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1 MWE 2019 WE6B-1 MIMO 技術の基本と応用 Fundamentals of MIMO Techniques and Their Applications 小川恭孝 Yasutaka OGAWA 北海道大学 Hokkaido University 概要 送信側と受信側に複数のアンテナを設置し, 信号を空間的に多重化することによって通信速度を向上させる MIMO 技術は,LTE-Advanced や無線 LAN において既に実用化されている. 第 5 世代移動通信 (5G) においては基地局に多数のアンテナ素子を設置し, 更に, ミリ波帯を利用することにより,10 Gbps を超える極めて高速な通信が期待されている. 本稿では,MIMO システムによる空間多重の基本とその応用を解説している. この技術は, 送信側でチャネル情報が未知の場合と既知の場合で用いる手法が異なっている. 前者の場合は, 各送信アンテナから独立な信号を等電力 等伝送レートで送信することになる. これを空間分割多重と呼んでいる. 受信側ではこれらの信号が互いに干渉するので, それを分離する必要がある. 空間フィルタリングと, それを発展させた順序付け逐次復号, 更に, 最尤推定について本稿では説明を行っている. 次に, 送信側でチャネル情報を有しているときに用いられる固有ビーム空間分割多重と重み付き空間分割多重を解説している. 最後に, 誤り率特性を用いて, これら多重方式の評価を行っている. MIMO 技術は, 通信方式, 信号処理, アンテナ伝搬, 情報理論と関連する分野が多岐に及ぶ. 本稿が 5G における MIMO システムを理解する一助になれば幸いである. #j h ij #i #N #L 図 MIMO システムモデル 図実験用 5G MIMO 基地局とアンテナ Abstract MIMO techniques employing multiple antennas at both the transmitter and receiver can increase transmission speed by spatially multiplexing signals, and are essential for the fifth generation mobile communication system. This paper presents fundamentals of MIMO techniques. First, we introduce multiplexing techniques used for a case where a transmitter does not have channel state information (CSI). Then, we explain techniques for a system where a transmitter has CSI. Furthermore, we evaluate the performance of MIMO spatial multiplexing using bit error rates.

2 1. MIMO (Multiple-Input Multiple-Output) [1] [3] LTE-Advanced LAN 5G10 Gbps MIMO (bit/s/hz) MIMO MIMO MIMO 5G 2. MIMO MIMO 1 N L j #j #N h ij #i #L 1: MIMO i h ij i j h ij L N H h ij OFDM h ij N s(t) L y(t) y(t) = Hs(t) + n(t) (1) n(t) L MIMO SN γ 1 Hz [4] C = log 2 (γ + 1) [bit/s/hz] (2)

3 2 SN 2 C = log 2 (2γ + 1) C + 1 [bit/s/hz] (3) SN (γ 1) 2 1 [bit/s/hz] SN γ γ 2 2 C = 2 log 2 (γ + 1) = 2C [bit/s/hz] (4) 2 MIMO [1] MIMO MIMO H 3. H MIMO H 2 (SDM: Space Division Multiplexing) data MUX 2: SDM stream 1 stream N stream 1 weight matrix #L stream N 3: 3 L N W W T y(t) [2], [3] s o (t) s o (t) = W T y(t) = W T Hs(t) + W T n(t) (5) N L * 1 * 1 L L 1 L 1 [5]

4 W W ZF (Zero-forcing) MMSE (Minimum Mean Square Error) 3.1 ZF ZF W ZF W T ZF H = I N (6) I N N N W ZF W ZF = H ( H T H ) 1 (7) y(t) W T ZF H Moore-Penrose [4] ) 1 WZF (H T = H H H H (8) (5) (6) ZF s o (t) = s(t) + W T n(t) (9) ZF (8) N N H H H ZF (6) W T n(t) 3.2 MMSE ZF MMSE j L w j j e j (t) e j (t) = w T j y(t) s j(t) (10) s j (t) j N s(t) j J N [ J = E ej (t) 2] (11) j=1 E[ ] (1) W 0 MMSE W MMSE [3] W MMSE = E [ y(t) y(t) T ] 1 [ E y(t) s(t) T ] (12) H H H H L n(t) ZF E [ y(t) y(t) T ] = (P x /N)H H T + P z I L (13) E [ y(t) s(t) T ] = (Px/N)H (14) P x P z 1 P x = E [ s H (t)s(t) ] (15) P z = E [ n H (t)n(t) ] /L (16) I L L L

5 (12) (13) (14) MMSE W MMSE = = ( H H T + (NP z /P x ) I L ) 1 H ( H H T + (N/γ 0 ) I L ) 1 H γ 0 (17) (18) γ 0 = P x /P z (19) H 0 1 P x γ 0 P x 1 SN (18) [3] W MMSE = H ( H T H + (N/γ 0 ) I N ) 1 (20) y(t) W T MMSE W T MMSE = (H H H + (N/γ 0 ) I N ) 1 H H (21) (8) W T ZF γ 0 SN W T MMSE W T ZF γ 0 SN (21) W T MMSE HH MMSE W T MMSE y(t) H H y(t) [3] MMSE MMSE SN 3.3 (OSD: Ordered Successive Detection) [6]L N N (MLD: Maximum Likelihood Detection) [4] y(t) Hs(t) 2 N L L M M N [7], [8] 4. H MIMO N

6 4.1 E-SDM (E-SDM: Eigenbeam-Space Division Multiplexing) N K T e K K H R (R = rank(h) min{n, L}) K R K R G = H H H G N N N e n (n = 1,..., N) e H j Ge j = λ j (λ 1 λ R > λ R+1 = = λ N = 0) (22) e H i Ge j = 0 (i j) (23) λ j j e j N R K (K R) N K T e = [e 1 e 2... e K ] (24) p 1, p 2,..., p K 1 j p j P x P x (15) K s(t) K j j data stream MUX stream 1 p 1 stream K p K weight matrix 4: E-SDM #N K K A ) A = diag ( p p 1, 2,..., p K (25) E-SDM 4 x(t) = T e As(t) (26) y(t) = Hx(t) + n(t) = HT e As(t) + n(t) (27) L K W e = (HT e ) (28) r(t) = W T e y(t) = T H e H H HT e As(t) + W T e n(t) = T H e GT e As(t) + W T e n(t) (29) (22) (23) T H e GT e = diag (λ 1, λ 2,..., λ K ) = Λ (30) (29) r(t) = ΛAs(t) + W T e n(t) (31) Λ A K K ΛA K K

7 ZF SDM E-SDM W T e = (HT e ) H SN SN ZF SDM SN j p j P x (31) j λ 2 j p j P x (28), (30) P z { ( ) ( ) } H E We T n(t) We T n(t) = P z Te H GT e = P z Λ (32) j j λ j P z j SN γ e, j = λ j p j P x/p z = λ j p j γ 0 (33) γ 0 (19) P x 1 SN E-SDM 5 (33) SN p j data stream MUX stream 1 p 1 stream K p K λ 1 λ K 5: E-SDM [3] (28) ZF MMSE ZF MMSE 4.2 W-SDM E-SDM K (25) (W- SDM: Weighted-Space Division Multiplexing) ZF MMSE [2] 5. MIMO n 1 n K

8 1 2 [bit/s/hz] SDM 4 QPSK 8 [bit/s/hz] 1 8 E-SDM W-SDM 256QAM 1 64QAM 1+QPSK 1 16QAM 2 16QAM 1+QPSK 2, QPSK 4 5 ZF MMSE OSD 2 OSD-ZF OSD-MMSE MLD E-SDM (28) ZF MMSE ZF W-SDM ZF ZF SDM E- SDM W-SDM [3] E-SDM SDM 1 1 E s /N 0 0 [db] Average BER Average BER SDM (ZF) SDM (MMSE) SDM (OSD-ZF) SDM (OSD-MMSE) SDM (MLD) W-SDM (ZF) E-SDM (ZF) 2-tx, 2-rx 4 [bps/hz] Normalized TX Power [db] (a) 2-tx, 2-rx (4 [bit/s/hz]) SDM (ZF) SDM (MMSE) SDM (OSD-ZF) SDM (OSD-MMSE) SDM (MLD) W-SDM (ZF) E-SDM (ZF) 4-tx, 4-rx 8 [bps/hz] Normalized TX Power [db] (b) 4-tx, 4-rx (8 [bit/s/hz]) 6: [2] copyright 2004 IEICE SDM E s /N 0 6 BER SDM MLD 6(a) 6(b) 6(a) 2 6(b)

9 4 MLD 6(a) 6(b) ZF MMSE 10 [db] 1 ZF MMSE ZF MMSE MMSE SN ZF 6 6(a), (b) SDM (ZF) SDM(MMSE)?? MMSE ZF 6 (BER) (Average BER) ZF MMSE OSD OSD- ZF 2-tx, 2-rx 15 [db] 4-tx, 4-rx 20 [db] ZF OSD-MMSE 4 20 [db] 2 OSD- MMSE MLD SDM W-SDM E-SDM 2 MLD SDM BER=10 4 W-SDM 5 [db] E-SDM 6 [db] E-SDM 4 3 [db] E-SDM 6. MIMO MIMO 1

10 MIMO MIMO [9] [11] 5G MIMO [12] Very Large MIMO Massive MIMO MIMO [13], [14] [1] E. Telatar, Capacity of multi-antenna Gaussian channels, European Trans. Telecommnications, vol. 10, no. 6, pp , Nov./Dec [2] MIMO, B vol. J87-B, no. 9, pp , Sept [3] MIMO [4] J. G. Proakis and M. Salehi, Digital Communications, Fifth ed., McGraw-Hill, New York, [5], [I], vol. 81, no. 12, pp , Dec [6] G. J. Foschini, G. D. Golden, R. A. Valenzuela, and P. W. Wolniansky, Simplified processing for high spectral efficiency wireless communication employing multi-element arrays, IEEE J. Sel. Areas Commun., vol. 17, no. 11, pp , Nov [7] K. J. Kim and R. A. Iltis, Joint detection and channel estimation algorithms for QS- CDMA signals over time-varying channels, IEEE Trans. Commun., vol. 50, no. 5, pp , May [8] M. O. Damen, H. El Gamel, and G. Caire, On maximum-likelihood detection and the search for the closest lattice point, IEEE Trans. Inf. Theory, vol. 49, no. 10, pp , Oct [9] MIMO vol. 97, no. 4, pp , April [10] MIMO [11] D. Gesbert, M. Kountouris, R. W. Heath Jr., C. B. Chae, and T. Sälzer, Shifting the MIMO paradigm, IEEE Signal Process. Mag., vol. 24, no. 5, pp , Sept [12] F. Rusek, D. Persson, B. K. Lau, E. G. Larsson, T. L. Marzetta, O. Edfors, and F. Tufvesson, Scaling up MIMO: Opportunities and challenges with very large arrays, IEEE Signal Process. Mag., vol. 30, no. 1, pp , Jan [13] F. Boccardi, R. W. Heath Jr., A. Lozano, T. L. Marzetta, and P. Popovski, Five disruptive technology directions for 5G, IEEE Commun. Mag., vol. 52, no. 2, pp , Feb [14] Y. Okumura, S. Suyama, J. Mashino, and K. Muraoka, Recent activities of 5G experimental trials on massive MIMO technologies and 5G system trials toward new services creation, IEICE Trans. Commun., vol. E102-B, no. 8, pp , Aug

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