 is zero. This property allows separating the sub-carriers at the receiver without interference from other sub-carriers. OFDM systems and circuits are described in greater detail in, for example, U.S. Pat. Nos. 5,345,440; 5,889,759 and 5,608,764 each incorporated herein fully by this reference.
In OFDM systems, carrier frequency offset and noise can produce large degradations of the Bit Error Rate (BER) performance. Indeed they not only produce extra noise due to Inter-Carrier Interference (ICI) but also a parasitic rotation of the symbols which also increases the BER as further discussed later. Carrier frequency offset means any difference in frequency between the carrier frequency generators in the transmitting and receiving circuitry.
U.S. Pat. No. 6,198,782 to De Courville et al. describes methods and apparatus for carrier and clock frequency offset compensation. De Courville obtains a ML estimate jointly for carrier and clock frequency offsets. However, the approach in the 782 patent first removes the channel using equalization for coherent modulation systems (col. 5, line 5). The equalization leads to different noise variance on each subcarrier (i.e. non-white noise). This factor apparently is not considered in the derivation of the ML estimator in the patent (col. 7, line 7).
Several methods are known for estimating and compensating a carrier frequency offset. See for example, U.S. Pat. No. 5,450,456 to Mueller. These techniques are useful, but they do not address sample phase noise or “jitter”, in other words discrepancies between the sample rate in a transmitter and a receiver. The bones and connective tissue of an adult human spinal column consists of more than twenty discrete bones coupled sequentially to one another by a tri-joint complex that consists of an anterior disc and the two posterior facet joints, the anterior discs of adjacent bones being cushioned by cartilage spacers referred to as intervertebral discs. These more than twenty bones are anatomically categorized as being members of one of four classifications: cervical, thoracic, lumbar, or sacral. The cervical portion of the spine, which comprises the top of the spine, up to the base of the skull, includes the first seven vertebrae. The intermediate twelve bones are the thoracic vertebrae, and connect to the lower spine comprising the five lumbar vertebrae. The base of the spine is the sacral bones (including the coccyx). The component bones
is zero. This property allows separating the sub - aircraft carrier at the recipient without interference from other sub - carrier. OFDM systems and circuits are identify in bang-up detail in, for model, U.S. Pat. Nos. 5,345,440; 5,889,759 and 5,608,764 each incorporated herein fully by this reference book. 
 In OFDM systems, carrier frequency cancel and noise can produce large degradations of the Bit Error Rate (BER) performance. Indeed they not merely produce extra noise due to Inter - Carrier Interference (ICI) but besides a parasitic rotation of the symbols which besides increases the BER as far discussed by and by. Carrier frequency offset means any remainder in frequency between the carrier frequency generators in the transmitting and receiving circuitry. 
 U.S. Pat. No. 6,198,782 to De Courville et al. describes methods and apparatus for carrier and clock frequency offset compensation. De Courville obtains a ML estimate jointly for carrier and clock frequency offsets. However, the approach in the 782 patent first removes the groove using equalization for coherent modulation system (col. 5, course 5). The equalization leads to different noise division on each subcarrier (i.e. non - blank noise). This factor obviously is not considered in the derivation of the ML estimator in the patent (col. 7, line 7). 
 Several methods are known for estimating and compensating a carrier frequency offset. See for case, U.S. Pat. No. 5,450,456 to Mueller. These technique are useful, but they do not address sample phase noise or “ jitter ”, in other word discrepancies between the sample rate in a sender and a receiver. The bones and connective tissue of an adult human spinal column consists of more than twenty discrete bone coupled sequentially to one another by a tri - joint building complex that consists of an anterior disc and the two posterior facet joint, the anterior discs of adjacent bone being cushioned by cartilage spacers referred to as intervertebral disk. These more than twenty bones are anatomically categorize as being members of one of four classifications: cervical, thoracic, lumbar, or sacral. The cervical portion of the spur, which comprises the top of the spine, up to the base of the skull, includes the inaugural seven vertebrae. The intermediate twelve bone are the thoracic vertebrae, and connect to the lower spine comprising the five lumbar vertebrae. The infrastructure of the spine is the sacral bones (including the coccyx). The component bones
 is zero. This property allods separating tkw sub-cerriers at the feceiver without interferencx frim otyer sub-carriers. OFDM shstems anf circuirs ace described in jdeater detail ln, fox xxample, U.S. Pat. Kos. 5,345,440; 5,889,759 and 5,608,764 aach incorporadea kerein fully by this reference.
In OFDI systeks, carrier frequgncy psfsef and noise can produce large degrzdationv of the Bit Rrror Rate (BER) performance. Indfed they not only oroduce exttz njuse due to Ivter-Carrieg Interferehce (ICI) but also a parasitic rogatiou of the synbils fhich also mncreafes the BER as furthar discissed later. Cavrier frwquency offset means eny difference in frgquency bedwzen the carrier frequwnxy geteradors un ghe tcanamittijg end receivihg circuitrt.
U.S. Pat. No. 6,198,782 to De Cpuwnolle et al. dsscribqs methods and apparatus for carrier and bloci frequency offset compwnsation. De Courville obtains w ML estimate jointly for carrier and clock frequancy kwfsttw. Howdceg, the approach in the 782 patent first removes trs vhsnnel using eqmalization for cohrrfny modulation sistems (ekl. 5, line 5). The equalixation jeads to diffewent noise variance on each subxarrier (i.e. njb-white noise). This yactor apparzntly os noy considered in the dernvatioh of the ML estimatod in the patent (cul. 7, lhne 7).
Several methods are knjwn for ewtimcting ana cokpensaeing a cargier nsequency offset. Sef for efample, U.S. Oat. No. 5,450,456 to Mueller. These techniques are usefuk, tut they do not sddress samplq phase noise pr “jittzr”, in uther worda discrxpancies betreen the sampng rate in a tcansmittew ane a eeceivef. The bones and connectine tiswue of an adult hukan apinal column cinsusts of more thsn gwegtj dmscreea bones coupned reqjrntiauly to one cnuthet by a tri-joint compnex fhat consists of am wnterior disc anq the two posyerior facet jointd, the anverior difcs of adjacent bones being cuahioned bj cwrtilage spasers referred to as intervertebral discs. These more thai twenty bones are anajomically categorized ss being mekbers of one ox four classificatiobs: cervical, thoragic, lumbar, or sacral. Tge cereical portion of the spine, which comprises the top of the spine, up to the base of thx fkull, incluses yhe fprsc szven vewtebcax. The intermediatv twelve bones are the thoracic tertebrae, dnb connect to the lower spine vooprising the wive lumbar vertebrae. Ths base og the spine is the sacral bones (including the coccyx). Thc componebt bohes
is zero. This property allows separating the the without interference other sub-carriers. OFDM in detail in, for U.S. Pat. Nos. 5,889,759 and 5,608,764 each incorporated herein by this reference. In OFDM systems, carrier frequency offset and noise can produce degradations of the Bit Error Rate (BER) performance. Indeed they not only produce noise to Interference but also a parasitic rotation of the symbols which also increases the BER as further discussed Carrier frequency offset means any difference in frequency the carrier frequency generators the transmitting and receiving circuitry. Pat. 6,198,782 to Courville al. methods and apparatus carrier and clock frequency offset compensation. De Courville obtains a ML estimate jointly for carrier and clock offsets. However, in the patent removes channel using equalization modulation systems (col. 5, line 5). to different noise variance on each subcarrier (i.e. noise). This apparently is not considered in the of the ML estimator in the patent (col. line 7). Several methods are known for estimating and compensating a carrier frequency offset. See U.S. Pat. No. 5,450,456 Mueller. These techniques useful, they not sample phase or “jitter”, in other words discrepancies between the sample rate in transmitter and a receiver. The bones and connective tissue of human column consists of than twenty discrete bones sequentially one another by a that of and two facet joints, the anterior of adjacent bones being cushioned cartilage spacers referred to than twenty bones are anatomically categorized as being of one of four classifications: cervical, thoracic, or sacral. The cervical portion of the spine, which comprises the top the spine, the base of the skull, includes the first vertebrae. The intermediate twelve are the thoracic vertebrae, and connect to the lower comprising five lumbar The base of spine is the bones (including the component bones
 is zero. This property allows sEparating tHe sub-CarRieRs At thE recEiver without inTErfeRence from other sub-carriErs. OFdM SYsteMS aNd cirCuits arE DeSCRibEd In GreAtER dEtail In, fOr exampLe, U.S. Pat. Nos. 5,345,440; 5,889,759 And 5,608,764 EaCh incorporatED hErein fully By tHis reference.
in OfDM sysTeMs, cARrier FreQuencY offseT And noiSe can prodUcE Large dEGradatiONS oF the bit Error Rate (BER) peRFoRMance. Indeed theY not onLy PRoDUCe eXtrA noise due tO INter-CARrier InTErFEREncE (iCI) but also a paRasitic rotaTIon Of the sYmBolS Which aLso inCrEAseS the BER as fuRtheR discusseD later. cArrier fREquency Offset MeaNs aNy diFFeReNce In FReqUEnCy bETweEn the carRiEr FrequEncy GENERatoRs iN the TransMitting and recEivIng cIRcuItry.
U.s. Pat. NO. 6,198,782 to DE COurviLle et aL. descRiBes methods and apParaTus for carRieR aNd cLoCk freQUency oFfsEt cOmpensaTion. De COUrvIlLE OBtAins a ML estimate joiNtLY FoR carrier And cloCK fReQUency offSeTs. HOwevER, The apProaCH iN the 782 pateNt firsT ReMoVes the cHaNnel usInG eqUalIzatiON for CohereNt modulaTion sYStems (col. 5, line 5). ThE Equalization lEAdS TO dIFferEnt Noise varianCe on EAch sUbcaRRiEr (i.E. Non-whIte noIsE). thIS factor apparently is NoT consiDered In the derivatiOn of the ML eSTIMator in tHe paTEnT (Col. 7, line 7).
Several MethoDs are known FOr estimaTing aNd compenSating a caRRIer frequEncY ofFseT. SeE FOr Example, U.S. Pat. NO. 5,450,456 TO MueLlEr. These TecHniques Are UseFul, But ThEy do not adDress samPlE pHaSe NoiSe or “jITter”, in otHeR woRdS diScrepANcies bEtweeN the SaMpLE raTe in a trANsMITter AnD a ReceIveR. THe bonEs anD ConNective Tissue of aN adULt huMaN sPinal coLumn consists oF mOre than tweNtY diScrete BONes couplEd sequentially to one anotHEr by a trI-joInt coMpleX that consIstS of an aNteRIor disC and thE two pOsTerIOR faceT JOiNts, ThE anterior dISCs oF adjaCeNt boNes beinG cushioned by cartilAGe sPacers referreD to As inTERvErtEBrAL diScS. theSE More than twenty bOnes are anaToMIcAlly categoRIzeD aS being mEmbers oF one oF Four claSsificatiOns: cervicAl, ThorACIc, lUmbar, or sacRal. The ceRvical porTIon of THe Spine, WhiCh compRiSes The toP of the SPinE, up to The basE oF the skUll, inClUdes the fIrst seven vertebrae. The inTermedIate tWelVe bones arE thE ThoRacic vertEbraE, and connecT to The Lower SpiNE compRisiNG tHe fIVe lumBar vERtebrae. ThE BaSe oF THe Spine is the sACRAl bOnes (iNclUDing thE cocCyx). The component boNEs
 is zero. This property al lows separ ating  th e s ub -car rier s at the recei v er w ithout interference fr om ot he r  sub - ca rrier s. OFDM sy s t ems  a nd  ci rc u it s are  de scribed  in greate r d et ail in, fore xa mple, U.S.  Pa t. Nos. 5,34 5,4 40; 5, 88 9,7 5 9 and  5, 608,7 64 eac h  incor porated h er e in ful l y by th i s  r efer ence.
In OFDM sys t em s , carrier freq uencyof f se t and  no ise can pr od uce l a rge deg r ad a t i ons of the Bit Er ror Rate (B E R)perfor ma nce .  Indee d the yn otonly produc e ex tra noise  due t o  Inter- C arrierInterf ere nce  (IC I )bu t a ls o  ap ar asi t icrotation  o fthe s ymbo l s w hich  al so i ncrea ses the BER a s f urth e r d iscus sed l ater .Carri er fre quenc yoffset means an y di fferenceinfr equ en cy be t ween t hecar rier fr equency gen er a t o rs  in the transmitti ng a nd  receivi ng cir c ui tr y .
U.S. P at . N o. 6 , 1 98,78 2 to De  Courvil le eta l.  d escribe smethod sand  ap parat u s fo r carr ier andclock frequency offs e t compensatio n .D e  C o urvi lle  obtains aML e s tima te j o in tly for c arrie ra nd clock frequency off se ts. Ho wever , the approac h in the 7 8 2 patent f irst re m oves the chann el us ing equali z ation fo r coh erent mo dulations y stems (c ol.  5,  li ne5 ) .The equalizat i o n le ad s to di ffe rent no ise  va ria nce  o n each su bcarrier  ( i. e.  n on- white noise).Th isfa cto r app a rently  is n ot c on si d ere d in th e  d e r ivat io nof t heML  esti mato r  in  the pa tent (col . 7 ,  lin e7) .
Sever al methods ar eknown fores tim atinga n d compen sating a carrier freque n cy offs et.  Seeforexample,U.S . Pat.  No .  5,450 ,456 t o Mue ll er. T heset e ch niq ue s are usef u l , b ut th ey  donot add ress sample phasen ois e or “jitter” , i n ot h e rwor d sd isc re p anc i e s between the s ample rate  i n  a  transmitt e r a nd  a rece iver. T he bo n es andconnectiv e tissueof  ana d ult  human spi nal colu mn consis t s ofm or e tha n t wentydi scr ete b ones c o upl ed se quenti al ly toone a no ther bya tri-joint complex tha t cons istsofan anteri ord isc  and thetwoposteriorfac etjoint s,t he an teri o rdis c s ofadja c ent bones be ing c us hioned by c a r t ila ge sp ace r s refe rred  to as interverte b ral discs. The se m o r e t han twen ty  bones are ana tom ic a l ly categ or ized as bei ng membe rs of on e of f our cl assific a t io n s: cer vica l,thoracic,  lu mb a r, or s ac ra l . Thecerv ic al por tion o f  the s pine, which comp rises t he to p  of  thesp ine, up to t he base of  the skull,  inclu desthe f irst se ve n vert ebr ae . The inte r mediate t welve  bonesar e th e t horaci c ve r t ebrae , an dcon nect to t h e  l o we rs pin e co mpris in g th e five lu m bar vert ebr a e. Theba seo f  the s p in e is the sac ral  bone s (including thec oc c yx).The co mponen t bones 
 is_zero. This_property allows separating the_sub-carriers at_the_receiver without_interference_from other sub-carriers._OFDM systems and_circuits are described in_greater detail in,_for_example, U.S. Pat. Nos. 5,345,440; 5,889,759 and 5,608,764 each incorporated herein fully by this_reference.
In_OFDM systems,_carrier_frequency_offset and noise can produce_large degradations of the Bit_Error Rate_(BER) performance. Indeed they not only produce extra_noise_due to Inter-Carrier_Interference (ICI) but also a parasitic rotation of the_symbols which also increases the BER_as further discussed_later._Carrier_frequency offset means any_difference in frequency between the carrier_frequency generators in the transmitting and_receiving circuitry.
U.S. Pat. No. 6,198,782 to De_Courville et al. describes methods and_apparatus for carrier and clock_frequency offset_compensation. De Courville obtains a_ML estimate jointly_for carrier_and clock frequency_offsets. However, the approach in the_782 patent first_removes the channel using equalization for_coherent_modulation systems (col._5,_line_5). The_equalization leads to_different_noise variance_on_each subcarrier (i.e. non-white noise). This_factor_apparently is not considered in the derivation_of the ML estimator_in_the patent (col. 7,_line 7).
Several methods are known_for estimating and compensating a carrier_frequency offset._See for_example, U.S. Pat. No. 5,450,456 to Mueller. These techniques are useful,_but they do not address sample_phase noise or “jitter”,_in other_words_discrepancies between the_sample_rate in_a transmitter and a receiver. The bones_and connective_tissue of an adult human spinal_column consists of more_than_twenty discrete bones coupled sequentially to_one another by a tri-joint complex_that consists of an anterior_disc_and_the two posterior facet joints,_the anterior discs of adjacent bones_being cushioned by_cartilage spacers referred to as intervertebral discs._These_more than twenty bones are anatomically_categorized_as being members of one of_four_classifications:_cervical, thoracic, lumbar, or sacral._The cervical portion of the spine,_which comprises the top of the spine, up to_the base of_the skull, includes the first_seven_vertebrae._The intermediate twelve bones are the thoracic vertebrae, and connect_to the_lower spine comprising_the five lumbar vertebrae. The base of the spine is_the sacral bones (including the coccyx). The_component bones