Estimation of Fading Characteristics Based on Multiple Observed Signals at Remote Locations

Estimation of Fading Characteristics Based on Multiple Observed Signals at Remote Locations

Keisuke I

NOUE^*

, Hisato I

WAI^*

and Hideichi S

ASAOKA^*

(Received October 29, 2009)

Wireless communications have become popular and are used in various environments such as outdoor, offices, homes, etc. As the use of the wireless communications becomes common, security issues have become one of the most important technical subjects.

In order to realize secure communications, a new wireless security technique based on wireless propagation characteristics has been proposed. The proposed technique is based on the reversibility and the locality of the wireless propagation characteristics to generate a common encryption key sequence between two wireless stations without pre-assignment and sharing of the key. The generated key can be used to realize secure secret wireless communications. The security performance of the technique has been analyzed in a viewpoint of encryption, however it has not been discussed from a viewpoint of radio propagation. The security of the technique relies on the fact that the received signal cannot be estimated from a remote point where the distance from the target point of the estimation is larger than the correlation length of the multipath fading environment. However it may be possible if an eavesdropper uses a higher performance receiving system such as directional antennas or multiple antenna systems, etc. In this paper, the possibility to break the locality is discussed. A method to estimate the received signal characteristics is presented based on the observed signals at multiple different points at a certain distance from the target and the estimation performance of the technique is evaluated quantitatively via computer simulations. The dependence of the estimation parameters on the estimation performance is analyzed. The mechanism of the estimation method is clarified through the analysis assuming a simpler propagation model. Based on the results of the analysis, a theoretical expression for the requirement to achieve successful estimation is derived.

.H\ZRUGV

Estimation of propagation characteristics, multipath fading, secret key agreement, theoretical analysis

࣮࣮࢟࣡ࢻ

ఏᦙ≉ᛶ᥎ᐃ㸪࣐ࣝࢳࣃࢫࣇ࢙࣮ࢪࣥࢢ㸪⛎ᐦ㘽ඹ᭷᪉ᘧ㸪⌮ㄽ᳨ウ

」ᩘᆅⅬほ ಙྕ࡟ᇶ࡙ࡃ௚ᆅⅬఏᦙ㊰≉ᛶࡢ᥎ᐃ

஭ୖ ᜨ㍜㸪ᒾ஭ ㄔே㸪➲ᒸ ⚽୍

ࡲ࠼ࡀࡁ

㏆ᖺ㸪↓⥺㏻ಙࡢⓎᒎ࡜㟂せࡢᣑ኱࡟క࠸㸪✀ࠎ ࡢ᪂ࡋ࠸↓⥺ࢩࢫࢸ࣒ࡀᥦ᱌㸪᳨ウࡉࢀ࡚࠸ࡿ㸬ࡋ

࠿ࡋ㸪↓⥺㏻ಙࡣ㟁Ἴࢆ฼⏝ࡋ࡚࠸ࡿࡓࡵ㸪୙≉ᐃ ከᩘࡢ➨୕⪅(┐⫈ᒁ)ࡀഐཷྍ⬟࡛࠶ࡿ࡜࠸࠺᝟ሗ

ࢭ࢟ࣗࣜࢸ࢕㠃࡛ࡢ⬤ᙅᛶࡀㄢ㢟࡜࡞ࡿ㸬ࡇࢀ࡟ᑐ ࡍࡿ↓⥺㏻ಙࡢࢭ࢟ࣗࣜࢸ࢕ྥୖᢏ⾡ࡢ୍ࡘ࡜ࡋ

࡚㸪↓⥺㏻ಙࡢఏᦙ㊰≉ᛶ࡟ᇶ࡙ࡃ⛎ᐦ㘽ඹ᭷᪉ᘧ ࡀ᳨ウࡉࢀ࡚࠸ࡿ ^1-3)㸬ࡇࢀࡽࡢ᪉ᘧࡣ㸪࣐ࣝࢳࣃ

ࢫࣇ࢙࣮ࢪࣥࢢࡢሙᡤ౫Ꮡᛶཬࡧ㟁Ἴఏᦙࡢྍ㏫

* Department of Electronics, Doshisha University, Kyotanabe, Kyoto, 610-0321, Japan

ᛶ࡟ࡼࡾ㸪ఏᦙ㊰≉ᛶࡣ㏦ཷಙᒁ㛫࡛ࡢࡳඹ᭷࡛ࡁ㸪

࠶ࡿ⛬ᗘ㊥㞳ࡀ㞳ࢀࡓ௚ᆅⅬ࡛ࡣࡑࡢ᝟ሗࢆᚓࡿ

ࡇ࡜ࡀ࡛ࡁ࡞࠸࡜࠸࠺ཎ⌮࡟ᇶ࡙࠸࡚࠸ࡿ㸬ࡇࡢ᪉ ᘧࡣ≀⌮⌧㇟࡟ᇶ࡙࠸࡚࠸ࡿࡇ࡜࠿ࡽ᝟ሗ⌮ㄽⓗ

࡞Ᏻ඲ᛶࢆ᭷ࡋ࡚࠾ࡾ㸪ᑐ┐⫈≉ᛶࡣ┐⫈ᒁࡢィ⟬

㈨※࡟౫Ꮡࡋ࡞࠸࡜࠸࠺≉ᚩࡀ࠶ࡿ㸬

ࡋ࠿ࡋ㸪┐⫈ᒁࡀఱࡽ࠿ࡢ᪉ἲ࡟ࡼࡗ࡚ṇつᒁ㛫 ࡢఏᦙ㊰≉ᛶࢆ᥎ᐃ࡛ࡁࡿ࡜ࡍࢀࡤ㸪ࡇࡢ᪉ᘧࡼࡾ

⏕ᡂࡉࢀࡿ⛎ᐦ㘽ࡢᏳ඲ᛶࡣኻࢃࢀࡿ㸬ࡋࡓࡀࡗ࡚㸪

┐⫈ᒁ࡟ࡼࡿṇつᒁࡢఏᦙ㊰≉ᛶࡢ᥎ᐃྍ⬟ᛶࢆ

᫂☜࡟ࡍࡿࡇ࡜ࡣ㸪ఏᦙ㊰≉ᛶ࡟ᇶ࡙ࡃ⛎ᐦ㘽ඹ᭷

᪉ᘧࡢᏳ඲ᛶ᳨ウࡢ࠺࠼࡛㔜せ࡞ㄢ㢟࡜࡞ࡿ㸬 ࡑࡇ࡛ᮏ◊✲࡛ࡣ㸪⛎ᐦ㘽ඹ᭷᪉ᘧࡢᏳ඲ᛶ᳨ウ

࡟㈨ࡍࡿࡓࡵ㸪」ᩘほ Ⅼࡢཷಙ᝟ሗࢆ⏝࠸࡚㞳ࢀ

ࡓᆅⅬࡢཷಙⅬࡢఏᦙ㊰≉ᛶࢆ᥎ᐃࡍࡿ᪉ᘧ࡟ࡘ

࠸᳨࡚ウࡋ㸪ࡇࡢᡭἲ࡟ࡼࡿ᥎ᐃ≉ᛶࢆヲ⣽࡟ศᯒ ࡍࡿ㸬࣐ࣝࢳࣃࢫఏᦙ⎔ቃ࡟࠾ࡅࡿ᥎ᐃ࣓࢝ࢽࢬ࣒

ࢆ᫂ࡽ࠿࡟ࡍࡿࡓࡵ࡟㸪ィ⟬ᶵࢩ࣑࣮ࣗࣞࢩࣙࣥ࡟

ࡼࡾ༢୍Ἴࡀ฿᮶ࡍࡿఏᦙ⎔ቃ࡟࠾ࡅࡿ᥎ᐃ≉ᛶ

ࢆヲ⣽࡟ศᯒࡍࡿ㸬ࡲࡓ㸪ࡇࡢ᥎ᐃ≉ᛶࡢศᯒ⤖ᯝ

ࡼࡾ᥎ᐃࡀṇ☜࡟⾜ࢃࢀࡿ᮲௳ࢆᑟฟࡍࡿ㸬

ఏᦙ㊰≉ᛶ࡟ᇶ࡙ࡃ⛎ᐦ㘽ඹ᭷᪉ᘧ

⌧ᅾ㸪↓⥺ࢆ฼⏝ࡋࡓ㏻ಙࡀᗈࡃ⏝࠸ࡽࢀ࡚࠸ࡿ

ࡀ㸪↓⥺ࢆ฼⏝ࡋࡓ㏻ಙࡣ㸪ࡑࡢᛶ㉁ୖ㸪᝟ሗࡢ┐

⫈ࡀᐜ࡛᫆࠶ࡾ᝟ሗࢭ࢟ࣜࣗࢸ࢕࣮㠃࡛ࡢ⬤ᙅᛶ ࡀㄢ㢟࡜࡞ࡿࡓࡵ㸪᝟ሗࢆᬯྕ໬ࡍࡿᚲせࡀ࠶ࡿ㸬

୍⯡࡟฼⏝ࡉࢀ࡚࠸ࡿᬯྕ᪉ᘧ࡜ࡋ࡚㸪බ㛤㘽ᬯྕ

᪉ᘧ࡜⛎ᐦ㘽ᬯྕ᪉ᘧࡀ࠶ࡿ^{4, 5)}㸬

බ㛤㘽ᬯྕ᪉ᘧࡣ㸪බ㛤ࡉࢀࡓᬯྕ໬㘽ࢆ⏝࠸࡚

ᬯྕ໬ࢆ⾜࠸㸪᚟ྕࡢ㝿࡟ࡣ㸪⛎ᐦࡢ᚟ྕ㘽ࢆ⏝࠸

࡚᚟ྕࢆ⾜࠺࡜࠸࠺ᬯྕ࡛࠶ࡿ㸬බ㛤ࡉࢀࡓᬯྕ໬

㘽(බ㛤㘽)ࢆ▱ࡿࡇ࡜࡛㸪ㄡ࡛ࡶᬯྕ໬ฎ⌮ࢆ⾜࠺

ࡇ࡜ࡣ࡛ࡁࡿࡀ㸪᚟ྕฎ⌮ࢆ⾜࠺ࡇ࡜ࡀ࡛ࡁࡿࡢࡣ㸪 ࡑࡢ᚟ྕ㘽ࡢᣢࡕ୺࡛࠶ࡿṇつࡢ฼⏝⪅࡟㝈ࡽࢀ

ࡿ㸬ࡲࡓ㸪ᬯྕ໬⏝ࡢ㘽࠿ࡽ᚟ྕ⏝ࡢ㘽ࢆᑟࡇ࠺࡜

ࡍࡿ࡜Ⳙ኱࡞ィ⟬㔞ࡀᚲせ࡞ࡇ࡜࠿ࡽ㸪᚟ྕ㘽ࡢゎ ㄞࡣᴟࡵ࡚ᅔ㞴࡛࠶ࡿ㸬ࡇࡢࡼ࠺࡞᪉ᘧࡣᬯྕ᪉ᘧ

࡜ࡋ࡚ィ⟬㔞ⓗ࡟Ᏻ඲࡛࠶ࡿ࡜ゝࢃࢀࡿ㸬ࡋ࠿ࡋ㸪

᚟ྕ㘽ࢆ⏝࠸࡚᚟ྕࢆ⾜࠺ሙྜࡶ₇⟬㔞ࡀከࡃ࡞

ࡿࡓࡵ㸪᚟ྕฎ⌮࡟ᚲせ࡞᫬㛫ࡀከࡃ࡞ࡿ࡞࡝㸪ฎ

⌮⬟ຊ࡟ไ⣙ࡢ࠶ࡿ⛣ື㏻ಙ➃ᮎ࡟㐺⏝ࡋ࡟ࡃ࠸

࡜࠸࠺ၥ㢟ࡀ࠶ࡿ⁵⁾㸬

୍᪉㸪⛎ᐦ㘽ᬯྕ᪉ᘧࡣ㸪ᬯྕ໬࡜᚟ྕ࡛ྠࡌ㘽

ࢆ⏝࠸ࡿ᪉ᘧ࡛࠶ࡾ㸪ࡑࡢ㘽ࢆ㏦ཷಙ⪅ࡢ㛫࡛ඹ᭷

ࡍࡿ᪉ᘧ࡛࠶ࡿ㸬ࡇࡢ᪉ᘧ࡛ࡣ㸪᝟ሗࡢᬯྕ໬࡜᚟

ྕ࡛ྠࡌ㘽ࢆ⏝࠸ࡿࡓࡵ㸪᚟ྕࡢࡓࡵࡢ₇⟬㔞ࡀᑡ

࡞ࡃ࡞ࡿ㸬₇⟬㔞ࡀᑡ࡞ࡃ࡚ࡍࡴࡢ࡛㸪኱㔞ࡢࢹ࣮

ࢱࢆ㧗㏿࡟ఏ㏦ࡍࡿሙྜ࡟᭷ຠ࡛࠶ࡿ㸬ࡓࡔࡋ㸪⛎

ᐦ㘽ᬯྕ᪉ᘧࡢሙྜࡣ㸪ᬯྕ㏻ಙࢆ⾜࠸ࡓ࠸┦ᡭࡈ

࡜࡟ಶูࡢ⛎ᐦ㘽ࢆᏳ඲࡟ඹ᭷ࡋ⟶⌮ࡍࡿᚲせࡀ

࠶ࡾ㸪⛎ᐦ㘽ࡢ㓄㏦ࡸಖ⟶ࡢ㝿࡟⛎ᐦ㘽ࡀ➨୕⪅࡟

ゎㄞࡉࢀࡿ༴㝤ᛶࡀ࠶ࡿ࡞࡝ࡢၥ㢟ࡀ࠶ࡿ㸬ࡇࢀࡽ

ࡢၥ㢟ࢆゎỴࡍࡿࡓࡵ㸪㘽ࡢ㓄㏦ࢆᚲせ࡜ࡋ࡞࠸⛎

ᐦ㘽ඹ᭷᪉ᘧࡢ୍ࡘ࡜ࡋ࡚㸪ఏᦙ㊰≉ᛶ࡟ᇶ࡙ࡃ⛎

ᐦ㘽ඹ᭷᪉ᘧࡀᥦ᱌ࡉࢀ࡚࠸ࡿ^1-3)㸬

ఏᦙ㊰≉ᛶ࡟ᇶ࡙ࡃ⛎ᐦ㘽ඹ᭷᪉ᘧࡢᴫせࢆ

Fig.

1

࡟♧ࡍ㸬

Multipath fading

Eavesdroppe

Reversibility of radio propagation

Authorized _Tx.

Rx.

Authorized

Rx.

Rx.

Tx.

Fig. 1. Concept of wireless security technique based on wireless propagation characteristics.

㟁Ἴఏᦙ࡟࠾࠸୍࡚⯡࡟㏦ཷಙⅬ㛫࡛ྍ㏫ᛶࡀ ᡂࡾ❧ࡘࡇ࡜࠿ࡽ㸪ṇつࡢ㏦ཷಙ⪅㛫࡛ఏᦙ㊰ࡢ≉

ᛶࢆඹ᭷ࡍࡿࡇ࡜ࡀ࡛ࡁࡿ㸬

Fig. 2

ࡣ༢୍࢔ࣥࢸࢼ

ࢆ⏝࠸ࡓሙྜࡢ࢔ࣥࢸࢼኚ఩࡟ᑐࡍࡿࣇ࢙࣮ࢪࣥ

ࢢࡢ┦㛵≉ᛶࢆ♧ࡋ࡚࠸ࡿ㸬ྠᅗ࠿ࡽཷಙᆅⅬ࠿ࡽ

1/4

Ἴ㛗௨ୖ㞳ࢀࡿ࡜ࣇ࢙࣮ࢪࣥࢢኚືࡣ┦㛵ࡀ༑

ศపࡃ࡞ࡾ㸪↓┦㛵࡜⪃࠼࡚ࡼ࠸㸬ࡋࡓࡀࡗ࡚㸪ࣇ

࢙࣮ࢪࣥࢢ⎔ቃ࡟࠾ࡅࡿఏᦙ㊰ࡢ≉ᛶࡣ㸪ṇつࡢ㏦

ཷಙ⪅㛫࡛➨୕⪅࡟⛎ᐦ⿬࡟ඹ᭷ࡍࡿࡇ࡜ࡀ࡛ࡁ

ࡿ᝟ሗ࡜⪃࠼ࡿࡇ࡜ࡀ࡛ࡁࡿ㸬ࡇࢀࡀ㸪ఏᦙ㊰≉ᛶ

࡟ᇶ࡙ࡃ⛎ᐦ㘽ඹ᭷᪉ᘧࡢᇶᮏཎ⌮࡛࠶ࡿ㸬

0 0.5 1 1.5 2 2.5 3 3.5 4

0 0.2 0.4 0.6 0.8 1

Normalized distance[wavelength]

Spatial correlation

Fig. 2. Spatial correlation in multipath fading environment.

Fig. 3

ࡣ㸪㟁Ἴఏᦙ㊰≉ᛶ࡟ᇶ࡙࠸࡚⛎ᐦ㘽(2್

⣔ิ

)

ࢆ⏕ᡂࡍࡿ௦⾲ⓗ࡞᪉ἲࢆᴫᛕⓗ࡟♧ࡋ࡚࠸

ࡿ㸬ࣇ࢙࣮ࢪࣥࢢኚືࡢᙉᗘศᕸ࠿ࡽࡑࡢ୰ኸ್ࢆ

ồࡵ㸪ࣇ࢙࣮ࢪࣥࢢࡀኚືࡍࡿྛ᫬Ⅼࡢಙྕᙉᗘࡢ

኱ᑠࢆ୰ኸ್ࢆࡋࡁ࠸್࡜ࡋุ࡚ᐃࡋ㸪0ࡲࡓࡣ

1

࡟

2

್໬ࡍࡿ㸬

Median

Signal strength

Time

1 0 0 1 0 1 0 1 1 1

Fig. 3. Binarization by median value.

ḟ࡟㸪┐⫈ᒁࡀṇつᒁࡢࣇ࢙࣮ࢪࣥࢢኚື࡜࠶ࡿ

⛬ᗘ┦㛵ࡢ࠶ࡿఏᦙ㊰≉ᛶࢆᚓࡓ࡜⪃࠼ࡓሙྜ࡟㸪

┐⫈ᒁࡀṇつᒁࡢ⛎ᐦ㘽࡜࡝ࡢ⛬ᗘ୍⮴ࡍࡿ㘽ࢆ

ᚓࡿࡇ࡜ࡀ࡛ࡁࡿ࠿ࢆ♧ࡍ㸬ࣇ࢙࣮ࢪࣥࢢኚືࡢ┦

㛵ࡀU࡜࡞ࡿ஧ࡘࡢࣞ࢖࣮ࣜࣇ࢙࣮ࢪࣥࢢࢆ⪃࠼㸪

Fig. 3

࡟♧ࡋࡓ⏕ᡂ᪉ἲ࡟ࡼࡾ

2

್⣔ิࢆࡑࢀࡒࢀ

⏕ᡂࡋࡓሙྜࡢ⛎ᐦ㘽ࡢ୍⮴≉ᛶࢆ

Fig. 4

࡟♧ࡍ㸬

┦㛵U=0.5 ⛬ᗘ࡛ࡣ୍⮴⋡ࡣ↓┦㛵ࡢሙྜ࡜኱ᕪ ࡣ࡞࠸㸬ࡲࡓ㸪ࡓ࡜࠼┦㛵U=0.9 ࡛ࡶ୍⮴⋡ࡣ

0.8

⛬ᗘ࡟཰ࡲࡿࡇ࡜ࡀࢃ࠿ࡿ㸬౛࠼ࡤ

128

ࣅࢵࢺࡢᬯ

ྕ㘽⏕ᡂࢆ⪃࠼ࡿ࡜㸪ᖹᆒࡋ࡚

8

๭⛬ᗘࡢ୍⮴⋡࡛

ࡣ

128

ࣅࢵࢺ඲࡚ࡀ᏶඲࡟୍⮴ࡍࡿ☜⋡ࡣ࡯ࡰ

0

࡛

࠶ࡿ㸬ࡇࡇ࡛㸪

Fig. 2

ࡼࡾࣞ࢖࣮ࣜࣇ࢙࣮ࢪࣥࢢ⎔

ቃ࡟࠾࠸࡚┦㛵್ࡀ

0.9

࡜࡞ࡿ㊥㞳ࡣ

0.1

Ἴ㛗

(800Hz

࡟࠾࠸࡚⣙

4cm

㸪

2.4GHz

࡟࠾࠸࡚⣙

1.25cm)

⛬ᗘ࡜࡞ࡾ⿕┐⫈ഃ࡟࡯ࡰ㞄᥋ࡋࡓ≧ែ࡜࡞ࡿ㸬┐

⫈⾜Ⅽࡣ୍⯡࡟⿕┐⫈ഃ࠿ࡽ㞃ࢀ࡚⾜࠺ࡶࡢ࡛࠶

ࡿࡇ࡜ࢆ⪃៖ࡍࡿ࡜㸪ࡇࡢ᪉ἲ࡟ࡼࡾ⏕ᡂࡉࢀࡓ⛎

ᐦ㘽ࢆ┐⫈ࡍࡿࡇ࡜ࡣ⌧ᐇⓗ࡟ࡣ୙ྍ⬟࡛࠶ࡿ࡜

ゝ࠼ࡿ㸬

0 0.2 0.4 0.6 0.8 1

0.4 0.5 0.6 0.7 0.8 0.9 1

Correlation

Average ratio of agreement bit

Fig. 4. Average agreement rate for variation of spatial correlation.

௚ᆅⅬఏᦙ㊰≉ᛶࡢ᥎ᐃἲ࡜ᇶᮏᛶ⬟ホ౯ 」ᩘᆅⅬほ ಙྕ࡟ᇶ࡙ࡃ௚ᆅⅬఏᦙ㊰≉ᛶ

᥎ᐃἲ

๓❶࡛♧ࡋࡓࡼ࠺࡟㸪༢୍࢔ࣥࢸࢼࢆ⏝࠸ࡓሙྜ㸪

ࣇ࢙࣮ࢪࣥࢢࡢ┦㛵㊥㞳௨ୖ࡟ཷಙⅬࡀ㞳ࢀࡿ࡜㸪

௚ᆅⅬࡢఏᦙ㊰≉ᛶࢆ▱ࡿࡇ࡜ࡣᅔ㞴࡛࠶ࡿ㸬ᮏ◊

✲࡛ࡣ㸪⛎ᐦ㘽ඹ᭷᪉ᘧࡢᏳ඲ᛶ᳨ウ࡜࠸࠺ほⅬ࠿

ࡽ┐⫈⪅࡟࡜ࡗ࡚ࡼࡾ᭷฼࡞≧ἣ

(

┐⫈⪅ࡀṇつࡢ

ཷಙᒁ࡟ẚ࡭࡚ࡼࡾᛶ⬟࣭ᶵ⬟ࡢ㧗࠸ཷಙࢩࢫࢸ࣒

ࢆ᭷ࡋ࡚࠸ࡿሙྜ

)

ࢆ⪃࠼ࡿ㸬౛࠼ࡤ᥎ᐃᒁࡀ」ᩘ

࢔ࣥࢸࢼࡸᣦྥᛶ࢔ࣥࢸࢼࢆ⏝࠸࡚࠸ࡿሙྜ࡟ࡣ㸪

௚ᒁࡢఏᦙ㊰≉ᛶࡢ᥎ᐃ

(

ࡇࢀࡣ⛎ᐦ㘽ඹ᭷᪉ᘧ࡛

ࡣࠕ┐⫈ࠖ࡜࠸࠺⾜Ⅽ࡟࠶ࡓࡿ)ࡢྍ⬟ᛶࡀ࠶ࡿ࡜

⪃࠼ࡽࢀࡿ㸬ࡑࡇ࡛㸪ᮏ◊✲࡛ࡣ┐⫈⪅ࡀṇつཷಙ ᒁࡢ࿘ᅖࡢ」ᩘᆅⅬ࡛ṇつᒁ࡜ྠ᫬࡟ཷಙࡍࡿࣔ

ࢹࣝࢆ⪃࠼㸪㟁Ἴᖸ΅ィࡢཎ⌮⁸⁾࡟㢮ఝࡋࡓ฿᮶ࣃ

ࢫࡢ᪉ྥ᳨ฟ(=௬᝿ࣃࢫ)ཬࡧࡑࡢྜᡂ࡟ࡼࡗ࡚┠

ⓗᆅⅬࡢఏᦙ≉ᛶࢆ᥎ᐃࡍࡿ᪉ᘧࢆ⪃࠼ࡿ㸬

ࡇࡢ᥎ᐃ᪉ᘧࡢᴫᛕࢆ

Fig. 5

࡟♧ࡍ㸬࡞࠾㸪ᮏ✏

࡛ࡣ஧ḟඖࡢၥ㢟ࢆ⪃࠼ࡿ㸬᥎ᐃࢆ⾜࠺๓ᥦ᮲௳࡜

ࡋ࡚㸪᥎ᐃᑐ㇟࡛࠶ࡿṇつཷಙᒁࢆ୰ᚰ࡜ࡋࡓ༙ᚄ R(ᮏㄽᩥ࡛ࡣἼ㛗࡛ṇつ໬ࡋࡓṇつ໬㊥㞳࡜ࡋ࡚

⾲ࡍࡇ࡜࡜ࡍࡿ

)

ࡢ෇࿘

(

ࡇࢀࢆほ ෇࡜࿧ࡪ

)

ࢆ⪃

࠼㸪ほ ෇࿘ୖ࡟」ᩘࡢほ ⅬPn

(n=1, …, N:N

ࡣほ  Ⅼᩘ

)

ࢆ➼ゅᗘ㛫㝸࡛⌮᝿ⓗ࡟㓄⨨ࡍࡿࡶࡢ࡜ࡍ

ࡿ㸬ࡲࡓ㸪᥎ᐃᑐ㇟ᒁ࠿ࡽࡢ Pnࡢゅᗘ᪉ྥࢆJn࡜

⾲ࡍ㸬ࡉࡽ࡟㸪Pn࡟࠾࠸࡚ほ ࡉࢀࡿཷಙಙྕ Zn

ࡣ඲࡚᪤▱࡛࠶ࡿ࡜ࡋ㸪ࡇࢀࡽࡢほ ಙྕࡣ᥎ᐃᑐ

㇟ᒁࡀཷಙࡍࡿࢱ࢖࣑ࣥࢢ࡜ྠ᫬࡟ཷಙࡍࡿࡶࡢ

࡜ࡍࡿ㸬

Observation points

Target point of estimation

Radius J_n

P_n(Z_n)

P_n-1(Z_n-1)

G_m

Observation circle

Hypothetical plain wave

Fig. 5. Estimation model.

᥎ᐃ᪉ἲࡣ௨ୗࡢ㏻ࡾ࡛࠶ࡿ㸬ࡲࡎ㸪ᐇ㝿ࡢ฿᮶

ࣃࢫࢆ࠶ࡿ฿᮶᪉ྥG_mࡢᖹ㠃Ἴ࡜ࡍࡿ௬᝿ⓗ࡞ࣃ

ࢫAm

(m=1, …, M:M

ࡣ௬᝿ࣃࢫᩘ)ࢆ⪃࠼㸪ࡑࢀࡒࢀ

ࡢ௬᝿ࣃࢫࡈ࡜࡟ほ ಙྕ Znࢆ⏝࠸࡚᥎ᐃᑐ㇟ᒁ

࡟࠾ࡅࡿཷಙಙྕࡢ᣺ᖜ࣭఩┦ࢆ᥎ᐃࡍࡿ㸬ᮏ◊✲

࡛ࡣG_mࡣ

2Sm/M

࡜➼㛫㝸࡟タᐃࡍࡿ㸬ࡇࡇ࡛㸪Zn

࠿ࡽ᥎ᐃࡉࢀࡿಙྕࡣZn

exp(-j2SRcos(J

n

-G

m

))࡜࡞ࡿ㸬

ࡉࡽ࡟඲࡚ࡢほ Ⅼ࡟ࡘ࠸࡚ࡇࡢ್ࢆᖹᆒࡍࡿࡇ

࡜࡟ࡼࡾ㸪௬᝿ࣃࢫ Am࡟ᑐࡍࡿ᥎ᐃᑐ㇟ᒁ࡟࠾ࡅ

ࡿ᥎ᐃಙྕXmࡣ௨ୗࡢࡼ࠺࡟ᚓࡽࢀࡿ㸬

) ʌ cos(

2 j 1

¹

exp(

0

m n N

n n

m

Z R

X N ¦

J G ⁽¹⁾

ࡇࡇ࡛㸪X_mࡢ್ࡣ㸪ᐇ㝿ࡢࣃࢫࡢ฿᮶ゅᗘࡀ௬

᝿ⓗ࡞ゅᗘG_m࡜୍⮴ࡍࡿሙྜࡣ㸪n࡟ᑐࡍࡿྛ㡯ࡀ ࡑࢀࡒࢀྠ఩┦࡜࡞ࡾࡑࡢ࿴(=|X_m

|)ࡢ⤯ᑐ್ࡣ኱

ࡁࡃ࡞ࡿ㸬ࡑࢀ࡟ᑐࡋ୍࡚⮴ࡋ࡞࠸ሙྜࡣ㸪ྛ㡯ࡢ

఩┦ࡣࣛࣥࢲ࣒࡟࡞ࡾࡑࡢ࿴ࡣ఩┦ࡀ୍⮴ࡍࡿሙ

ྜ࡟ẚ࡭࡚ᑠࡉࡃ࡞ࡿ㸬ࡇࡇ࡛㸪ࡍ࡭࡚ࡢ฿᮶᪉ྥ

ᡂศࡢᐤ୚࡟ࡘ࠸࡚⪃࠼ࡿࡓࡵ㸪ồࡵࡓ Xmࢆࡍ࡭

࡚ࡢ m ࡟ࡘ࠸࡚඲࿘᪉ྥ࡛ᖹᆒࡋ㸪௨ୗࡢࡼ࠺࡟

᥎ᐃᑐ㇟ᒁ࡟࠾ࡅࡿ᥎ᐃཷಙಙྕXࢆᚓࡿ㸬

m M

m

M X X ¦

¹

0

1 (2)

ࢩ࣑࣮ࣗࣞࢩࣙࣥ࡟ࡼࡿᇶᮏᛶ⬟ホ౯ ಙྕᙉᗘኚືࡢ᥎ᐃ

๓⠇࡛ㄝ᫂ࡋࡓ᳨ウᡭἲࡢ᥎ᐃ౛ࢆィ⟬ࢩ࣑ࣗ

࣮ࣞࢩࣙࣥ࡟ࡼࡾ♧ࡍ㸬ࡇࡇ࡛ࡣ㸪ఏᦙ⎔ቃࡢࣔࢹ

ࣝ࡜ࡋ࡚㸪」ᩘࡢᖹ㠃Ἴࡀ࿘ᅖ୍ᵝࡢ᪉ྥ࠿ࡽ฿᮶

ࡍࡿ

Jakes

ࣔࢹࣝ⁹⁾࡟㢮ఝࡍࡿఏᦙ⎔ቃࢆ௬ᐃࡍࡿ㸬

ࡇࡢࣔࢹࣝࡢᴫᛕࢆ

Fig. 6

࡟♧ࡍ㸬฿᮶࣐ࣝࢳࣃࢫ ࡣᖹ㠃Ἴ࡜ࡋ㸪ࡑࡢᩘࢆ

5

࡜ࡍࡿ㸬ࡲࡓ㸪඲࡚ࡢ฿

᮶࣐ࣝࢳࣃࢫࡣ➼ࡋ࠸᣺ᖜ(=1)ࢆࡶࡘࡶࡢ࡜ࡍࡿ㸬 ࡉࡽ࡟㸪᥎ᐃᑐ㇟ᒁ࡟࠾ࡅࡿྛࣃࢫࡢ฿᮶᪉ྥ㸪ཷ

ಙ఩┦ࡣ[0, 2S)ࡢ⠊ᅖ୍࡛ᵝศᕸ࡟ᚑ࠺ࣛࣥࢲ࣒

್࡛࠶ࡿ࡜ࡍࡿ㸬ࡇࡢఏᦙ⎔ቃࣔࢹࣝ࡟࠾࠸࡚

3.1

⠇࡟♧ࡋࡓ᥎ᐃᡭἲࢆ㐺⏝ࡋࡓሙྜࡢ᥎ᐃ⤖ᯝࢆ

♧ࡍ㸬

Target point of estimation Observation

points

Fig. 6. Multipath model.

Fig. 7

ཬࡧ

Fig. 8

ࡣಙྕᙉᗘࡢ᥎ᐃ⤖ᯝ࡛࠶ࡿ㸬

Fig. 7

ࡣほ ⅬᩘNࢆ

20

࡜ࡋࡓሙྜ㸪Fig. 8ࡣ

40

ࡢሙྜࡢ⤖ᯝ࡛࠶ࡿ㸬ࡲࡓ㸪ほ ෇༙ᚄR=4Ἴ㛗㸪 ௬᝿ࣃࢫᩘM=1000࡜௬ᐃࡋ࡚࠸ࡿ㸬ᮏㄽᩥ࡛ࡣ⛎

ᐦ㘽ඹ᭷᪉ᘧࡢᏳ඲ᛶ᳨ウ࡜࠸࠺❧ሙ࡛㆟ㄽࢆ⾜

࠺ࡓࡵ㸪௬᝿ࣃࢫࡢᩘࡣ༑ศ࡟኱ࡁࡃタᐃࡍࡿࡇ࡜

ࡀ㐺ษ࡛࠶ࡿ

(

௬᝿ࣃࢫᩘࡢኚ໬࡟ᑐࡍࡿ≉ᛶ࡟ࡘ

࠸࡚ࡣᚋ࡟ヲࡋࡃ㏙࡭ࡿ)㸬ࡋࡓࡀࡗ࡚ࡇࡇ࡛ࡣ㸪 ௬᝿ࣃࢫᩘ M=1000 ࡜ࡋ࡚࠸ࡿ

(

ᚋ㏙ࡢࢩ࣑࣮ࣗࣞ

ࢩࣙࣥホ౯࡛ࡣ≉࡟᩿ࡾࡀ࡞࠸㝈ࡾM=1000࡜ࡋ࡚

࠸ࡿ

)

㸬

Fig. 7

࠾ࡼࡧ

Fig. 8

ࡢᶓ㍈ࡣ㸪ࣇ࢙࣮ࢪࣥࢢ

⎔ቃ(฿᮶᪉ྥཬࡧྛ฿᮶Ἴࡢ఩┦)ࢆኚ໬ࡉࡏ࡚␗

࡞ࡿࣇ࢙࣮ࢪࣥࢢ⎔ቃ࡜ࡋࡓሙྜࡢヨ⾜ᅇᩘࢆ♧

ࡋ࡚࠸ࡿ㸬ࡲࡓ୧ᅗ࡟ࡣ㸪ᐇ㝿ࡢཷಙಙྕᙉᗘ㸪᥎ ᐃಙྕᙉᗘ࡟ຍ࠼࡚㸪ࡇࢀࡽࡢẚࢆేࡏ࡚♧ࡋ࡚࠸

ࡿ㸬Fig. 7࡛ࡣᐇ㝿ࡢ್࡜᥎ᐃ್ࡢẚࡀࣇ࢙࣮ࢪࣥ

ࢢ⎔ቃࢆኚ໬ࡉࡏࡿࡈ࡜࡟ኚືࡋ࡚࠸ࡿࡀ㸪

Fig. 8

࡛ࡣࡇࡢ್ࡀ୍ᐃ࡜࡞ࡗ࡚࠸ࡿ㸬ࡍ࡞ࢃࡕ㸪ᐇ㝿ࡢ

್࡜᥎ᐃ್ࡀẚ౛ࡢ㛵ಀ࡛࠶ࡾ㸪ࡇࢀࡼࡾࣇ࢙࣮ࢪ

ࣥࢢ࡟ࡼࡿಙྕᙉᗘኚືࢆṇ☜࡟᥎ᐃ࡛ࡁ࡚࠸ࡿ

ࡇ࡜ࡀࢃ࠿ࡿ㸬

0 20 40 60 80 100

0 0.05 0.1 0.15

Trial count Estimated signal level Ratio of Etimated/Actual

䢢

䢢

0 20 40 60 80 1000

2 4 6

Actual signal level

Estimated Estimated/Actual Actual

Fig. 7. Actual and estimated signal variations (N=20).

0 20 40 60 80 100

0 0.02 0.04 0.06

Trial count Estimated signal level Ratio of Estimated/Actual

䢢

䢢

0 20 40 60 80 1000

2 4 6

Actual signal level

Estimated Estimeted/Actual Actual

Fig. 8. Actual and estimated signal variations (N=40).

┦㛵್ࢆ⏝࠸ࡓ᥎ᐃ≉ᛶࡢᐃ㔞໬

ḟ࡟㸪

3.2.1

⠇ࡢ⤖ᯝࢆ㋃ࡲ࠼㸪

Fig. 7

ཬࡧ

Fig. 8

࡟♧ࡉࢀࡓࡼ࠺࡞ࣇ࢙࣮ࢪࣥࢢ⎔ቃࡢኚ໬࡟క࠺

ಙྕᙉᗘኚື࡟ࡘ࠸࡚㸪ᐇ㝿ࡢ್ࡢኚື࡜᥎ᐃ್ࡢ ኚື࡜ࡢ㛫ࡢ┦஫┦㛵ಀᩘࢆィ⟬ࡋ㸪ࡇࡢ┦㛵ࢆ᥎ ᐃ⢭ᗘࡢᣦᶆ࡜ࡋ࡚᥎ᐃ≉ᛶࡢᐃ㔞໬ࢆ⾜࠺㸬

Fig.

8

ࡢࡼ࠺࡞≧ἣ࡛ࡣ┦㛵ࡣ࡯ࡰ

1

࡜࡞ࡾ㸪Fig. 7࡛ ࡣ┦㛵್ࡣ

1

ࡼࡾࡶᑠࡉࡃ࡞ࡿ㸬ࡇࡢ᪉ἲࢆ⏝࠸࡚㸪 ほ ෇ࡢ༙ᚄ㸪ほ Ⅼᩘ࡞࡝ࢆኚ໬ࡉࡏࡓሙྜࡢ᥎ ᐃ≉ᛶࡢኚ໬ࢆ♧ࡍ㸬

Fig. 9

ࡣほ ෇ࡢ༙ᚄRࢆኚ໬ࡉࡏࡓሙྜࡢ┦㛵

≉ᛶࢆ♧ࡋ࡚࠸ࡿ㸬ࡇࡇ࡛ࡣほ Ⅼᩘ N=100 ࡜ࡋ

࡚࠸ࡿ㸬N=100ࡢሙྜ࡟ࡣほ ෇༙ᚄࡀ

15

Ἴ㛗⛬

ᗘ௨ୗ࡛┠ⓗࡢཷಙᙉᗘኚື≉ᛶࡀṇ☜࡟᥎ᐃ࡛

ࡁࡿࡇ࡜ࡀࢃ࠿ࡿ㸬

0 10 20 30 40

-0.2 0 0.2 0.4 0.6 0.8 1

Normalized radius[wavelength]

Correlation

Fig. 9. Correlation characteristics when radius of observation circle is changed.

᥎ᐃ≉ᛶ࡟㛵ࡍࡿヲ⣽᳨ウ ᥎ᐃ࣓࢝ࢽࢬ࣒࡜᥎ᐃ≉ᛶ࡟㛵ࡍࡿศᯒ ௬᝿ࣃࢫࡢ฿᮶᪉ྥ࡟ᑐࡍࡿ᥎ᐃ್ࡢኚ໬

Fig. 9

ࡼࡾほ ෇༙ᚄࡀ

15

Ἴ㛗⛬ᗘࡲ࡛࡯ࡰṇ

☜࡞᥎ᐃ(┦㛵ࡢ್ࡀ࡯ࡰ

1

࡜࡞ࡿ)ࡀᐇ⌧ࡉࢀ࡚࠸

ࡿࡀ㸪ほ ෇༙ᚄࡀࡑࢀ௨ୖ࡟኱ࡁࡃ࡞ࡿ࡜ᛴ࡟᥎ ᐃࡀ୙ྍ⬟࡜࡞ࡿ≉ᛶ࡜࡞ࡿࡇ࡜ࡀࢃ࠿ࡿ㸬ᮏ⠇࡛

ࡣ㸪ࡇࡢࡼ࠺࡞᥎ᐃ≉ᛶࡀᚓࡽࢀࡿ࣓࢝ࢽࢬ࣒ࢆヲ ࡋࡃศᯒࡍࡿࡓࡵ࡟

Fig. 6

࡟♧ࡍࣔࢹࣝࡼࡾࡶ⡆᫆

࡞ࣔࢹࣝࢆ⪃࠼ࡿ㸬

Fig. 10

࡟㸪ࡓࡔ୍ࡘࡢᖹ㠃Ἴࡀ

Fig. 5

ࡢ

0[rad.]࠿ࡽ฿᮶ࡍࡿ⎔ቃࣔࢹࣝࢆ♧ࡍ㸬ほ

 Ⅼࡣ

0[rad.]

࠿ࡽ㓄⨨ࡋ࡚࠸ࡿࡢ࡛㸪୍ࡘ┠ࡢほ 

Ⅼࡢゅᗘ᪉ྥJ1࡜ᖹ㠃Ἴࡢ฿᮶᪉ྥ࡜ࡢゅᗘᕪࡣ

࡞࠸㸬ࡇࡢ⎔ቃ࡟࠾࠸࡚㸪௬᝿ࣃࢫࡢ฿᮶᪉ྥG_m

ࢆኚ໬ࡉࡏࡿሙྜ࡟ࡘ࠸࡚⪃࠼ࡿ㸬࡞࠾㸪ࡇࡢ฿᮶ Ἴࡢ᥎ᐃᑐ㇟ᒁ࡛ࡢཷಙ఩┦ࢆȧ

/2

࡜ࡍࡿ㸬

Target point of estimation

Single wave - Incident angle : 0

-

Phase at center : S

Fig. 10. Single wave model.

Fig. 11

ࡣ㸪

Fig. 10

࡟♧ࡋࡓࣔࢹࣝ࡟࠾࠸࡚㸪N=100㸪 M=1000࡜ࡋ㸪ほ ෇༙ᚄR=1Ἴ㛗㸪

15

Ἴ㛗࡜ࡋࡓ ሙྜ࡟࠾ࡅࡿ㸪௬᝿ࣃࢫࡢ฿᮶᪉ྥ࡟ᑐࡍࡿᘧ

(1)

࡛ᚓࡽࢀࡿ᥎ᐃ್ Xmࡢ᣺ᖜ࡜఩┦ࡢኚ໬ࢆ♧ࡋ࡚

࠸ࡿ㸬ࡇࡇ࡛ࡣ㸪ࡇࡢ᣺ᖜ≉ᛶࡀ࢔ࣥࢸࢼࣃࢱ࣮ࣥ

࡟㢮ఝࡍࡿࡇ࡜࠿ࡽ㸪ࡓ࡜࠼ࡤ

Fig. 11(a)࡟࠾࠸

࡚

,G

_mࡀ

±0.4[rad.]

ࡢ⠊ᅖෆࡢ≉ᛶࢆ࣓࢖࣮ࣥࣟࣈ㸪

ࡑࡢ୍ࡘእഃࡢ≉ᛶࢆ➨୍ࢧ࢖ࢻ࣮ࣟࣈ㸪ࡑࡢࡉࡽ

࡟እഃࢆ➨஧ࢧ࢖ࢻ࣮ࣟࣈ࡞࡝࡜౽ᐅⓗ࡟࿧ࡪࡇ

࡜࡟ࡍࡿ㸬

(a)R=1[wavelength]

(b)R=15[wavelength]

Fig. 11. Estimated amplitude and phase when azimuth direction of hypothetical wave is changed

(Arrival direction =0[rad.]).

ࡑࢀࡒࢀࡢ఩┦≉ᛶ࠿ࡽ㸪᥎ᐃ఩┦ࡣṇࡋ࠸఩┦

࡜㸪ࡑࢀࡀ཯㌿ࡋࡓ఩┦㸪ࡢ஧ࡘࡢሙྜࡋ࠿Ꮡᅾࡋ ᚓ࡞࠸ࡇ࡜ࡀࢃ࠿ࡿ㸬ࡇࢀࡣ㸪ほ Ⅼࡢ㓄⨨ࡀ᥎ᐃ ᑐ㇟ᒁࡢ࿘ࡾ࡟ᑐ⛠࡟㓄⨨ࡉࢀ࡚࠸ࡿࡓࡵ࡛࠶ࡾ㸪 ᚋ࡟⌮ㄽⓗ࡟᳨ウࡍࡿ㸬

ࡲࡓ㸪᭱⤊ⓗ࡞᥎ᐃ್ࡣྛ௬᝿ࣃࢫ࡟ᑐࡍࡿ᥎ᐃ

್ Xmࢆᖹᆒࡍࡿࡇ࡜࡟ࡼࡗ࡚ᚓࡽࢀࡿࡀ㸪᥎ᐃࡀ

ྍ⬟࡞ᚲせ᮲௳㸪ࡘࡲࡾࡇࡢᖹᆒ್ࡀ༑ศ࡟኱ࡁࡃ

࡞ࡿ᮲௳㸪࡜ࡋ࡚࣓࢖࣮ࣥࣟࣈࡢ⠊ᅖෆ࡟ᑡ࡞ࡃ࡜

ࡶ୍ࡘࡢ௬᝿ࣃࢫࢆ⪃࠼ࡿࡇ࡜ࡀᚲせ࡜⪃࠼ࡽࢀ

ࡿ㸬

Fig. 11

ࡼࡾ㸪఩┦≉ᛶࡀ࣓࢖࣮ࣥࣟࣈ࡟ᑐࡋ࡚

ወᩘ␒┠ࡢࢧ࢖ࢻ࣮ࣟࣈࡀ㏫┦㸪അᩘ␒┠ࡢࢧ࢖ࢻ

࣮ࣟࣈࡀྠ┦࡛࠶ࡿࡇ࡜࠿ࡽ㸪ࡑࡢᖹᆒ್ࡣほ ෇

༙ᚄࡢኚ໬࡟ᑐࡋ࡚᣺ືⓗ࡟ኚ໬ࡍࡿࡇ࡜ࡀண᝿

ࡉࢀࡿ㸬ࡲࡓ㸪ほ ෇༙ᚄࡀ኱ࡁࡃ࡞ࡿ࡟క࠸㸪ᖹ ᆒ್࡛࠶ࡿ᥎ᐃ್࡟ᑐࡍࡿ࣓࢖࣮ࣥࣟࣈ㒊ศࡢᐤ

୚ࡀᑠࡉࡃ࡞ࡾ㸪ᖹᆒ್ࡢ᣺ᖜࡣᑠࡉࡃ࡞ࡿ㸪ࡲࡓ ࡣ㸪ᖹᆒ್ࡀ㏫┦࡟࡞ࡿྍ⬟ᛶࡶ⏕ࡌࡿ࡜⪃࠼ࡽࢀ

ࡿ㸬

ḟ࡟㸪J₁

(0[rad.]

᪉ྥ

)

࡜ᐇ㝿࡟฿᮶ࡍࡿᖹ㠃Ἴ࡜

ࡢ㛫࡟ゅᗘᕪࡀ࠶ࡿሙྜࢆ⪃࠼ࡿ㸬ᖹ㠃Ἴࡢ฿᮶᪉

ྥࢆほ Ⅼ㛫ゅᗘࡢ

1/4

࡜ࡋࡓሙྜࡢ

Fig. 11

࡜ྠᵝ

ࡢ≉ᛶࢆ

Fig.12

࡟♧ࡍ㸬ࡇࡇ࡛ࡣN=100࡜ࡋ࡚࠸

ࡿࡢ࡛ほ Ⅼ㛫ゅᗘࡣ

1/4

™

2S/100

㸻

0.0157[rad.]

࡛

࠶ࡿ㸬ࡲࡓ㸪M=1000࡜ࡋ㸪ほ ༙ᚄR=1Ἴ㛗㸪15 Ἴ㛗ࡢሙྜࢆ⪃࠼ࡿ㸬ྠᅗࡼࡾ㸪ゅᗘᕪࡀ࠶ࡿሙྜ

࡟ࡶ㸪ゅᗘᕪࡀ࡞࠸ሙྜ࡜ྠᵝ࡟᥎ᐃ఩┦ࡣṇࡋ࠸

఩┦࡜ࡑࢀࡀ཯㌿ࡋࡓ఩┦㸪ࡢ஧ࡘࡋ࠿Ꮡᅾࡋ࡞ࡃ㸪 ほ ෇༙ᚄࡀ኱ࡁࡃ࡞ࡿ࡟క࠸㸪ᖹᆒ್࡛࠶ࡿ᥎ᐃ

್࡟ᑐࡍࡿ࣓࢖࣮ࣥࣟࣈ㒊ศࡢᐤ୚ࡀᑠࡉࡃ࡞ࡿ

ࡇ࡜ࡀࢃ࠿ࡿ㸬࡞࠾㸪Fig. 12 ࡟࠾࠸࡚㸪ほ Ⅼᩘ

N=100࡛ṇ☜࡞᥎ᐃࡀ୙ྍ⬟࡛࠶ࡿほ ༙ᚄ R=15 Ἴ㛗ࡢሙྜ࡟ࡣ㸪ࣃࢱ࣮ࣥࡣࢃࡎ࠿࡟㠀ᑐ⛠࡟࡞ࡗ

࡚࠸ࡿ㸬

ࡇࢀࡽࡢ≉ᛶࡼࡾ㸪ほ Ⅼࡢ᥎ᐃᑐ㇟ᒁ࡜ࡢゅᗘ ᪉ྥJ₁࡜ᖹ㠃Ἴࡢ฿᮶᪉ྥ࡜ࡢゅᗘᕪࡀ࠶ࡿሙྜ

࡛ࡶ㸪᣺ᖜ࣭఩┦≉ᛶ࡜ࡶ࡟㸪ゅᗘᕪࡀ࡞࠸ሙྜ࡜

࡯ࡰྠᵝࡢ≉ᛶࢆ♧ࡍࡇ࡜ࡀࢃ࠿ࡿ

(

ࡓࡔࡋ㸪

Fig. 12

ࡢR=15Ἴ㛗࡞࡝ṇ☜࡞᥎ᐃࡀ⾜࠼࡞࠸᮲௳࡛ࡣ㸪

᣺ᖜ≉ᛶ࡟࠾࠸࡚ࣃࢱ࣮ࣥࡀࢃࡎ࠿࡟㠀ᑐ⛠࡞ࡿ

ࡇ࡜࠿ࡽ㸪᥎ᐃ್Xࡢ᣺ᖜ್ࡣゅᗘ᪉ྥJ1࡜ᖹ㠃Ἴ

-2 0 2

0 0.5 1

Angle of hypothetical plain wave

Estimated amplitude

-2 0 2

-2 -1 0 1 2

Angle of hypothetical plain wave

Estimated phase[rad.]

-2 0 2

0 0.5 1

Angle of hypothetical plain wave

Estimated amplitude

-2 0 2

-2 -1 0 1 2

Angle of hypothetical plain wave

Estimated phase[rad.]

ࡢ฿᮶᪉ྥ࡜ࡢゅᗘᕪ࡟ࡼࡾኚ໬ࡍࡿࡇ࡜ࡀ⪃࠼

ࡽࢀࡿ)㸬ࡇࡇ࡛ᚓࡽࢀࡓ⤖ᯝࡼࡾ㸪ࣃࢫࡀࣛࣥࢲ

࣒᪉ྥ࡟฿᮶ࡍࡿఏᦙ⎔ቃ࡟࠾࠸࡚ࡶࡇࡇ࡛♧ࡋ ࡓ⪃࠼᪉ࡣ୍⯡࡟㐺⏝ྍ⬟࡛࠶ࡾ㸪௨㝆ࡢゎᯒࢆ⡆

᫆໬ࡍࡿࡇ࡜ࡀ࡛ࡁࡿ࡜⪃࠼ࡽࢀࡿ㸬

(a)R=1[wavelength]

(b)R=15[wavelength]

Fig. 12. Estimated amplitude and phase when azimuth direction of hypothetical wave is changed

(Arrival direction =0.0157[rad.]).

᣺ᖜཬࡧ఩┦᥎ᐃ☜⋡ࡢኚ໬

ḟ࡟㸪๓⠇ࡢ⤖ᯝࢆ㋃ࡲ࠼㸪ほ ෇༙ᚄࡢኚ໬࡟

ᑐࡍࡿ᭱⤊ⓗ࡞᥎ᐃ್ X ࡢ᣺ᖜཬࡧ఩┦᥎ᐃ☜⋡

ࡢኚ໬ࢆ

Fig. 13

࡟♧ࡍ㸬

๓㏙ࡢࡼ࠺࡟㸪ࡇࢀࡣ

Fig. 11

㸪

Fig. 12

ࡢ≉ᛶࢆ࿘

᪉ྥ࡟✚ศࡋࡓ್࡜࡞ࡿ㸬ࡇࡇ࡛㸪

(a)ࡣࡓࡔ୍ࡘࡢ

ᖹ㠃Ἴࡢ฿᮶᪉ྥࡀ

[0, 2S)

ࡢ⠊ᅖ࡛ࣛࣥࢲ࣒࡟฿

᮶ࡍࡿఏᦙ⎔ቃ࡟࠾࠸࡚

100

ᅇヨ⾜ࡋࡓ⤖ᯝ࡛࠶

ࡿ

(R=15

Ἴ㛗௨ୗ࡛ࡣ᥎ᐃ⢭ᗘࡣ฿᮶᪉ྥ࡟౫Ꮡࡏ

ࡎ

100

ᅇヨ⾜ࡋࡓ࡜ࡋ࡚ࡶ୍ᐃ್࡛࠶ࡿࡀ㸪R=15 Ἴ㛗௨ୖࡢሙྜࡣ฿᮶᪉ྥ࡟ࡼࡾ᥎ᐃ᣺ᖜ್ࡀኚ

໬ࡍࡿࡢ࡛

100

ヨ⾜ࡢᖹᆒ್ࢆ♧ࡋ࡚࠸ࡿ)㸬(b)ࡣ

఩┦᥎ᐃ☜⋡࡛࠶ࡿ㸬๓⠇࡛♧ࡋࡓࡼ࠺࡟᥎ᐃ఩┦

ࡣṇࡋ࠸఩┦࡜㏫┦ࡢࡳ࡛࠶ࡿࡇ࡜ࢆ⪃៖ࡋ࡚㸪఩

┦᥎ᐃࡢᣦᶆ࡜ࡋ࡚㸪ṇࡋ࠸᥎ᐃ఩┦್ࢆᚓࡓ๭ྜ

ࢆ⏝࠸࡚࠸ࡿ㸬

๓⠇࡟࠾࠸࡚ࡶ᥎ ࡉࢀࡓࡼ࠺࡟㸪᥎ᐃ್ࡢ᣺ᖜ ࡣほ ෇༙ᚄࡢቑຍ࡟కࡗ࡚᣺ືⓗ࡟ῶᑡࡋ࡚࠸

ࡃࡇ࡜ࡀࢃ࠿ࡿ㸬ほ ෇༙ᚄࡀ

15

Ἴ㛗⛬ᗘࡲ࡛ࡣ

᣺ᖜࡀ࠿࡞ࡾᑠࡉࡃ࡞ࡗ࡚ࡶ఩┦ࡣṇࡋࡃ᥎ᐃࡉ

ࢀ࡚࠸ࡿ㸬ࡋ࠿ࡋ㸪

Fig. 9

࡜ྠᵝ࡟ほ ෇༙ᚄࡀ

15

Ἴ㛗⛬ᗘࢆ㉸࠼ࡿ࡜㸪఩┦ࡀ㏫㌿ࡍࡿྍ⬟ᛶࡀ⏕ࡌ ṇ☜࡟᥎ᐃ࡛ࡁ࡞࠸ሙྜࡀ⏕ࡌࡿ㸬ࡇࢀࡣ㸪࣓࢖ࣥ

࣮ࣟࣈࡢ⠊ᅖࡀ್ࡀ཯㌿ࡋࡓ఩┦㒊ศ࡟ᑐࡋ࡚┦

ᑐⓗ࡟ᑠࡉࡃ࡞ࡾ㸪㏫┦㒊ศࢆ༑ศ࡟⿵࠺ࡔࡅࡢ኱

ࡁࡉࢆᚓࡿࡇ࡜ࡀ࡛ࡁ࡞ࡃ࡞ࡗࡓࡇ࡜࡟ࡼࡿ࡜⪃

࠼ࡽࢀࡿ㸬

0 5 10 15 20

-100 -80 -60 -40 -20 0

Normalized radius[wavelength]

Estimated amplitude[dB]

(a)Amplitude

0 5 10 15 20

0.4 0.5 0.6 0.7 0.8 0.9 1

Normalized radius[wavelength]

Detection probability

䢢

䢢

(b)Phase

Fig. 13. Estimated amplitude and probability of correct estimation of phase.

㞧㡢ࡀᏑᅾࡍࡿሙྜࡢ᥎ᐃ≉ᛶ

ࡇࡇࡲ࡛ࡣ㞧㡢ࡢᙳ㡪ࢆ↓どࡋ㸪ಙྕࡢࡳࡀᏑᅾ ࡍࡿሙྜ࡟ࡘ࠸࡚㆟ㄽࡋ࡚ࡁࡓ㸬ࡋ࠿ࡋ࡞ࡀࡽ㸪ᐇ 㝿ࡢ⎔ቃࢆ⪃࠼ࡓሙྜ࡟ࡣ㞧㡢ࡣᚲࡎᏑᅾࡍࡿ㸬ࡋ ࡓࡀࡗ࡚㸪ࡑࡢᙳ㡪ࢆホ౯ࡍࡿࡇ࡜ࡣ㔜せ࡛࠶ࡿ㸬

ࡇࡇ࡛ࡣ

Fig. 6

ࡢఏᦙ⎔ቃࣔࢹࣝ࡟࠾࠸࡚㸪㞧㡢

ࡀᏑᅾࡍࡿ⎔ቃࢆ᝿ᐃࡍࡿ㸬

Fig. 13(a)

ࡼࡾ᥎ᐃ್ࡢ

᣺ᖜࡣほ ෇༙ᚄࡢኚ໬࡟ᑐࡋ࡚኱ࡁࡃ᣺ືࡋ࡚

࠸ࡿࡢ࡛㸪㞧㡢ࡀᏑᅾࡍࡿ⎔ቃ࡛ࡣ᥎ᐃ≉ᛶࡣ

Fig.

9

ࡼࡾࡶຎࡿࡇ࡜ࡀ⪃࠼ࡽࢀࡿ㸬

N=100 M=100

-2 0 2

0 0.5 1

Angle of hypothetical plain wave

Estimated amplitude

䢢

䢢

-2 0 2

0 0.5 1

Angle of hypothetical plain wave

Estimated amplitude

-2 0 2

-2 -1 0 1 2

Angle of hypothetical plain wave

Estimated phase[rad.]

䢢

䢢

-2 0 2

-2 -1 0 1 2

Angle of hypothetical plain wave

Estimated phase[rad.]

䢢

䢢

N=100 M=100

Fig. 14

ࡣ㸪ಙྕᑐ㞧㡢㟁ຊẚ

SNR (Signal to Noise Ratio)=0dB㸪20dB㸪40dB

࡜ࡋࡓሙྜࡢ㸪Fig. 9࡜ྠ

ᵝ࡞ほ ෇༙ᚄࡢኚ໬࡟ᑐࡍࡿ┦㛵≉ᛶࢆ♧ࡋ࡚

࠸ࡿ㸬ࡇࡇ࡛㸪SNR ࡣ୍ほ Ⅼ࡟࠾ࡅࡿ฿᮶Ἴࡢ

ྜᡂಙྕࡢᖹᆒ㟁ຊ࡜㞧㡢ᖹᆒ㟁ຊࡢẚ࡛࠶ࡿ㸬

Fig. 9

࡛ࡣࣇࣛࢵࢺ࡛࠶ࡗࡓほ ෇༙ᚄࡀ

15

Ἴ㛗

⛬ᗘ௨ୗࡢ㒊ศ࡟࠾࠸࡚ࡶ㸪

Fig. 13(a)

࡟♧ࡍ᥎ᐃ್

ࡢ᣺ᖜࡢ᣺ື࡟కࡗ࡚┦㛵≉ᛶࡀ኱ࡁࡃኚືࡋ࡚

࠸ࡿࡇ࡜ࡀࢃ࠿ࡿ㸬ࡓࡔࡋ㸪

SNR=40dB

࡜࠸࠺

SNR

ࡀ኱ࡁ࠸⎔ቃ࡛ࡣ㸪Fig. 9ࡢ᥎ᐃ≉ᛶ࡜ࡢᕪࡣ኱ࡁ ࡃ࡞࠸㸬

Fig. 14. Correlation characteristics in a noisy channel when radius of observation circle is changed.

᥎ᐃ≉ᛶ࡟㛵ࡍࡿ⌮ㄽ᳨ウ ఩┦᥎ᐃ≉ᛶ

௨ୗ࡛ࡣ㞧㡢ࡀ↓࠸⎔ቃ࡟ࡘ࠸࡚⪃࠼ࡿࡶࡢ࡜

ࡍࡿ㸬

ࡇࡇ࡛ࡣ㸪ࡇࢀࡲ࡛♧ࡋࡓ᥎ᐃ≉ᛶࡀᚓࡽࢀࡿ࣓

࢝ࢽࢬ࣒ࢆ⌮ㄽⓗ࡟᳨ウࡍࡿ㸬4.1.1 ⠇ࡢ≉ᛶศᯒ

࡟ࡼࡾ㸪༢୍ࡢᖹ㠃Ἴࡀ฿᮶ࡍࡿఏᦙ⎔ቃ࡛ࡣ᥎ᐃ

఩┦ࡣṇࡋ࠸఩┦࡜㸪ࡑࢀࡀ཯㌿ࡋࡓ఩┦㸪ࡢ஧ࡘ ࡢሙྜࡋ࠿Ꮡᅾࡋᚓ࡞࠸ࡇ࡜ࡀࢃ࠿ࡗࡓ㸬ࡇࢀࡣ௨

ୗࡢࡼ࠺࡟ㄝ᫂ࡍࡿࡇ࡜ࡀ࡛ࡁࡿ㸬

ࡲࡎ㸪࠶ࡿほ Ⅼ

n1

P (

ゅᗘ᪉ྥ

n1

J )

࡟ᑐࡋ࡚᥎ᐃ ᑐ㇟ᒁࢆ୰ᚰ࡜ࡋࡓⅬᑐ㇟࡞ほ Ⅼ

P

n₂

( J

ⁿ₂

= J

ⁿ₁

+S,

n2

= n

1

+N/2)

ࢆ⪃࠼ࡿ㸬ࡇࡇ࡛㸪฿᮶Ἴࡀᖹ㠃Ἴ࡜ࡍ

ࡿ࡜ᘧ(1)ࡢZnࡣ௨ୗࡢᘧ࡛⾲ࡍࡇ࡜ࡀ࡛ࡁࡿ㸬

))) ʌ cos(

2 j(

exp( Z J

_n

M

n

r R

Z (3)

ࡇࡇ࡛㸪r㸪Z㸪Mࡣᑐ㇟࡜ࡍࡿ฿᮶Ἴࡢ᣺ᖜ㸪᥎ ᐃᑐ㇟ᒁ࡟࠾ࡅࡿ఩┦㸪฿᮶ゅ࡛࠶ࡿ㸬

ᘧ

(1)

࡜ᘧ

(3)

࠿ࡽ௬᝿ࣃࢫAm࡟ᑐࡍࡿほ Ⅼ

P

n₁

,

n2

P

࡟࠾ࡅࡿ᥎ᐃಙྕ

X

m,n₁

, X

m,n₂^{ࡣࡑࢀࡒࢀ௨ୗࡢ}

ᘧ࡛⾲ࡍࡇ࡜ࡀ࡛ࡁࡿ㸬

))) cos(

) (cos(

ʌ

2 j(

exp(

))) cos(

) (cos(

ʌ

2 j(

exp(

2 2

2

1 1

1

, ,

m n n

n m

m n n

n m

R r

X

R r

X

G J M

J Z

G J M

J Z

(4)

n2

J = J

n₁

+Sࢆ⏝࠸ࡿ࡜㸪௨ୗࡢ⤖ᯝࡀᚓࡽࢀࡿ㸬

) j exp(

cos

2

2

1 ,

,

X r Q Z

X

^{m n}

^{m n}

(5)

ࡇࡇ࡛㸪Q

= 2SR (cos( J

n₁

^{-M)- cos(} J

n1

^-G

m

)

࡛࠶ࡿ㸬ࡇ ࡢ⤖ᯝ࠿ࡽ㸪࠶ࡿほ Ⅼࡢಙྕ᝟ሗࡢ఩┦࡜Ⅼᑐ㇟

࡟఩⨨ࡍࡿほ Ⅼࡢಙྕ᝟ሗࡢ఩┦ࢆ㊊ࡋྜࢃࡏ

ࡿ࡜㸪஫࠸ࡢ఩┦ᡂศࡀ┦ẅࡉࢀṇࡋ࠸఩┦ᡂศ

(Z)

ࡔࡅࡀṧࡾ㸪

cos Q

ࡢ್ࡀṇ࡞ࡽࡤ᥎ᐃ఩┦ࡣṇ ࡋ࠸఩┦㸪㈇࡞ࡽࡤࡑࢀࡀ཯㌿ࡋࡓ఩┦࡟࡞ࡿ㸬ࡉ

ࡽ࡟㸪ᘧ

(5)

ࡢ㛵ಀࡣࡍ࡭࡚ࡢほ Ⅼ࡟࠾࠸࡚ᡂࡾ❧

ࡕ㸪ࡑࢀࡽࢆ඲࡚ຍ࠼ࡓ᥎ᐃ್ࡢ఩┦ࡣ฿᮶ᖹ㠃Ἴ ࡢ఩┦ࡸ฿᮶ゅ࡞࡝ࡢఏᦙ⎔ቃࡸ㸪ほ Ⅼᩘࡸほ 

෇༙ᚄ࡞࡝ࡢ᥎ᐃᡭἲࡢࣃ࣓࣮ࣛࢱ࡟౫Ꮡࡏࡎ࡟

ṇࡋ࠸఩┦࡜㸪ࡑࢀࡀ཯㌿ࡋࡓ఩┦㸪ࡢ஧ࡘࡢሙྜ

ࡋ࠿Ꮡᅾࡋᚓ࡞࠸㸬

᥎ᐃྍ⬟᮲௳

ḟ࡟㸪๓⠇ࡢ᳨ウࢆ㋃ࡲ࠼࡚㸪࣐ࣝࢳࣃࢫఏᦙ⎔

ቃ࡟࠾ࡅࡿṇ☜࡟᥎ᐃࡀ⾜࠼ࡿ᮲௳

(

᥎ᐃྍ⬟᮲௳

)

࡟ࡘ࠸࡚⪃࠼ࡿ㸬ࡇࡇ࡛㸪௬ᐃࡍࡿ࣐ࣝࢳࣃࢫఏᦙ

⎔ቃ࡟࠾ࡅࡿ᥎ᐃ≉ᛶࡣ༢୍฿᮶Ἴࡢఏᦙ⎔ቃࡢ 㔜ࡡྜࢃࡏ࡛࠶ࡿࡢ࡛㸪᥎ᐃྍ⬟᮲௳࡜ࡋ࡚༢୍฿

᮶Ἴࡢఏᦙ⎔ቃ࡟࠾࠸࡚఩┦ࢆṇ☜࡟᥎ᐃ࡛ࡁࡿ

᮲௳ࢆ⪃࠼ࡿ㸬ᘧ(5)ࡼࡾ

cos Q

ࡢ್ࡀṇ࡟࡞ࡿሙྜ㸪

఩┦ࡀṇ☜࡟᥎ᐃ࡛ࡁࡿ㸬ࡋࡓࡀࡗ࡚㸪᥎ᐃྍ⬟᮲

௳ࡣ௨ୗࡢᘧ࡛⾲ࡍࡇ࡜ࡀ࡛ࡁࡿ㸬

0 ))) cos(

) (cos(

ʌ

2 2

¹

cos(

0 21

0

t

¦ ¦

^{n n m}

M

m N

n

MN R

J I J G ⁽⁶⁾

ࡇࡇ࡛㸪᥎ᐃྍ⬟࡞ほ Ⅼᩘ N ࡜ほ ෇༙ᚄ R ࡢ㛵ಀ࡟ࡘ࠸࡚↔Ⅼࢆ⤠ࡿࡶࡢ࡜ࡍࡿ㸬N࡜Rࡣ᥎ ᐃࢩࢫࢸ࣒ࡢ≀⌮ⓗ࡞኱ࡁࡉࡸ⿦⨨ᩘ࡟ࡼࡗ࡚㝈 ᐃࡉࢀࡿࡶࡢ࡛࠶ࡿࡢ࡟ᑐࡋ࡚㸪௬᝿ࣃࢫᩘ M ࡣ ィ⟬ࡢࣉࣟࢭࢫෆ࡛ࡢࡳ⏝࠸ࡿࡶࡢ࡛࠶ࡿ㸬ࡲࡓ㸪

᪤࡟♧ࡋࡓࡼ࠺࡟ M ࡣ኱ࡁ࠸⛬᥎ᐃ⬟ຊࡢྥୖࡀ ᚓࡽࢀࡿࡢ࡛㸪࠶ࡿ᥎ᐃࢩࢫࢸ࣒࡟ࡘ࠸࡚ࡢ᥎ᐃྍ

0 5 10 15 20

-0.2 0 0.2 0.4 0.6 0.8 1

Normalized radius[wavelength]

Correlation

䢢

䢢

SNR = 0dB SNR = 20dB SNR = 40dB

N=100 M=100

⬟᮲௳ࢆㄽࡌࡿሙྜ࡟ࡣ㸪Mࢆ⌮᝿ⓗ

(

↓㝈኱

)

࡟タ ᐃࡍࡿࡢࡀ㐺ษ࡛࠶ࡿ㸬ࡇࡢ᮲௳ࡢࡶ࡜࡛㸪ᘧ(6) ᕥ㎶ࡣ௨ୗࡢࡼ࠺࡟⾲ࡍࡇ࡜ࡀ࡛ࡁࡿ㸬

䌥 䌥

䌥 䌥

1

0 ʌ

ʌ 1

0

ʌ ʌ 1

0

ʌ ʌ 1

0 ʌ

ʌ 1

0 21

0 1

0 21

0

2 2

2 2

)) ʌ cos(

2 cos(

)) ʌ cos(

2 ʌ cos(

1

)) ʌ cos(

2 sin(

)) ʌ cos(

2 ʌ sin(

1

)) ʌ cos(

2 cos(

)) ʌ cos(

2 ʌ cos(

1

)) cos(

- ) (cos(

ʌ 2 ʌ cos(

1

ʌ ))) cos( 2 ) (cos(

ʌ 2 ʌ cos(

2 ʌ

1

))) cos(

) (cos(

ʌ 2 2 cos(

³

³

³

³

¦ ¦

¦ ¦

˜

N N

N N

n

n n

n

n n

n

n n

n

n n

n n

M

m N

n

m n n

M

m N

n

R d

N R

d R

N R

d R

N R

d N R

Mm M R

N NM R

M J G

G J

G G J M

J

G G J M

J

G G J M J

J I J

G J I J

ࡇࡇ࡛㸪ᘧ(7)࡟࠾ࡅࡿ✚ศࡣゅᗘᡂศJn࡟ᑐࡋ࡚

Gࢆ඲࿘᪉ྥ࡛✚ศࡍࡿࡢ࡛㸪G^’

=

G-J_n࡜⨨ࡃ࡜ᘧ

(8)

࡟♧ࡍࡼ࠺࡟Jnࡣ↓どࡍࡿࡇ࡜ࡀ࡛ࡁࡿ㸬

ʌ ' ʌ

' ʌ '

ʌ

' ʌ

ʌ ʌ

ʌ

)) ʌ cos(

2 cos(

)) ʌ cos(

2 cos(

)) ʌ cos(

2 cos(

)) ʌ cos(

2 cos(

G G

G G

G J G G

G J

J J

d R

d R

d R

d R

n

n

n n

³

³

³

³

ࡇࡇ࡛㸪ࢩ࣮ࣗࣞࣇࣜࡢ✚ศබᘧ

T T

T z d

m z

J

^m

³

0^ʌ

cos( ˜ cos ) ˜ ʌ

) 1

( (9)

ࢆ⏝࠸ࡿ࡜㸪ᘧ(6)ࡣ᭱⤊ⓗ࡟௨ୗࡢᙧ࡟ኚᙧࡉࢀࡿ㸬

¦

³

³

1

0 0

1

0 ʌ

0

1

0 ʌ

ʌ

2

2 2

)) ʌ cos(

2 cos(

ʌ ) 2 2 (

)) ʌ cos(

2 cos(

)) ʌ cos(

2 ʌ cos(

2

)) ʌ cos(

2 cos(

)) ʌ cos(

2 ʌ cos(

1

䌥 䌥

N

N N

n

n n

n n

n

n n

R R

NJ

R d

N R

R d

N R

M J

M J G

G J

M J G

G J

ࡘࡲࡾ㸪ࡇࡢᘧࡢ್ࡀ᥎ᐃྍྰࡢ᮲௳࡜࡞ࡿ㸬Fig.

15

࡟ほ ෇༙ᚄRࡢኚ໬࡟ᑐࡍࡿᘧ(10)ࡢ್ࡢኚ໬

ࢆ♧ࡍ㸬ྠᅗࡢ⤖ᯝ࠿ࡽ㸪R=15 Ἴ㛗⛬ᗘ௨ୖ࡟࡞

ࡿ࡜ᘧ(10)ࡢ್ࡀ

0

௨ୗ࡟࡞ࡿሙྜࡀ࠶ࡾ㸪ࡑࡢ⤖

ᯝ࡜ࡋ࡚R=15Ἴ㛗⛬ᗘ௨ୖ࡟࡞ࡿ࡜᥎ᐃ୙ྍ⬟࡟

࡞ࡿࡇ࡜ࡀࢃ࠿ࡿ㸬

ࡲࡓ㸪ᘧ(10)࡟࠾࠸࡚ほ ⅬᩘNࢆ↓㝈኱࡟௬ᐃ ࡍࡿ࡜㸪ᘧ(7)-(9)࡜ྠᵝ࡞⤖ᯝ࡞ᒎ㛤࡟ࡼࡾ㸪᭱⤊

ⓗ࡟ᘧ(6)ࡢᕥ㎶ࡣ௨ୗ࡜࡞ࡿ㸬

0

²

1

0

0(2ʌ ) cos(2ʌ cos( )) (2ʌ )

2 ²

R J R

R NJ

N

n

n ˜

¦

^{J M}

⁽¹¹⁾

ࡇࡇ࡛㸪ᘧ(11)ࡣ್ࡀᖖ࡟

0

௨ୖ࡛࠶ࡿࡢ࡛㸪ほ  ෇༙ᚄ࡟౫Ꮡࡍࡿࡇ࡜࡞ࡃᖖ࡟᥎ᐃࡀྍ⬟࡞ࡇ

࡜ࡀࢃ࠿ࡿ㸬ࡇࡢࡇ࡜࠿ࡽほ ⅬᩘNࢆ↓㝈኱࡟ࡍ

ࡿ࡜㸪ほ ෇༙ᚄRࢆ࡝ࢀࡔࡅ኱ࡁࡃࡋ࡚ࡶ᥎ᐃྍ

⬟࡜࡞ࡿ㸬ࡓࡔࡋ㸪ᘧ(11)ࡢ್ࡀ

0

࡜࡞ࡿRࡀ࠶ࡾ

ࡑࡢሙྜ࡟ࡣ㸪᥎ᐃࡉࢀࡓಙྕࡀ↓㝈ᑠ࡟ࡲ࡛ᑠࡉ ࡃ࡞ࡿࡢ࡛㸪㞧㡢ࡀᏑᅾࡍࡿ࡜᥎ᐃ≉ᛶࡣຎ໬ࡍࡿ㸬

10 12 14 16 18 20

-0.02 -0.01 0 0.01 0.02 0.03 0.04

Normalized radius[wavelength]

Value of Eq.(10)

Fig. 15. Value of Eq.(10) when radius of observation circle is changed.

0 5 10 15 20

-120 -100 -80 -60 -40 -20 0

Normalized radius[wavelength]

Estimated amplitude[dB]

䢢

䢢

Theory Fig.12(a)

Fig. 16. Comparison of estimated amplitude, theory (Eq. (11)) and simulated (Fig. 13(a)).

ᘧ

(11)

ࢆ⏝࠸࡚ィ⟬ࡋࡓほ ෇༙ᚄࡢኚ໬࡟ᑐࡍ

ࡿ᥎ᐃ᣺ᖜࢆ

Fig. 16

࡟♧ࡍ㸬R=15Ἴ㛗⛬ᗘ௨ୗ࡟

࠾࠸࡚㸪ᘧ

(11)

ࡣ㸪ࢩ࣑࣮ࣗࣞࢩࣙࣥ࠿ࡽᚓࡽࢀࡓ

Fig. 13(a)ࡢ᥎ᐃ᣺ᖜ≉ᛶ࡟➼ࡋ࠸≉ᛶࢆ♧ࡍࡇ࡜

ࡀࢃ࠿ࡿ㸬ࡘࡲࡾ㸪ほ ෇༙ᚄࡢ᥎ᐃྍ⬟⠊ᅖ࡛ࡣ㸪

᣺ᖜ≉ᛶࡣ➨୍✀

0

ḟ࣋ࢵࢭࣝ㛵ᩘࡢ

2

஌࡟๎ࡍࡿ

᣺ື≉ᛶࢆ♧ࡍࡇ࡜ࡀࢃ࠿ࡿ㸬ࡲࡓ㸪ࡇࡢ⤖ᯝ࠿ࡽ

㞧㡢ࡀᏑᅾࡍࡿ⎔ቃ࡛ࡣ㸪

Fig. 14

࡟♧ࡍᵝ࡟᥎ᐃྍ

¸¹

¨ ·

©

§ {

dG M2ʌ

(7)

(8)

(10)

Eq.(11) Fig. (13)a

⬟࡞ࣃ࣓࣮ࣛࢱ⎔ቃ࡟࠾࠸࡚ࡶ┦㛵್ࡀほ ෇༙

ᚄࡢኚ໬࡟ᑐࡋ࡚᣺ືࡍࡿ㸬

ศᯒ⤖ᯝ࡟ᇶ࡙ࡃ⛎ᐦ㘽ඹ᭷᪉ᘧࡢ㘽┐⫈

ྍ⬟ᛶ࡟㛵ࡍࡿ⪃ᐹ

๓⠇ࡲ࡛ࡢศᯒ࠿ࡽ㸪௚ᆅⅬࢆᑐ㇟࡜ࡋࡓఏᦙ㊰

≉ᛶࡢ᥎ᐃࡣ⌮ㄽⓗ࡟ྍ⬟࡛࠶ࡿࡇ࡜ࡀ᫂ࡽ࠿࡜

࡞ࡗࡓ㸬ࡇࡢศᯒ⤖ᯝࢆᇶ࡟

2

❶࡛♧ࡋࡓఏᦙ㊰≉

ᛶ࡟ᇶ࡙ࡃ⛎ᐦ㘽ඹ᭷ᘧࡢ㘽┐⫈ࡢྍ⬟ᛶ࡟ࡘ࠸

࡚⪃࠼ࡿ㸬ࡇࡇ࡛㸪ఏᦙ⎔ቃࡣᦙ㏦࿘Ἴᩘࡀ

2.4GHz

ࡢ࿘ᅖ୍ᵝࡢ᪉ྥ࠿ࡽ࣐ࣝࢳࣃࢫࡀ฿᮶ࡍࡿࣞ࢖

࣮ࣜࣇ࢙࣮ࢪࣥࢢ⎔ቃ࡜ࡍࡿ㸬౛࠼ࡤ㸪┐⫈┦ᡭ࡜

࡞ࡿ᥎ᐃᑐ㇟ᒁ࠿ࡽ㞃ࢀ࡚┐⫈ࡍࡿࡇ࡜ࢆ᝿ᐃࡋ㸪 ᑐ㇟ᒁ࠿ࡽ

10m

ࡢ༙ᚄࡢほ ෇༙ᚄࢆ⪃࠼ࡓ࡜ࡍ

ࡿ࡜㸪᥎ᐃࢆṇ☜࡟⾜࠺ࡓࡵ࡟ࡣ㸪๓⠇ࡲ࡛ࡢศᯒ

࠿ࡽ㸪᭱ప࡛ࡶ

530

Ⅼ⛬ᗘࡢほ Ⅼࡀᚲせ࡜࡞ࡿ㸬 ࡇࡢᩘࡢཷಙࢆ᥎ᐃᑐ㇟ᒁࡢཷಙಙྕ࡜᏶඲࡟᫬

㛫ྠᮇࡉࡏࡿᚲせࡀ࠶ࡿ㸬ࡲࡓ㸪఩┦᥎ᐃ⢭ᗘࢆຎ

໬ࡉࡏ࡞࠸ࡓࡵ࡟ࡣ┐⫈ᒁ࡜᥎ᐃᑐ㇟ᒁࡢ఩⨨㛵

ಀࡶ

1/10

㹼

1/100

Ἴ㛗ࡢ⢭ᗘ࡛᪤▱࡛࡞ࡅࢀࡤ࡞ࡽ

࡞ ࠸ 㸬 ࡘ ࡲ ࡾ 㸪

10m

㞳 ࢀ ࡓ ᆅ Ⅼ ࡜ ࡢ ㊥ 㞳 ࢆ

1.25mm~12.5mm

ࡢ࣮࢜ࢲ࡛ṇ☜࡟ᚓࡿࡇ࡜ࡀᚲせ

࡜࡞ࡿ㸬ࡇࡢࡼ࠺࡞ఏᦙ㊰≉ᛶࡢ᥎ᐃࡣ⌧ᐇⓗ࡟ࡣ 㠀ᖖ࡟ᅔ㞴࡛࠶ࡿ㸬㏫࡟㸪᫬㛫ⓗ࡞ྠ᫬ཷಙࡀ⌧ᐇ

ⓗ࡟ྍ⬟࡞ᩘ࡜ࡋ࡚౛࠼ࡤほ Ⅼᩘࢆ

10

Ⅼ࡜ࡍࡿ

࡜㸪᥎ᐃྍ⬟࡞᥎ᐃᑐ㇟ᒁ࡜ࡢ㊥㞳ࡣ᭱㛗࡛ࡶ

18.8cm

⛬ᗘ࡜࡞ࡿ㸬┐⫈⾜Ⅽࡣ୍⯡࡟⿕┐⫈ഃ࠿

ࡽ㞃ࢀ࡚⾜࠺ࡶࡢ࡛࠶ࡿࡢ࡛㸪ࡇࡢ㊥㞳࡛ࡣ┐⫈⾜

Ⅽࢆ⾜࠺ࡇ࡜ࡣ⌧ᐇⓗ࡟୙ྍ⬟࡛࠶ࡿ㸬

௨ୖࡢ⪃ᐹࡼࡾ㸪┐⫈ࡢほⅬ࡟࠾࠸࡚ほ Ⅼᩘࡸ

᥎ᐃᑐ㇟࡜ࡢ㊥㞳ࢆኚ໬ࡉࡏ࡚ࡶ௚ᆅⅬࢆᑐ㇟࡜

ࡋࡓఏᦙ㊰≉ᛶࡢ᥎ᐃࡣ⌧ᐇⓗ࡟୙ྍ⬟࡛࠶ࡿ࡜

⤖ㄽ࡙ࡅࡿࡇ࡜ࡀ࡛ࡁࡿ㸬

ࡲ࡜ࡵ

⛎ᐦ㘽ඹ᭷᪉ᘧࡢᏳ඲ᛶ᳨ウ࡟㈨ࡍࡿࡓࡵ㸪」ᩘ

ᆅⅬ࡛ࡢほ Ⅼࡢཷಙ᝟ሗࢆ⏝࠸࡚㞳ࢀࡓᆅⅬࡢ

ཷಙⅬࡢఏᦙ㊰≉ᛶࢆ᥎ᐃࡍࡿ᪉ᘧ࡟ࡘ࠸᳨࡚ウ

ࡋ㸪ࡇࡢᡭἲ࡟ࡼࡿ᥎ᐃ≉ᛶࢆヲ⣽࡟ศᯒࡋࡓ㸬

࣐ࣝࢳࣃࢫఏᦙ⎔ቃ࡟࠾ࡅࡿ᥎ᐃ≉ᛶࡢ᥎ᐃ࣓

࢝ࢽࢬ࣒ࢆ᫂ࡽ࠿࡟ࡍࡿࡓࡵ࡟㸪༢୍฿᮶Ἴࡢఏᦙ

⎔ቃ࡟࠾ࡅࡿ᥎ᐃ≉ᛶࢆヲ⣽࡟ศᯒࡋࡓ㸬௬᝿ࣃࢫ ࡢ࢔ࢪ࣐ࢫゅ࡟ᑐࡍࡿ᣺ᖜ≉ᛶ࡜఩┦≉ᛶࢆศᯒ ࡋ㸪ほ Ⅼ࠾ࡼࡧ௬᝿ࣃࢫᩘ➼ࡢ᥎ᐃᡭἲࡢࣃ࣓ࣛ

࣮ࢱ࡟㛵ࡍࡿ᥎ᐃྍྰࡢ᮲௳ࢆ᫂ࡽ࠿࡟ࡋࡓ㸬ࡉࡽ

࡟㸪ほ ෇༙ᚄࡢቑຍ࡟కࡗ࡚᥎ᐃ್ࡢ᣺ᖜࡀ᣺ື

ⓗ࡟ኚ໬ࡍࡿࡇ࡜࠿ࡽ㸪㞧㡢ࡀᏑᅾࡍࡿሙྜࡢ≉ᛶ

࡟ࡘ࠸࡚ࡶ⤖ᯝࢆ♧ࡋࡓ㸬ࡲࡓ㸪ࡇࡢ᥎ᐃ≉ᛶࡢศ ᯒ⤖ᯝ࡟ᇶ࡙ࡃ㸪᥎ᐃྍྰࡢ᮲௳ࢆ⌮ㄽᘧ࡟ࡼࡾ⾲

ࡋࡓ㸬᭱ᚋ࡟㸪ఏᦙ㊰≉ᛶ࡟ᇶ࡙ࡃ⛎ᐦ㘽ඹ᭷ᘧࡢ 㘽┐⫈ࡢྍ⬟ᛶ࡟ࡘ࠸᳨࡚ウࡋࡓ㸬ほ Ⅼᩘࡸ᥎ᐃ ᑐ㇟࡜ࡢ㊥㞳ࢆኚ໬ࡉࡏ࡚ࡶ㸪⌧ᐇⓗ࡟ࡣ௚ᆅⅬࢆ

ᑐ㇟࡜ࡋࡓఏᦙ㊰≉ᛶࡢ᥎ᐃࡣ୙ྍ⬟࡛࠶ࡿࡇ࡜

ࢆ♧ࡋࡓ㸬

ཧ⪃ᩥ⊩

1) ໭ᾆ᫂ே, ➲ᒸ⚽୍, “㝣ୖ⛣ື㏻ಙ࡟࠾ࡅࡿOFDM ࡢఏᦙ㊰≉ᛶ࡟ᇶ࡙ࡃ⛎ᐦ㘽ඹ᭷᪉ᘧ,” ಙᏛㄽ(A), vol. J87-A, no. 10, pp. 1320-1328, Oct., 2004㸬

2) T.Aono, K.Higuchi, T.Ohira, B.Komiyama and H.Sasaoka, “Wireless secret key generation exploiting reactance-domain scalar response of multipath fading channels,” IEEE Trans. Antennas & Propagt., vol. 53, no.

11, pp. 3776-3784, Nov. 2005.

3) ᒾ஭ㄔே, ➲ᒸ⚽୍, “㟁Ἴఏᦙ≉ᛶࢆά⏝ࡋࡓ⛎ᐦ

᝟ሗࡢఏ㏦࣭ඹ᭷ᢏ⾡,” ಙᏛㄽ(B), vol. J90-B, no. 9, pp. 770-783, Sep. 2007.

4) ᒸᮏ㐩᫂, ᬯྕ࡜᝟ሗࢭ࢟ࣗࣜࢸ࢕, ᪥⤒ BP ♫, 1998.

5) ᒸᮏ㱟᫂, ⌧௦ᬯྕ, ⏘ᴗᅗ᭩ᰴᘧ఍♫, 1997.

6) K.Inoue, H.Iwai, and, H.Sasaoka, “Estimation of fading characteristics based on multiple observed signals at different locations,” Proc.2008 International Symposium on Antennas and Propagation (ISAP2008), TP-A05, Oct.

2008.

7) ஭ୖᜨ㍜, ୹ᚋಇᏹ, ᒾ஭ㄔே, ➲ᒸ⚽୍, “௚ᆅⅬ ほ ಙྕ࡟ᇶ࡙ࡃఏᦙ㊰≉ᛶ᥎ᐃࡢ≉ᛶゎᯒ,”ಙᏛ ᢏሗ, AP2007-74, Sep. 2007.

8) ஭ཱྀ⪷, ᕝཱྀ๎ᖾ, “㉸㛗ᇶ⥺ᖸ΅ィ(VLBI)࡟࠾ࡅࡿ

᭱㐺ࣇ࢕ࣝࢱࣜࣥࢢ,” ಙᏛㄽ(B), Vol.J82-B, No.3, pp. 420-426, Mar, 1999.

9) W.C.Jakes, “Microwave Mobile Communications,”

Wiley-IEEE Press, 1994.