CA2086548C - A method for optimizing an adaptive filter update coefficient - Google Patents
A method for optimizing an adaptive filter update coefficientInfo
- Publication number
- CA2086548C CA2086548C CA002086548A CA2086548A CA2086548C CA 2086548 C CA2086548 C CA 2086548C CA 002086548 A CA002086548 A CA 002086548A CA 2086548 A CA2086548 A CA 2086548A CA 2086548 C CA2086548 C CA 2086548C
- Authority
- CA
- Canada
- Prior art keywords
- signal
- error
- mean square
- square error
- adaptive filter
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired - Fee Related
Links
Classifications
-
- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
- H03H21/00—Adaptive networks
- H03H21/0012—Digital adaptive filters
- H03H21/0043—Adaptive algorithms
-
- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
- H03H17/00—Networks using digital techniques
- H03H17/02—Frequency selective networks
- H03H17/0223—Computation saving measures; Accelerating measures
- H03H17/0227—Measures concerning the coefficients
-
- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
- H03H21/00—Adaptive networks
- H03H21/0012—Digital adaptive filters
- H03H21/0025—Particular filtering methods
Landscapes
- Engineering & Computer Science (AREA)
- Computing Systems (AREA)
- Theoretical Computer Science (AREA)
- Physics & Mathematics (AREA)
- Computer Hardware Design (AREA)
- Mathematical Physics (AREA)
- Filters That Use Time-Delay Elements (AREA)
- Cable Transmission Systems, Equalization Of Radio And Reduction Of Echo (AREA)
Abstract
The method of the present invention generates an opti-mal adaptive filter update coefficient by first generating three error signals using a signal input and three update coeffi-cients (301- 303). Mean Square Error (MSE) values are esti-mated (307 and 308) for the first and third error signals. The first MSE value (307) is subtracted (309) from the third MSE
value (308) to generate a difference signal. The difference sig-nal is used to generate (310) an update signal that is used to modify the update coefficients. The process of the present in-vention is repeated until the difference signal is substantially zero, thus optimizing the second update coefficient. This pro-cess enables an update coefficient for an adaptive filter to quickly adapt to a changing environment.
value (308) to generate a difference signal. The difference sig-nal is used to generate (310) an update signal that is used to modify the update coefficients. The process of the present in-vention is repeated until the difference signal is substantially zero, thus optimizing the second update coefficient. This pro-cess enables an update coefficient for an adaptive filter to quickly adapt to a changing environment.
Description
- 1 - 20865~ 8 A METHOD FOR opTrM~ G AN ADAl~IVE FILTER
UPDATE COEFFICIENT
E~dof~be ~lvention s The present invention relates generally to the field of commnnic~tio~ and particularly to digital cellular commu-nications.
1 0 B~ground of 1 be Il,~lion U.S. digital cellular com~nllnic~;Qn~ uses digitized voice and data Pigr~ for co ~ qtio- belween a mobile telephone and a base ~t~tin When the mn~ile moves, it may 15 enco lnter de~l 19-1 com_~lnic~*on rh~nnPl~ due to noise and mllltip~tl distortion; both noise and distortion varying with time. The multipath distortion is due to a signal being leca;ved by the mo~ile at difre~ nt times when it bow~cas off blfil-lings and terrain. Multipath ~h~nn~ can cause inter-2 0 symbol inte~re~e~ce (ISI) that can be removed with an adap-tive eq~ li7er, a spe~ific type of an adayl ive filter.
A typical adaptive Iter is illustrated in FIG. 1. The in-put signal (106) is y.oce~e~ by the adal l iv~ filter (101), pro fln~ng the ada~,Lve filter out~ut signal (102). The oul~ 1, of 2 5 the filter is then subtracted (105) from a, efe~c,~ce signal (103), to produce an error signal (104). This error signal (104) is used by an adaptive algorithm with an llp~ te coPffi~çnt, Il, in the ada~ve filter to llrYl~te the filter coeffi~ nte. The ll~te coeffi~ient is also ~ferLed to as a k~rlring coeffi~ent or mem-3 0 ory coPffirient~ It is assumed that the m~mory of the adaptivealgorithm increases as the value of ~1 increases.
The llp~l~te coef~i~ent controls the memory of the adap-tive algorithm and its determin~tion is a trade-off betwee~ the rate that the filter can track the l~h~n~ing ~h~nn~l character-3 5 istics and the amount of noise averaging that will be accom-pl;ghe-l by the adaptive algorithm. As the adaptive algorithm *
~086~48 m~m.^,ry is shortened, the algorithm is better able to track time va~tion~ in the co~ ..ic~tion çh-onnsl but will become more sensitive to noise on the communication rh~nnel If the coefficiçnt is çhosçn to filter out more noise, then filter's 5 ch^nnel tracking c-o-peh;lity will be re-lllce~3 The adaptive algorithm can be a Kolmon, Re~aive Least Square, or Least Mean Square (LMS) algorithm. The typical goal of the adaptive algorithm is to minimi7e the mean square value of the error signal (104). This value is typically 10 ~le~ign-t~l mean square error (MSE).
FIGs. 2A, B, ant C illustrate the three po~sihle rlo-~se~
of ataptive filter oye~ g e~vi~ n~nts. FIG. 2A is a time invariant ~ tem in a noisy environm^~t In this case, the to-tal MSE, 13e~ignote~l ET, comes only from the noise, ~3esignote~
1 5 En~ since the system is not time varying. The total MSE is pro-portional to 1l.
FIG. 2B is a time varying but st^-~;Q~ry system in a noisy environmPnt a stationary B~ having higher order signal st-t;s';cs that do not change over time. In this esam-2 0 ple, ET (203) con~ip~ of the sum of two in~lep-n~l~nt comp~
nents, the lag error (201) and the noise (202). The lag error (201) is due to the filter .,tta~ ~g to tracl~ the time V~ ~
system. The lag error (201), ~^Fign~te~l EL, is ill~e~sely pro-portional to ~. The noise co~..yQ--~nt (202) is due to the noisy 2 5 e,.~;~o-----ent as ill~l~ted in FIG. 2A. It can be seen in FIG.
2B that the total MSE can be minimi7ecl by ~ oo~i~ the value of ~ co,.e~ondi~g to the int~, ~ec' ;on of the curves (204).
The last e.lvi.~ Pnt is a time varying, non-~t~ion~ly ~ystem in a noisy e~vi.o.~mPnt. The total MSE in this case 3 0 consists of the same components as in FIG. 2B. The differ-ence betwee~ the tv~o s~lel.ls is that in this case, the curves are shif~ing or rh~n~inE- slope over time c~llsing the mini-mum point on the curve to shift thus rh~n~ine the opt;m~l value of ~ over time. This ~.lvho-.mant is illustrated by com-3 5 panng FIGs. 2B and 2C. FIG. 2B represents the MSE charac-~ 3 ~ 2086548 teristic at some time tl w ile FIG. 2C represent~ the MSEcharacteristic at some later time t2.
A fL~ed ~ te coefficient in t_e lsst e~vilo~.ment would not provide adequate filter performance due to the rhs~n~inf~
5 e~Yi.~-.m~nt There i8 a resulting need for alltom~ticslly P~n~ the ~ te coeffi~ent acco~ g to t_e vehicle speed and rhs~nnel conditions thereby i~lOVi~g filter pe.Ço- ~snce.
&mmalyof the I~i;on The method of the present invention generates an optimum memory co-efficient in an apparatus having two adaptive filters. Each adaptive filter has an input signal and a reference signal. A first adaptive filter of the two adaptivefilters has a first memory coefficient and a second adaptive filter has a second 15 memory coefficient. The method starts by generating an error signal for each adaptive filter in response to the input signal and the reference signal. Then, each error signal is averaged to generate an average error for each adaptive filter.
The average error of the two adaptive filters is compared, and the first and 20 second memory coefficients are modified in response to a difference in the average errors.
Bri~Descri~tion of 1~e D _.. ;~
FIG. 1 shows a block diagram of a typical ada~ive fil-ter.
FIGs. 2A, B, and C show three different adaptive filter operating e~vn~ments.
FIG. 3 shows a block diagram of the preferred eml~li-ment of the lJ-OC~39 of the present inv~n*Qn 3 0 FIG. 4 shows a block diagram of an alternate ~mbo li.
ment of the process of the present invention.
FIG. 5 shows a graph of MSE versus ~ in accordance with the process of the present invention.
FIG. 6 shows a plot of a fixed update coefficient and an optimi7e-1 update coefficient in accordance with the process of the present invention.
A
UPDATE COEFFICIENT
E~dof~be ~lvention s The present invention relates generally to the field of commnnic~tio~ and particularly to digital cellular commu-nications.
1 0 B~ground of 1 be Il,~lion U.S. digital cellular com~nllnic~;Qn~ uses digitized voice and data Pigr~ for co ~ qtio- belween a mobile telephone and a base ~t~tin When the mn~ile moves, it may 15 enco lnter de~l 19-1 com_~lnic~*on rh~nnPl~ due to noise and mllltip~tl distortion; both noise and distortion varying with time. The multipath distortion is due to a signal being leca;ved by the mo~ile at difre~ nt times when it bow~cas off blfil-lings and terrain. Multipath ~h~nn~ can cause inter-2 0 symbol inte~re~e~ce (ISI) that can be removed with an adap-tive eq~ li7er, a spe~ific type of an adayl ive filter.
A typical adaptive Iter is illustrated in FIG. 1. The in-put signal (106) is y.oce~e~ by the adal l iv~ filter (101), pro fln~ng the ada~,Lve filter out~ut signal (102). The oul~ 1, of 2 5 the filter is then subtracted (105) from a, efe~c,~ce signal (103), to produce an error signal (104). This error signal (104) is used by an adaptive algorithm with an llp~ te coPffi~çnt, Il, in the ada~ve filter to llrYl~te the filter coeffi~ nte. The ll~te coeffi~ient is also ~ferLed to as a k~rlring coeffi~ent or mem-3 0 ory coPffirient~ It is assumed that the m~mory of the adaptivealgorithm increases as the value of ~1 increases.
The llp~l~te coef~i~ent controls the memory of the adap-tive algorithm and its determin~tion is a trade-off betwee~ the rate that the filter can track the l~h~n~ing ~h~nn~l character-3 5 istics and the amount of noise averaging that will be accom-pl;ghe-l by the adaptive algorithm. As the adaptive algorithm *
~086~48 m~m.^,ry is shortened, the algorithm is better able to track time va~tion~ in the co~ ..ic~tion çh-onnsl but will become more sensitive to noise on the communication rh~nnel If the coefficiçnt is çhosçn to filter out more noise, then filter's 5 ch^nnel tracking c-o-peh;lity will be re-lllce~3 The adaptive algorithm can be a Kolmon, Re~aive Least Square, or Least Mean Square (LMS) algorithm. The typical goal of the adaptive algorithm is to minimi7e the mean square value of the error signal (104). This value is typically 10 ~le~ign-t~l mean square error (MSE).
FIGs. 2A, B, ant C illustrate the three po~sihle rlo-~se~
of ataptive filter oye~ g e~vi~ n~nts. FIG. 2A is a time invariant ~ tem in a noisy environm^~t In this case, the to-tal MSE, 13e~ignote~l ET, comes only from the noise, ~3esignote~
1 5 En~ since the system is not time varying. The total MSE is pro-portional to 1l.
FIG. 2B is a time varying but st^-~;Q~ry system in a noisy environmPnt a stationary B~ having higher order signal st-t;s';cs that do not change over time. In this esam-2 0 ple, ET (203) con~ip~ of the sum of two in~lep-n~l~nt comp~
nents, the lag error (201) and the noise (202). The lag error (201) is due to the filter .,tta~ ~g to tracl~ the time V~ ~
system. The lag error (201), ~^Fign~te~l EL, is ill~e~sely pro-portional to ~. The noise co~..yQ--~nt (202) is due to the noisy 2 5 e,.~;~o-----ent as ill~l~ted in FIG. 2A. It can be seen in FIG.
2B that the total MSE can be minimi7ecl by ~ oo~i~ the value of ~ co,.e~ondi~g to the int~, ~ec' ;on of the curves (204).
The last e.lvi.~ Pnt is a time varying, non-~t~ion~ly ~ystem in a noisy e~vi.o.~mPnt. The total MSE in this case 3 0 consists of the same components as in FIG. 2B. The differ-ence betwee~ the tv~o s~lel.ls is that in this case, the curves are shif~ing or rh~n~inE- slope over time c~llsing the mini-mum point on the curve to shift thus rh~n~ine the opt;m~l value of ~ over time. This ~.lvho-.mant is illustrated by com-3 5 panng FIGs. 2B and 2C. FIG. 2B represents the MSE charac-~ 3 ~ 2086548 teristic at some time tl w ile FIG. 2C represent~ the MSEcharacteristic at some later time t2.
A fL~ed ~ te coefficient in t_e lsst e~vilo~.ment would not provide adequate filter performance due to the rhs~n~inf~
5 e~Yi.~-.m~nt There i8 a resulting need for alltom~ticslly P~n~ the ~ te coeffi~ent acco~ g to t_e vehicle speed and rhs~nnel conditions thereby i~lOVi~g filter pe.Ço- ~snce.
&mmalyof the I~i;on The method of the present invention generates an optimum memory co-efficient in an apparatus having two adaptive filters. Each adaptive filter has an input signal and a reference signal. A first adaptive filter of the two adaptivefilters has a first memory coefficient and a second adaptive filter has a second 15 memory coefficient. The method starts by generating an error signal for each adaptive filter in response to the input signal and the reference signal. Then, each error signal is averaged to generate an average error for each adaptive filter.
The average error of the two adaptive filters is compared, and the first and 20 second memory coefficients are modified in response to a difference in the average errors.
Bri~Descri~tion of 1~e D _.. ;~
FIG. 1 shows a block diagram of a typical ada~ive fil-ter.
FIGs. 2A, B, and C show three different adaptive filter operating e~vn~ments.
FIG. 3 shows a block diagram of the preferred eml~li-ment of the lJ-OC~39 of the present inv~n*Qn 3 0 FIG. 4 shows a block diagram of an alternate ~mbo li.
ment of the process of the present invention.
FIG. 5 shows a graph of MSE versus ~ in accordance with the process of the present invention.
FIG. 6 shows a plot of a fixed update coefficient and an optimi7e-1 update coefficient in accordance with the process of the present invention.
A
4 208~18 FIG. 7 shows a plot of an llp~l~ta coefficient, in accor-dance with the process of the present invention, in a delay spread environment.
~e~ibd Desdp~on of ffle Pn~ned Embo&~
The l..ocess of the present invention provides ~l~tom~tic adjustment and optimi7p~;on of an adaptive filter llp~3~ts coef-ficient in a ch~ ing el~vil~o ~ment The llp~l~te coçffir~Pnt is 1 0 continllously llr~l~t9tl by a fee~lh~ck signal that is generated by the filtered di~r~ence b.:tweel, MSE estim~tes for two adaptive filters.
A block diagram of the l,lefel~cd çmbotlimçnt of the process of the present i~v~tion is illustrated in FIG. 3. The 1 5 l..ocess is c~ r;sed ofthree adaptive filters (301- 303). Each of the filters is irl ~ntic~ql e~cept for having dia`e~t llp~l~ta co-effi~ent~ 2. and ~13. The secon~ llp~te coçffirient~ ~2. is the coefflcient that is optimi~e~l by the process. The optimal llpA~t9 coeffi~ent is subsequently Lefe~.ed to as 11*. Since 112 is 2 0 the optimi7e~l llp~l~ts coefficient, the secon~l adaptive filter (302) is the filter used to l,e-ru~ the actual desired adaptive filtering filnction The update coefficients have the following rel~t~ n~hip:
~ 2 < 1l3 2- ~d ~3 = ~2 + ~d.
where ~d is a CQn~tqnt rhosen for the particular system in 3 0 which the comml)nil~tion device i8 to operate as well as the particular adaptive algorithm used. In an alternate emhotli ment, llt would vary with time ag the l~p~3S~tg coefflciQnt~
change. In the ~efe-.ed emboAime- t llt is 0.01 using an LMS adaptive algorithm.
3 5 The lJ~OCe98 first generates error ~ign~lR from the adap-tive filters (301 - 303). This is ~ comrli~he~l by the adaptive fil-- 5 - ~0865~
ters (301 - 303) filtering the input signal in such a way that it fonns a 8ignal that m~trhss t_e reference signal as close as pQ88ih1e In the l,lefelled emho~limpnt~ the input is the de-tected symbols in the cG~~ tion rcæiver. These output S ~ are fefelLed to as OUTPUT1, 0UTPUT2, and OUTPUT3 in FIG. 3. Each output signal from the filters is tben subtracted (304 - 306) from a ~efef~hce signal. In the pre-ferred ~mho~liment~ the ~eÇefc,lce signal is the le~eived The ~1;~re~,c~ ~el- ecn these two ~i~n~l~ is the error l 0 si~n~1.
Mean square error estim~tes are l,c,ro,~ed (307 and 308) on the error ~ from the first and third adaptive fil-ters (301 and 303). The MSE for each error signal is es~;m~te-3 as follows:
Ic+n ET1= i=~
n + l Ic+n ~ 1e~3 ET3 = i = lC
n + l 2 0 where k i8 the start value and n i~ the number of s~mp1es of the error siE~ For P~mr1e, if k = 1 and n = 10 for the first e~l :"~ c~cle, k will start at 12 for the next cycle.
The ~ e.cllce between the estimD~te~l MSE's (309), Ed = ET1 - ET3 . provides an in-lir~l1;on of which direction to 2 5 move along the ~ asis to get closer to ~1*. In the ~,efer,~d em-b~;..~,-.t, Ed i8 input to a co~ ator (310) where it is com-pared to 0. If Ed < 0, then ~1l is closer to ,u* than ,U3. The coeffi-cients, thelcfo~, should be decremented in order to move ~2 closer to ~*. In this case, the coefflcient 1lr~l~tes are illus-3 0 trated as follows:
if Ed < 0 then:
~1 = )1l - ~
~e~ibd Desdp~on of ffle Pn~ned Embo&~
The l..ocess of the present invention provides ~l~tom~tic adjustment and optimi7p~;on of an adaptive filter llp~3~ts coef-ficient in a ch~ ing el~vil~o ~ment The llp~l~te coçffir~Pnt is 1 0 continllously llr~l~t9tl by a fee~lh~ck signal that is generated by the filtered di~r~ence b.:tweel, MSE estim~tes for two adaptive filters.
A block diagram of the l,lefel~cd çmbotlimçnt of the process of the present i~v~tion is illustrated in FIG. 3. The 1 5 l..ocess is c~ r;sed ofthree adaptive filters (301- 303). Each of the filters is irl ~ntic~ql e~cept for having dia`e~t llp~l~ta co-effi~ent~ 2. and ~13. The secon~ llp~te coçffirient~ ~2. is the coefflcient that is optimi~e~l by the process. The optimal llpA~t9 coeffi~ent is subsequently Lefe~.ed to as 11*. Since 112 is 2 0 the optimi7e~l llp~l~ts coefficient, the secon~l adaptive filter (302) is the filter used to l,e-ru~ the actual desired adaptive filtering filnction The update coefficients have the following rel~t~ n~hip:
~ 2 < 1l3 2- ~d ~3 = ~2 + ~d.
where ~d is a CQn~tqnt rhosen for the particular system in 3 0 which the comml)nil~tion device i8 to operate as well as the particular adaptive algorithm used. In an alternate emhotli ment, llt would vary with time ag the l~p~3S~tg coefflciQnt~
change. In the ~efe-.ed emboAime- t llt is 0.01 using an LMS adaptive algorithm.
3 5 The lJ~OCe98 first generates error ~ign~lR from the adap-tive filters (301 - 303). This is ~ comrli~he~l by the adaptive fil-- 5 - ~0865~
ters (301 - 303) filtering the input signal in such a way that it fonns a 8ignal that m~trhss t_e reference signal as close as pQ88ih1e In the l,lefelled emho~limpnt~ the input is the de-tected symbols in the cG~~ tion rcæiver. These output S ~ are fefelLed to as OUTPUT1, 0UTPUT2, and OUTPUT3 in FIG. 3. Each output signal from the filters is tben subtracted (304 - 306) from a ~efef~hce signal. In the pre-ferred ~mho~liment~ the ~eÇefc,lce signal is the le~eived The ~1;~re~,c~ ~el- ecn these two ~i~n~l~ is the error l 0 si~n~1.
Mean square error estim~tes are l,c,ro,~ed (307 and 308) on the error ~ from the first and third adaptive fil-ters (301 and 303). The MSE for each error signal is es~;m~te-3 as follows:
Ic+n ET1= i=~
n + l Ic+n ~ 1e~3 ET3 = i = lC
n + l 2 0 where k i8 the start value and n i~ the number of s~mp1es of the error siE~ For P~mr1e, if k = 1 and n = 10 for the first e~l :"~ c~cle, k will start at 12 for the next cycle.
The ~ e.cllce between the estimD~te~l MSE's (309), Ed = ET1 - ET3 . provides an in-lir~l1;on of which direction to 2 5 move along the ~ asis to get closer to ~1*. In the ~,efer,~d em-b~;..~,-.t, Ed i8 input to a co~ ator (310) where it is com-pared to 0. If Ed < 0, then ~1l is closer to ,u* than ,U3. The coeffi-cients, thelcfo~, should be decremented in order to move ~2 closer to ~*. In this case, the coefflcient 1lr~l~tes are illus-3 0 trated as follows:
if Ed < 0 then:
~1 = )1l - ~
- 6 - 208~ ~ 8 = ~12 ~ ~
~3 = ~3 - ~.
otherwise, if Ed ~ O then the coeffi~Pnt~ should be incre-5 mented:
1 +
~2 = ~12 + ~
1l3 = 1l3 + ~.
where ~ is the llp~l~te coeffi~çnt step size. This value is appli-cation depçn~l~nt ~ can be rhosçn as a very small value for time invariant and st~ti~n~ry e~viro ~ments and slightly larger for non-stationary e~vi~o ~m^nt~ This value deter-1 5 mines the resolution of the llpclPte coeffi~ent, eetim~te and theadaptation speed of the l~p~l~te coeffi~ent In the preferred emhoAim~nt ~ is 0.005 using an LMS adaptive algorithm. As with ~ld. in an alternate emho~limpnt~ ~ could vary with time.
In an alternate emho~lim~nt, illustrated in FIG. 4, Ed is 2 0 input to a filter (410) in~te~ of a co...~.~. ator. The filter pro vides a time varying step size (co---r~- cd to the fised step size ~) that is ~eL~ -~ ve to the size of the error difference ~ignsll For e~mple~ when the error difference signal becomes large, the step size ~ om~t~ y increases resulting in faster con-2 S ~e~ ce of the algorithm. Using the filter, ho~ er, in-creases the cQmrlçrity of the invention and m~y cause stabil-ity problçm~ if a higher order filter is used. A first order digi-tal infinite impulse response (IIR) filter is preferred due to stability and simpli~ty cor qicler~tion~ In this case, the up-3 0 date coeffiriçnt~ are ~lPpte~l by ~ ng the value of the o~l~utof the filter to the coefflrients.
A~er several adaptation iter~ti~An~ is slightly ~m-ller than 1l*, ~13 iB Blightly larger than ~*, 112 is apl~ro~ i-mately equal to ~*, and the error difference signal is appro~c-3 5 imately zero. Adaptive filter 2 (302) is now optimi~e~ for thec~leut euvi~o~m^nt If the enviro^m~nt changes, the pro-7 20865~8 cess of the present invention detects and tracks the change to~A;~ the optimality of adaptive filter 2 (302).
The above described process can be illustrated graphi-cally as seen in FIG. 5, a plot of MSE versus ~. In the case 5 where Ed ~ . ET1 and ET3 (501) are on the right part of the curve and must move down the curve to the left in orter to lo-cate ~2 at the bollolu of the curve which is the optimum point.
This lequ,.es decrement;ng the tlp~lAte coçfficients by ~ to move ~2 closer to the l1~ point. ~:imil~-ly~ if Et > . ET1 and ET3 l 0 (502) are on the left part of the curve and must move down the curve to the right to locate ~2 at the op ;.~ m point. This re-quire~ increm~nt;~ te coefficiçnt~ by ~ to move ~2 closer to the 1l~ point (503).
The i~.o~c~ent using the proceas of the y.e&cht in-1 5 vention over a fi ed ~ te coeffir~ent is illusl~ated in FIGs. 6and 7. In these ~ hs, the l,.oce~3 is uset with a least mean square (LMS) adaptive rh~nnsl estim~tor in simlll~t;ons of a M~im~lm T.ilr~lihoo-l Sequence Est;m~1ion eqll~li7~r for the U.S. digital cellular ~le~. The fi~ced ~ te co~ffi~i~nt is set 2 0 at 11 = 0.38 to allow adequate pe-f~.~ance when the mobile ra-diotelephone is traveling in vehicle at high spee~ls~ By using the ~ s of the present inven~ n~ the y~ço~ance of the eq~li7er is i~y~o~ed at signifiç~ntly lower vehicle speeds, as illustrated in FIG. 6. FIG. 6 shows the ye,fo,. lance of the 2 5 eq~ i7sr as a fimr~;on of multipath delay and the vehicle speed is apy,Q~ tely 5 mph. FIG. 7 shows how the p,ocess operates in a ch~nnel with delay spread and co-rh~nnel inter-Çe~chce when the vehicle speed drops in~ntqnP,ously from 63 mph to 5 mph. It can be seen that the llp~l~te coefficient, 3 0 quicldy decreases to a new lower level suitable for the lower vehicle speed.
In the preferred embo~iment the process of the present invention is implçmPnte~ as an algorithm. Alternate emho~l-imPnt~ of the invention can be implçmçnte~ in hardware or 3 5 combin~tion~ of ha,dwa,e and software; each block of the pro-- 8 - ~0365~8 cess being either an algorithm or a hardware circuit equiva-lent of that block.
In sllmm~ry~ a process of a~tom~tic~lly optimi7ine an adaptive filter l~p~l~te coefficient in a ch~ngine envirQnmPnt S has been described. By comr~ring the perfulluance of each adaptive algûrithm to deter~e how to change the l~r~ts co-~ffi~i~nt~, an optimal l~ t~ coeffirient for that particular en-vironmsnt can be obt~ine~l- Cornm~ni~tion devices using the process of the ~lcee-~t invention can out-~ folm devices using 10 a fLsed l~p~3~t'~ coPffit~iPn~
~3 = ~3 - ~.
otherwise, if Ed ~ O then the coeffi~Pnt~ should be incre-5 mented:
1 +
~2 = ~12 + ~
1l3 = 1l3 + ~.
where ~ is the llp~l~te coeffi~çnt step size. This value is appli-cation depçn~l~nt ~ can be rhosçn as a very small value for time invariant and st~ti~n~ry e~viro ~ments and slightly larger for non-stationary e~vi~o ~m^nt~ This value deter-1 5 mines the resolution of the llpclPte coeffi~ent, eetim~te and theadaptation speed of the l~p~l~te coeffi~ent In the preferred emhoAim~nt ~ is 0.005 using an LMS adaptive algorithm. As with ~ld. in an alternate emho~limpnt~ ~ could vary with time.
In an alternate emho~lim~nt, illustrated in FIG. 4, Ed is 2 0 input to a filter (410) in~te~ of a co...~.~. ator. The filter pro vides a time varying step size (co---r~- cd to the fised step size ~) that is ~eL~ -~ ve to the size of the error difference ~ignsll For e~mple~ when the error difference signal becomes large, the step size ~ om~t~ y increases resulting in faster con-2 S ~e~ ce of the algorithm. Using the filter, ho~ er, in-creases the cQmrlçrity of the invention and m~y cause stabil-ity problçm~ if a higher order filter is used. A first order digi-tal infinite impulse response (IIR) filter is preferred due to stability and simpli~ty cor qicler~tion~ In this case, the up-3 0 date coeffiriçnt~ are ~lPpte~l by ~ ng the value of the o~l~utof the filter to the coefflrients.
A~er several adaptation iter~ti~An~ is slightly ~m-ller than 1l*, ~13 iB Blightly larger than ~*, 112 is apl~ro~ i-mately equal to ~*, and the error difference signal is appro~c-3 5 imately zero. Adaptive filter 2 (302) is now optimi~e~ for thec~leut euvi~o~m^nt If the enviro^m~nt changes, the pro-7 20865~8 cess of the present invention detects and tracks the change to~A;~ the optimality of adaptive filter 2 (302).
The above described process can be illustrated graphi-cally as seen in FIG. 5, a plot of MSE versus ~. In the case 5 where Ed ~ . ET1 and ET3 (501) are on the right part of the curve and must move down the curve to the left in orter to lo-cate ~2 at the bollolu of the curve which is the optimum point.
This lequ,.es decrement;ng the tlp~lAte coçfficients by ~ to move ~2 closer to the l1~ point. ~:imil~-ly~ if Et > . ET1 and ET3 l 0 (502) are on the left part of the curve and must move down the curve to the right to locate ~2 at the op ;.~ m point. This re-quire~ increm~nt;~ te coefficiçnt~ by ~ to move ~2 closer to the 1l~ point (503).
The i~.o~c~ent using the proceas of the y.e&cht in-1 5 vention over a fi ed ~ te coeffir~ent is illusl~ated in FIGs. 6and 7. In these ~ hs, the l,.oce~3 is uset with a least mean square (LMS) adaptive rh~nnsl estim~tor in simlll~t;ons of a M~im~lm T.ilr~lihoo-l Sequence Est;m~1ion eqll~li7~r for the U.S. digital cellular ~le~. The fi~ced ~ te co~ffi~i~nt is set 2 0 at 11 = 0.38 to allow adequate pe-f~.~ance when the mobile ra-diotelephone is traveling in vehicle at high spee~ls~ By using the ~ s of the present inven~ n~ the y~ço~ance of the eq~li7er is i~y~o~ed at signifiç~ntly lower vehicle speeds, as illustrated in FIG. 6. FIG. 6 shows the ye,fo,. lance of the 2 5 eq~ i7sr as a fimr~;on of multipath delay and the vehicle speed is apy,Q~ tely 5 mph. FIG. 7 shows how the p,ocess operates in a ch~nnel with delay spread and co-rh~nnel inter-Çe~chce when the vehicle speed drops in~ntqnP,ously from 63 mph to 5 mph. It can be seen that the llp~l~te coefficient, 3 0 quicldy decreases to a new lower level suitable for the lower vehicle speed.
In the preferred embo~iment the process of the present invention is implçmPnte~ as an algorithm. Alternate emho~l-imPnt~ of the invention can be implçmçnte~ in hardware or 3 5 combin~tion~ of ha,dwa,e and software; each block of the pro-- 8 - ~0365~8 cess being either an algorithm or a hardware circuit equiva-lent of that block.
In sllmm~ry~ a process of a~tom~tic~lly optimi7ine an adaptive filter l~p~l~te coefficient in a ch~ngine envirQnmPnt S has been described. By comr~ring the perfulluance of each adaptive algûrithm to deter~e how to change the l~r~ts co-~ffi~i~nt~, an optimal l~ t~ coeffirient for that particular en-vironmsnt can be obt~ine~l- Cornm~ni~tion devices using the process of the ~lcee-~t invention can out-~ folm devices using 10 a fLsed l~p~3~t'~ coPffit~iPn~
Claims (10)
1. A method for generating an optimum memory coefficient in an apparatus having two adaptive filters, each adaptive filter having an input signal and a reference signal, a first adaptive filter of the two adaptive filters having a first memory coefficient and a second adaptive filter of the two adaptive filters having a second memory coefficient, the method comprising the steps of:
generating an error signal for each adaptive filter in response to the input signal and the reference signal;
averaging each error signal to generate an average error for each adaptive filter;
comparing the average error of the two adaptive filters; and modifying the first and second memory coefficients in response to a difference in the average errors.
generating an error signal for each adaptive filter in response to the input signal and the reference signal;
averaging each error signal to generate an average error for each adaptive filter;
comparing the average error of the two adaptive filters; and modifying the first and second memory coefficients in response to a difference in the average errors.
2. A method for generating an optimal adaptive filter update coefficient in an apparatus having an input signal, the method characterized by the steps of:
generating a first error signal in response to the input signal and a first update coefficient;
generating a second error signal in response to the in-put signal and a second update coefficient;
estimating a third error signal in response to the input signal and a third update coefficient;
estimating a first mean square error in response to the first error signal;
estimating a second mean square error in response to the third error signal;
subtracting the second mean square error from the first mean square error to produce a mean square error difference;
generating an adaptation signal in response to the mean square error difference;
modifying the first, second, and third update coeffi-cients in response to the adaptation signal; and the method further characterized by repeating from the first step to make the mean square error difference substantially zero.
generating a first error signal in response to the input signal and a first update coefficient;
generating a second error signal in response to the in-put signal and a second update coefficient;
estimating a third error signal in response to the input signal and a third update coefficient;
estimating a first mean square error in response to the first error signal;
estimating a second mean square error in response to the third error signal;
subtracting the second mean square error from the first mean square error to produce a mean square error difference;
generating an adaptation signal in response to the mean square error difference;
modifying the first, second, and third update coeffi-cients in response to the adaptation signal; and the method further characterized by repeating from the first step to make the mean square error difference substantially zero.
3. The method of claim 2 and further characterized in that the first, second, and third error signals are generated by adaptive filters.
4. The method of claim 3 and further characterized in that the adaptive filters are adaptive equalizers.
5. The method of claim 2 and further characterized in that the adaptation signal is generated by comparing the mean square error difference to zero.
6. A method for generating an adaptive filter update coeffi-cient in an apparatus having an input signal, the method characterized by the steps of:
filtering the input signal, in a first adaptive filter hav-ing a first update coefficient, to generate a first error signal;
filtering the input signal, in a second adaptive filter having a second update coefficient, to generate a second error signal;
filtering the input signal, in a third adaptive filter hav-ing a third update coefficient, to generate a third error signal;
estimating a first mean square error in response to the first error signal;
estimating a second mean square error in response to the third error signal;
subtracting the second mean square error from the first mean square error to produce a mean square error difference;
filtering the mean square error difference to produce an adaptation signal;
modifying the first, second, and third update coeffi-cients in response to the adaptation signal; and the method further characterized by repeating from the first step to make the mean square error difference substantially zero.
filtering the input signal, in a first adaptive filter hav-ing a first update coefficient, to generate a first error signal;
filtering the input signal, in a second adaptive filter having a second update coefficient, to generate a second error signal;
filtering the input signal, in a third adaptive filter hav-ing a third update coefficient, to generate a third error signal;
estimating a first mean square error in response to the first error signal;
estimating a second mean square error in response to the third error signal;
subtracting the second mean square error from the first mean square error to produce a mean square error difference;
filtering the mean square error difference to produce an adaptation signal;
modifying the first, second, and third update coeffi-cients in response to the adaptation signal; and the method further characterized by repeating from the first step to make the mean square error difference substantially zero.
7. The method of claim 6 and further characterized in that the first, second, and third adaptive filters are adaptive equalizers.
8. A method for generating an adaptive filter update coeffi-cient in an apparatus having an input signal, the method characterized by the steps of:
filtering the input signal, in a first adaptive filter hav-ing a first update coefficient, to generate a first error signal;
filtering the input signal, in a second adaptive filter having a second update coefficient, to generate a second error signal;
filtering the input signal, in a third adaptive filter hav-ing a third update coefficient, to generate a third error signal;
estimating a first mean square error in response to the first error signal;
estimating a second mean square error in response to the third error signal;
subtracting the second mean square error from the first mean square error to produce a mean square error difference;
comparing the mean square error difference to a prede-termined value to produce an adaptation signal;
modifying the first, second, and third update coeffi-cients in response to the adaptation signal; and the method further characterized by repeating from the first step to make the mean square error difference substantially zero.
filtering the input signal, in a first adaptive filter hav-ing a first update coefficient, to generate a first error signal;
filtering the input signal, in a second adaptive filter having a second update coefficient, to generate a second error signal;
filtering the input signal, in a third adaptive filter hav-ing a third update coefficient, to generate a third error signal;
estimating a first mean square error in response to the first error signal;
estimating a second mean square error in response to the third error signal;
subtracting the second mean square error from the first mean square error to produce a mean square error difference;
comparing the mean square error difference to a prede-termined value to produce an adaptation signal;
modifying the first, second, and third update coeffi-cients in response to the adaptation signal; and the method further characterized by repeating from the first step to make the mean square error difference substantially zero.
9. The method of claim 8 and further characterized in that the first, second, and third adaptive filters are adaptive equalizers.
10. The method of claim 8 and further characterized in that the predetermined value is zero.
Applications Claiming Priority (2)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| US722,825 | 1991-06-28 | ||
| US07/722,825 US5230007A (en) | 1991-06-28 | 1991-06-28 | Method for optimizing an adaptive filter update coefficient |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CA2086548C true CA2086548C (en) | 1996-06-04 |
Family
ID=24903548
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA002086548A Expired - Fee Related CA2086548C (en) | 1991-06-28 | 1992-05-08 | A method for optimizing an adaptive filter update coefficient |
Country Status (9)
| Country | Link |
|---|---|
| US (2) | US5230007A (en) |
| JP (1) | JP2960165B2 (en) |
| KR (1) | KR960011120B1 (en) |
| BR (1) | BR9205341A (en) |
| CA (1) | CA2086548C (en) |
| DE (2) | DE4292034T1 (en) |
| GB (1) | GB2264600B (en) |
| MX (1) | MX9203306A (en) |
| WO (1) | WO1993000741A1 (en) |
Families Citing this family (37)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CA2089154C (en) * | 1991-06-28 | 1999-08-03 | Kevin L. Baum | Automatic frequency control by an adaptive filter |
| CA2076997C (en) * | 1991-09-30 | 1996-12-10 | James C. Baker | Apparatus and method for adaptively filtering a time-varying signal using multiple filtering algorithms |
| US5615233A (en) * | 1992-07-22 | 1997-03-25 | Motorola, Inc. | Method for channel estimation using individual adaptation |
| US5390364A (en) * | 1992-11-02 | 1995-02-14 | Harris Corporation | Least-mean squares adaptive digital filter havings variable size loop bandwidth |
| US5424881A (en) | 1993-02-01 | 1995-06-13 | Cirrus Logic, Inc. | Synchronous read channel |
| JP3102221B2 (en) * | 1993-09-10 | 2000-10-23 | 三菱電機株式会社 | Adaptive equalizer and adaptive diversity equalizer |
| DE19506324C1 (en) * | 1995-02-23 | 1995-10-12 | Siemens Ag | Adaptive balance filter guaranteeing optimal matching to line |
| JP2685031B2 (en) * | 1995-06-30 | 1997-12-03 | 日本電気株式会社 | Noise cancellation method and noise cancellation device |
| US5844941A (en) * | 1995-07-20 | 1998-12-01 | Micro Linear Corporation | Parallel adaptive equalizer circuit |
| US5694423A (en) * | 1996-08-06 | 1997-12-02 | Lucent Technologies Inc. | Method and apparatus for detecting and correcting misconvergence of a blind equalizer |
| US6263030B1 (en) | 1998-07-01 | 2001-07-17 | Ericsson Inc. | Equalizer with channel tracker switching |
| GB2348092B (en) * | 1999-01-12 | 2001-04-18 | Motorola Inc | Adapative step size for filter and method therefor |
| US6233276B1 (en) | 1999-09-13 | 2001-05-15 | Virata Corporation | XDSL modem having time domain filter for ISI mitigation |
| US6115419A (en) * | 1999-10-21 | 2000-09-05 | Philips Electronics North America Corporation | Adaptive digital beamforming receiver with π/2 phase shift to improve signal reception |
| KR100500810B1 (en) * | 1999-10-29 | 2005-07-12 | 마츠시타 덴끼 산교 가부시키가이샤 | Waveform equalization controller |
| EP1484325B1 (en) * | 2002-03-08 | 2014-06-18 | Japan Science and Technology Agency | Isoxazole derivatives and process for producing the same |
| JP4246562B2 (en) * | 2003-08-19 | 2009-04-02 | パイオニア株式会社 | Multipath distortion filter |
| KR100556401B1 (en) * | 2003-12-04 | 2006-03-03 | 엘지전자 주식회사 | Equalizer in VSB receiver |
| US7483479B2 (en) * | 2004-09-16 | 2009-01-27 | Keyeye Communications | Scaled signal processing elements for reduced filter tap noise |
| FR2878745B1 (en) | 2004-12-07 | 2007-03-09 | Oreal | TRANSUNGEAL DEVICE |
| US7702053B2 (en) * | 2005-05-05 | 2010-04-20 | Broadcom Corporation | State based algorithm to minimize mean squared error |
| US7436615B2 (en) * | 2005-12-08 | 2008-10-14 | International Business Machines Corporation | Using a measured error to determine coefficients to provide to an equalizer to use to equalize an input signal |
| FR2895555B1 (en) * | 2005-12-28 | 2008-05-09 | Jean Claude Odent | "METHOD AND INTERACTIVE SYSTEM FOR SOUND INTENSITY REDUCTION" |
| FR2946880B1 (en) | 2009-06-22 | 2011-07-15 | Oreal | COMPOSITION CONTAINING FILAMENTARY BACTERIUM EXTRACT AND PROCESS FOR COSMETIC TREATMENT OF AGING SIGNS |
| FR2956812B1 (en) | 2010-03-01 | 2013-03-08 | Oreal | COSMETIC COMPOSITION BASED ON ELLAGIC ACID OR ONE OF ITS DERIVATIVES AND A BACTERIA EXTRACT. |
| FR2964565B1 (en) | 2010-09-14 | 2012-09-07 | Oreal | COSMETIC COMPOSITION COMPRISING A FIXING POLYMER AND ANTIPELLICULAR AGENT |
| EP2627311A1 (en) | 2010-10-12 | 2013-08-21 | L'Oréal | Cosmetic composition comprising a particular silicon derivative and one or more acrylic thickening polymers |
| FR2966357A1 (en) | 2010-10-26 | 2012-04-27 | Oreal | COSMETIC COMPOSITION COMPRISING A FATTY CHAIN ALCOXYSILANE AND ANTIPELLICULAR AGENT |
| FR3001145B1 (en) | 2013-01-18 | 2015-07-17 | Oreal | FLEXIBLE SOLID COSMETIC COMPOSITION COMPRISING ANIO-NITIC SURFACTANTS AND POLYOLS, AND COSMETIC TREATMENT METHOD |
| FR3001144B1 (en) | 2013-01-18 | 2015-07-17 | Oreal | FLEXIBLE SOLID COSMETIC COMPOSITION COMPRISING ANIONIC SURFACTANTS AND POLYMERIC CONDITIONING AGENTS, AND COSMETIC TREATMENT METHOD |
| FR3001147B1 (en) | 2013-01-18 | 2015-07-17 | Oreal | FLEXIBLE SOLID COSMETIC COMPOSITION COMPRISING ANTI-ANSIAL SURFACTANTS AND SOLID PARTICLES, AND COSMETIC TREATMENT METHOD |
| WO2015085376A1 (en) | 2013-12-10 | 2015-06-18 | L'oreal | Cosmetic composition comprising cationic surfactant(s), antidandruff agent(s), liquid non-siliceous fatty substance(s), and non-polymeric thickening agent(s) |
| JP2015209380A (en) | 2014-04-24 | 2015-11-24 | ロレアル | Cosmetic composition |
| FR3044898B1 (en) | 2015-12-15 | 2019-11-01 | L'oreal | COSMETIC COMPOSITION COMPRISING ANIONIC SURFACTANT, AT LEAST 3.5% BY WEIGHT OF A FATTY ACID AND ANTIPELLICULAR AGENT |
| FR3060324B1 (en) | 2016-12-16 | 2019-04-12 | L'oreal | COMPOSITION COMPRISING AT LEAST TWO ANIONIC SURFACTANTS, NON-IONIC SURFACTANT AND AMPHOTERIC SURFACTANT, AND AT LEAST ONE ANTI-DELL AGENT |
| FR3072287B1 (en) | 2017-10-18 | 2019-10-25 | Basf Beauty Care Solutions France Sas | USE OF A CASSIA ALATA EXTRACT AGAINST HAIR AGING |
| TWI790000B (en) * | 2021-11-18 | 2023-01-11 | 立積電子股份有限公司 | Doppler radar apparatus and narrowband interference suppression method thereof |
Family Cites Families (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US4038536A (en) * | 1976-03-29 | 1977-07-26 | Rockwell International Corporation | Adaptive recursive least mean square error filter |
| US4577330A (en) * | 1984-04-19 | 1986-03-18 | At&T Bell Laboratories | Cross-polarization interference cancellation arrangement for digital radio channels |
| US4947363A (en) * | 1988-12-12 | 1990-08-07 | Motorola, Inc. | Pipelined processor for implementing the least-mean-squares algorithm |
| FR2641922B1 (en) * | 1988-12-30 | 1991-03-22 | Alcatel Transmission | SELF-ADAPTIVE EQUALIZATION DEVICE FOR A DIFFERENTIALLY CONSISTENT DEMODULATION INSTALLATION |
-
1991
- 1991-06-28 US US07/722,825 patent/US5230007A/en not_active Expired - Fee Related
-
1992
- 1992-05-08 KR KR1019930700465A patent/KR960011120B1/en not_active IP Right Cessation
- 1992-05-08 JP JP5501453A patent/JP2960165B2/en not_active Expired - Fee Related
- 1992-05-08 CA CA002086548A patent/CA2086548C/en not_active Expired - Fee Related
- 1992-05-08 DE DE4292034T patent/DE4292034T1/de active Pending
- 1992-05-08 BR BR9205341A patent/BR9205341A/en not_active Application Discontinuation
- 1992-05-08 WO PCT/US1992/003767 patent/WO1993000741A1/en active Application Filing
- 1992-05-08 GB GB9303631A patent/GB2264600B/en not_active Expired - Fee Related
- 1992-05-08 DE DE4292034A patent/DE4292034C2/en not_active Expired - Fee Related
- 1992-06-25 MX MX9203306A patent/MX9203306A/en not_active IP Right Cessation
-
1993
- 1993-03-30 US US08/040,064 patent/US5276707A/en not_active Expired - Lifetime
Also Published As
| Publication number | Publication date |
|---|---|
| DE4292034T1 (en) | 1993-06-03 |
| BR9205341A (en) | 1994-06-21 |
| JPH06500913A (en) | 1994-01-27 |
| KR960011120B1 (en) | 1996-08-20 |
| JP2960165B2 (en) | 1999-10-06 |
| GB2264600A (en) | 1993-09-01 |
| US5230007A (en) | 1993-07-20 |
| GB2264600B (en) | 1996-01-17 |
| GB9303631D0 (en) | 1993-05-05 |
| US5276707A (en) | 1994-01-04 |
| KR930701866A (en) | 1993-06-12 |
| DE4292034C2 (en) | 1995-04-27 |
| MX9203306A (en) | 1992-12-01 |
| WO1993000741A1 (en) | 1993-01-07 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CA2086548C (en) | A method for optimizing an adaptive filter update coefficient | |
| US5581585A (en) | Phase-locked loop timing recovery circuit | |
| KR100253539B1 (en) | Adaptive noise reduction circuit for a sound reproduction system | |
| EP1415403B1 (en) | System and method for canceling interference in a communication system | |
| US5566214A (en) | Automatic noise normalization and reacquisition control for a QPSK demodulator symbol tracking loop | |
| US4777640A (en) | Frequency adaptive phase jitter canceler | |
| WO2003034784A1 (en) | Improved hearing aid | |
| US20020093908A1 (en) | Noise/interference suppression system | |
| US5233633A (en) | Automatic frequency control by an adaptive filter | |
| KR20060094078A (en) | Voice activity detection with adaptive noise floor tracking | |
| CA2197001A1 (en) | Equalization system for timing recovery in electronic data transmission | |
| US20030048858A1 (en) | Method of reconstructing data transmitted over a transmission path in a receiver and corresponding device | |
| US6574576B2 (en) | Equalizer with auto-calibration and self-test | |
| US6922440B2 (en) | Adaptive signal latency control for communications systems signals | |
| WO1984001641A1 (en) | Adaptive filter including controlled tap gain coefficient drift | |
| EP1154586B1 (en) | Equaliser | |
| US5428834A (en) | Method and circuit for processing and filtering signals | |
| US7385913B2 (en) | Method and apparatus for compensating for variations in a receive portion of a wireless communication device | |
| US6888938B2 (en) | Dynamically adjustable digital gyrator having extendable feedback for stable DC load line | |
| Olika et al. | Adaptive noise cancellation for speech signal | |
| US5410741A (en) | Automatic gain control of transponded supervisory audio tone | |
| JP2003502910A (en) | Method and system for binary information detection in the presence of slowly changing disturbances | |
| CA2089154C (en) | Automatic frequency control by an adaptive filter | |
| Frank et al. | Efficient equalization of nonlinear communication channels | |
| Hariharan et al. | HF channel estimation using a fast transversal filter algorithm |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| EEER | Examination request | ||
| MKLA | Lapsed |