Pongs of h 5 IEEE onfn on onol pplons oono, n, gs 8-, 5 n Sf Mgn n Fl-oln Pv onoll M l-gll, E n, G oon L, Unvs of Mnnh, Gn lgll@n-nnh, n@n-nnh, g@n-nnh s n sf gn SM s nw pfon n s o s h sn wn pfn sf on n h s sp n h ss jo s volvs onoll sgn s on SM s pon o nn pfn gn of sf ng h nsn n n h psn of lg sns pll n sf-l sss In hs pp, fl oln onol sgn, sng pv onoll s on SM, o ov ss pfon f so ss fls s sss In on, l- sls of onol ss, whh ws pln n wo-n ss, psn o ons h fflnss of hs sgn I IOUIO h vlon of onol ss pns nl on h ffn wn h s pfon ong o h gvn spfons n h l pfon Sf s on of h os pon spfons fo h onoll ss Sf onol pol s ovng h ss fo gvn s of nl ss n s s sp o pn sf gon n Sf Mgn SM s nw pfon n fo h onol ss sgn, whh ws no n [], [] n [6] hs n ss how f h ss s jo s fo pfn sf on n h s sp h s vls of ns hv o ns h on gon n nol opon n n s of nns n/o sns hs, onoll sgn s on SM ps o nn pfn gn of sf ng nsn n s s of sf-l sss Moov, n s n Fl oln onol ss sgn F [], [] n o o sp p pfon ov n so ss of fls So hos fo nong SM no onoll sgn s n [] n [6] In hos onons, png ps of PI onolls, swhng onoll n/o opl onol hghlgh n lgoh fo h opon of SM n h s of SM n fl gnoss n solon s sss n [] Mol-s Pv onol MP longs o lss of ppohs h ns h opl onol pofl ong o pon of h ss hvo ov ng hozon, sn of f onol ons s hosn n o o p h volon of h ss n s ppl o h pln nl nw sns vll hn, nw sn s n, whh pl h pvos on [5]- [7] SM n no n MP s h h onsn o n onl n h pfon n sof onsns h w o o hs, h nlss fo F n h pl pplon n l- s h n onon of hs wo h pp s ognz s follow: Fs, SM fo sf-l ss n h F pol pln, ssp pv onoll sgn s on SM o nn pfn gn of sf ng h ss opon s vlop n slon sls psn I follows n llsv l- pl on wo-n loo poop wh nsl oponns Fnll, onlsons n f wo wn II EFIIIO OF F SM n F ss s onol ss h n oo oponns fls n s l o nn sl n pl g of pfon whn no onl h ss s fl-f lso whn h oponn lfnons h F pvns fls n sss fo vlopng no fls ss lvl h sgn of F sss n lssf s pssv s wll s v PF n F In PF, ss ol onl l n of fls, whh ss o nown po o h sgn of h onoll On h onoll s sgn, n opns np fls who n ss of on-ln fl nfoon F opnss h ff of fls h slng pop onol lw, o snhszng nw onol low on-ln n l- In h followng, h gnl wll fl pln s [] fo ls L X h s sp n n, n ons h ssp X, whh fns h sf opon gon fo so ss of s vls, n h s ssp, n spf s of nls {,=,}, wh : > ns nsf opon Fg I s ss h h ss s sl n h sns of Lpnov n h h sf gon s fll onn n h sl gon Sng wh h nl onon o, h ss jo wll volv o h opng pon s vsng h s sp wh vng sn o h sf on SM s fn s h nsnnos shos sn, wn h s vls of ns n pfn ons { =,=,}n hs ssp of s vls Whn h ss hs h opng pon / = n hs onsn vl nng h Son Sf Mgn SSM Mos nsl -78-95-6/5/$ 5 IEEE 8
n n ˆ shos sn fo o, spvl Vl s h n of fn nls n h n of s vls lvn o sf o h n h nson of h s-sp In os ss, h sf opon gon n fn s of ln nls { In s h h on fnon s nonln, n sv no wo o o ln onsns pws ln ppo- sgns on ng o ssf spf vls of SSM on I s nss o sngsh wn sf on If s onv fn ln on onsns n n nvl s ls of pls n on h vls of ns gvn h whol s vo, Sos, so of h sf ons fn = n, hn h sf gon s polop n fn h s ls no lws Fg shows h ffn wn pl on of vls n sf on I s ln nls n h fo l fo Fg h ll s vls ls ns s nvl pl on so s vos o no wh n, s onsn n = s = - ssf sf on onsns In gnl, h sf-opon gon s fn s of nls gvn ssp of s vo wh = hs, fo h s vo, n ll [] s,, ff 5 ff Sf on = o Sf Opon gon < Sf ls fo n SM s fn s s Fg : SM fnon Sf opon gon Unsf Opon gon > Fg SM n s ls Sf ls fo n s, [,,, ] n wh s s gvn s f ns h sf opon gon f os h sf opon gon Fo ll ons, h sn vo = [,,, ] n on fo = - 6 wh =,, = n g,,, n, SM, s h n ln n ong o III FUL OLE OOL SM ong o h fnon of SM n [] n [], SM shol ohws h s fl o lg sn Hn, F sgn s on SM ssfs h s spons n nns h ss s whn h sf gon Moov, shol hv h l o ng h ss ss o h sf gon s fs s possl whn, fo so son, h n nol son F s on SM n pssv o v [],[] If h pssv F wh SM hs no h l o ov h ss hn v F wh SM s pf h nvolvn of SM n v F sss s pon s h nfoon of fl on n solon FI ss, n os ss, s no Hn, SM wh v F n pov h F ss In hs wo, SM onl n pssv F sss s no, wh h s no nfoon o h fl IV PEIIVE OOLLE WIH SM In gnl, os of h onol lgohs s o ov h ss pfon sll s fo ln, pv o os onol hs, hs son plns how SM n nvolv no pv onolls o hv sf ns n on o ss pfon h onol lw of pv onoll, fo ss fn h s-sp ol, s n fo h nzon of -no s of p pfon [5] 8
n n J S 7 n sj o 8 wh ] [ - s h o wn h s n s spons n s h ss s vo, s h fn op vo, s h s op vo, s h np vo,,, n ss p of nsons, S, h o wghng, s h np wghng,, n h, n n onol hozons, spvl ` h nvolvn of SM no h pv onoll n hnl n wo ffn fos, wh oh psn vngs n svngs oh hos ons h h ss ol s s s-sp ol n h h sf gon s fn ln ons n onsn s ll fo 6 h ojv fnon ong o s Mho n n J H M o onol SM SM posv ll lns of h sn vo n 6 s posv hs, h vo n no n h pv onol pol s onl Ln M nl LMI onsns Hn, h onol sgnl s on nzng on 7 sj o sj o, wh H M,,, o 9 ons 5 n 8 hn gnl fo of o pon n sn vo S Eon s nown s pogng P pol, fo whh sn solvs s [8]-[] On ln opzon of on gvs h s onol sn, whh hvs h op pfon n h sf pfon o,, S,,, n f sgn ps SM onsns ons h s h onsns wh h fsl of h ov MP wh SM onsns n nls s n [7] n hs no n nl n hs wo Moov, h sf gon n ons s n nvn s [] n n nls ong o h hs ho n gv goo sls h opon n s so hgh h n onl ppl, wh h poss onsns slow n n Mho In o o psn h son ho, h followng l s nss: L : f h sf opng gon,, s onv, hn h onon o nz n-no of sj o ss 85
ol s o ov h ss o ns h sf gon h poof of l s spl n sl poof ong o h onv s pops Hn, h -no of n no s onl n h n ojv fnon 7 h ojv fnon of h pv onoll n hs s n wn n h followng fo [ n J n S ] sj o 7 n, wh S,, S P n P Po P hs s n nonsn pol, wh P s h wghng fo n pns on h vl of SM f s ngv hn h wghng ns n v-vs P s onsn wghng h n of f sgn ps n hs s ns P o SM onsns, h, s ons s sof onsns hs opzon pol n solv n wo ffn ws On-sho Opzon Solvng pol n h fo of sng opzon n fon n [5],[] Ssng n n n J n P s on, wh P P h onol lw s gvn P K K K wh K P K K h fs oponn n, nl, s h onol vo ppl o h ss hs onol vo n on fo s :: : I K K K 5 sp spl of h opzon lgoh, ns h o sp s h s sll hv lg nsons Moov, h pol ol nl nsl whn h hozons v lg n pogng h solon of h onol pol pplng n pogng s gvn h ffn onol lw [6] who ngl on w 6 wh w psns h onol vo o h fn n h onol on s on h s f P K, wh j P- s ll solvng h ffn Eon E j j j P P M P K j fo j =, -, n spf P S K s ll fo K j K j [ M P j ], wh M j n j h s n on fo n n h s n fn s j j j I j n j j j j h onol vo w s gvn w jw p wh w p- s on fo p j j K j w j K j p j n p S w h vng of sng n pogng opzon ns of opzon s h h s nsons sll Howv, h n of llon sps s ns o h oh hos o pln SM n pv onoll gnl fo MIMO sss h followng pl shows h vngs of h ho Epl S-sp ol ps of spl oo, s n [], [] 86
n S SM - - n SM OP [/s] -6 6 8 [s] [/s] - 5 [s] Ss 5 5 5 n sp 6 8 [s] onol Vol Fg oo spons wh PI S: on n OP: jo 5 6 8 [s] wh n = v s h oo sp ngl vlo, n, v np volg [,5] h sf opon gon s fn -w+5 < -w > < n w< 7 Fg shows h oo s jo Fg, SM von Fg n sp spons Fg o sp np /s sng PI onoll wh K p =, K = n K = h spons of h onoll s p w h o n s- h s jo ls os h sf ons nsn Fg SM s ngv o pov SM nsn, h onoll shol sgn ong o SM So ho of solvng hs pol s s n [] n [] sng swh PI, pv PI n opl s-f onolls s on SM Fg shows h oo spons sng pv onoll n h fo of 9 sj o ho wh h followng ps g 7, 7,,,,, S [ ] [] Fg 5 shows h s oo spons n on, w sf n nsn pfon, sng pv onoll n h fo of 5 ho wh h followng ps P o = g,,,,, = S = [] = [] = = =5 o h h s n Fg s sl o Fg h s jo Fg s fo o ns h sf gon ng nsn po spons n Fg 5 ssfs h sf ons h s- ns Fg 5 h pfon of ho s o p h opon lgoh s ffl On h oh hn, lgohs of ho s n pov sooh onol sgnls h ovll pfon of h ss s fo pl pl wos n h f sgn ps Ss n Ss n sp 5 [s] 5 5 5 ns onol Vol 5 5 [s] Fg Moo spons wh pv onoll ho n sp [/s] 5 [s] SM onol Vol - 5 [s] 5 5 5 5 5 [s] Fg 5 Moo spons wh pv onoll ho V EXPEIMEL ESULS h ov lgohs s n l- opon of n pnl loo poss s n [5] h poss, shown n Fg 6, onsss of wo-n ss Eh n hs onol vlv h op ln o onol h lvl n h n In h n pn, h nonnng vlv ws fll opn, h lg vlv onol vlv of n n ws js o sl onsn lg n h onol vlv, of h fs n, ws s o js h lvl n oh ns h wo-n ss ws f onsn flow l/s n h fs n h s ln ol of h ss splng l o Hz s gvn n l Lvl ns h onol vlv Inp flow l/s Lg vlv Lvl ns Fg 6 Sh g of wo-n ss 87
l : Ln s-sp ol of h wo-n-ss 978 9-6 -66-5555 - -8 7 - -5-7 [ ] [] h/ [/s] 5 - -5-5 [/s] 5 SM - - - - 5 [s] h op h s h lvl n h n n h np s h vlv opnng ons h h vls, whh lvn o ss sf, h n lvl h/ n v, h vlv l ovn whh sls h vlv opnng h sf opon gon s gvn : h/ + 8 v - 8 h/ + 75 v + - h/ -5 v 5 8 wh h vlv opnng s nolz whn [-5, 5] 5 ns fll opn n -5 opll los h lvl h/ hngs n /s pv onolls wh n who SM s, ong o Son, o gl h lvl of h lf n s pon of n s of lg fl Fg 7 shows l- sls who onsng SM n pv onoll fo h l wo-n ss whn h lg vlv s opn % f 5 s, f 65 s, n 5% f 8 s fl sno Fg 8 shows h l sls of h ov lgoh wh onsng SM n pv onoll fo h s fls I s l fo Fg 8 h n s of fl h onoll hs h l o op h ss whn h sf l nl h fl p o sol VI OLUSIOS onoll sgn s on SM povs sfssssn of sf-l sss pll sng MP sls of slon pl s wll s of l plnon on wo-n poss ons h vng of hs ppoh nl n F Howv, h fsl of MP wh SM onsn ws no n hs wo h so opn s n pplng hs h/ [/s] Ss 5 - -5-5 5 vlv opnng 5 [s] h h SM onol sgnl 5 - - 5 [s] -5 5 [s] Fg 7: Lvl spons sng pv onoll who SM - Ss h h 5 [s] onol Sgnl - - - - -5 5 [s] Fg 8: Lvl spons sng pv onoll wh SM ppoh, whh shol ov n h f: Fo pl, SM sng fo lg-sl ss n h pol of nng sf ons Hn, ll hs ops wll nn n h f wo s wll s h pol of pplng SM o fl pognoss EFEEES [] E n n M l-gll n Sf Mgn Pnpl n pplon n onol of Sf l Ss, IEEE Innonl onfn of onol pplon onfn, Sp -,, wn 689-695 [] M l-gll n E n, n Sf Mgn n Fl gnoss n Isolon, Eopn Sf n ll ESEL onf, Poln, Jn 7-, 5 [] M ln, M Sosw n Ev W, onp n Mhos n Fl-oln onol, ol n onol onfn, Jn [] M Mho, J Jng, n Y Zhng, v Fl oln onol Ss: L os n onol n nfoon Sns, Spng, [5] J oss, Mol-s Pv onol: Pl ppoh,, [6] G n H Unhn, Mlvl Gnlz S- Sp ng Hozon onol n l- Envonn, o, 5, 787-797, 999 [7] Mn, J wlngs, V o n Po M So, onsn Mol Pv onol: Sl n Opl, o, 6, 789-8, [8] EF ho n oons, Mol Pv onol, Spng, 999 [9] F oln, n Y L, flv won Mho Fo Mnzng Fnon Sj o ons on So of h Vls, SIM Jonl on Opzon, Vol 6,, -58, 996 [] JM Mjows, Pv onol wh onsn, Pn Hll, [] F oll, onsn Opl onol of Ln n H sss: L os n Infoon Sn, Spng, [] hos, M nh n G, Opzon oolo, Mh Wo, In, 999 []F lnhn S Invn n onol, o, 5:77-767, 999 [] G S-sp sgn of Pv onol fo MIMO Sss, Ph hss, oh Unvs, Gn, 995 [5] G, Msh n E n, onol Loo Pln o Epn wh H Ss, Po of n onol onfn, nv, [6] M l-gll n E n, pv onoll sng n sf gn fo h loo pln, Po of n onol onfn 5, Poln, Ogon, US, -8 88