coefficient vector by updating a frequency-domain tap coefficient vector making use of a frequency-domain LMS method with an error value defined as a difference of a product of the training vector and the windowed target impulse response to a product of the frequency-domain tap coefficient vector and a reception signal vector, the frequency-domain tap coefficient vector being obtained by transforming the windowed tap coefficients into the frequency-domain, and the reception signal vector being obtained by transforming the transmission signal received through the transmission channel into the frequency-domain;
a tap-coefficient windowing means for producing the windowed tap coefficients by transforming the updated tap coefficient vector into updated tap coefficients, selecting the first number of consecutive coefficients giving a maximum total power from coefficients of the updated tap coefficients, normalizing the selected cosecutive coefficients and shifting the normalized consecutive coefficients to be assigned from a top of the windowed tap coefficients and;
a control means for initializing the windowed tap coefficients to some predetermined values, controlling the transmitter, the target-impulse-response update means, the target-impulse-response windowing means, the tap-coefficient update means and the tap-coefficient windowing means to update the windowed target impulse response and the windowed tap coefficients alternately and recursively by generating the PRBS and the replica of the PRBS repeatedly until a certain convergence condition of the windowed tap coefficients is attained, and out-putting the windowed tap coefficients as the tap coefficients of the adaptive equalizer after the certain convergence condition is attained.

9. A training circuit as recited in claim 8; wherein the selected consecutive coefficients are normalized by the tap-coefficient windowing means to give a standard deviation of a value of 1.

10. A training, circuit as recited in claim 8; wherein a condition that a total power of the selected consecutive coefficients selected by the tap-coefficient windowing means becomes sufficiently large compared to a total power of other coefficients of the updated tap coefficients is included in the certain convergence condition of the windowed tap coefficients.

11. A training circuit as recited in claim 8; wherein a condition that a number of repetition times of updating the windowed target impulse response and the windowed tap coefficients reaches a predetermined number is included in the certain convergence condition of the windowed tap coefficients.

12. A training circuit for training tap coefficients of an adaptive equalizer having a first number of taps to be used for equalizing duration of an impulse response of a transmission channel to be shorter than a second number of taps with a sufficiently small error; the training circuit comprising:
a transmitter for transmitting a transmission signal which is produced by transforming a frequency-domain transmission vector encoded with a PRBS into a time-domain;
a target-impulse-response update means for producing an updated target impulse response by updating the windowed target impulse response multiplied by a normalization coefficient making use of a frequency-domain LMS method with an error value defined as a difference of a product of the normalization coefficient, a training vector and the windowed target impulse response to a product of a frequency-domain tap coefficient vector and a reception signal vector, the training vector being produced by encoding a frequency-domain vector with a replica of the PRBS, the frequency-domain tap coefficient vector being obtained by transforming the windowed tap coefficients into a frequency-domain, and the reception signal vector being obtained by transforming the transmission signal received through the transmission channel into the frequency-domain;
a target-impulse-response windowing means for producing a windowed target impulse response by transforming the updated target impulse response into a time-domain updated target impulse response signal, selecting the second number of consecutive tap values giving a maximum total power from tap values of the time-domain updated target impulse response and transforming the selected consecutive tap values into the frequency-domain;
a tap-coefficient update means for producing an updated tap coefficient vector by dividing a product of the windowed target response and the reception signal vector with the training vector;
a tap-coefficient windowing means for outputting the windowed tap coefficients together with the normalization coefficient, the windowed tap coefficients being produced by transforming the updated tap coefficient vector into updated tap coefficients, selecting the first number of consecutive coefficients giving a maximum total power from coefficients of the updated tap coefficients, normalizing the selected consecutive coefficients and shifting the normalized consecutive coefficients to be assigned from a top of the windowed tap coefficients, and the normalization coefficient being obtained by dividing the normalized consecutive coefficients with the selected consecutive coefficients before normalization; and a control means for initializing the windowed target impulse response and the windowed tap coefficients to some predetermined values, controlling the transmitter, the target-impulse-response update means, the target-impulse-response windowing means, the tap-coefficient update means and the tap-coefficient windowing means to update the windowed target impulse response and the windowed tap coefficients alternately and recursively by generating the PRBS and the replica of the PRBS repeatedly until a certain convergence condition of the windowed tap coefficients is attained, and outputting the windowed tap coefficients as the tap coefficients of the adaptive equalizer after the certain convergence condition is attained.

13. A training circuit as recited in claim 12; wherein the selected consecutive coefficients are normalized by the tap-coefficient windowing means to give a standard deviation of a value of 1.

14. A training circuit as recited in claim 12; wherein a condition that a total power of the selected consecutive coefficients selected by the tap-coefficient windowing means becomes sufficiently large compared to a total power of other coefficients of the updated tap coefficients is included in the certain convergence condition of the windowed tap coefficients.

15. A training circuit as recited in claim 12; wherein a condition that a number of repetition times of updating the windowed target impulse response and the windowed tap coefficients reaches a predetermined number is included in the certain convergence condition of the windowed tap coefficients.