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1F02
2 ͭͷ৴߸ͷҐ૬͕ࠩ 2 ࣍Ґ૬ CAZAC ‫ྻܥ‬ͷ৔߹ͷҐ૬‫ݶ‬ఆ૬ؔؔ਺
˓෱ҪҰ߂*ɼീ‫ר‬ढ़ี**ɼѨ෦ ਖ਼ӳ*ɼ઒ຢ ੓੐*
*౦๺େֶେֶӃ޻ֶ‫ڀݚ‬Պిࢠ޻ֶઐ߈
**౦๺େֶαΠόʔαΠΤϯεηϯλʔ‫ڀݚ‬։ൃ෦
1.
αk
0
-20
0
Ґ૬‫ݶ‬ఆ૬ؔؔ਺ͱ PCE
௕͞ N ͷ 2 ͭͷෳૉ৴߸ x(n) ͱ y(n) ͷҐ૬‫ݶ‬ఆ૬
ؔ (POC) ؔ਺ r(m) ͸ҎԼͷࣜͰఆٛ͞ΕΔɽ
=
1
N
k=0
ejαk WN−mk
(1)
͜͜ͰɼX(k) ͱ Y (k) ͸ͦΕͧΕ x(n) ͓Αͼ y(n) ͷ
प೾਺εϖΫτϧͰ͋Γɼ|X(k)| ͱ |Y (k)| ͸ৼ෯εϖ
ΫτϧͰ͋Δɽ·ͨɼαk ͸ x(n) ͱ y(n) ͷҐ૬εϖΫ
)Ͱ͋Δɽ‫ ∗ ߸ه‬͸ෳૉ‫ڞ‬໾Λද͠ɼ
τϧͷࠩ (Ґ૬ࠩ
jαk
WN = exp −j 2π
͸Ґ૬Ҽ
N ͸ճసҼࢠͰ͋Δɽe
ࢠͱ‫ݺ‬͹ΕΔɽPOC ؔ਺͸Ґ૬Ҽࢠͷ཭ࢄϑʔϦΤ‫ٯ‬
ม‫ʹ׵‬ΑΓ‫·ٻ‬Δɽ
࣍ʹ PCE ͷఆٛࣜΛҎԼʹࣔ͢ɽ
(2)
͜͜Ͱɼp ͸ POC ؔ਺ͷઈର஋ |r(m)| ͕࠷େͱͳΔΠ
ϯσοΫεͰ͋Δɽ
3.
20
30
1
0.5
0
0
10
ͷ৔߹ͷҐ૬ (্) ͱ POC ؔ਺ (Լ)
(m = 0, 1, 2, ..., N − 1)
|r(p)|2
PCE = N −1
2
m=0 |r(m)|
30
ਤ 1: P4 ‫( ྻܥ‬N = 32, u = 4, N/gcd(N, u) = 8)
k=0
=
20
m
N −1
1 X(k)Y ∗ (k)
W −mk
N
|X(k)| |Y (k)| N
N
−1
10
k
2.
r(m)
-10
|r(m)|
·͕͖͑
Ґ૬‫ݶ‬ఆ૬ؔ (Phase-Only Correlation: POC) ؔ਺
͸ɼ2 ͭͷ৴߸ͷҐ૬ࠩʹண໨ͨ͠૬ؔؔ਺Ͱ͋Δɽ2 ͭ
ͷ৴߸ͷҐ૬͕ࠩप೾਺ʹରͯ͠ઢ‫ܗ‬ͷ৔߹ʹɼPOC
ؔ਺͸σϧλؔ਺ͱͳΔɽ͜ͷੑ࣭Λࠜ‫ͯ͠ͱڌ‬ɼPOC
ؔ਺ͷ PCE(Peak to Correlation Energy) Λ༻͍ͯը
૾ϚονϯάͳͲʹԠ༻͞ΕΔɽ͜ͷΑ͏ʹɼҐ૬ࠩ
͕ઢ‫ܗ‬ͷ৔߹ʹ͍ͭͯ͸ POC ؔ਺ͷ༗ޮੑΛೝΊΔ͜
ͱ͕Ͱ͖Δɽ͔͠͠ɼҐ૬͕ࠩඇઢ‫ͳͱܗ‬Δ৔߹͕࣮
ࡍʹ͸ଟ͘ଘࡏ͢Δɽྫ͑͹ɼޫ఻ૹʹ͓͍ͯɼϑΝΠ
όʔதͰͷ೾௕෼ࢄʹΑΓ 2 ࣍Ґ૬͕ࠩੜ͡Δɽຊߘ
Ͱ͸ɼ2 ͭͷ৴߸ͷҐ૬͕ࠩ 2 ࣍Ґ૬ CAZAC ‫ͱྻܥ‬
ͳΔ৔߹ͷҐ૬‫ݶ‬ఆ૬ؔؔ਺ͷੑ࣭Λௐ΂Δɽ
ఆৼ෯ྵࣗ‫ݾ‬૬ؔ (CAZAC) ‫ྻܥ‬
CAZAC ‫ͱྻܥ‬͸ɼৼ෯͕ҰఆͰࣗ‫ݾ‬૬ؔؔ਺͕σ
ϧλؔ਺ͱͳΔ‫ྻܥ‬ͷ͜ͱͰ͋Δ [1]ɽCAZAC ‫ྻܥ‬͸ɼ
Ұൠʹͦͷ཭ࢄϑʔϦΤม‫׵‬΋·ͨ CAZAC ‫ͳʹྻܥ‬
Δͱ͍͏ੑ࣭Λ࣋ͭɽҐ૬Ҽࢠ ejαk ͱͯ͠ CAZAC ‫ܥ‬
ྻΛԾఆ͢Δ͜ͱʹΑͬͯɼCAZAC ‫ྻܥ‬ͷੑ࣭Λ༻
͍ͯ POC ؔ਺ͷੑ࣭Λௐ΂Δ͜ͱ͕Ͱ͖Δ [2], [3]ɽ
ຊߘͰ͸ɼ2 ࣍Ґ૬ࠩΛ࣋ͭ POC ؔ਺ͷੑ࣭Λղੳ
͢ΔͨΊʹɼҐ૬Ҽࢠͱͯ͠ 2 ࣍Ґ૬ CAZAC ‫ྻܥ‬Λߟ
͑Δɽ2 ࣍Ґ૬ CAZAC ‫ ྻܥ‬C(k) ͸ɼप೾਺Πϯσο
Ϋε k ͷ 2 ࣍ଟ߲ࣜ P (k) Λ༻͍ͯ
π
C(k) = exp j P (k)
(k = 0, 1, ..., N − 1) (3)
N
Ͱද͞ΕΔ‫͋Ͱྻܥ‬Δɽ୅දతͳ 2 ࣍Ґ૬ CAZAC ‫ܥ‬
ྻͱͯ͠ Zadoff-Chu ‫ྻܥ‬ɼP4 ‫ྻܥ‬ɼWiener CAZAC
‫͕͋ྻܥ‬Δ [1]ɽͦΕͧΕͷ‫ྻܥ‬ͷఆٛࣜΛ࣍ʹࣔ͢ɽ
• Zadoff-Chu ‫ྻܥ‬: P (k) = uk(k − 1)
• P4 ‫ྻܥ‬: P (k) = uk(k − N )
• Wiener CAZAC ‫ྻܥ‬: P (k) = uk 2
͜͜Ͱɼu ͸੔਺Ͱ͋Δɽ
4.
2 ࣍Ґ૬ CAZAC ‫ྻܥ‬Λ༻͍ͨ POC ؔ਺
Zadoff-Chu ‫ྻܥ‬ɼP4 ‫ྻܥ‬ɼWiener CAZAC ‫ྻܥ‬Λ
Ґ૬Ҽࢠͱͯ͠ɼPOC ؔ਺ΛͦΕͧΕ‫ͨ͠ࢉܭ‬ɽਤ 1
ʹ P4 ‫ྻܥ‬ͷҐ૬͓Αͼ POC ؔ਺ͷྫΛࣔ͢ɽ৴߸௕
N ͓Αͼ੔਺ u ͕‫ʹ͍ޓ‬ૉͷ৔߹ɼ͢΂ͯͷ‫ؔʹྻܥ‬
√
ͯ͠ɼPOC ؔ਺͸Ұఆ஋ 1/ N ΛͱΔؔ਺ͱͳͬͨɽ
·ͨɼN ͱ u ͕‫ʹ͍ޓ‬ૉͰͳ͍৔߹ɼ͢΂ͯͷ‫ʹྻܥ‬
ؔͯ͠ POC ؔ਺͸ৼ෯ gcd(N, u)/N ͷप‫ظ‬తͳΠ
ϯύϧεؔ਺ͱͳͬͨɽ͕ͨͬͯ͠ɼҐ૬͕ࠩ 2 ࣍Ґ
૬ CAZAC ‫ͳͱྻܥ‬ΔΑ͏ͳ৴߸ʹରͯ͠ɼPCE Λ༻
͍ͨ POC ؔ਺ͷԠ༻͸༗ޮͰ͸ͳ͍͜ͱ͕෼͔Δɽ
ࢀߟจ‫ݙ‬
[1] J. J. Benedetto, I. Konstantinidis and M. Rangaswamy IEEE Signal Processing Magazine, Vol.
26, No.1, pp. 502–503, 2009.
[2] ҏ౻, খࢁ, ീ‫ר‬, Ѩ෦, ઒ຢ ୈ 27 ճ৴߸ॲཧγϯ
ϙδ΢Ϝߨԋ࿦จू, pp. 472–477, 2012.
[3] ҏ౻, ീ‫ר‬, Ѩ෦, ઒ຢ ୈ 28 ճ৴߸ॲཧγϯϙδ΢
Ϝߨԋ࿦จू, pp. 73–78, 2013.

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