修士論文の和文要旨研究科専攻大学院情報理工学研究科情報. 通信工学専攻博士前期課程

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1 修士論文の和文要旨研究科専攻大学院情報理工学研究科情報. 通信工学専攻博士前期課程氏名 ova aras urul Khamsah 学籍番号論文題目 Channel Estimation for SC-FDA in LTE Uplink using Data-Domain Pilot Signals and B-Spline Approximation データ領域パイロット信号と B スプライン近似を用いた LTE 上り回線のための通信路推定要旨 LTE アップリンク上でシングルキャリア周波数分割多元接続 (SC-FDA) において通信路速い変動があると間干渉 (ICI) が生ずるそのためチャネル推定は LTE アップリンクシステムの堅牢な性能を得るために特別な注意が必要である通信路推定のために我々は高速フェージング下での SC-FDA システムにおけるデータ領域におけるパイロット信号の挿入を提案する我々は通信路推定のために支援するためのデータ領域でパイロット信号を使用して数学的モデルを開発した移動体通信ではドップラー効果がよく Rayleigh fading のモデルによって記述さるがこのモデルは 3 次 B-スプライン関数で近似することができることが知られているそこで LTE-アップリンクにおける通信路推定を支援するためにデータ領域内のパイロット信号と 3 次 B-スプライン近似適用を提案するコンピュータシミュレーションは他の方式ではツイスト-OFDA で実施されているこれはパイロットが挿入された提案されたスキーム B スプライン近似の性能を示すために行わ結果は SE チャネル推定による SC-FDA システムとの性能を比較したドップラースプレッドに対する弱点に正規化されたドップラー周波数が増加するにつれて SC-FDA の性能低下となる結果は B スプライン近似が SC-FDA システムにおいて実現することが非常に有望な候補であることを示している私たちは今後の研究への SC-FDA システムにおける B スプライン近似の C モデルの実装のままにしておきます

2 Channel Estimation for SC-FDA in LTE Uplink using Data-Domain Pilot Signals and B-Spline Approximation OVA ARAS URUL KHASAH A DISSERTATIO PRESETED TO THE DEPARTET OF COUICATIO EGIEERIG AD IFORATICS I CADIDACY FOR THE ASTER S DEGREE RECOEDED FOR ACCEPTACE BY THE DEPARTET OF COUICATIO EGIEERIG AD IFORATICS ADVISOR: TAKESHI HASHIOTO, Professor ADVISOR: HISAAKI TAAKA, Professor JAUARY 30, 2015

3 Abstract In Single Carrier Frequency Division ultiple Access (SC-FDA) on the LTE uplink, fast variations of channel result in inter-carrier-interference(ici). Therefore, the channel estimation needs a special care in order to robust performance of LTE uplink system. In order to estimate the channel, we propose pilot signals insertion in data-domain, for design of SC-FDA systems under fast fading. We developed a mathematical model which uses pilot signals in data domain to aid for channel estimation. In mobile communication the Doppler effect is well described by Rayleigh fading model, and this model can be accurately approximated by the cubic B-spline function. Therefore, we propose cubic B-spline approximation and pilot signals in data domain to aid for channel estimation in LTE-Uplink. The computer simulations are conducted in other scheme, Twisted-OFDA. This done to illustrate the performance of the proposed scheme B-spline approximation with pilot insertion. The results then compared to the performance with SC-FDA system with SE channel estimation. Due to its weakness against Doppler spread, as the normalized Doppler frequency increased, so become the degradation in the performance of SC-FDA. The result shows that B-Spline approximation is very promising candidate to be implemented in SC-FDA system. We leave the C model implementation of B-Spline approximation in SC-FDA system to future research. i

4 Contents Abstract i 1 Introduction 1 2 SC-FDA in LTE Uplink SC-FDA System odel Pilot Aided System odel Channel Estimation Response odel Vector atrix odel Equivalent Channel Performance Evaluation Simulation Setups Simulation Result Conclusion 22 ii

5 List of Figures 2.1 Uplink transmission - receiver model for LTE LTE Uplink Transmitter - Receiver Block Pilot Insertion BER performance comparison of the Twisted-OFDA system and the SC-FDA system for user = 7, 14, f dt = BER performance comparison of the Twisted-OFDA system and the SC-FDA system for user = 7, 14, f dt = BER performance comparison of the Twisted-OFDA system and the SC-FDA system for user = 7, 14, f dt = BER performance comparison of the Twisted-OFDA system and the SC-FDA system for user = 7, 14, f dt = iii

6 List of Tables 4.1 Simulation parameters iv

7 Chapter 1 Introduction LTE Uplink uses SC-FDA to keep a low peak to average power ratio (PAPR). Since the radio channel is highly dynamic, the transmitted signal travel by undergoing many effects that corrupt the signals and lower the performance of the system. SC-FDA has similar throughput performance and complexity as OFDA and is highly sensitive the Doppler spread of the channel [1],[2]. Doppler spread caused frequency offset which leads to Inter Carrier Interference (ICI) [3] and results in the degradation of bit error rate (BER). Channel estimation techniques allow the receiver to approximate the impulse response of the channel, therefore choosing the best channel estimation technique is essential in order to robust performance of LTE uplink system. There have been several researches concerning in improving channel estimation in LTE uplink system over fast fading channel [3]-[7]. In [3] and [4], time domain Kalman filter is introduced to mitigate ICI in high mobility environment, but this only applied in single user system, and also these techniques involve high complexity. Thus in [7] channel estimation is conducted using Basis Expansion odel (BE) which easy to use and no need of prior channel statics if compared to Kalman filter, however for mobility more than 350 km/h, least square proposition has no solution. Zhang in [6] shows that the poor performance in LTE uplink is mainly caused by limited time-domain pilot symbols. Zhang in [6] also describes that using cubic spline interpolation for channel 1

8 Chapter1. Introduction estimation improve bit error rate (BER) in fast fading channel. In mobile communication the Doppler effect which causes time-varying fading of multipath components, is well described by Clarke s model. This model can be accurately approximated by the cubic B-spline function [8]. Therefore we propose cubic B-spline approximation and pilot signals in data domain to aid for channel estimation in LTE-Uplink. The rest of the paper is organized as follows: Chapter 2 introduces SC-FDA system model and the performance over fast fading channels. Theoretical analyses are conducted to help understand the impacts of Doppler spreads in SC-FDA system for determining optimal solutions. Chapter 3 presents the theory of cubic B-spline approximation in pilot signals for channel estimation in SC-FDA system, and the mathematical solution of equivalent channel is presented. Chapter 4 shows the performance of cubic B-spline approximation in Twisted-OFDA to illustrate the proposed scheme, and then the performance of SC-FDA with SE channel estimation is conducted and compared to that of the Twisted- OFDA performance. Chapter 5 conludes the thesis and gives study for the further research. 2

9 Chapter 2 SC-FDA in LTE Uplink SC-FDA is utilized in LTE uplink which has similarity multiple access scheme with the downlink, has some desirable attributes, such as orthogonal uplink transmission by different user, flexibility to support a wide range of data ranges, sufficiently low Peak to Average Power Ratio (PAPR), exploit the frequency diversity even at low data rates transmission, etc [9]. In order to estimate the channel, we propose pilot signals insertion in data-domain, for design of SC-FDA systems under fast fading. 2.1 SC-FDA System odel Transmitter and receiver structure in LTE Uplink is shown in Fig The transmitted signal is distorted by multipath propagation in the channel and is received together with an additive white Gaussian noise (AWG). In this research we only focused on single antenna case. domain signal d(n) into frequency domain Assuming an -point DFT for spreading the uth users time D (u) (κ) = 1 1 d (u) (n)e j2πnκ, (2.1) n=0 After spreading, then D (u) (κ)is mapped onto the k th subcarrier S (u) (k) given by 3

10 Chapter2. SC-FDA in LTE Uplink D (u) (κ), k = Γ,(u) (κ) S (u) (k) = 0, otherwise (2.2) where Γ,(u) (κ) denotes -element mapping set of u th user. Consecutively Γ,(u) (κ) = κ + u it called localized mapping, and if it is not consecutive Γ,(u) (κ) = κu + u, it called distributed mapping. Using -point IDFT, where is the minimum power of 2 and larger than, the transmitted signal is then expressed by s (u) (m) = 1 S (u) (k)e j2πmk, (2.3) k=0 Assuming a quasi-static multipath fading channel with CIR h = [h 0, h 1,, h L ] T, the signal received r(m), at the output of the channel after CP removal is given by U 1 L 1 r(m) = h (u) (m, l)s (u) (m l) + w(m) (2.4) u=0 l=0 where h (u) (m, l) is sample spaced channel response of l th path during time m of u th user, and w(m) denotes the white Gaussian noise. From (2.3) and (2.4) we can get where U 1 L 1 1 r(m) = S (u) (k)h (u) (m, l)e j2πk(m l) u=0 l=0 = 1 U 1 u=0 k=0 k=0 + w(m) S (u) (k)h (u) (k, m)e j2πkm + w(m) (2.5) L 1 H(k, m) = h(m, l)e j2πkl (2.6) l=0 The FFT output at k th subcarrier can be expressed as 4

11 Chapter2. SC-FDA in LTE Uplink R(k) = 1 2πmk j r(m)e ( = 1 = 1 = 1 U 1 u=0 k =0 u=0 U 1 1 u=0 k =0 + 1 ) S (u) (k )H (u) (k, m)e j2πk m + w(m) e j2πmk S (u) (k )H (u) (k, m)e j2πm(k k) w(m)e j2πmk U 1 S (u) (k) H (u) (k, m) + 1 U 1 u=0 k k,k =0 S (u) (k ) H (u) (k, m)e j2πm(k k) + 1 w(m)e j2πmk (2.7) Data obtained after subcarrier demapping block with k = κ + u for localized mapping and k = κu + u for interleaved mapping, is defined by ˆD (u) (κ) = R(k) = 1 U 1 u =0 S (u )(k) k k,k =0 U 1 H (u )(k, m) S (u) (k ) H (u) (k, m)e j2πm(k k) u u,u =0 k k,k =0 We can also write equ. (2.8) as S (u )(k ) H (u )(k, m)e j2πm(k k) + 1 w(m)e j2πmk (2.8) ˆD (u) (κ) = D (u) (κ)h (u) (k, m) + I UI (k) + W (k) (2.9) 5

12 Chapter2. SC-FDA in LTE Uplink where H (u) (k, m) represents frequency domain channel response, I ISI (k)and I UI (k) represents inter-symbol interference and multi-user interference respectively, and W (k) as is Fourier transform of noise w(m). After -point IDFT, data for each user can be expressed by ˆd (u) (n) = 1 1 κ=0 = 1 1 κ=0 κ=0 ˆD (u) (κ)e j2πnκ e j2πnκ ( D(u) (κ)h (u) (k, m) + I UI (k) + W (k) ) = 1 1 e j2πnκ D(u) (κ)h(k) κ=0 e j2πnκ (IUI (k) + W (k)) (2.10) let the inverse Fourier of inter-symbol interference, the inverse Fourier of multi-user interference, and noise in data domain as then from (2.1) and (2.6) we get κ=0 ı UI (n) = 1 1 I UI (k)e j2πnκ κ=0 w(n) = 1 1 W (k)e j2πnκ κ=0 ˆd (u) (n) = 1 1 e j2πnκ D(u) (κ)h(k) + ı UI (n) + w(n) where we let = 1 1 = 1 κ=0 1 n =0 e j2πnκ 1 d (u) (n ) ( 1 1 κ=0 n =0 d (u) (n )e j2πn κ + ı UI (n) + w(n) e j2πκ(n n) L 1 l=0 ) ( L 1 l=0 h(m, l)e j2πkl h(m, l)e j2πkl ) + ıui (n) + w(n) = d (u) (n )ĥ(n, n ) + ı UI (n) + w(n) (2.11) ĥ(n, n ) = 1 as apparent channel response. 1 κ=0 e j2πκ(n n) 6 L 1 l=0 h(m, l)e j2πkl, (2.12)

13 Chapter2. SC-FDA in LTE Uplink 2.2 Pilot Aided System odel For channel estimation purposes, pilot is added after constellation mapping block (see Figure 2.2) with p as number of pilots in a symbol, and λ as length of pilot guards, to avoid mutual interference between data and pilot. In cubic b-spline interpolation there is a need for equally distance knots (pilots). Then the pilot d p (n) with p = (0, 1, 2,..., p 1) are spreaded by d p (n) = b p, (2.13) Then, the number of data in a block (symbol) of SC-FDA is d = p λ, (2.14) where is number of point DFT in the following block. Then, the position of pilots in a symbol can be shown in the Figure 2.3. Assuming that with an appropriate pilot guard λ, there are no interference between the pilot and the data signals, the received pilot of the ξth SC-FDA symbol (for ξ = 0, 1,..., B 1) is given by ˆd ξ p = d p,(u) (n )ĥ(n, n ) + ı UI (n) + w(n) = b p ĥ(n, n ) + z m, (2.15) where we let z m = ı UI (n) + w(n). 7

14 Chapter2. SC-FDA in LTE Uplink Figure 2.1: Uplink transmission - receiver model for LTE 8

15 Chapter2. SC-FDA in LTE Uplink Figure 2.2: LTE Uplink Transmitter - Receiver Block 9

16 Chapter2. SC-FDA in LTE Uplink Figure 2.3: Pilot Insertion 10

17 Chapter 3 Channel Estimation In mobile communication the Doppler effect which causes time-varying fading of multipath components, is well described by Clarke s model. This model can be accurately approximated by the cubic B-spline function [8]. We propose channel estimation using pilot signals and cubic B-spline approximation for SC-FDA system in LTE uplink. 3.1 Response odel To estimate the inter-shift response ĥ(n, n ), first we estimate the physical channel impulse response h(m, l) which is approximated by a series of cubic B-splines B+2 h m,l = a l,γ ϕ γ (m), (3.1) γ=0 where ϕ γ (m) denotes the B-spline basis located at knot γ. The whole transmission duration B s is divided into B intervals by equally-distanced knots ε γ, γ = 0, 1,, B 2, and 4 additional knots, ε B 1,, ε B+2, are introduced in order to generate the necessary B-spline basis (note that in each spline base function, there are at most four polynomial terms (segment)). ϕ γ (m) can be calculated using the recurrence relations, and for γ = 3, 4,, B 1, we have 11

18 Chapter3. Channel Estimation ϕ γ (m) = ϕ(m γ s + 3 s ) (3.2) for ϕ(m) = m 3, 0 m < 6s 3 s m3 2 3 s m s + 2m2 2 s 4m2 2 s 2m s + 2 3, s m < 2 s + 10m s 7 1 3, 2 s m < 3 s (4 s m) 3, 3 6s 3 s m < 4 s 0, otherwise. (3.3) where s = +L is symbol length of SC-FDA including CP. The first three B-spline base functions which are prototype base functions, are given by [11] ( s m) 3, 0 m < s ϕ 0 (m) = 3 s, (3.4) 0, otherwise ϕ 1 (m) = 7m s 9m2 2 2 s + 3m s, 0 m < s (2 s m) 3, 4s 3 s m < 2 s 0, otherwise, (3.5) ϕ 2 (m) = 11m s 7m s + 3m2, 0 m < 2s 2 s 3m2 2 s + 9m 2 s 3 2, s m < 2 s (3 s m) 3, 2 6s 3 s m < 3 s 0, otherwise, (3.6) and the last three base functions are given as ϕ B (m) = ϕ 2 (B s ), ϕ B+1 (m) = ϕ 1 (B s ), ϕ B+2 (m) = ϕ 0 (B s ), (3.7) 12

19 Chapter3. Channel Estimation ϕ B (m) = ϕ B+1 (m)= (m (B 3) s) 3, (B 3) 6s 3 s m<(b 2) s 7(m (B 2)s)3 12s 3 + (m (B 2)s)2 2 2 s + m (B 2)s 2 s + 1,(B 2) 6 s m < (B 1) s (11(m (B 1) s)+7 s)( s m+(b 1) s) 2, (B 1) 12s 3 s m<b s 0, otherwise (m (B 2) s) 3 4s 3 7(m (B 1)s)3 4 3 s 0, otherwise (3.8), (B 2) s m<(b 1) s + 3(m (B 1)s)2 4 2 s + 3(m (B 1)s) 4 s + 1,(B 1) 4 s m < B s (3.9),, (m (B 1) s) 3, (B 1) s ϕ B+2 (m) = 3 s m B s 0, otherwise. (3.10) For the pilot signal in symbol ξ = 0, 1,..., B 1, the channel output at the receiver with CP removed is L 1 rp(m) ξ = h l,t s p (m l) + z p l=0 L 1 = h l,m+ξs+ls p (m l) + z p (3.11) l=0 where we define t = l, m + ξ s + L. Then, the corresponding matched filter output is rp ξ 2πpk L j = b p e e j 2πk(m l) h l,m+ξs+l + z p 2πpk j = b p e 2πpk j = b p e = b p L l=0 l=0 L l=0 L l=0 e j 2πk(m l) e j 2πk(m l) B+2 γ=0 3 d=0 a l,γ a l,ξ+d ϕ γ (m + ξ s + L) + z p ϕ ξ+d (m + ξ s + L) + z p 3 a l,ξ+d β ξ l,d (p) + z p (3.12) d=0 13

20 Chapter3. Channel Estimation where we define β ξ l,d 2πpk (p) = e j e j 2πk(m l) ϕ ξ+d (m + ξ s + L) (3.13) Employing the prototype base function in (3.2), we can express (3.13) based on the prototype base functions where for 0 ξ + d 3, β ξ l,d β ξ l,d for 3 ξ + d B, and β ξ l,d for B ξ + d B πpk (p) = e j 2πpk (p) = e j 2πpk (p) = e j e j 2πk(m l) e j 2πk(m l) e j 2πk(m l) ϕ ξ+d (m + ξ s + L) (3.14) ϕ(m + [3 d] s + L) (3.15) ϕ ξ+d (m + [3 d] s + L) (3.16) 3.2 Vector atrix odel Let r ξ p = [ r ξ p1,ζ s, r ξ p2,ζ s,, r ξ p1,ζ e, r ξ p2,ζ e ] T, shows the pilot in ξth symbol of SC-FDA has output from ζ s to ζ e, we can introduce the following vectors. r= [ r 0T p, r 1T p ],, rp B 1T T, a l =[a l,0, a l,1,, a l,b+2 ] T, a= [ a T 0, a T 2,, a T L ] T (3.17) then, with the response matrix Ψ we can express y as r = Ψa + z (3.18) 14

21 Chapter3. Channel Estimation where Ψ = [Ψ 0 Ψ 1 Ψ L ] yields L path response matrix. From this expression, the maximum likelihood (L) estimator is given by â = ( Ψ H Ψ ) 1 Ψ H r. (3.19) 3.3 Equivalent Channel Since the calculation of apparent channel response ĥ(n, n ) is difficult to obtain, therefore as stated before we estimate the physical channel impulse response h l,m calculate ĥ(n, n ) from the estimated h l,m. express ĥ(n, n ) = 1 1 κ=0 e j2πκ(n n) L 1 l=0 3 d=0 then From equation (2.12) and (3.1) we can â l,d+3 ϕ d+3 (m + ξ s + L)e j2πkl, (3.20) The apparent channel response is obtained by using pilot signals which transmitted in data domain parallel with data signals. With this proposed scheme, the mathematical solution of the apparent channel response is presented. 15

22 Chapter 4 Performance Evaluation The performance of B-spline approximation of pilot signals which modeled in 3 has been developed in Twisted-OFDA [12]. In this chapter we present the performance of B-Spline approximation in Twisted-OFDA, compared to SC-FDA with SE channel estimation. 4.1 Simulation Setups The performance of the proposed B-Spline approximation is evaluated using pilot signals in Twisted-OFDA. This is done, in order to gives an overview of B-spline approximation capability in estimating fast-fading channel transmission. Twisted-OFDA itself is a scheme, that is introduced in [12] to suppress the effect of Doppler Spread. The transmitted signal of Twisted-OFDA is solely an OFD signal, which are twisted over the full frequency band. The performance characteristic of proposed B-Spline approximation in Twisted- OFDA then compared with SC-FDA system, which uses SE channel estimation. Bit Error Rate (BER) to SR characteristic of both systems is compared in various Doppler frequency with various number of users. The system parameter for both Twisted-OFD and SC-FDA is presented in Table

23 Chapter4. Performance Evaluation Table 4.1: Simulation parameters Parameters Twisted-OFDA SC-FDA Carrier Frequency f c =2.0 GHz Chip Rate R c =3.84 cps Chip Duration T c = ns umber of Pilot p ξ =8 Channel Estimation B-Spline Approx. SE ormalized Doppler Freq. f D T =0, 0.05, 0.1, 0.2, 0.3 umber of User 7, Simulation Result Here, computer simulations are conducted to illustrate the performance of the proposed scheme B-spline approximation with pilot insertion in Twisted-OFDA, and to compare the performance with SC-FDA system with SE channel estimation. Figure 4.1 compares bit error rate (BER) performance in normalized Doppler frequency f D T = We can see that the performance of SC-FDA with SE channel estimation is inferior if compared to the performance of Twisted-OFDA with B-Spline approximation. The increase of number of user in SC-FDA is effecting to lower performance due to the Doppler spread. However in Twisted-OFDA, the increase of the number of user seems does not infecting the performance. In Figure 4.2, Figure 4.3, and Figure 4.4 respectively, shows the BER performance comparison with increasing of normalized Doppler frequency for f D T = 0.1, f D T = 0.2, and f D T = 0.3. Clearly the performance of Twisted-OFDA is stable in each normalized Doppler frequency with various number of user. However for SC-FDA we can see the degradation of performance, especially for number of user u ser = 7, starting from normalized frequency f D T =

24 Chapter4. Performance Evaluation Figure 4.1: BER performance comparison of the Twisted-OFDA system and the SC-FDA system for user = 7, 14, f dt = 0.05 From the performance in Twisted-OFDA system, it can be concluded that, B- Spline approximation method using pilot signals can be used as channel estimator in system with fast fading channel transmission. Such system is not limited to Twisted- OFDA. Other system, such as SC-FDA also can take advantage of B-Spline approximation method to deal with fast fading channel transmission. 18

25 Chapter4. Performance Evaluation Figure 4.2: BER performance comparison of the Twisted-OFDA system and the SC-FDA system for user = 7, 14, f dt =

26 Chapter4. Performance Evaluation Figure 4.3: BER performance comparison of the Twisted-OFDA system and the SC-FDA system for user = 7, 14, f dt =

27 Chapter4. Performance Evaluation Figure 4.4: BER performance comparison of the Twisted-OFDA system and the SC-FDA system for user = 7, 14, f dt =

28 Chapter 5 Conclusion This paper has proposed a scheme to implement B-Spline approximation method as channel estimator in SC-FDA system. We developed a mathematical model of B- Spline approximation for SC-FDA system. This mathematical model uses pilot signal in data domain to aid for channel estimation. The calculation of apparent channel response is difficult to obtain, therefore we estimate the physical channel impulse response using B-Spline approximation then calculate the apparent channel response. We also introduced C model simulation of B-Spline approximation in Twisted- OFDA system. It showed that B-Spline approximation able to estimate fast fading channel channel transmission. We compare our result with existing SC-FDA C model simulation, which uses SE as chnanel estimator. From the simulation we can see that the performance of SC-FDA with SE channel estimation is inferior if compared to the performance of Twisted-OFDA with B-Spline approximation, due to its weakness against Doppler spread. As the normalized Doppler frequency increased, so become the degradation in the performance of SC-FDA. The result shows that B-Spline approximation is very promising candidate to be implemented in SC-FDA system. We leave the C model implementation of B-Spline approximation in SC-FDA system to future research. 22

29 Bibliography [1] P. Robertson, S. Kaiser, The effects of Doppler spreads in OFD(A) mobile radio systems, in Proc Vehicular Technology Conference (VTC 1999-Fall), vol. 1, pp [2] T. Wang, J. G. Proakis, and E. asry, and J. R. Zeidler, Performance of degradation of OFD systems due to Doppler spreading, IEEE Trans. Wireless Communications, vol. 5, no. 6, pp , June [3] B. Karakaya, H. Arslan, and H. A. Cirpan, Channel estimation for LTE Uplink in high Doppler spread, IEEE Communication Society WCC, [4] B. Karakaya, H. Arslan, and H. A. Cirpan, An Adaptive Channel Interpolator Based on Kalman Filter for LTE Uplink in High Doppler Spread Environments, EURASIP Journal on Wireless Communications and etworking, Vol. 2009, Article ID [5] d.. RAA, J. Kim, and WK. Cho, LS based adaptive channel estimation for LTE Uplink, Radioengineering, Vol. 19, o. 4, pp , December [6] L. Zhang, Z. Hong, and R. Boudreau, Improved Doppler itigation Techniques for LTE Uplink Transmission, 2013 IEEE ilitary Communications Conference,

30 BIBLIOGRAPHY [7] Dan Li, Feng Ke, Fast Time-Varying Channel Estimation ethod for LTE SC- FDA Systems, IEEE International Conference on Accoustic, Speech, and Signal Processing (ICASSP), [8] Y. V. Zakharov, T. C. Tozer, and J. F. Adlard, Polynomial spline-approximation of Clarkefs model, IEEE Trans. Signal Processing, vol. 52, pp , ay [9] S. Sesia, I. Toufik, and. Baker, LTE The UTS Long Term Evolution, from theory to practice. John Wiley and Sons Ltd, [10] D.C. Chu, Polyphase codes with good periodic correlation properties, IEEE Trans. Information Theory, vol. 19, no. 4, pp , July [11] Y. Li, On the Performance of Convolutional Spreading CDA with Cyclic Prefix over Fast Fading Channels, PhD Thesis, University of Electro Communication, arch [12] Y. Li, C. Han, and T. Hashimoto, Twisted OFDA: A Robust Scheme for ultiuser Downlink Transmission over Doubly Selective Channels, 2013 IEICE Society Conference, September

D80 を使用したオペレーション GSL システム周波数特性アンプコントローラー設定. Arc 及びLine 設定ラインアレイスピーカーを2 から7 までの傾斜角度に湾曲したアレイセクションで使用する場合 Arcモードを用います Lineモード

D80 を使用したオペレーション GSL システム周波数特性アンプコントローラー設定. Arc 及びLine 設定ラインアレイスピーカーを2 から7 までの傾斜角度に湾曲したアレイセクションで使用する場合 Arcモードを用います Lineモード D8 を使用したオペレーション GSL システム周波数特性アンプコントローラー設定 Arc 及びLine 設定ラインアレイスピーカーを2 から7 までの傾斜角度に湾曲したアレイセクションで使用する場合 Arcモードを用います Lineモードアンプ1 台あたりの最大スピーカー数 SL-SUB SL-GSUB - - - - は 3つ以上の連続したから1 までの傾斜設定のロングスローアレイセクションで使用する場合に用います

修士論文の和文要旨 研究科 専攻大学院情報理工学研究科情報. 通信工学専攻博士前期課程

修士論文の和文要旨研究科専攻大学院情報理工学研究科情報. 通信工学専攻博士前期課程