A massive MIMO-based adaptive multi-stream beamforming scheme for high-speed railway

Abstract

The throughput of high-speed railway (HSR) communication systems is limited not only by frequency spectrum but also by high mobility. Under the HSR scenario, one of the promising solutions to improve the throughput is multi-stream beamforming. However, severe performance degradation occurs due to larger inter-beam interference (IBI) as the number of beams is constant. In order to maximize the throughput, a massive multiple input and multiple output (MIMO)-based adaptive multi-stream beamforming scheme is proposed, which utilizes an adaptive beam-selection proposal by exploiting the location information of the train. By adaptively selecting the optimal subset of beams, including active subset size and active receive antenna indices, with respect to the location of the train, the proposed scheme significantly outperforms single/dual-stream beamforming and conventional massive MIMO. We also find that the throughput is not proportional to, but a nonlinear function of, the number of active receive antennas in this scenario.

1 Introduction

High-speed railway (HSR) communication systems are defined to satisfy the requirements of train-ground data transmission [1]. On the one hand, safety-critical railway signaling (e.g., train control information, security monitoring, and operational services) needs to be transmitted to the ground. On the other hand, the passenger’s travelling experience, such as high-rate Internet access, must be supported by more reliable communication quality. Thus, there is practical motivation and interest to investigate how to improve the data rate and transmission reliability of HSR communication systems efficiently to address the different requirements of data transmission.

To fulfill these requirements, several important issues are needed to be investigated, such as serious Doppler effect, synchronization, and frequent handover. Seamless connectivity, soft handover, and fast handover were proposed to provide continuous system connection [2–6]. The timing-frequency training and compressive sensing techniques are used to confirm synchronization [7, 8]. Doppler diversity is one of the most common methods to overcome the Doppler effect [9–11]. The computational complexity can be further reduced by utilizing location and velocity information of the train [12]. In addition, it was proved that the frequency offset estimation and correction are very good in a near constant velocity scenario [13]. Therefore, we assume that the Doppler effect caused by high mobility can be almost compensated by other elaborated solutions. And synchronization can be achieved in the systems.

In this paper, we focus on mitigating the inter-beam interference (IBI) to improve the throughput by utilizing massive multiple input and multiple output (MIMO)-based multi-stream beamforming.

Massive MIMO [14, 15] (also known as large-scale antenna array and very large MIMO) is one of the promising technologies for 5G wireless communication systems, which uses antenna arrays with tens or even hundreds of antennas simultaneously serving many tens of terminals to enhance the system throughput and transmission reliability. Theoretically, as the number of base station (BS) antennas grows without bound, the effects of uncorrelated noise and fast fading disappear [16], the high degree of freedom (DoF) is provided [17], and the distribution of the singular values of the channel matrix approaches to a deterministic function [18]. Besides, extra antennas focus energy into a small region [14], which can be helpful to improve the throughput when multi-stream beamforming is employed. Nevertheless, massive MIMO will result in pilot contamination and lower energy efficiency problems [19]. More particularly, performance limitation [20] (i.e., it eventually saturates at a certain value) or degradation [21, 22] can be caused by the transmitters’ size.

For HSR, one of the typical terrains is the viaduct (e.g., 86.5 % of the Chinese Beijing-Shanghai HSR) [23]. Since the viaduct raises the height of transmit antennas leading to a relatively clear line-of-sight (LOS) and few scatters [24], the benefit of multiple antenna gain is barely harvested. Therefore, there are some limitations to apply massive MIMO to a HSR scenario.

Beamforming can be regarded as forming a signal beam towards the receiver, if there is LOS between the transmitter and receiver. Beamforming can also be applied in non-LOS, if the multipath channel state information (CSI) is known [25]. Several beamforming-based schemes were conceived for HSR communication systems [5, 26–30]. A WiMAX-based route-tracking beamforming was proposed, and field tests over Taiwan HSR were carried out [26]; the experimental results showed that the received signal strength indicator (RSSI), carrier to interference plus noise ratio (CINR), and throughput were improved. In [5, 27–30], location information-assisted opportunistic beamforming, beamforming and location-assisted handover scheme, beamforming and Alamouti STBC combined scheme, location assistant beamforming, and distributed beamforming were proposed to improve system throughput and transmission reliability under HSR scenario by exploiting the regular and predictive location and velocity information of the train. However, in the above schemes, only single-stream beamforming and dual-stream beamforming were adopted but the performance of multi-stream beamforming is not analyzed and discussed in this scenario either.

Based on the above background, multi-stream beamforming is introduced to improve the throughput under HSR scenario. However, performance degradation is caused by the increased IBI with a larger distance between the trackside BS and onboard mobile relay station (MRS) as the number of beams is constant. To overcome the degradation, a massive MIMO-based adaptive multi-stream beamforming (AMSB) scheme is proposed. The proposed scheme is based on an adaptive beam-selection procedure by exploiting the regular and predictive location information provided by train control systems. By adaptively selecting the optimal subset of beams, including active subset size and active receive antenna indices, the maximum throughput has been achieved under HSR scenario.

The rest of this paper is organized as follows. In Section 2, the HSR scenario is presented. Then, in Section 3, the proposed massive MIMO-based AMSB scheme and benchmark conventional massive MIMO are described and analyzed under LOS MIMO channel. Performances of these schemes are evaluated in Section 4. Finally, Section 5 concludes by summarizing the main results and suggests some future work.

2 System model of HSR

Consider that the system model by activating all beams with equal power allocation for HSR communication systems is depicted in Fig. 1. The projection of BS and N _R th receive antenna onto ground are denoted as O and A, respectively. The perpendicular distance between BS and track is d _min. The track-side BS is equipped with uniform linear antenna arrays (ULAA), where the N _T antennas are evenly spaced along a straight line. The transmit antennas are separated by Δ _t λ _c , where λ _c is carrier wavelength (e.g., if f _c =2.5 GHz, then λ _c =0.12 m) and Δ _t is the normalized transmit antenna separation, normalized to the unit of the carrier wavelength. In addition, the train is moving along the direction of the velocity vector as seen in Fig. 1. The receive antennas of MRS are deployed on the top of each carriage of the train, while the length of the train, l _T , with eight carriages (e.g., CRH-3C train) is used exclusively. The receive antenna separation is Δ _r λ _c , where Δ _r is the normalized receive antenna separation. Since the receive antennas are far apart from each other, we assume that the receive antennas are geographically separated [31].

Fig. 1

System model of HSR

For the sake of mathematical analysis, the distance between BS and reference receive antenna (i.e., the first receive antenna) is denoted as d and the angle between BS and the ith receive antenna is denoted as ϕ _i as seen in Fig. 1. For the sake of simplicity, one data stream per active receive antenna (i.e., the number of beams is equal to the number of active receive antennas) and the number of transmit antennas at BS being not less than the number of receive antennas on the train (i.e. N _T ≥N _R ) are considered. Furthermore, it is assumed that the CSI can be estimated by the BS due to channel reciprocity in TDD systems [32]; the Doppler shift and channel selectivity caused by high mobility can be almost eliminated by some offset compensation techniques (see, e.g., [9–11, 33–40] and references therein). Many literatures have been devoted to the issues of antenna tracking, training, and synchronization (see [7, 8, 41–44] and the references therein). Therefore, we assume that these problems can be maintained via location prediction and other technologies. Only the downlink is considered in this paper; the uplink will be investigated in our future work. A simple way for the uplink is to activate one or all antennas which is equivalent to the SIMO or MIMO system.

According to the system model depicted above, for the multi-stream beamforming with a subset of active receive antennas Υ⊂Ω (details on the beam-selection procedure given in Section 3), the received signal for ith receive antenna on the train with ith beam can be expressed as:

$$ y_{i} = \sqrt{p_{i} \beta_{i}} \boldsymbol{h}_{i} {\boldsymbol{w}_{i}^{H}} x_{i} + \sum_{j \in \Upsilon, j \neq i} \sqrt{p_{j} \beta_{j}} \boldsymbol{h}_{i} {\boldsymbol{w}_{j}^{H}} x_{j} + n_{i} $$

((1))

where the three terms on the right-hand side of equality represent desired signal, interference signal, and additive white Gaussian noise (AWGN), respectively. p _i is the optimal transmit power for the signal x _i and n _i is independent and identically distributed (i.i.d.) with zero-mean and variance ${\sigma _{n}^{2}}$ (i.e., $n_{i} \sim CN(0,{\sigma _{n}^{2}})$). β _i is the large-scale fading from the BS to ith receive antenna, which is determined by both path loss and shadowing modeled using the WINNER II D2a [45]. $\boldsymbol {h}_{i} = \alpha _{i} \exp {(I2 \pi d_{i} / \lambda _{c})} \boldsymbol {f}(\phi _{i}) \in \mathbb {C}^{1 \times N_{T}}$ is the small-scale fading [31], d _i is the distance from BS to ith receive antenna (specifically, for the first receive antenna, d ₁=d), α _i ∼N(0,1), $I=\sqrt {-1}$. A simple direction-of-arrival (DoA)-based method is used [46], $\boldsymbol {w}_{i} = \frac {1}{\sqrt {N_{T}}}\, \boldsymbol {f}(\phi _{i}) = \frac {1}{\sqrt {N_{T}}} \left [\!1, e^{-I2 \pi \Delta _{t} \cos {\phi _{i}}}, e^{-I2 \pi 2 \Delta _{t} \cos {\phi _{i}}}, \!\cdots \!, e^{-I2 \pi (N_{T}-1) \Delta _{t} \cos {\phi _{i}}}\right ] \in \mathbb {C}^{1 \times N_{T}}$ with power constraint $\sum _{i \in \Upsilon } \|{\boldsymbol {w}_{i}}\|^{2} \leq P$, P is the total transmit power of BS, [ ·]^H denotes Hermitian transportation.

To satisfy the angular resolvability of the receive antenna, the angular separation of any two receive antennas should be of the order of or larger than the length of the transmit antenna array, normalized to the carrier wavelength [31], i.e., for any i,j=1,⋯,N _R ,i≠j; the angular resolvability requirement is given by:

$$ |\cos{\phi_{i}} - \cos{\phi_{j}}| \geq \frac{1}{N_{T} \Delta_{t}} $$

((2))

where ϕ _i and ϕ _j represent the directional angles for departure of the path from BS to the ith and jth receive antennas, respectively.

Since cosϕ _i and cosϕ _j in (2) can be expressed as:

Submitting (3) into (2) yields

$$ \begin{aligned} \Bigg|\frac{\sqrt{d^{2}-d_{\text{min}}^{2}}+\frac{i-1}{8} l_{T}}{\sqrt{d_{\text{min}}^{2}+\left(\sqrt{d^{2}-d_{\text{min}}^{2}}+\frac{i-1}{8} l_{T} \right)^{2}}} - \\ \frac{\sqrt{d^{2}-d_{\text{min}}^{2}}+\frac{j-1}{8} l_{T}}{\sqrt{d_{\text{min}}^{2}+\left(\sqrt{d^{2}-d_{\text{min}}^{2}}+\frac{j-1}{8} l_{T} \right)^{2}}}\Bigg| \geq \frac{1}{N_{T} \Delta_{t}} \end{aligned} $$

((4))

3 Massive MIMO-based AMSB design and performance analysis of HSR

In this section, a massive MIMO-based adaptive multi-stream beamforming scheme is proposed to maximize the throughput by selecting the optimal subset of beams, including active subset size and active receive antenna indices, under HSR scenario. Then, the benchmark conventional massive MIMO is described briefly.

3.1 Massive MIMO-based adaptive multi-stream beamforming scheme

For the selected subset of active receive antennas, Υ, the corresponding signal to interference plus noise ratio (SINR) for ith beam amounts to:

$$ \begin{aligned} \text{SINR}_{i} &= \frac{p_{i} \beta_{i} |\boldsymbol{h}_{i} {\boldsymbol{w}_{i}}^{H}|^{2}}{{\sigma_{n}^{2}} + \sum_{j \in \Upsilon, j \neq i} p_{j} \beta_{j} |\boldsymbol{h}_{i} {\boldsymbol{w}_{j}^{H}}|^{2}} \\ &= \frac{p_{i} \beta_{i} |\boldsymbol{h}_{i} {\boldsymbol{w}_{i}}^{H}|^{2} / {\sigma_{n}^{2}}}{1 + \sum_{j \in \Upsilon, j \neq i} p_{j} \beta_{j} |\boldsymbol{h}_{i} {\boldsymbol{w}_{j}^{H}}|^{2} / {\sigma_{n}^{2}} } \end{aligned} $$

((5))

The optimal p _i in (1) can be found by the waterfilling power allocation policy [47, 48]:

$$ p_{i} = (\mu \lambda_{i} - 1)^{+} $$

((6))

where λ _i =1/∥w _i ∥², (x)⁺= max(0,x), and μ is the water level satisfying:

$$ \sum_{i \in \Upsilon} \left(\mu - \lambda_{i}^{-1}\right)^{+} = P $$

((7))

Then, the throughput is given by:

$$ \begin{aligned} C(\Upsilon) &= E \bigg\{ \sum_{i \in \Upsilon} B \log_{2} (1+\text{SINR}_{i}) \bigg\} \\ &= B \times E \bigg\{ \sum_{i \in \Upsilon} \log_{2} (1+\text{SINR}_{i}) \bigg\} \end{aligned} $$

((8))

where B is the bandwidth and E[ ·] denotes expectation.

Here, several typical configurations of beamforming are taken as an example. The parameter settings are listed in Table 1 in Section 4 and the performances of single-, dual-, and eight-stream beamforming are shown in Fig. 2. To be specific, the N _R th receive antenna is activated for single-stream beamforming, both first and N _R th receive antennas are activated for dual-stream beamforming, and all receive antennas are activated for eight-stream beamforming. It illustrates that more active beams do not simply mean an increased system performance under HSR scenario (i.e., the throughput is not proportional to the number of active receive antennas), which is bottlenecked by IBI, which is the interference from the other beams sharing the same frequency band. Performance degradation occurs as the number of beams is constant with larger distance between trackside BS and onboard MRS. Thus, to maximize the throughput, the beam-selection procedure is required to determine the optimal subset of beams (i.e., active subset size and active receive antenna indices) with respect to the regular and predictive location of the train.

Fig. 2

Throughputs with different number of beams

Table 1 Simulation parameters

Based on the above analysis, a massive MIMO-based adaptive multi-stream beamforming scheme is proposed. At the BS, a massive MIMO is used and multi-stream beamforming is introduced. Then, an adaptive beam-selection procedure is applied to select beams. Furthermore, on the top roof of the train, one receive antenna is deployed on each carriage connected by a system bus to a central unit where received signals are processed.

The maximum throughput can be optimized with respect to the selected beam subset Υ. Thus, the beam-selection problem can be formulated as:

$$\begin{array}{*{20}l} (P1) &\max\,\, B \times E \bigg\{ \sum_{i \in \Upsilon} \log_{2} (1+\text{SINR}_{i}) \bigg\} \\ & \begin{array}{r@{\quad}r@{}l@{\quad}l} \mathrm{s.t.}& \\ & \Upsilon \subset \Omega \\ & \sum_{i \in \Upsilon}^{} {\|{\boldsymbol{w}_{i}}\|^{2}} \leq P \\ \end{array} \end{array} $$

((9))

The greedy and discrete stochastic iterative algorithms are commonly used for beam-selection process [49, 50]. However, the greedy algorithm needs to search all possible beam subsets exhaustively, thus leading to high computational complexity. While the discrete iterative algorithm starts by selecting all beams and then performs set reduction. It may result in redundant beams in the selected subset.

Thus, we propose a beam-selection procedure that selects both active subset size and active receive antenna indices with respect to the regular and predictive location of the train to resolve the problem. Let Ω denote the candidate beam subset and Υ denote the selected beam subset. C _temp is the maximum system throughput. The proposed procedure is illustrated as follows. Firstly, the single beam with the highest capacity is selected as the initial maximum throughput. And the beam index of the highest capacity is obtained as the initial selected beam subset. Secondly, the beam to maximize the throughput together with the selected beams is found. Then, the algorithm replaces the maximum throughput and updates the selected beam subset. It is terminated when all beams are selected or the throughput drops when more beams are selected. Finally, the algorithm outputs the maximum system throughput and the selected beam subset. The detailed steps are listed in Table 1.

3.2 Conventional massive MIMO scheme

The proposed scheme described in the previous section is based on the massive MIMO technology for 5G. Therefore, the performance of the conventional massive MIMO is used as a benchmark to compare with other techniques. Different from the proposed scheme, conventional massive MIMO activates all transmit/receive antennas simultaneously at transmission and only gets multiplexing gain of the system. The throughput can be expressed as [17, 51]

$$ {\footnotesize{\begin{aligned} {}C_{\text{MIMO}} &= E_{\boldsymbol{H}} \left\{ B \log_{2} \det \bigg(\boldsymbol{I}_{N_{R}} + \frac{P \boldsymbol{\beta} \boldsymbol{H} \boldsymbol{H}^{H}}{N_{T} {\sigma_{n}^{2}}} \bigg) \right\} \\ &= E \left\{ \sum_{i=1}^{N_{R}}{B \log_{2} \left(1 + \frac{P \beta_{i} \boldsymbol{h}_{i} \boldsymbol{h}_{i}^{H}}{N_{T} {\sigma_{n}^{2}}} \right)} \right\} \\ &= B N_{R} \!\times \!E\!\! \left\{\! \log_{2}\!\left(\!\!1\! +\! \frac{P \beta_{i} \sum_{j=1}^{N_{T}}{{\alpha_{i}^{2}}\! \exp{\left(\!\frac{I4 \pi d_{i}}{\lambda_{c}}\,-\,I 4 \pi (j-1) \Delta_{t} \cos{\phi_{i}}\!\right)}} }{N_{T} {\sigma_{n}^{2}}}\!\right)\!\right\} \end{aligned}}} $$

((10))

where $\boldsymbol {I}_{N_{R}}$ is the N _R ×N _R identity matrix, $\boldsymbol {\beta } = \text {diag}{\left [\beta _{1},\beta _{2},\cdots,\beta _{N_{R}}\right ]} \in \mathbb {C}^{N_{R} \times N_{R}}$ is diagonal matrix, and det[ ·] denotes the matrix determinant.

4 Numerical results

The HSR scenario depicted in Fig. 1 is constructed to verify the performance analysis in the previous section. The performance of the proposed scheme is compared to single/dual-stream beamforming and conventional massive MIMO. The detailed values of simulation parameters are listed in Table 1 [45, 52].

Figure 3 illustrates the throughputs of the single/dual-stream beamforming, conventional massive MIMO, and proposed scheme with a different distance between the BS and train as Δ _t =0.5, N _T =1024. For single-stream beamforming, the N _R th receive antenna is activated. Furthermore, for dual-stream beamforming, both the first and N _R th receive antennas are activated. In contrast to the single/dual-stream beamforming, the throughput of the conventional massive MIMO is strongly influenced by the location of the train and decreased rapidly when the distance between the BS and train increases. This is because the HSR scenario with the dominance of LOS and few scatters has restricted the multiplexing gain of the MIMO channel. Whereas, the advantages of single/dual-stream beamforming are validated in the LOS environment. The throughputs of single/dual-stream beamforming decrease gradually and do not change drastically, when the distance between the BS and train increases. Meanwhile, the performance of dual-stream beamforming is worse than single-stream beamforming when the influence of IBI becomes more significant as the distance between the BS and train is larger than 570 m. The proposed scheme adjusts the active subset size and active receive antenna indices adaptively with respect to the location of the train. More beams are activated when the train is close to the BS, and fewer beams are activated to reduce IBI when the train is far from the BS. Thus, for the proposed scheme, the maximum throughput has been achieved.

Fig. 3

Throughputs of different schemes

Both the throughput and number of active (selected) beams of the proposed scheme are charted in Fig. 4 with a different distance between the BS and train as Δ _t =0.5, N _T =1024. It is shown that the optimal number of active beams decreases and degenerates to single-stream beamforming finally when the train travels from the cell center to cell edge and changes periodically when the train travels through the cells. Besides, we also find that the throughput is not proportional to, but a nonlinear function of, the number of active beams, which is bottlenecked by IBI. Obviously, the proposed scheme designed in Section 3 maximizes the system throughput.

Fig. 4

Throughput and number of active beams

5 Conclusions

The typical terrain for the HSR scenario is the viaduct in which exists a dominant LOS component. Therefore, the benefit of multiple antenna gain is hardly harvested, and that is one of the challenges for massive MIMO applied under HSR scenario. Although beamforming can form a signal beam towards the given direction which is better than MIMO in a strong LOS environment, the IBI problem of multi-stream beamforming is not yet mitigated. Thus, to maximize the throughput, a massive MIMO-based adaptive multi-stream beamforming scheme is proposed, which selects the active subset size and active receive antenna indices adaptively by exploiting the regular and predictive location information of the train. Numerical results also show that the throughput is not proportional to, but a nonlinear function of, the number of active beams, which is bottlenecked by IBI. Hence, the adaptive beam-selection design is needed in this scenario. Our future work will focus on further research on beam-selection procedure and design a massive MIMO-based multi-stream beamforming scheme for uplink transmission.