HIGH-reliability high-throughput wireless links are required

Beamforming and Alamouti Combined Downlink Transmission Schemes in Communication Systems For High-Speed Railway Meng Cheng, Xuming Fang, Li Yan Abstract In this paper, we propose a reliable downlink (DL) transmission scheme exploiting both location- and speed- related information in a high-speed railway scenario, which relies on a multi-functional antenna array (MFAA) combining spacetime block coding () with adaptive receive beamforming techniques. Firstly, the state-of-the-art and adaptive beamforming techniques are reviewed and analyzed in the context of both block-fading and time-varying channels. Then we propose to employ an antenna array on board of a high-speed train to form two beams for receiving the signals from the DL transmit antennas in order to improve the reliability of the system. It is demonstrated that in the context of combined schemes, receive beamforming is more beneficial than transmit beamforming under high-speed railway linear topology to achieve low bit error rate (). Hence it is more attractive to employ receive beamforming antennas on the top of the train. Index Terms, beamforming, block fading, time varying, high speed train I. INTRODUCTION HIGH-reliability high-throughput wireless links are required for high-speed trains. Both and beamforming may be employed at the Base Station (BS) relying on multiple antennas for achieving transmit diversity gain and beamforming gain, respectively, for the sake of increasing the Signal-to-Noise Ratio (SNR). However, requires the antenna spacing of the array elements to be sufficiently high, such as 5 to 0 times the wavelength of the carrier for a Uniform Linear Array (ULA), in order to achieve the independent fading of the multipath components, and hence to achieve the maximum attainable diversity gain. By contrast, beamforming achieves angular selectivity with the aid of half-wavelength antenna spacing. Owing to these different antenna-spacing requirements, it is a challenge to construct the combination of and beamforming. A beamforming scheme combined with was proposed in 2, while its switched-beam counterpart was proposed in 3. This combined scheme has been analyzed under specific conditions, when the transmitter has imperfect knowledge of the channel in 4, while correlated MIMO fading channels were assumed in 5. Cooperative BS scenarios were considered in 6. The beamforming weight vector generation methods used in all the above-mentioned solutions were based on the decomposition of the channel s covariance matrix, which opt for using the large eigenvectors as the beamforming weight vectors for maintaining a high SNR 7. A simple way to generate the beamforming weight vector is to calculate it based on Direction-of-Arrival (DoA) 8 2. The influence of the angular spread experienced on the performance of combined scheme is illustrated in 8. The authors also suggest that in radio environments associated with small angular spreads a beneficial strategy would be to avoid steering a beam by ensuring that maximum array gain coincides with the DoA, but instead to create a pair of beams so that they are symmetrical at both sides of the DoA. The author of 9 applied this combined scheme in indoor communications. Instead of a single antenna array, a pair of subarrays was conceived in 0 and the achievable array gain was also calculated, which was then further extended to a system equipped with more than three transmit antennas in. The authors of 2 combined Minimum Bit Error Rate (M) Beamforming proposed in 3 with for the sake of achieving both a full diversity gain and a high beamforming gain. In the context of DL transmission, the employment of transmit beamforming is more common than that of receive beamforming due to the constraints of the user equipment size, complexity and power consumption. However, in high-speed railway scenarios this situation is different, because multiple antennas can be accommodated on the top of the carriages which make combined with receive beamforming an attractive proposition. A combined scheme relying on matrix decomposition aided receive beamforming weight vector generation was proposed in 4. It also shows that Alamouti decoder outperforms the MMSE decoder when there are sufficient degrees of freedom at the receiver antenna array. A system structure based on the combination of and beamforming is used to realize the design of 5, 6. However, they are not considered in the high-speed scenario. In the considered scenario, the influence of delay on the accuracy of channel estimation is very obvious which will further have bad effect on the generation of beamforming weight vectors based on matrix decomposition. Thus the combined scheme which applies DOA based weight vector generation to receive beamforming is proposed in this paper to achieve higher mobility with lower complexity. The rest of this paper is structured in five sections. Section II reviews the system model of high speed railway communications. The expressions of the received signals are also analyzed. Section III introduces combined with transmit beamforming, while the focus of Section IV is on combined with receive beamforming, where an improved version is proposed. Section V illustrates the achievable performances of different schemes. Finally, Section VI concludes the paper. 978--4799-0308-5/3/$3.00 203 IEEE

2 v R Fig.. Linear Topology of Communication Systems for High-Speed Railway. d min II. SYSTEM AND SIGNAL MODEL In our high-speed railway scenario, we consider a nondispersive scenario associated with an M-element transmitter antenna array, which performs for DL transmission. The communication system in a high-speed railway scenario may have a linear topology and the cell radius is R. The antennas of BS radiate towards the track side directionally. The vertical distance from BS to the track is d min, as depicted in Figure. It may be reasonable to assume that both the train moving speed and location information can be obtained. In this communication system the receiver is mounted on the top of the carriage and only the hop from the BS to the onboard receiver is considered. The communication between passengers and onboard receivers is beyond the scope of this study. As high-speed trains are operated in diverse environments, such as open rural areas where Line of Sight (LOS) scenarios are typical, as well as in tunnels and suburban areas, where no LOS propogation is feasible, both Rayleigh and Rician fading channels will be taken into consideration. To model these two types of channel, the sum-of-sinusoids simulation models 7 proposed by Xiao can be used. Generally, the channel is assumed at least block fading in Alamouti s 2x transmission structure, which means the channel cofficients remain constant during the period of two transmit symbols. However, the velocity of high-speed trains will be over 350km/h, thus the channel s complex envelope fluctuates in line with the Doppler spread associated with rapidly time-varying channels. In this paper, the situation in which the channel coefficients are different for two continuous transmit periods is also taken into account to verify the performance of the proposal. There are two basic methods of combining with beamforming. The first one is to conceive and beamforming at the BS, which we represent as -. The second one is to perform at the BS and beamfoming at the receiver since the receiver of high speed railway DL scenario is on the top of the carriage, which has practically no size limitations. This scheme is represented by - RxBF. In the first and the second techniques, the beamforming antenna array has to be configured differently. For example, the array can generate either one or two beams according to the beamforming weight generation model. Furthermore, the array can also be divided into two subarrays, in which the inter-element spacing Δ may be set to half the wavelength, λ 2, but the distance between two subarrays is large enough to generate two independently fading beams. Details of the configuration will be illustrated in Section III. When beamforming is applied, the instantaneous channel can be characterized as h(t) = L α l (t)sθ l (t), l =,...L, () l= where L is the number of spatially separated paths and s(θ l ) is the DL steering vector at the DOA θ l, which can be expressed as,e j2πsin(θl)δ/λ,...,e j2π(m )sin(θ l)δ/λ. Furthermore, α l (t) is the fading coefficient of path l. Since the receiver s location information and the parameters of the cell are known, the DOA θ l can be readily calculated at time instant t. Generally, for the combined and beamforming schemes 3, the transmitted signal is first encoded using an encoder, yielding the pair of outputs as x (t) and x 2 (t). Then they are processed by two transmit beamformers having the weights w and w 2, respectively, and summed for producing a vector of signals for transmission over the channel. Hence the received signal r(t) can be represented as r(t) =w H H(t) x (t)+w H 2 H(t) x 2 (t)+v(t), (2) where v(t) is the additive white Gaussian noise(awgn) and H(t) =h (t)+h 2 (t). There are two methods of generating the beamforming weights. The first one is based on calculating the two largest eigenvalues of the DL channel s covariance matrix (DCCM) and retaining the two eigenvectors corresponding to these two eigenvalues as beamforming weights, as defined in 2 7. This method is capable of achieving the maximal SNR with the aid of the optimal beamforming weights, which is accomplished at the cost of eigenvalue-decomposing (EVD) of the DCCM for every transmission. The second one is of lower complexity, where we generate the beamforming weights with the aid of the DL steering vectors 8 2, w i = 2M s(θ i ),i =, 2. In the next section, the abovementioned weight generation methods will be applied to - and -RxBF schemes. III. COMBINED BEAMFORMING AND ALAMOUTI DOWNLINK TRANSMISSION A. Combining beamforming with As mentioned above, Equation (2) describes a specific structure combining and, which is referred to as - I in this paper. The difference between - I and the method proposed in 3 is that the weight vectors are generated with the aid of the DL steering vector, rather than by the EVD of the DCCM. The structure of - I is seen in Figure 2(a). The equivalent channels β (t) =w H (t)h(t) and β 2 (t) =w2 H (t)h(t) are uncorrelated owing to spacing the subarrays far apart for achieving diversity gain of the. The using the twin-antenna array group proposed in 0 is denoted as - II, which

3 w w2 w w2 M α(t),θ(t) (a) - I α(t),θ(t) M/2 M/2 4 is denoted as -RxBF I and its structure is shown as Figure 2(c). It has the potential of maximizing the SNR at the cost of a high computational overhead since it employs DCCM EVD, which is formulated as: R = E h(t) h H (t) B = E α b (t) 2 s(θ b ) s(θ b ) H. (4) b= Following processing by the beamformer, the received signal vector at the receive antenna is: w ỹ = H (n)h (n) w H (n)h 2 (n) w T (n +)h 2(n +) w T (n +)h (n +) x w + H (n)v(n) x 2 w T (n +)v. (n +) (5) Fig. 2. Fig. 3. (b) - II α(t),θ(t) M (c) -RxBF I w Structures of different and Beamforming combined schemes α(t),θ(t) Structure of Improved -RxBF scheme. M w w2 is characterized here in a time-varying scenario. The - II scheme is shown in Figure 2(b). In case of timevarying channels, the received signal vector is: r = βx + ṽ, (3) w where β = H (n)h (n) w2 H (n)h 2 (n) w2 T (n +)h 2(n +) w T (n +)h (n +) r(n) v(n) while r = r and ṽ = (n +) v. In - (n +) I, the two branches of the signals pass through the same physical channel h(t) described by Equation (), while in - II the pair of transmit signals propogate through two independently fading physical channels h (t) and h 2 (t), h i (t) =α i (t)sθ i (t), i =, 2. So far there are less studies in combining with receive beamforming in the literatures than for combined and transmit beamforming. The scheme proposed in, B. Improved -RxBF Scheme Since -RxBF I only generates one beam using the receive antenna array which employs the DCCM EVD model, on one hand, it has not utilized the features of high-speed railway scenario such as the train moving speed and location information as well as the spacious carriage top which can bear sufficient antennas, and on the other, the performance of DCCM EVD model depends on channel estimation which leads to big amount of overhead and high complexity of receiver to obtain enough accuracy under high mobility. The potential of the spacious carriage top of the train to deploy sufficent large number of antennas which achieves high angular resolvability makes it possible for the onboard receiver to serve the different spatial streams from the BS simultaneously with two different beams. Thus an improved scheme denoted as -RxBF II is proposed to overcome the shortcoming of -RxBF I and seize the benefits provided by the scenario. It employs the M-elements antenna array at the receiver to generate two beams to receive the signals r (t) and r 2 (t) from different transmit antennas seperately, where r i (t) =h i (t)x i + v i (t), t = n, n +, i =, 2, and w (t) and w 2 (t) are simply generated by downlink steering vectors related method,that is, w i = 2M s(θ i ),i =, 2, which has less computational overhead than -RxBF I. Its structure is illustrated in Figure 3. The two branches of signals are summed up after processing by two beamformers respectively, then the received signal vector can be expressed as: w ỹ = H (n)h (n) w2 H (n)h 2 (n) x w2 T (n +)h 2(n +) w T (n +)h (n +) x 2 w + H (n)v (n)+w2 H (n)v 2 (n) w T (n +)v(n +)+w2 T (n +)v2(n. (6) +) C. Detection of the received signals Under time-varying channels, either Simple Maximum Likelihood (SML) or Joint Maximum Likelihood (JML) criteria can be used to detect signals. Take - RxBF II for example, applying SML first. Denote G = w H (n)h (n) w2 H (n)h 2 (n) w2 T (n +)h 2(n +) w T (n +)h, then after match filtering, x = G H ỹ.for x choose x i if and (n +) only

4 I II RxBF I RxBF II I II RxBF I RxBF II 0 4 0 4 0 5 0 5 0 6 0 5 0 5 20 25 0 6 0 5 0 5 20 25 I II RxBF I RxBF II I II RxBF I RxBF II 0 4 0 4 0 5 0 5 0 5 20 25 0 5 0 5 0 5 20 25 Fig. 4. vs. SNR over Rayleigh Fading Channels Fig. 5. vs. SNR over Rician Fading Channels if: ( α 2 + α2 2 ) x i 2 + d 2 ( x,x i ) ( α 2 + α2 2 ) x k 2 + d 2 ( x,x k ), i k where d 2 (x, y) is the squared Euclidean distance between signals x and y. When using JML, which is a full searching method with high computation and good performance, x i is chosen from min ỹ Gx i 2 (8) x i A where A is the constellation set from which x i is drawn. For block-fading channels, the receiver structure of - schemes is the same with that of classic Alamouti 2x, thus the maximum likelihood detection rule can be simply employed to detect signals. IV. SIMULATION RESULTS AND PERFORMANCE ANALYSIS In our simulations, an M-elements ULA antenna is assumed in the enodeb while the onboard receiver has single antenna for - schemes. When the subarray case is considered, the total elements are kept constant which means 2 subarrays with M/2 elements each, where M is an even (7) number such as 6. For -RxBF schemes, the onboard receiver has M-elements ULA antenna while the enodeb uses two antennas to perform transmission. To observe the performance through the whole cell under high-speed railway, we define the initial time t =0when the train enters the cell. The speed of the train is 360km/h and QPSK is employed. Assume there exist 3 paths and the power of each path obeys negative exponential distribution. Both Rayleigh and Rician fading channels are considered and the Rician K factor is 6 db in the simulation according to the parameters provided in Winner II report which also suggests a medium Angular Spread as 60 degrees. Accurate compensation for Doppler shift and perfect channel estimation are assumed. For both fading channels, block fading and time varying fading are simulated respectively. For comparison, two conventional schemes are included, which are Alamouti 2x and 6-elements ULA transmit beamforming technique. Figure 4 and Figure 5 illustrate how performances of these schemes change with SNR under Rayleigh and Rician channels separately, both including block fading channel and time varying channel. It is shown in Figure 4 that the performance of traditional transmit beamforming outperforms that of Alamouti 2x when the SNR is small under

5 I II RxBF I RxBF II I II RxBF I RxBF II 0 200 400 600 800 000 200 400 600 800 2000 0 200 400 600 800 000 200 400 600 800 2000 I II RxBF I RxBF II I II RxBF I RxBF II 0 200 400 600 800 000 200 400 600 800 2000 0 200 400 600 800 000 200 400 600 800 2000 Fig. 6. vs. Location over Rayleigh Fading Channels Fig. 7. vs. Location over Rician Fading Channels Rayleigh block fading, however, this advantage is weakened in the case of time varying as the diversity structure of is better at coping with fast fluctuation. In the combined schemes of and transmit beamforming, - II always performs better than Alamouti since it is the extension of traditional using two independent subarrays instead of two independent single antennas which always benefits from beamforming gains. Its performance is better than traditional beamforming when SNR is larger than 0dB under Rayleigh block-fading channels but when it turns to time varying Rayleigh, - II almost outperforms traditional beamforming for the whole SNR range and this trend becomes obvious as the SNR increases, by which approximate 4dB improvement is achieved around =. It can be seen from Figure 5 that the performance of traditional beamfoming changes little under block fading and time varying Rician channels because most energy is focused on the LOS path which results in less fluctuation compared with Rayleigh channels and this will benefit the beamforming gain. Under Rician fading channels, both Alamouti and its extension, - II, can outperform the tradition beamforming only when the SNR is large as the less fluctuation caused by LOS path will decrease the effect of diversity. However, - I is the only scheme which performs better under time varying channels other than block fading channels based on the assumption of perfect channel estimation. As seen from the operating principle shown in Figure 2(a), two transmit signals pass through the same physical channel which is turned into two independent equivalent channels using two beamformers. It is more possible to get two separate and strong orthogonal equivalent channels when the physical channel varies faster. It is also shown in these figures that the performances of -RxBF shemes are always the best, especially the proposed improved scheme -RxBF II which can achieve about db gain than the -RxBF I for the whole SNR range. Figure 6 and Figure 7 illustrate the performances of these schemes during the whole process when the train moves across the cell under different channel conditions. All the combined schemes outperform those two comparison algorithms. In simulation of this time, SNR is set as 5dB and angular spread is assumed 60. Among four combined schemes, - II performs steadily worst and very closely to that of traditional beamforming. - I is better than - II but experiences sudden change in the range around the enodeb, especially under Rayleigh

6 time varying channels its performance degrading seriously in the district which is enodeb-centered and 600 meters long. Similarly, -RxBF I also encounters this kind of problem almost in any channel conditions we mentioned in this simulation. The performance of proposed improved scheme -RxBF II is the best and most stable across the entire cell. V. CONCLUSION Different combination structures of and beamforming technique for communications in high-speed railway are illustrated and analyzed, respectively, in this paper. The combined techniques improve the performance considerably. To further decrease computational overhead, we propose to improve the -RxBF scheme by generating beamforming weights according to steering vectors and the proposed scheme is shown to achieve lower and perform most stable during the whole transmission. In the future work, imperfect channel estimation will be considered. The extention from Alamouti 2x to multiple transmit and receive antennas will also be discussed. ACKNOWLEDGMENT The work of authors was supported partially by the 973 Program under the Grant 202CB3600, NSFC under the Grant 60708, 6032002, the Major Program of Technological R&D of the Ministry of Railway under the Grant 203X06- A. REFERENCES S. Alamouti, A simple transmit diversity technique for wireless communications, J. Sel. Areas Commun., vol. 6, no. 8, pp. 45 458, 998. 2 Z. Lei, F. Chin, and Y. Liang, Combined beamforming with spacetime block coding for wireless downlink transmission, in IEEE 56th Vehicular Technology Conference, VTC 2002-Fall, vol. 4. IEEE, 2002, pp. 245 248. 3, Orthogonal switched beams for downlink diversity transmission, IEEE Transactions on Antennas and Propagation, vol. 53, no. 7, pp. 269 277, 2005. 4 G. Jongren, M. Skoglund, and B. Ottersten, Combining beamforming and orthogonal space-time block coding, IEEE Transactions on Information Theory, vol. 48, no. 3, pp. 6 627, 2002. 5 M. Lin, M. Li, L. Yang, and X. You, Adaptive transmit beamforming with space-time block coding for correlated mimo fading channels, in IEEE International Conference on Communications, ICC 07. IEEE, 2007, pp. 5879 5884. 6 M. Lin, J. Ouyang, and Y. Niu, A simple downlink diversity transmit scheme for cooperative base stations, in 20 International Conference on Wireless Communications and Signal Processing (WCSP). IEEE, 20, pp. 5. 7 Y. Liang and F. Chin, Downlink channel covariance matrix (dccm) estimation and its applications in wireless ds-cdma systems, IEEE Journal on Selected Areas in Communications, vol. 9, no. 2, pp. 222 232, 200. 8 M. Katz and J. Ylitalo, Extension of space-time coding to beamforming wcdma base stations, in IEEE 5st Vehicular Technology Conference, VTC 2000-Spring Tokyo, vol. 2. IEEE, 2000, pp. 230 234. 9 R. Morelos-Zaragoza, M. Ghavami et al., Combined beamforming and space-time block coding for high speed wireless indoor communications, in 4th International Symposium on Wireless Personal Multimedia Communications (WPMC 0), Aalborg, Denmark, 200, pp. 427 43. 0 F. Zhu and M. Lim, Combined beamforming with space-time block coding using double antenna array group, Electronics Letters, vol. 40, no. 3, pp. 8 83, 2004. L. Liu and M. Lim, An efficient selective transceiver for beamforming and transmit diversity combining scheme, in Antennas and Propagation Conference, LAPC 2007. Loughborough. IEEE, 2007, pp. 33 36. 2 S. Elnoubi, W. Abdallah, and M. Omar, Minimum bit error rate beamforming combined with space-time block coding, in International Conference on Communications and Information Technology (ICCIT). IEEE, 20, pp. 203 206. 3 S. Chen, N. Ahmad, and L. Hanzo, Adaptive minimum bit-error rate beamforming, IEEE Transactions on Wireless Communications, vol. 4, no. 2, pp. 34 348, 2005. 4 C. Sun, M. Taromaru, and N. Karmakar, On the combination of receive beamforming with alamouti decoders, in IEEE 63rd Vehicular Technology Conference, VTC 2006-Spring, vol. 6. IEEE, 2006, pp. 2798 2802. 5 A. Pascual-Iserte, A. Pirez-Neira, and M. A. Lagunas, A maximin approach for robust mimo design: Combining ostbc and beamforming with minimum transmission power requirements, in Acoustics, Speech, and Signal Processing, 2004. Proceedings.(ICASSP 04). IEEE International Conference on, vol. 2. IEEE, 2004, pp. ii. 6 D. Arora and P. Agathoklis, Performance evaluation of uplink transmission using space time block coding and beamforming, in Signal Processing and Information Technology, 2004. Proceedings of the Fourth IEEE International Symposium on. IEEE, 2004, pp. 405 408. 7 C. Xiao, Y. Zheng, and N. Beaulieu, Novel sum-of-sinusoids simulation models for rayleigh and rician fading channels, IEEE Transactions on Wireless Communications, vol. 5, no. 2, pp. 3667 3679, 2006.