▼■◆■❙❚❘❨ ❖❋ ◆❆❚■❖◆❆▲ ❉❊❋❊◆❙❊ ▼■▲■❚❆❘❨ ❚❊❈❍◆■❈❆▲ ❆❈❆❉❊▼❨ ◆●❯❨❊◆ ❚❍❆◆❍ ◆❖◆▲■◆❊❆❘ ❉■❙❚❖❘❚■❖◆❙ ❆◆❉ ❈❖❯◆❚❊❘▼❊❆❙❯❘❊❙ ❋❖❘ P❊❘❋❖❘▼❆◆❈❊ ■▼P❘❖❱❊▼❊◆❚❙ ■◆ ❈❖◆❚❊▼P❖❘❆❘❨ ❘❆❉■❖ ❈❖▼▼❯◆■❈❆❚■❖◆ ❙❨❙❚❊▼❙ ❙♣❡❝✐❛❧✐③❛t✐♦♥ ✿ ❊❧❡❝tr♦♥✐❝ ❊♥❣✐♥❡❡r✐♥❣ ❙♣❡❝✐❛❧✐③❛t✐♦♥ ❝♦❞❡ ✿ ✾ ✺✷ ✵✷ ✵✸ ❙❯▼▼❆❘❨ ❖❋ ❚❊❈❍◆■❈❆▲ ❉❖❈❚❖❘❆▲ ❚❍❊❙■❙ ❍❛ ◆♦✐ ✲ ✷✵✶✾ ▲■❙❚ ❖❋ P❯❇▲■❈❆❚■❖◆❙ ❚❍■❙ ❲❖❘❑ ■❙ ❈❖▼P▲❊❚❊❉ ❆❚ ▼■▲■❚❆❘❨ ❚❊❈❍◆■❈❆▲ ❆❈❆❉❊▼❨ ✲ ▼■◆■❙❚❘❨ ❖❋ ◆❆❚■❖◆❆▲ ❉❊❋❊◆❙❊ ✶✳ ◆❣✉②❡♥ ❚❤❛♥❤ ✱ ◆❣✉②❡♥ ❚❛t ◆❛♠✱ ❛♥❞ ◆❣✉②❡♥ ◗✉♦❝ ❇✐♥❤✱ ✏❆✉t♦♠❛t✐❝ ♣❤❛s❡ ❝♦♠♣❡♥s❛t✐♦♥ ✐♥ ▼■▼❖✲❙❚❇❈ s②st❡♠s ✇✐t❤ ♥♦♥❧✐♥❡❛r ❞✐st♦rt✐♦♥ ✐♥✲ ❝✉rr❡❞ ❜② ❤✐❣❤ ♣♦✇❡r ❛♠♣❧✐❢✐❡rs✱✑ ✐♥ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✷✵✶✼ ❆❞✈❛♥❝❡❞ ❚❡❝❤✲ ♥♦❧♦❣② ❢♦r ❈♦♠♠✉♥✐❝❛t✐♦♥s ❈♦♥❢❡r❡♥❝❡ ✲ ❆❚❈ ✷✵✶✼✱ ◗✉② ◆❤♦♥✱ ❱✐❡t ◆❛♠✱ ♣♣✳ ✽✻✲✾✶✱ ❖❝t✳ ✶✽✲✷✵✱ ✷✵✶✼✳ ❙✉♣❡r✈✐s♦r✿ ❆ss♦❝✳ Pr♦❢✳ ❉r✳ ◆●❯❨❊◆ ◗❯❖❈ ❇■◆❍ ✷✳ ◆❣✉②❡♥ ❚❤❛♥❤ ✱ ◆❣✉②❡♥ ❚❛t ◆❛♠✱ ❛♥❞ ◆❣✉②❡♥ ◗✉♦❝ ❇✐♥❤✱ ✏P❡r❢♦r♠❛♥❝❡ ♦❢ ❛ ♣❤❛s❡ ❡st✐♠❛t✐♦♥ ♠❡t❤♦❞ ✉♥❞❡r ❞✐❢❢❡r❡♥t ♥♦♥❧✐♥❡❛r✐t✐❡s ✐♥❝✉rr❡❞ ❜② ❤✐❣❤ ♣♦✇❡r ❛♠♣❧✐❢✐❡rs ✐♥ ▼■▼❖✲❙❚❇❈ s②st❡♠s✱✑ ✐♥ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ❈♦♥❢❡r❡♥❝❡ ♦♥ ■♥❢♦r♠❛t✐♦♥ ❛♥❞ ❈♦♠♣✉t❡r ❙❝✐❡♥❝❡ ✲ ◆■❈❙ ✷✵✶✼✱ ❍❛ ◆♦✐✱ ❱✐❡t ◆❛♠✱ ♣♣✳ ✹✷✲✹✼✱ ◆♦✈✳ ✷✹✲✷✺✱ ✷✵✶✼✳ ❖♣♣♦♥❡♥t ✶✿ ❆ss♦❝✳ Pr♦❢✳ ❉r✳ ◆●❯❨❊◆ ❍❯❯ ❚❍❆◆❍ ✸✳ ◆❣✉②➵♥ ❚❤➔♥❤ ✱ ◆❣✉②➵♥ ❚➜t ◆❛♠✱ ◆❣✉②➵♥ ◗✉è❝ ❇➻♥❤✱ ✏❷♥❤ ❤÷ð♥❣ ❝õ❛ ♠➨♦ ♣❤✐ t✉②➳♥ ❞♦ ❜ë ❑✣❈❙ ✤➳♥ ❤➺ t❤è♥❣ ▼■▼❖✲❙❚❇❈ tr♦♥❣ tr÷í♥❣ ❤đ♣ ❝â sû ❞ư♥❣ trữợ t t ❚↕♣ ❝❤➼ ❑❤♦❛ ❤å❝ ✈➔ ❑ÿ t❤✉➟t✱ ❍å❝ ✈✐➺♥ ❑ÿ t❤✉➟t ◗✉➙♥ sü✱ tr❛♥❣ ✼✹✲✽✽✱ sè ✶✽✽✱ t❤→♥❣ ✷ ♥➠♠ ✷✵✶✽✳ ❖♣♣♦♥❡♥t ✷✿ ❆ss♦❝✳ Pr♦❢✳ ❉r✳ ▲❊ ◆❍❆❚ ❚❍❆◆● ✹✳ ◆❣✉②❡♥ ❚❤❛♥❤ ✱ ◆❣✉②❡♥ ◗✉♦❝ ❇✐♥❤✱ ◆❣✉②❡♥ ❚❤✐ P❤✉♦♥❣ ❍♦❛✱ ✏P❤❛s❡ ❡s✲ t✐♠❛t✐♦♥ ❛♥❞ ❝♦♠♣❡♥s❛t✐♦♥ ✉♥❞❡r ❞✐❢❢❡r❡♥t ♥♦♥❧✐♥❡❛r✐t✐❡s ✐♥❝✉rr❡❞ ❜② ❤✐❣❤ ♣♦✇❡r ❛♠♣❧✐❢✐❡rs ✐♥ ▼■▼❖✲❙❚❇❈ s②st❡♠s✱✑ ❏♦✉r♥❛❧ ♦❢ ❙❝✐❡♥❝❡ ❛♥❞ ❚❡❝❤✲ ♥✐q✉❡ ✲ ▼✐❧✐t❛r② ❚❡❝❤♥✐❝❛❧ ❆❝❛❞❡♠②✱ ♣♣✳ ✺✾✲✼✹✱ ◆♦✳ ✶✾✶✱ ❏✉♥✳ ✷✵✶✽✳ ❖♣♣♦♥❡♥t ✸✿ ❉r✳ P❍❆◆ ❍❯❨ ❆◆❍ ✺✳ ◆❣✉②❡♥ ❚❤❛♥❤ ✱ ◆❣✉②❡♥ ❚❛t ◆❛♠✱ ◆❣✉②❡♥ ◗✉♦❝ ❇✐♥❤✱ ✏❖♥ t❤❡ r❡❛s♦♥❛❜❧❡✲ ♥❡ss ♦❢ ♥♦♥❧✐♥❡❛r ♠♦❞❡❧s ❢♦r ❤✐❣❤ ♣♦✇❡r ❛♠♣❧✐❢✐❡rs ❛♥❞ t❤❡✐r ❛♣♣❧✐❝❛t✐♦♥s ✐♥ ❝♦♠♠✉♥✐❝❛t✐♦♥ s②st❡♠ s✐♠✉❧❛t✐♦♥s✱✑ ❏♦✉r♥❛❧ ♦❢ ▼✐❧✐t❛r② ❙❝✐❡♥❝❡ ❛♥❞ ❚❡❝❤✲ ♥♦❧♦❣② ✲ ❆❝❛❞❡♠② ♦❢ ▼✐❧✐t❛r② ❙❝✐❡♥❝❡ ❛♥❞ ❚❡❝❤♥♦❧♦❣②✱ ♣♣✳ ✽✻✲✾✾✱ ◆♦✳ ✺✺✱ ❏✉♥✳ ✷✵✶✽✳ ❚❤✐s t❤❡s✐s ✇✐❧❧ ❜❡ ❞❡❢❡♥❞❡❞ ❜❡❢♦r❡ ❚❤❡ ❆❝❛❞❡♠②✲▲❡✈❡❧ ❉♦❝t♦r❛❧ ❊①❛♠✐♥❛t✐♦♥ ❇♦❛r❞ ❛❝❝♦r❞✐♥❣ t♦ t❤❡ ❉❡❝✐s✐♦♥ ◆♦ ✳✳✳✴✳✳✳✳✳✳ ❞❛t❡ ✳✳✳ ♠♦♥t❤ ✳✳✳ ②❡❛r ✳✳✳✳✳ ♦❢ t❤❡ Pr❡s✐❞❡♥t ♦❢ ▼✐❧✐t❛r② ❚❡❝❤♥✐❝❛❧ ❆❝❛❞❡♠②✱ ♠❡❡t✐♥❣ ❛t t❤❡ ▼✐❧✐t❛r② ❚❡❝❤♥✐❝❛❧ ❆❝❛❞❡♠② ❛t t✐♠❡ ✳✳✳ ❞❛t❡ ✳✳✳ ♠♦♥t❤ ✳✳✳ ②❡❛r ✳✳✳✳✳ ❚❤✐s t❤❡s✐s ❝♦✉❧❞ ❜❡ ❢♦✉♥❞ ❛t✿ ✲ ◆❛t✐♦♥❛❧ ▲✐❜r❛r② ♦❢ ❱✐❡t♥❛♠ ✲ ▲✐❜r❛r② ♦❢ ▼✐❧✐t❛r② ❚❡❝❤♥✐❝❛❧ ❆❝❛❞❡♠② ❋✐♥❛❧ ❈♦♥❝❧✉s✐♦♥s ❛♥❞ ❙✉❣❣❡st❡❞ ❊①t❡♥s✐♦♥s ■◆❚❘❖❉❯❈❚■❖◆ ❙✉♠♠❛r② ♦❢ ♠❛❥♦r ❢✐♥❞✐♥❣s ❛♥❞ ❝♦♥tr✐❜✉t✐♦♥s ✶✳ ❇❛❝❦❣r♦✉♥❞ ♦❢ r❡s❡❛r❝❤✿ ▼❛❥♦r ❝♦♥tr✐❜✉t✐♦♥s ♦❢ t❤❡ t❤❡s✐s ❛r❡ ❛s ❢♦❧❧♦✇s✳ ❆ ♣r❛❝t✐❝❛❧ ❤✐❣❤ ♣♦✇❡r ❛♠♣❧✐❢✐❡r ✭❍P❆✮ ❞♦❡s ❤❛✈❡ ❛ ♥♦♥❧✐♥❡❛r ✐♥♣✉t✲♦✉t♣✉t ✶✳ ❊✈❛❧✉❛t✐♥❣ ♥♦♥❧✐♥❡❛r ❍P❆ ♠♦❞❡❧s r❡❣❛r❞✐♥❣ t♦ ♣r♦❜❧❡♠ ♦❢ s✐♠✉❧❛t✐♥❣ ✐♥✲ ❝❤❛r❛❝t❡r✐st✐❝✱ t❤✉s✱ ❞✐st♦rt✐♥❣ t❤❡ ♦✉t♣✉t s✐❣♥❛❧ ❬✹✺✱ ✺✺❪✳ ❍❡♥❝❡✱ ♠♦❞❡❧✐♥❣ ❛♥❞ t❡r♠♦❞✉❧❛t✐♦♥ ♣r♦❞✉❝ts ✭■▼P✮✳ Pr♦♣♦s✐♥❣ t❤❡ ♣♦❧②s✐♥❡ ♠♦❞❡❧ ❢♦r ♣r❡❝✐s❡ ❛♥❛❧②③✐♥❣ ♥♦♥❧✐♥❡❛r ❍P❆ tr❛♥s❢❡r ❢✉♥❝t✐♦♥s✱ ❛♥❞ s♣❡❝✐❢✐❝❛❧❧②✱ ✐♥✈❡st✐❣❛t✐♥❣ ❡❢✲ s✐♠✉❧❛t✐♦♥ ♦❢ ■▼Ps✱ ❡s♣❡❝✐❛❧❧② ❢♦r s✐❣♥❛❧s ✇✐t❤ ❝♦♠♣❧❡① str✉❝t✉r❡s✳ ❢❡❝ts ♦❢ t❤❡s❡ ❝❤❛r❛❝t❡r✐st✐❝s t♦ ♠♦❞❡r♥ ❞✐❣✐t❛❧ ❝♦♠♠✉♥✐❝❛t✐♦♥ s②st❡♠s ❛r❡ st✐❧❧ ✷✳ Pr♦♣♦s✐♥❣ t❤❡ ✉s❡ ♦❢ ♣r❡❞✐st♦rt✐♦♥ s❝❤❡♠❡s ❢♦r ▼■▼❖✲❙❚❇❈ s②st❡♠s ❝♦♥t❡♠♣♦r❛r② t♦♣✐❝s ✇✐❞❡❧② st✉❞✐❡❞✳ ❚❤♦✉❣❤t❢✉❧ ✉♥❞❡rst❛♥❞✐♥❣ t❤❡ ❝❛✉s❡s ♦❢ ❜❛s❡❞ ♦♥ t❤♦r♦✉❣❤ ❛♥❛❧②s❡s ♦❢ t❤❡ ♥♦♥❧✐♥❡❛r ❍P❆ ❡❢❢❡❝ts ♦♥ t❤❡s❡ s②st❡♠s ❡rr♦rs ✐♥ s✐♠✉❧❛t✐♥❣ ✐♥t❡r♠♦❞✉❧❛t✐♦♥ ♣r♦❞✉❝ts ❢♦r ❝♦♥✈❡♥t✐♦♥❛❧ ♠♦❞❡❧s s✉❝❤ ✇✐t❤ tr❛♥s♠✐t✴r❡❝❡✐✈❡ ❢✐❧t❡rs ✐♥tr♦❞✉❝❡❞ ✐♥ t❤❡ ♠♦❞❡❧✳ ❛s ❙❛❧❡❤✱ ❘❛♣♣✱ ♣♦❧②♥♦♠✐❛❧✱✳✳✳ ❛♥❞ ♦✈❡r❝♦♠✐♥❣ t❤❡s❡ ❞❡❢❡❝ts ❜② ❝♦♥str✉❝t✐♥❣ ❛ ✸✳ Pr♦♣♦s✐♥❣ ❛♥ ❛✉t♦♠❛t✐❝✱ ❡❢❢✐❝✐❡♥t ♣❤❛s❡ ❡st✐♠❛t✐♦♥ ❛♥❞ ❝♦♠♣❡♥s❛t✐♦♥ ❞✐✲ ❛❣r❛♠ ❢♦r ▼■▼❖✲❙❚❇❈ s②st❡♠s ✉s✐♥❣ M ✲◗❆▼ s✉✐t❛❜❧❡ ❍P❆ ♠♦❞❡❧ ❛r❡ t❤❡♥ r❡❛❧❧② str♦♥❣ ❜✉t ❝❤❛❧❧❡♥❣✐♥❣ r❡s❡❛r❝❤ ♠♦t✐✈❛t✐♦♥s✳ s✐❣♥❛❧✐♥❣ ✐♥❝✉rr❡❞ ✇✐t❤ ❋♦r ❙■❙❖ s②st❡♠s✱ ❬✶✱ ✹✱ ✶✶✱ ✶✸❪ r❡s♦❧✈❡❞ s❡✈❡r❛❧ ♥♦♥❧✐♥❡❛r ❍P❆✲r❡❧❛t❡❞ ♣r♦❜✲ ♥♦♥❧✐♥❡❛r ❞✐st♦rt✐♦♥s ❢r♦♠ ❞✐❢❢❡r❡♥t ❍P❆ t②♣❡s ♦❢ ❜♦t❤ ❚❲❚❆s ❛♥❞ ❙❙✲ ❧❡♠s s✉❝❤ ❛s ❡✈❛❧✉❛t✐♥❣ s❡♣❛r❛t❡✴❝♦♥❝✉rr❡♥t ❡❢❢❡❝ts ♦❢ ♥♦♥❧✐♥❡❛r✴❧✐♥❡❛r ❞✐st♦r✲ P❆s✳ t✐♦♥s✱ ❛♣♣❧②✐♥❣ ♦♣t✐♠✉♠ ❛❞❞✐t✐♦♥❛❧ ♣❤❛s❡ s❤✐❢t✐♥❣ s♦❧✉t✐♦♥✳ ❘❡❝❡♥t❧②✱ ❬✸❪ ❡①✲ ❙✉❣❣❡st❡❞ ❡①t❡♥s✐♦♥s t❡♥❞❡❞ t❤❡s❡ r❡s✉❧ts t♦ ▼■▼❖✲❙❚❇❈ s②st❡♠s ❛❝❝❡♥t✐♥❣ ♦♥ s❛t❡❧❧✐t❡ ❝♦♠♠✉♥✐✲ ✶✳ ❚❤❡ s✐♠✉❧❛t✐♦♥ r❡s✉❧ts ❤❛✈❡ ✐♥✐t✐❛❧❧② ❝♦♥❢✐r♠❡❞ t❤❡ ❛❞✈❛♥t❛❣❡s ♦❢ t❤❡ ♣r♦✲ ❝❛t✐♦♥s✳ ❍♦✇❡✈❡r✱ t❤❡r❡ ❛r❡ s❡✈❡r❛❧ t♦♣✐❝s ✇❤✐❝❤ ❛r❡ ♥♦t r✐❣♦r♦✉s❧② ❞✐s❝✉ss❡❞ ♣♦s❡❞ ♣♦❧②s✐♥❡ ♠♦❞❡❧ ❛s ✇❡❧❧ ❛s t❤❡ ♣r❡✲❝♦♠♣❡♥s❛t✐♦♥ ❛♥❞ ♣♦s✲❝♦♠♣❡♥s❛t✐♦♥ ❛♥❞ ❛❧s♦ ❛r❡ ♥♦t ❡①t❡♥❞❡❞ t♦ ♥❡✇ ❞✐r❡❝t✐♦♥s✳ ❚❤❡r❡❢♦r❡✱ t❤✐s ✇♦r❦ ❡♥t✐t❧❡❞ ✏◆♦♥✲ s❝❤❡♠❡s ❢♦r ♥♦♥❧✐♥❡❛r ❞✐st♦rt✐♦♥s✱ t❤❡ ❤❛r❞✇❛r❡ ❡①♣❡r✐♠❡♥t❛❧ t❡sts ✇✐❧❧ ❧✐♥❡❛r ❞✐st♦rt✐♦♥s ❛♥❞ ❝♦✉♥t❡r♠❡❛s✉r❡s ❢♦r ♣❡r❢♦r♠❛♥❝❡ ✐♠♣r♦✈❡♠❡♥ts ✐♥ ❝♦♥✲ s♦❧✐❞✐❢② t❤❡ ❛❝❤✐❡✈❡❞ r❡s✉❧ts ❛♥❞ ❝♦♥❢✐r♠ t❤❡ ♣r❛❝t✐❝❛❧ ❛♣♣❧✐❝❛❜✐❧✐t② ♦❢ t❡♠♣♦r❛r② r❛❞✐♦ ❝♦♠♠✉♥✐❝❛t✐♦♥ s②st❡♠s✑✱ ❢♦❝✉s❡s ♦♥ ❞❡❛❧✐♥❣ t♦ s✉❝❤ ♣r♦❜❧❡♠s✳ t❤❡s❡ ♣r♦♣♦s❛❧s❀ ✷✳ ▼❛❥♦r ❢✐♥❞✐♥❣s ❛♥❞ ❝♦♥tr✐❜✉t✐♦♥s✿ ✷✳ ❘❡s❡❛r❝❤❡s ♦♥ t❤❡ ❡❢❢❡❝ts ♦❢ ♥♦♥❧✐♥❡❛r ❞✐st♦rt✐♦♥s ❢♦r ✉♣❞❛t❡❞ ▼■▼❖ t❡❝❤♥♦❧♦❣✐❡s ❛♥❞ s②st❡♠s s✉❝❤ ❛s s♣❛t✐❛❧ ♠♦❞✉❧❛t✐♦♥✱ ♠✉❧t✐✲✉s❡r ▼■▼❖✱ ❡t❝✳ ❛r❡ st✐❧❧ ✈❡r② ❧✐♠✐t❡❞❀ ✸✳ ❆♥♦t❤❡r r❡s❡❛r❝❤ ❞✐r❡❝t✐♦♥ t❤❛t ❤❛s ♥♦t ❜❡❡♥ ✇✐❞❡❧② ❞✐s❝✉ss❡❞ ❢♦r ▼■▼❖✲ ❙❚❇❈ s②st❡♠s ✐s t❤❡ ❡✈❛❧✉❛t✐♦♥ ♦❢ s②st❡♠ ♣❡r❢♦r♠❛♥❝❡ ❞❡❣r❛❞❛t✐♦♥ ✉♥❞❡r t❤❡ s✐♠✉❧t❛♥❡♦✉s ❡❢❢❡❝ts ♦❢ ♥♦♥❧✐♥❡❛r ❞✐st♦rt✐♦♥s ❛♥❞ ♦t❤❡r ❡❢❢❡❝ts s✉❝❤ ❛s ❧✐♥❡❛r ❞✐st♦rt✐♦♥s✱ ♦r ❤❛r❞✇❛r❡ ✐♠♣❛✐r♠❡♥ts ❧✐❦❡ ❧♦❝❛❧ ♦s❝✐❧❧❛t♦r ♣❤❛s❡ ♥♦✐s❡✱ s❛♠♣❧✐♥❣ ❥✐tt❡r✱ s❛♠♣❧✐♥❣ ❢r❡q✉❡♥❝② ♦❢❢s❡t✱ ❝❛rr✐❡r ❢r❡q✉❡♥❝② ♦❢❢s❡t✱ ■◗ ✐♠❜❛❧❛♥❝❡✱ ❘❋ ❝♦✉♣❧✐♥❣✱ ❝r♦ss✲t❛❧❦✱✳✳✳ ✹✳ ❚❤❡ M ✲❆P❙❑ ♠♦❞✉❧❛t✐♦♥ s❝❤❡♠❡s ❛r❡ ♣r❡❢❡rr❡❞ ✐♥ t❤❡ ♥❡✇ s❛t❡❧❧✐t❡ ❝♦♠✲ ♠✉♥✐❝❛t✐♦♥ st❛♥❞❛r❞s s✐♥❝❡ t❤❡② ❤❛✈❡ ♠❛♥② ❛❞✈❛♥t❛❣❡s ♦✈❡r M ✲◗❆▼ s❝❤❡♠❡s✳ ❍♦✇❡✈❡r✱ ♥♦♥❧✐♥❡❛r ❞✐st♦rt✐♦♥s ✇✐t❤ t❤❡ ♣❤❛s❡ r♦t❛t✐♦♥ ❡❢❢❡❝t ❛r❡ ❛❧✇❛②s ♣r❡s❡♥t✳ ❚❤❡ ❛❜✐❧✐t② t♦ ❛♣♣❧② ❛ ♣❤❛s❡ ❡st✐♠❛t✐♦♥ ❛♥❞ ❝♦♠♣❡♥✲ s❛t✐♦♥ s♦❧✉t✐♦♥ ❢♦r t❤❡s❡ M ✲❆P❙❑ ✷✹ ✶✳ ❊✈❛❧✉❛t✐♥❣ ♥♦♥❧✐♥❡❛r ❍P❆ ♠♦❞❡❧s r❡❣❛r❞✐♥❣ t♦ ♣r♦❜❧❡♠ ♦❢ s✐♠✉❧❛t✐♥❣ ✐♥✲ t❡r♠♦❞✉❧❛t✐♦♥ ♣r♦❞✉❝ts ✭■▼P✮✳ Pr♦♣♦s✐♥❣ t❤❡ ♣♦❧②s✐♥❡ ♠♦❞❡❧ ❢♦r ♣r❡❝✐s❡ s✐♠✉❧❛t✐♦♥ ♦❢ ■▼Ps✱ ❡s♣❡❝✐❛❧❧② ❢♦r s✐❣♥❛❧s ✇✐t❤ ❝♦♠♣❧❡① str✉❝t✉r❡s✳ ✷✳ Pr♦♣♦s✐♥❣ t❤❡ ✉s❡ ♦❢ ♣r❡❞✐st♦rt✐♦♥ s❝❤❡♠❡s ❢♦r ▼■▼❖✲❙❚❇❈ s②st❡♠s ❜❛s❡❞ ♦♥ t❤♦r♦✉❣❤ ❛♥❛❧②s❡s ♦❢ t❤❡ ♥♦♥❧✐♥❡❛r ❍P❆ ❡❢❢❡❝ts ♦♥ t❤❡s❡ s②st❡♠s ✇✐t❤ tr❛♥s♠✐t✴r❡❝❡✐✈❡ ❢✐❧t❡rs ✐♥tr♦❞✉❝❡❞ ✐♥ t❤❡ ♠♦❞❡❧✳ ✸✳ ❆♣♣r♦①✐♠❛t✐♥❣ ♥♦♥❧✐♥❡❛r ♣❤❛s❡ ❞✐st♦rt✐♦♥ ❜② ❛ ❧✐♥❡❛r ♠♦❞❡❧✳ ❇❛s❡❞ ♦♥ t❤❛t✱ ♣r♦♣♦s✐♥❣ ❛♥ ❛✉t♦♠❛t✐❝✱ ❡❢❢✐❝✐❡♥t ♣❤❛s❡ ❡st✐♠❛t✐♦♥ ❛♥❞ ❝♦♠♣❡♥s❛✲ t✐♦♥ ❞✐❛❣r❛♠ ❢♦r ▼■▼❖✲❙❚❇❈ s②st❡♠s ✉s✐♥❣ ▼✲◗❆▼ s✐❣♥❛❧✐♥❣✳ ✸✳ ❚❤❡s✐s ♦✉t❧✐♥❡✿ ❚❤✐s t❤❡s✐s ✐♥❝❧✉❞❡s ❛❜♦✉t ✶✷✵ ♣❛❣❡s ❛♥❞ ✐s ♦r❣❛♥✐③❡❞ ✐♥ ❢♦✉r ❝❤❛♣t❡rs ❡①❝❡♣t ❢♦r t❤❡ ❢♦r❡✇♦r❞✱ ❝♦♥❝❧✉s✐♦♥ ❛♥❞ r❡❢❡r❡♥❝❡s✳ s❝❤❡♠❡s ✐s st✐❧❧ ❧❡❢t ♦♣❡♥✳ ✶ ❝♦♥✈❡rs✐♦♥s s✉❝❤ ❛s ❢♦r ❙❛❧❡❤ ♦r ♠♦❞✐❢✐❡❞ ●❤♦r❜❛♥✐ ♠♦❞❡❧s✳ ❈❤❛♣t❡r ✶ 30 ■♥tr♦❞✉❝t✐♦♥ t♦ ◆♦♥❧✐♥❡❛r ❉✐st♦rt✐♦♥ ❛♥❞ 25 TD Pr❛❝t✐❝❛❧ ▼■▼❖✲❙❚❇❈ ❙②st❡♠s ✶✳✶ Saleh, HPA only Saleh, phase comp M Saleh, HPA only M Saleh, phase comp M Ghorbani, HPA only M Ghorbani, phase comp M Rapp, HPA only M Rapp, phase comp 35 20 ▼❛✐♥ ❝❛✉s❡s ♦❢ ♥♦♥❧✐♥❡❛r ❞✐st♦rt✐♦♥s ✐♥ r❛❞✐♦ ❝♦♠♠✉♥✐✲ 15 ❝❛t✐♦♥ s②st❡♠s 10 ■♥ ♣r❛❝t✐❝❡✱ r❛❞✐♦ tr❛♥s♠✐tt❡rs ♦❢t❡♥ ❤❛✈❡ str✉❝t✉r❡ ❝♦♥s✐st✐♥❣ ♦❢ s❡✈❡r❛❧ t②♣✐❝❛❧ st❛❣❡s s✉❝❤ ❛s ❜❛s❡❜❛♥❞ s✐❣♥❛❧ ♣r♦❝❡ss✐♥❣✱ ❞✐❣✐t❛❧✲t♦✲❛♥❛❧♦❣ ❝♦♥✈❡r✲ 10 12 14 16 18 20 IBO [dB] ❋✐❣✉r❡ ✹✳✺✿ T D(IBO) ✇✐t❤✴✇✐t❤♦✉t ♣❤❛s❡ ❝♦♠♣❡♥s❛t✐♦♥ ❛t BER = 10−3 ✳ s✐♦♥✱ ♠♦❞✉❧❛t✐♦♥✱ ❢r❡q✉❡♥❝② ✉♣✲❝♦♥✈❡rs✐♦♥✱ ❢✐❧t❡r✐♥❣✱ ❛♠♣❧✐❢✐❝❛t✐♦♥s✱ ❛♥t❡♥♥❛✱✳✳✳ ❆♠♦♥❣ t❤❡s❡ ♣❛rts✱ r❛❞✐♦ ❢r❡q✉❡♥❝② ❍P❆ ✐s ♦♥❡ ♦❢ t❤❡ ♠♦st ♣♦✇❡r✲❝♦♥s✉♠✐♥❣ ✹✳✹✳✹ ❝♦♠♣♦♥❡♥ts ❛♥❞ ✐s t❤❡ ♠❛✐♥ ❝❛✉s❡ ♦❢ ♥♦♥❧✐♥❡❛r ❞✐st♦rt✐♦♥s ❬✾✱ ✷✷✱ ✷✸✱ ✺✺❪✳ ✶✳✷ ❇✐t ❡rr♦r r❛t✐♦ ❋r♦♠ ❋✐❣✉r❡ ✹✳✻✱ t❤❡ s❛✈✐♥❣s ♦❢ ◆♦♥❧✐♥❡❛r ❍P❆ ♠♦❞❡❧ ❝❧❛ss✐❢✐❝❛t✐♦♥ Eb /N0 ❢♦r ♣❤❛s❡✲❝♦♠♣❡♥s❛t❡❞ s②st❡♠s ✇✐t❤ ♥♦♥❧✐♥❡❛r✐t✐❡s ❤❛✈✐♥❣ s♠❛❧❧ ♣❤❛s❡ ❝♦♥✈❡rs✐♦♥s ❛r❡ st✐❧❧ s✐❣♥✐❢✐❝❛♥t ✭♠♦r❡ t❤❛♥ ✷ ❋✐❣✉r❡ ✶✳✶ ❞❡s❝r✐❜❡s t❤❡ ❍P❆ ♠♦❞❡❧ ❝❧❛ss✐❢✐❝❛t✐♦♥ ✇✐t❤ r❡❧❛t❡❞ ❢❡❛t✉r❡s✳ ❞❇ ❢♦r ♠♦❞✐❢✐❡❞ ❙❛❧❡❤ ♠♦❞❡❧ ❛♥❞ ♠♦r❡ t❤❛♥ ✸ ❞❇ ❢♦r ♠♦❞✐❢✐❡❞ ❘❛♣♣ ♠♦❞❡❧ BER = 10−3 ✮✳ ❍❡r❡✱ ♠♦❞❡❧s ♠❛r❦❡❞ ❜② ❣r❛② ✇✐❧❧ ❜❡ st✉❞✐❡❞ ✐♥ ❞❡t❛✐❧ t❤r♦✉❣❤♦✉t t❤❡ t❤❡s✐s✳ ❛t ▲❡t✬s ❝♦♥✈❡rs✐♦♥s ✭✇✐t❤ ❙❛❧❡❤✱ ♦r ♠♦❞✐❢✐❡❞ ●❤♦r❜❛♥✐ ♠♦❞❡❧s✮ ❛r❡ r❡❛❧❧② ❤✉❣❡✳ r(t) ❛♥❞ φ(t) ❛r❡ t❤❡ ❛♠♣❧✐t✉❞❡ ♠♦❞✉❧❛t✐♦♥ ✭❆▼✮ ❛♥❞ ♣❤❛s❡ ♠♦❞✉❧❛t✐♦♥ ✭P▼✮ ♦❢ t❤❡ ✐♥♣✉t x(t) = r(t)ejφ(t) ✳ ❚❤❡ ✐♥♣✉t✲♦✉t♣✉t ♥♦♥❧✐♥❡❛r r❡❧❛t✐♦♥ ❝♦✉❧❞ ❜❡ r❡♣r❡s❡♥t❡❞ ❜② ❆▼✲❆▼ ❛♥❞ ❆▼✲P▼ ❢✉♥❝t✐♦♥s Fa (r)✱ Fp (r) ■❞❡❛❧ ♠♦❞❡❧ F (.) 10 ❛s y(t) = F (x(t)) = Fa (r(t))ej(φ+Fp (r(t))) • ❚❤❡ ❣❛✐♥s ❢♦r ♣❤❛s❡✲❝♦♠♣❡♥s❛t❡❞ s②st❡♠s ✇✐t❤ str♦♥❣ ♣❤❛s❡ ✭✶✳✶✮ −1 10 ✐s t❤❡ ♣❡r❢❡❝t❧② ❧✐♥❡❛r✐③❡❞ ♠♦❞❡❧ ❢♦r ❍P❆ ✇✐t❤ −2 10 ✇❤❡r❡✱ • ♦r ❡q✉✐✈❛❧❡♥t❧② x = x(t)✱ y = y(t)✱ ▲✐♥❡❛r✐③❡❞ ♠♦❞❡❧ ❛♥❞ g>0 , Fa (r) = gr, Fp (r) = 0, ✭✶✳✷✮ BER y = gx, −3 10 ✐s t❤❡ ✭r❡❛❧✲✈❛❧✉❡❞✮ ❧✐♥❡❛r ❣❛✐♥✳ ✐s t❤❡ s✐♠♣❧❡st ❍P❆ ♠♦❞❡❧ ✇✐t❤♦✉t ❝♦♥s✐❞❡r✐♥❣ ♦✉t♣✉t −4 10 ♠❛❣♥✐t✉❞❡ ❝❧✐♣♣✐♥❣ ❢♦r ♥♦♥❧✐♥❡❛r ❝❤❛r❛❝t❡r✐st✐❝ ✭✶✳✸✮ y = gx + n, ✇❤❡r❡✱ g ❤❛s t❤❡ s❛♠❡ ♠❡❛♥✐♥❣ ❛s ✐♥ ✭✶✳✷✮✱ n ❙♦❢t ❧✐♠✐t❡r Fa (r) = |r| < A✐s A✐s , |r| Fp (r) = 0, ✷ A✐s , ✭✶✳✹✮ ✭✶✳✺✮ 10 12 14 16 r t❤❡ ❛♠♣❧✐t✉❞❡ ❛♥❞ ♣❤❛s❡ ♣r❡❞✐st♦r✲ Pam ❛♥❞ Ppm ✇❤❡r❡ t❤❡ tr✉❡ ❞❡r✐✈❛t✐✈❡s ♦❢ ❏❛❝♦❜✐❛♥ ♠❛tr✐① ❛r❡ ❛♣♣r♦①✐♠❛t❡❞ ❜② ❞✐❢❢❡r❡♥t✐❛❧ ❡♥tr♦♣②✿ ✸✳✸✳✹ h1 (Pam ,Ppm )−h1 (Pam−1 ,Ppm ) h1 (Pam ,Ppm )−h1 (Pam ,Ppm−1 ) J= Pam −Pam−1 h2 (Pam ,Ppm )−h2 (Pam−1 ,Ppm ) Pam −Pam−1 Ppm −Ppm−1 h2 (Pam ,Ppm )−h2 (Pam ,Ppm−1 ) Ppm −Ppm−1 ❛♥❞ Pp (r)✱ h❬n❪ ❂ h(t)|t=n T , − M ✭✸✳✶✶✮ ❆t t❤❡ k✲t❤ N −1 N −1 ≤n≤ 2 t✐♠❡ s❧♦t✱ t❤❡ ♦✉t♣✉t ♦❢ t❤❡ i✲t❤ ❢✐❧t❡r✱ x ˜i,k = xi,k h[0] + ❝♦✉❧❞ ❜❡ ❛♣♣r♦①✐♠❛t❡❞ ❜② t❤❡ ❢♦❧❧♦✇✐♥❣ ♣♦❧②♥♦♠✐❛❧s ❬✾✹❪ Pa (r) = a1 r + a2 r2 + a3 r3 + + al rl = aT , ✭✸✳✶✷✮ Pp (r) = p0 + p1 r + p2 r2 + + am rm = pT rp ✭✸✳✶✸✮ ✭✸✳✶✮ ■ts ❝❛✉s❛❧ ❞✐s❝r❡t❡✲t✐♠❡ r❡s♣♦♥s❡ ✐s ❣✐✈❡♥ ❜② ❆❞❛♣t✐✈❡ ▲▼❙ ♣♦❧②♥♦♠✐❛❧✲❛♣♣r♦①✐♠❛t❡❞ ♣r❡❞✐st♦rt✐♦♥ Pa (r) s②st❡♠ ♠♦❞❡❧ ❙✐❣♥❛❧s ♦✉t♣✉t ❙❚❇❈ ❡♥❝♦❞❡r ❛r❡ ♦❢ t❤❡ ❢♦r♠ ✭✶✳✻✮✳ ❚❤❡♥✱ t❤❡② ❛r❡ ✐♥♣✉t ❆❞❛♣t✐✈❡ ◆❡✇t♦♥ ♣r❡❞✐st♦rt✐♦♥ t✐♦♥ ❢✉♥❝t✐♦♥s✱ × nR −1 l=k,− N l i = 1, 2✱ ✭✸✳✷✮ t❤✉s ✐s ♦❢ t❤❡ ❢♦r♠ xi,l h[k − l] = xi,k h[0] + n■❙■ i,k ✭✸✳✸✮ n■❙■ i,k ✱ ✇❤✐❝❤ t❤❡♥ N −1 ❚❤❡r❡❢♦r❡✱ s✐❣♥❛❧s ✐♥♣✉t t♦ t❤❡ ❍P❆ ❛❧s♦ ❝♦♥t❛✐♥ t❤❡ ■❙■ t❡r♠ ②✐❡❧❞s ♥♦♥❧✐♥❡❛r ■❙■ ❛t t❤❡ ❍P❆ ♦✉t♣✉t✳ ❋♦r t❤❡ ♣✉r♣♦s❡❞ ♦❢ ❝♦♠♣❛r✐s♦♥ ✇✐t❤ ♣r❡✈✐♦✉s ♣✉❜❧✐❝❛t✐♦♥s✱ ✇✐t❤♦✉t ❝♦♥s✐❞❡r✐♥❣ t❤❡ s♣❡❝tr❛❧ r❡❣r♦✇t❤ ❡❢❢❡❝t ❛s ❛♥❛❧✲ ❚❤❡ ❧❡❛st ♠❡❛♥ sq✉❛r❡ ✭▲▼❙✮ ❛❧❣♦r✐t❤♠ ❬✹✹❪ ✐s t❤❡♥ ❡♠♣❧♦②❡❞ ❢♦r ❝❛❧❝✉❧❛t✐♥❣ ②s❡❞ ✐♥ ❈❤❛♣t❡r ✷✱ ❤❡r❡ ✇❡ ✉s❡ ❝♦♥✈❡♥t✐♦♥❛❧ ❍P❆ ♠♦❞❡❧s ✐♥❝❧✉❞✐♥❣ ❚❲❚❆ ❜② ❛♠♣❧✐t✉❞❡ ❛♥❞ ♣❤❛s❡ ❝♦❡❢❢✐❝✐❡♥ts ❙❛❧❡❤ ♠♦❞❡❧ ✭✷✳✸✮✱ ✭✷✳✹✮ ❛♥❞ ❙❙P❆ ❜② ❘❛♣♣ ♠♦❞❡❧ ✭✷✳✺✮✳ a(m)✱ p(m)✳ ✶✹ ✶✶ HPA1 x2, k SRRC x 2,k xˆ 2,k nnR ,k ynR ,k nR Tx2 SRRC Rx2 sˆk sˆk 1 s✐❣♥❛❧ st❛t✐st✐❝s✱ t❤❛t ❛❝t✉❛❧❧② r❡❢❧❡❝t t❤❡ ♥♦♥❧✐♥❡❛r ■❙■ ❛♥❞ ■❈■ ❡❢❢❡❝ts✱ ✐s ♥♦t ˆk m ♦❜s❡r✈❡❞ ✐♥ ❋✐❣✉r❡ ✸✳✷✭❜✮✱ ♠❛❦✐♥❣ ❞❡❝❡♣t✐✈❡ ❛ss✉♠♣t✐♦♥ ❢♦r ❛♥❛❧②t✐❝❛❧ ❛♥❛❧②s❡s✳ ˆ k 1 m HPA2 ✸✳✷✳✷ Quadrature Q ❋✐❣✉r❡ ✸✳✶✿ ▼■▼❖✲❙❚❇❈ ♠♦❞❡❧ ✇✐t❤ ❚①✲❘① ❢✐❧t❡rs ❛♥❞ ♥♦♥❧✐♥❡❛r ❍P❆s✳ ◆♦♥❧✐♥❡❛r ❞✐st♦rt✐♦♥ ❡❢❢❡❝ts ✐♥❝✉rr❡❞ ❜② ❍P❆s ❘❡❝❡✐✈❡ s✐❣♥❛❧s ♦♥ t❤❡ l✲t❤ ❜r❛♥❝❤✱ nR ✱ l ✐♥ t✐♠❡ s❧♦ts k ❛♥❞ (k + 1) ❛r❡ ✭✸✳✹✮ yl,k = hl,1 sˆk + hl,2 sˆk+1 + nl,k , yl,k+1 = −hl,1 sˆ∗k+1 + hl,2 sˆ∗k + nl,k+1 4 2.8 2.6 0.7 0.9 1.1 −1 −1 −2 −2 −3 −3 −4 −4 ✭✸✳✺✮ Quadrature Q sk 1 ❡❢❢❡❝ts ❛♥❞ ❣✐✈❡ ✭♠✉❝❤✮ ♠♦r❡ ♦♣t✐♠✐st✐❝ r❡s✉❧ts✳ ❋✉rt❤❡r✱ t❤❡ ❝❤❛♥❣❡ ♦❢ r❡❝❡✐✈❡ SRRC Rx1 ML detector mk 1 sk n1,k y1,k MRC combiner mk xˆ1,k Tx1 STBC encoder M-QAM x1,k SRRC x1,k −3 −2 −1 Inphase I −4 −4 −3 ✭❛✮ ❆♣♣❧②✐♥❣ ♠❛①✐♠✉♠ r❛t✐♦ ❝♦♠❜✐♥✐♥❣ ❬✼❪✱ t❤❡s❡ r❡❝❡✐✈❡ s✐❣♥❛❧s ❛r❡ ♣r♦❝❡ss❡❞ ❛s −2 −1 Inphase I ✭❜✮ ❋✐❣✉r❡ ✸✳✸✿ ❋♦r ❍P❆ ♠♦❞❡❧ ✉t✐❧✐③❡❞ ✐♥ ❬✽✶❪✿ ❛✮ ✇✐t❤ ❢✐❧t❡rs❀ ❜✮ ✇✐t❤♦✉t ❢✐❧t❡rs✳ ∗ s¯l,k = h∗l,1 yl,k + hl,2 yl,k+1 , s¯l,k+1 = h∗l,2 yl,k − ✭✸✳✻✮ ∗ hl,1 yl,k+1 ✭✸✳✼✮ ❯s✐♥❣ ❧✐♥❡❛r✐③❡❞ ♠♦❞❡❧ ✭✶✳✸✮ ❢♦r t❤❡ ❍P❆ ✐♥♣✉t✴♦✉t♣✉t s✐❣♥❛❧s ❛♥❞ sˆk ✱ t❤❡♥ 4 t❤❡ ▼■▼❖ s②st❡♠ ✐♥t♦ ❙■❙❖ ❡q✉✐✈❛❧❡♥t ♦♥❡s ❛s ❡q✉❛t✐♦♥ ✭✽✮ ✐♥ ❬✽✶❪ ✐s ❛♥ ♦✈❡r s✐♠♣❧✐❢✐❝❛t✐♦♥✱ ♦♥❧② r❡❛s♦♥❛❜❧❡ ✇❤❡♥ t❤❡ ♥♦♥❧✐♥❡❛r✐t② ✐s ✇❡❛❦✱ ❛♥❞ ✇✐t❤♦✉t ❆▼✲ P▼ ❞✐st♦rt✐♦♥✳ ❚❤❡♥✱ t❤❡ ■❈■ ✇✐❧❧ ❜❡ ♥❡❣❧✐❣✐❜❧❡✱ t❤❡ ❝❧✉st❡r ♣♦✐♥ts s❤r✐♥❦ ✐♥t♦ ❛ 2.9 2.7 s✐♥❣❧❡ ♣♦✐♥t ✇✐t❤ ♦♥❧② ❛♠♣❧✐t✉❞❡ ❝♦♠♣r❡ss✐♦♥ ❡❢❢❡❝t ❡①✐sts✳ ❚❤✐s ❢❛❝t ✐s ❞❡♠♦♥✲ str❛t❡❞ ❜② ❋✐❣✉r❡ ✸✳✸✭❜✮ ✇✐t❤ t❤❡ ❍P❆ ♣❛r❛♠❡t❡rs ✉s❡❞ ✐♥ ❬✽✶❪✳ ▼♦r❡♦✈❡r✱ ✐❢ t❤❡ s②st❡♠ ♠♦❞❡❧ ❤❛✈✐♥❣ ❚①✲❘① ❢✐❧t❡rs ❛s ✐t ♣r❛❝t✐❝❛❧❧② ✐s✱ t❤❡ s✐❣♥❛❧ q✉❛❧✐t② ✐s Quadrature Q 0.9 1.1 −1 ❛❧s♦ s✐❣♥✐❢✐❝❛♥t❧② ❞❡❣r❛❞❡❞ ❛s ✐❧❧✉str❛t❡❞ ✐♥ ❋✐❣✉r❡ ✸✳✸✭❛✮✳ ❖❜✈✐♦✉s❧②✱ t❤❡ r❡❝❡✐✈❡ −2 −2 s✐❣♥❛❧s ❛r❡ ♥♦♥✲●❛✉ss✐❛♥✱ ♠❛❦✐♥❣ ❛♥❛❧②t✐❝❛❧ ❛♥❛❧②s❡s ✐♠♣♦ss✐❜❧❡✳ −3 −3 −3 −2 −1 Inphase I −4 −4 ✭❛✮ ✸✳✸ −3 −2 −1 Inphase I Pr❡❞✐st♦rt✐♦♥ s❝❤❡♠❡s ❚❤❡ ♣r♦♣♦s❡❞ s②st❡♠ ♠♦❞❡❧ ✐s ✐❧❧✉str❛t❡❞ ✐♥ ❋✐❣✉r❡ ✸✳✹✳ ✭❜✮ x1,k s✐❣♥❛❧s ❛❢t❡r ▼❘❈ ❛r❡ ❛❢❢❡❝t❡❞ ❜② ♥♦♥❧✐♥❡❛r ♥♦✐s❡✱ ♥♦♥❧✐♥❡❛r ■❙■ ❛♥❞ ♥♦♥❧✐♥❡❛r ■❈■✳ ❚❤❡s❡ ❡❢❢❡❝ts ❛r❡ ✐❧❧✉str❛t❡❞ ✐♥ ❋✐❣✉r❡ ✸✳✷✭❛✮✱ s✐♠✉❧❛t❡❞ ❜②✿ ✶✻✲◗❆▼❀ ❢✐❧t❡rs✬ r♦❧❧♦❢❢ ❢❛❝t♦r Dl = 10❀ α = 0.2✱ ✐♥♣✉t✴♦✉t♣✉t s❛♠♣❧✐♥❣ r❛t❡s Fd = 1✱ Fs = 16Fd ✱ ❣r♦✉♣ ❞❡❧❛② ❍P❆ ❙❛❧❡❤ ♠♦❞❡❧ αa = 2✱ βa = 1✱ αp = π/3✱ βp = 1✱ IBO = 10 ❞❇✳ ❋✐❣✉r❡ ✸✳✷✭❜✮ ✐s ②✐❡❧❞❡❞ ❢r♦♠ t❤❡ s❛♠❡ ♠♦❞❡❧ ❜✉t ✇✐t❤♦✉t ❢✐❧t❡r✐♥❣✳ ❚❤✉s✱ mk mk 1 M-QAM ❋✐❣✉r❡ ✸✳✷✿ ❘❡❝❡✐✈❡ s✐❣♥❛❧s ❛❢t❡r ▼❘❈✿ ❛✮ ✇✐t❤ ❢✐❧t❡rs❀ ❜✮ ✇✐t❤♦✉t ❢✐❧t❡rs✳ sk sk 1 SRRC x1,k Tx1 PD x1,k xˆ1,k n1,k y1,k SRRC Rx1 HPA1 x2,k SRRC x 2,k Tx2 PD x2,k xˆ 2,k nR nnR ,k ynR ,k SRRC Rx2 sˆk sˆk 1 HPA2 ❋✐❣✉r❡ ✸✳✹✿ ▼■▼❖✲❙❚❇❈ s②st❡♠ ♠♦❞❡❧ ✇✐t❤ ♣r❡❞✐st♦rt❡rs✳ s✉❝❤ ♠♦❞❡❧s✱ ❛❧s♦ ❛s ✐♥ ❬✼✸✱✼✹✱✽✶✱✾✹❪✱ ❞♦ ♥♦t ❢✉❧❧② r❡♣r❡s❡♥t ❍P❆✬s ♥♦♥❧✐♥❡❛r ✶✷ ML detector −4 −4 MRC combiner −1 STBC encoder Quadrature Q sk ▼♦r❡♦✈❡r✱ ❜② ❋✐❣✉r❡ ✸✳✷✭❜✮✱ ❡✈❡♥ ✇✐t❤♦✉t ❢✐❧t❡r✐♥❣ ■❈■ st✐❧❧ ❡①✐sts ✉♥❞❡r ♥♦♥✲ ❧✐♥❡❛r ❍P❆ ❡❢❢❡❝ts✳ ❚❤❡r❡❢♦r❡✱ ✉s✐♥❣ ♦rt❤♦❣♦♥❛❧✐t② ♦❢ ❙❚❇❈ ❝♦❞❡ t♦ ❞❡❝♦♠♣♦s❡ ✶✸ ˆk m ˆ k 1 m ... s✉❝❤ ❛s ❧✐♥❡❛r ❞✐st♦rt✐♦♥s✱ ♦r ❤❛r❞✇❛r❡ ✐♠♣❛✐r♠❡♥ts ❧✐❦❡ ❧♦❝❛❧ ♦s❝✐❧❧❛t♦r ♣❤❛s❡ ♥♦✐s❡✱ s❛♠♣❧✐♥❣ ❥ tt r✱ s❛♠♣❧✐♥❣ ❢r❡q✉❡♥❝② ♦❢❢s❡t✱ ❝❛rr✐❡r ❢r❡q✉❡♥❝② ♦❢❢s❡t✱ ■◗ ✐♠❜❛❧❛♥❝❡✱ ❘❋ ❝♦✉♣❧✐♥❣✱ ❝r♦ss✲t❛❧❦✱✳✳✳... ❝❛✉s❡s ♦❢ ♥♦♥❧✐♥❡❛r ❞✐st♦rt✐♦♥s ✐♥ r❛❞✐♦ ❝♦♠♠✉♥✐✲ 15 ❝❛t✐♦♥ s②st❡♠s 10 ■♥ ♣r❛❝t✐❝❡✱ r❛❞✐♦ tr❛♥s♠ tt rs ♦❢t❡♥ ❤❛✈❡ str✉❝t✉r❡ ❝♦♥s✐st✐♥❣ ♦❢ s❡✈❡r❛❧ t②♣✐❝❛❧ st❛❣❡s s✉❝❤ ❛s ❜❛s❡❜❛♥❞ s✐❣♥❛❧ ♣r♦❝❡ss✐♥❣✱