Hybrid Spatial Modulation Beamforming for mmWave Railway

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 65, NO. 12, DECEMBER 2016

9597

Hybrid Spatial Modulation Beamforming for mmWave Railway Communication Systems Yaping Cui, Xuming Fang, Senior Member, IEEE, and Li Yan

Abstract—Using higher frequency bands [e.g., millimeter wave (mmWave)] is the most effective and straightforward way to alleviate the bands scarcity at lower frequency bands (e.g., microwave) while simultaneously supporting the ever-growing data rate demands for future cellular networks. Cellular-networks-based highspeed railway (HSR) wireless communication systems also need to be evolved to satisfy the requirements of train-ground data transmission by using higher frequency bands. An essential characteristic of HSR propagation channels is the strong line of sight, which results in high channel correlation. Therefore, the conventional multiple input multiple output (MIMO, e.g., VBLAST, STBC) is less effective under the HSR scenario. Moreover, the high complexity of the conventional MIMO makes it hard to achieve multiple antenna gain. Spatial modulation (SM) is a low complexity and high spectral efficiency multiple antenna technology that has emerged in recent years. The properties of SM imply that it may be a potential technique for improving the performance of HSR wireless communication systems. In this paper, a hybrid SM beamforming scheme operating at mmWave frequency bands is proposed for future 5G HSR wireless communication systems. The proposed scheme is designed in both analog and digital domains. In digital domain, SM is used to activate antenna array (AA) indices to convey information bits. RF beams are predefined and the optimal beams are selected to transmit modulation symbols in analog domain. Theoretical analysis and numerical results indicate that the proposed scheme achieves a good compromise between performance and complexity. Multiple antenna gain, which is difficult to achieve by the conventional MIMO, can be almost achieved by the proposed scheme due to analog beamforming. Numerical results further show that the performance of the proposed scheme is not sensitive to the number of predefined RF beams, but it is to some extent sensitive to both AAs at base station and antenna elements in an AA on the train. Index Terms—5th-generation (5G) networks, hybrid beamforming, massive multiple input multiple output (MIMO), millimeter wave (mmWave), spatial modulation (SM).

I. INTRODUCTION OWER frequency bands (e.g., microwave) for cellular communication systems have been almost used up in recent years, which means that there are not enough frequency bands in the current range for future cellular networks (e.g.,

L

Manuscript received February 23, 2016; revised June 15, 2016 and September 21, 2016; accepted September 24, 2016. Date of publication September 27, 2016; date of current version December 14, 2016. This work was supported in part by the 973 Program under Grant 2012CB316100, in part by the National Natural Science Foundation of China under Grant 61471303, and in part by the Program for Development of Science and Technology of China Railway Corporation under Grant 2015X007-B. The review of this paper was coordinated by Editors of CVS TVT. (Corresponding author: X. Fang.) The authors are with the Key Laboratory of Information Coding and Transmission, School of Information Science and Technology, Southwest Jiaotong University, Chengdu 610031, China (e-mail; [email protected]; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TVT.2016.2614005

5G networks). To support high data rate demands of future cellular networks, one of the most effective and straightforward ways is to exploit higher frequency bands [e.g., millimeter wave (mmWave)] [1]. Similarly, for cellular-networks-based highspeed railway (HSR) wireless communication systems, they also need to be evolved to satisfy the requirements of train-ground data transmission, such as safety-critical railway signaling, and passengers Internet access services [2]. Thus, the higher frequency bands are also needed for use in future HSR wireless communication systems. Theoretical analysis and measured data have indicated that higher frequency bands are potential sources for future cellular communication systems [1]. However, higher frequency signals will experience orders of magnitude and more path loss than the microwave frequency signals used in current cellular communication systems. Therefore, large scale antenna arrays with beamforming must be used to combat the severe path loss of higher frequency bands. Large scale antenna arrays [AA, also known as massive multiple input multiple output (MIMO)], which use tens or even hundreds of antenna elements simultaneously serving many terminals, has emerged in the last few years [3]. As the number of transmit antennas grows without bound, the effects of uncorrelated noise and fast fading disappear, and the high degree of freedom (DoF), spectral efficiency, and antenna gain are all achieved [3], [4]. Besides, when beamforming is employed, the signal energy can be focused on a small region to improve the throughput. Nevertheless, massive MIMO will result in pilot contamination and lower energy efficiency [4]. Moreover, the effect of hardware cost (e.g., one RF chain associated with each antenna) is more severe when a massive number of transmit antennas are equipped [5]. However, the performance improvement of multiple antennas is attributed to the assumption that the fading channels are uncorrelated, which is not necessarily true for HSR wireless communication systems. As we know, at least in China, the typical terrain for HSR is viaduct [6]. The measured data and theoretical analysis have shown that the viaduct terrain may lead to a relatively clear line of sight (LOS) and few scatters, thereby resulting in strong channel correlation [6]. Therefore, multiple antenna gain may be less achieved by the conventional MIMO (e.g., VBLAST, STBC) for HSR wireless communication systems in such scenarios. Besides, the high complexity of the conventional MIMO means that multiple antenna gain is difficult to be achieved. Therefore, there is strong motivation and interest to investigate an SM-based solution to take advantage of multiple antenna gain with massive MIMO while simultaneously reduce the number of RF chains for HSR wireless communication systems.

0018-9545 © 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications standards/publications/rights/index.html for more information.

9598

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 65, NO. 12, DECEMBER 2016

The first type of solution is to use spatial modulation (SM), which exploits the spatial dimension (i.e., transmit antenna indices) as an additional dimension to convey information bits in addition to information bits conveyed through modulation symbols (e.g., PSK, QAM) during transmission [7]. In SM, the spectral efficiency is improved, the intercarrier interference is completely eliminated, and only one single RF chain is required. Thus, the implementation cost and complexity can be reduced, which implies that SM has the potential advantages compared with the conventional MIMO solution. In addition, the spectral efficiency of SM can be further improved by a massive number of transmit antennas [8]. Measured data in [9] have also shown that the performance of SM under LOS is better than that under NLOS when the transmit power is constrained as a constant. Our previous work further shows that the better performance can be achieved with an appropriate scheme in SM systems under the HSR scenario [10]. These properties imply the feasibility of SM for HSR wireless communication systems. Investigations of SM can be also found in many other literatures. In [11]–[13], the average bit error probability (ABEP) of SM was analyzed over spatial correlated Rician fading channels. The upper bound on the ABEP was also exactly obtained. In [14]–[16], several low complexity detection algorithms were proposed to reduce the exponential complexity of the maximum likelihood (ML) detector for massive SM MIMO systems. In [17]–[19], the performance of SM was analyzed using the measured data and experimental testbed. In [10], [20], and[21], the performance of SM under vehicular channels, including vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2X), and HSR propagation channels were analyzed. A general survey of the SM design framework was provided in [22]. However, the multiple antenna gain has not been fully achieved due to strong LOS under an HSR scenario. The second type of solution is to use the hybrid beamforming architecture, which consists of analog and digital domains [23], [24]. In this architecture, the sharp RF beams formed by analog beamforming are used to compensate for the severe path loss at higher frequency bands, and digital baseband precoding is performed to provide the necessary flexibility. In [23], a hybrid beamforming architecture was proposed that jointly combines RF beamforming and baseband precoding to compromise between performance and complexity. In [24], an iterative hybrid precoding algorithm for single user was proposed that exploits both the sparse and reciprocal natures of higher frequency bands, and a variant of matching pursuit was also used to provide simple solutions to the hybrid beamforming problem to approach the rates achieved by digital beamforming. In [25], a multibeam transmission diversity scheme for the single user was proposed, which is based on a hybrid beamforming architecture that combines an analog beamforming with AAs and a digital baseband precoding with multiple RF chains. Kim et al. [26] extended this architecture to the architecture with the shared AA. In this novel architecture, the AA is shared by multiple analog beams. In [27], the spatial nature of higher frequency bands was exploited to formulate the precoding/combining problem as a sparse reconstruction problem. And the principle of basis pursuit was used to develop low hardware complexity spatially sparse precoding and minimum mean square error combining. Numerical results

of the proposed algorithms accurately approximated optimal unconstrained precoders and combiners. In [28], a low complexity hybrid analog/digital precoding algorithm was proposed for multiuser massive MIMO systems leveraging the sparse nature of higher frequency bands to approach the performance of unconstrained digital beamforming. Simulation results also showed that the hybrid precoding gain was not very sensitive to RF angles quantization, which is important to have a good quantization for the digital precoding layer to maintain a reasonable precoding gain over analog-only solutions. The performance of baseband precoding in the hybrid beamforming architecture depends on the accuracy of channel estimation. Various channel estimation schemes have been proposed to obtain accurate channel estimation under high mobility scenario [29]–[31]. Therefore, we assume that the channel estimation error can be almost well compensated by other elaborate solutions. This assumption is valid because the movement of the train is regular, and the location as well as the velocity information can be predictable in HSR wireless communication systems with linear coverage topology [32]–[34]. In HSR wireless communication systems, the location and velocity of the train are strictly controlled by control systems according to the predesigned velocity–distance operation diagram. Not only the safety-critical railway signaling (e.g., train control signaling) is transmitted but also the passengers Internet access is provided [2], [35]. Therefore, the communication system part and the control system part are normally jointly designed for professional HSR. In these jointly designed systems, additional hardware will never be required to obtain the location and velocity information since the regular location and velocity information has already been generated in the control systems. The train periodically reports the location and velocity information in signaling systems, which could be used to calculate the train movement authority [35], [36]. Furthermore, the location information could be exploited to further improve the accuracy of channel estimation in communication systems [31], [37]. Although in practical systems, the regular movement of the train may be influenced by sudden emergent events, it has negligible effect on the performance since the statistical regularity of the train movement is not changed. For HSR communication systems, there are many important issues that need to be investigated, such as accurate channel modeling, frequent handover, and reliable transmission. In [38]– [41], the geometry-based stochastic model and Markov chain were used to describe and develop the nonstationary properties of HSR wireless channels. In [32], [42], and [43], location information-assisted opportunistic beamforming, adaptive antenna-activation based beamforming, and massive MIMObased adaptive multistream beamforming were proposed to improve the system performance. In [44] and[45], the handover problem was formulated as a partially observable Markov decision process. Handover decisions were made and physical layer MIMO parameters were adapted to minimize the communication latency to optimize the train control performance in communication-based train control systems. Based on the aforementioned background, a hybrid SM beamforming scheme is proposed for HSR wireless communication systems at mmWave frequency bands. It is designed in both analog and digital domains. In digital domain, SM is used to

CUI et al.: HYBRID SPATIAL MODULATION BEAMFORMING FOR MMWAVE RAILWAY COMMUNICATION SYSTEMS

Fig. 1.

System model.

choose active transmit AA indices. In analog domain, RF beams are predefined and the optimal beams are selected to transmit modulation symbols. As mentioned previously, much essential work on SM has indeed been conducted by the authors in [7], [13], [17], [18], [20], and [22]. They have provided some important conclusions on the performance of SM over different fading channels. However, our contribution is to extend the work and propose an SM-based solution by exploiting the properties of SM under HSR scenario. Then, the proposed scheme is compared with the conventional SM and full digital dual beamforming. In dual beamforming, two beam streams are used to transmit data streams to AAs mounted at both the front and rear of the train, respectively. The AAs are connected by a system bus to a central unit where received signals are processed. Theoretical analysis and numerical results indicate that the proposed scheme can achieve a good compromise between performance and complexity. Multiple antenna gain, which is difficult to achieve in the conventional MIMO, can be almost achieved by the proposed scheme. Numerical results further show that the performance of the proposed scheme is not sensitive to the number of predefined RF beams, but it is to some extent sensitive to both AAs at the base station (BS) and antenna elements in the AA on the train. The rest of this paper is organized as follows. In Section II, the system model is presented. In Section III, the proposed hybrid SM beamforming scheme is described in details, which is then compared with the conventional SM and full digital dual beamforming. The performance of the proposed scheme is analyzed in Section IV. Numerical results and discussions are given in Section V. Section VI concludes this paper by summarizing the results and suggesting some future work. Notation: Boldface capital and lowercase symbols represent matrices and column vectors, respectively. [·]∗ , [·]T , and [·]H denote conjugate, transpose, and Hermitian transpose, respectively.  · F and | · | denote the Frobenius norm and absolute value, respectively. (·)! denotes factorial. log2 (·) denotes binary logarithm. E[·] denotes expectation. I(·) is an identity matrix and C n represents the set of complex n-vector.

evenly spaced in the form of a UPA. Thus, the total number of antenna elements at the BS can be calculated as NBS = NAA NT . Similarly, NU uniform linear arrays (ULAs) AA are evenly deployed on the roof of the train. And each AA comprises NR antenna elements in the form of an ULA. Thus, the total number of antenna elements on the train can be calculated as NMS = NU NR . For the sake of simplicity, each AA with equal antenna elements and interelement spacing at the BS and the train, respectively, are assumed. And we consider the total number of antenna elements at the BS is not less than that on the train (i.e., NBS ≥ NMS ). Since ULA AAs on the train are far from each other, we assume that each ULA AA is a virtually independent user. Furthermore, we assume that each virtual user is serviced by only one RF beam transmitted by one single data stream (i.e., NU = NB = NS ), where NB and NS are the number of selected beams and transmitted data streams, respectively. For the sake of mathematical analysis, the distance between the first UPA AA at the BS and the first ULA AA on the train is denoted as d, as seen in Fig. 1. Although only downlink is considered in this paper, the proposed scheme can be extended to the uplink because multiple AAs can be deployed on the roof of the train due to its size. The information bits are divided into two parts in the proposed scheme, which is described in Section III-A in detail. The first part is used to match the transmitted AA index and the second part is used to match the modulation symbol. Then, the modulation symbol is transmitted at the active AA by the selected analog RF beam. In the proposed scheme, the AAs are exploited as an additional dimension that is different from the conventional SM. Conventionally, the transmit antenna indices are exploited as the additional dimension invoked for transmitting information bits. Thus, the sampled transmitted signal x ∈ C N T ×1 can be expressed as x = F RF s

Consider the system model of hybrid SM beamforming for HSR wireless communication systems depicted in Fig. 1. The trackside BS is equipped with uniform planar arrays (UPA), where NAA UPA AAs are spaced along a straight line on the x-axes. Each AA comprises NT antenna elements, which are

(1)

N T ×N U U where F RF = [f 1RF , f 2RF , . . . , f N is the analog RF ] ∈ C transmit beamforming weight vectors. s = [s1j,q , s2j,q , . . . , N U ×1 U T sij,q , . . . , sN is the super symbols, including j,q ] ∈ C modulation symbol of each data stream, where sij,q denotes modulation symbol sq of ith data stream transmitted by jth AA at the BS, i = 1, 2, . . . , NU , and j ∈ {1, 2, . . . , NAA }. The modulation symbol depends on the used modulation order (e.g., M -QAM). Then, the received signal ri for ith data stream with ith RF beam processed by RF receive beamforming weight vector can be expressed as

ri = II. SYSTEM MODEL

9599

√

ρi

NU 

(wnRF )H H i,j f nRF sn + (wiRF )H ni

(2)

n =1

where ρi represents the average received power, which depends on path loss [46]. wiRF is the analog receive beamforming weight vector. H i,j ∈ C N R ×N T is the channel matrix between the jth active AA at the BS and the ith virtual user (i.e., ULA AA) on the train. ni ∈ C N R ×1 are independent identically

9600

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 65, NO. 12, DECEMBER 2016

distributed (i.i.d) complex Gaussian variables with zeros mean and variance σ 2 . A geometric channel model with Li scatterers is adopted [28]. Under this model, the channel matrix H i,j can be expressed as  Li NT NR  r t H (3) H i,j = αi,l ar (φri,l , θi,l )at (φti,l , θi,l ) Li l=1

 i r αi,l = 1. φri,l (θi,l ) and where αi,l is the complex gain with Ll=1 t t φi,l (θi,l ) are azimuth (elevation) arrival and departure angles, r t respectively. The vectors ar (φri,l , θi,l ) and at (φti,l , θi,l ) are the received and transmitted array response vectors (i.e., steering vectors) at the corresponding arrival and departure angles. In this paper, two types of array geometries are used: UPA and ULA. For an N -element ULA on the x-axis, the array response vector is [27] T 1  aULA (φ) = √ 1, eI k Δ sin (φ) , . . . , eI (N −1)k Δ sin (φ) (4) N √ where I = −1, k = 2π/λ, λ is carrier wavelength, and Δ is interelement spacing. For a UPA in the xz-plan with W and H elements on the zand x-axes, respectively, the array response vector is [27] 1  aUPA (φ, θ) = √ 1, eI k Δ (m sin (φ) sin (θ )+n cos (θ )) , . . . , N T eI k Δ ((W −1) sin (φ) sin (θ )+(H −1) cos (θ ))

(5)

where 0 ≤ m ≤ W and 0 ≤ n ≤ H are the z and x indices of an antenna element, respectively, and N = W H. Analog beamforming is supposed to be used at both the BS and the train. A simple direction-of-arrival-based estimation is used [23]. Then, analog beamforming weight vectors at the BS and the train can be, respectively, expressed as f iRF

= at (φi , θi )

(6a)

wiRF

= ar (φi ).

(6b)

III. HYBRID SM BEAMFORMING SCHEME In this section, the proposed hybrid SM beamforming scheme is described, then the proposed scheme is compared with the conventional SM and full digital dual beamforming. A. Implementation of the Proposed Scheme To facilitate understanding of the proposed hybrid SM beamforming under the HSR scenario, a simple case is used in this subsection. In this case, four UPA AAs (NAA = 4) are equipped with two data streams transmission (NS = 2) at the BS, and two ULA AAs (NU = 2) are mounted at the front and rear of a train, as depicted in Fig. 2. The channel state information (CSI) is measured adaptively by using beam-dedicated reference signals whenever the beams are changed. In the proposed scheme, the BS is designed in both analog and digital domains. In digital domain, SM is used to choose the active AA index according to the information bits. In this case, NAA = 4; thus, the number of information bits conveyed

Fig. 2. Cse of hybrid SM beamforming scheme. (a) Data streams with different information bits transmission. (b) Data streams with the same information bits transmission.

TABLE I SM MAPPING Information Bits

AA Index

00 01 10 11

AA 0 AA 1 AA 2 AA 3

through the index of the active AA is log2 (NAA ) = 2. The SM mapping between information bits and transmit AA index is defined in Table I. The situation in which different information bits are conveyed through two data streams is depicted in Fig. 2(a), where AA 0 will be activated for data transmission by the first data stream 00, and AA 3 will be activated by the second data stream 11, respectively. RF chains and analog components will be connected to both AA 0 and AA 3. If the same information bits are conveyed through two data streams as depicted in Fig. 2(b), AA 0 will be activated by the same data stream 00, and all RF chains and analog components will be connected to AA 0. In analog domain, a finite number of analog RF beams that uniformly cover the beam space of their service areas are

CUI et al.: HYBRID SPATIAL MODULATION BEAMFORMING FOR MMWAVE RAILWAY COMMUNICATION SYSTEMS

predefined as a candidate beams’ set (denoted as NTBSS ), and beam indices (BIs) are used to distinguish the different RF beams [23], [25]. Then, the optimal beams are selected based on the selection metric such as capacity maximization. The number of selected beams is identical to that of data streams, i.e., every data stream is transmitted by one analog RF beam. In this case, if different AAs are activated, one RF beam is selected in AA 0 to transmit the first data stream, and the other RF beam is selected in AA 3 to transmit the second data stream, respectively, depicted in Fig. 2(a). If the same AA is activated, such as AA 0 in this case, two RF beams are selected in AA 0 to transmit the two data streams, as depicted in Fig. 2(b). As for the train, two ULA AAs are supposed to be mounted at the front and rear of the train connected by a high-speed system bus to a central unit where received signals are processed. Each AA comprises two antenna elements in the form of an ULA. Furthermore, each ULA AA is assumed as a virtually independent user, which is serviced by one RF beam, and each RF beam transmits one single data stream. Then, the received signals are combined to achieve multiplexing gain. In Fig. 2(a), the ULA 0 receives the first data stream transmitted by analog RF beam from AA 0, and the ULA 1 receives the second data stream transmitted by analog RF beam from AA 3. Then, the two received data streams are converged and processed. In the conventional MIMO, all received antennas are utilized simultaneously to receive all the signals transmitted by the BS. Different from the conventional MIMO, one data stream is received through a certain ULA AA on the train in our proposed scheme, other data streams are considered as interference. Although the proposed scheme in this subsection is described using a simple case, which transmits only two data streams, it actually can be easily extended to transmit multiple data streams. However, the interbeam interference and hardware cost (e.g., one RF chain associated with each data stream) will become severer as the number of data streams increases. Thus, the tradeoff between performance and hardware cost must be considered for a generalized solution.

9601

TABLE II COMPARISONS AMONG DIFFERENT SCHEMES

Multiplexing gain Beamforming gain Beam tracking Cost and complexity Flexibility

Proposed Scheme

Conventional SM

Full Digital Dual Beamforming

Yes Yes No Moderate Low

Yes No Low -

Yes Yes Yes High High

to the location of the train. The high computational complexity is of course inevitable due to beam tracking in digital dual beamforming. In the proposed scheme, a candidate RF beams’ set is predefined in the service areas. Instead of beam tracking, beam selection is required in the proposed scheme, which reduces the complexity of calculating the solution. The hardware cost and complexity mainly depend on RF chains. In full digital dual beamforming, there is one RF chain associated with each transmit antenna, which results in high cost and complexity. In the conventional SM and the proposed scheme, only one RF chain is associated with each data stream, which reduces the cost and complexity. In addition, the analog components, such as phase shifter, mixer, and power amplifier, are needed in the proposed scheme. Thus, the cost of the proposed scheme is a little bit higher than the conventional SM. The proposed scheme comprises analog domain, which implies that the flexibility is less than full digital dual beamforming. The comparisons are summarized in Table II. In the proposed scheme, baseband precoding is replaced by SM in digital domain, which highly reduces the cost and complexity. In the analog domain, RF beams are used to compensate the large path loss, which results in less flexibility than that of digital beamforming. Thus, the proposed scheme is a compromise among hardware cost, complexity, and flexibility with multiplexing gain and beamforming gain. IV. PERFORMANCE ANALYSIS

B. Comparisons Among Different SM Schemes To demonstrate the features of different SM schemes, we compare the proposed hybrid SM beamforming with the conventional SM and full digital dual beamforming. In dual beamforming, two beams are similarly used to transmit data streams to AAs mounted at both the front and rear of the train, respectively. Multiplexing gain can be obtained by all these three schemes because multiple data streams transmission can be supported by multiple RF chains in these schemes. In the proposed scheme and full digital dual beamforming, the severe path loss caused by higher frequency bands can be overcome with beamforming gain. Meanwhile, the conventional SM will suffer a severe drop in the performance because large path loss cannot be compensated. In digital dual beamforming, the better performance to the proposed scheme can be achieved because the directions of beams can be adjusted and tracked simultaneously with respect

The performance of the proposed hybrid SM beamforming is analyzed in this section using sum rate and ABEP. A. Sum Rate The mutual information for ith virtual user (i.e., ULA AA) can be expressed as [47] I(sij,q ; ri ) = He(ri ) − He(ri |sij,q )

(7)

where He(z) denotes the differential entropy of a continuous random variable z, and it can be defined as  ∞ f (z) log2 f (z)dz He(z) = − (8) −∞

where f (z) is the probability density function of random variable z.

9602

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 65, NO. 12, DECEMBER 2016

TABLE III PARAMETER SETTINGS

Then, the upper bound of achievable rate for ith virtual user can be expressed as [28], [48]  N AA 1  ρi (wiRF )H H i,j f iRF 2  Ri = log2 1 + NAA (wnRF )H H i,j f nRF 2 + σ 2 j =1

n = i

+ log2 NAA (9) where H i,j ∈ C N R ×N T is the channel matrix between the jth active UPA AA at the BS and the ith virtual user at the train. Thus, the sum rate of the system can be expressed as Rsum =

NU 

Parameters

Values

Carrier frequency Channel bandwidth Subcarrier space Total BS transmit power Interelement spacing Number of ULA at train Cell radius Distance from BS to track Train length Noise figure Thermal noise

28 GHz 500 MHz 270 kHz 46 dBm 0.5λ 2 1.2 km 30 m 200 m 7 dB −174 dBm/Hz

(10)

Ri .

i=1

where Q(x) =

B. ABEP

√1 2π

∞ x

2

exp(− t2 )dt and zi =

ρi 2

i (hi,j ef f sj,q −

ˆ

The optimum ML detector proposed in [49] is supposed to be employed to estimate the active transmit UPA AA index jˆi and the selected modulation symbol index qˆi as

hi,efj f xij, qˆ ). Thus, ABEP of the system can be expressed as P¯b = E P¯bi .

(17)

[jˆi , qˆi ] = arg max pR (ri |sij q , (wiRF )H H i,j f iRF ) j i ,q i

= arg min(ri − (wiRF )H H i,j f iRF sij,q 2F ).

(11)

j i ,q i

hi,j ef f

For the sake of mathematical analysis, = (wiRF )H H i,j is defined. Thus, (10) can be rewritten as

f iRF

[jˆi , qˆi ] = arg max pR (ri |sij q , hi,j ef f ) j i ,q i

(12)

The ABEP of the hybrid SM beamforming for ith virtual user with optimum ML detector given in (11) can be computed as [50] AA  AA    N (j, ˆj, q, qˆ) ¯i ˆ 1 P (j, j, q, qˆ) NAA M − 1 log2 (NAA M ) s

N

P¯bi ≤

N

M

M

j =1 ˆj =1 q =1 qˆ=1

(13) where N (j, ˆj, q, qˆ) is the Hamming distance between the rei, ˆj i i spective channel and symbol pairs, (hi,j eff , sj,q ) and (heff , sj, qˆ ). P¯si (j, ˆj, q, qˆ) is the average pairwise symbol error probability (APEP) for ith virtual user. The average ratio N (j, ˆj, q, qˆ)/log2 (NAA M ) is given by [51] N (j, ˆj, q, qˆ) 1 ≈ . log2 (NAA M ) 2

(14)

Substituting (14) into (13), ABEP for ith virtual user can be rewritten as AA  AA    1 P¯si (j, ˆj, q, qˆ). 2(NAA M − 1)

N

P¯bi ≤

N

M

M

(15)

j =1 ˆj =1 q =1 qˆ=1

APEP for ith virtual user can be expressed as [12] 

 P¯si (j, ˆj, q, qˆ) = EH Q( zi 2 )

In this section, the theoretical analysis presented in the previous section is validated by numerical results. Then, some challenges of the proposed scheme are discussed. A. Numerical Results

j i ,q i

i 2 = arg min(ri − hi,j ef f sj,q F ).

V. NUMERICAL RESULTS AND DISCUSSIONS

(16)

Numerical results on the performance of the proposed scheme are given and compared with the conventional SM and full digital dual beamforming. In digital dual beamforming, the simple MRT precoding is used. And in the proposed scheme, there are four antenna elements on the z- and x-axis, respectively, for each UPA AA at the BS. Furthermore, the interelement spacing of UPA AA at the BS equals to that of ULA AA at the train. In [52], the feasibility of higher frequency bands have been investigated under HSR scenario. Thus, we use mmWave frequency bands in our numerical studies. The value of carrier frequency is set to 28 GHz. Besides, LTE standard is taken as a baseline to evaluate the performance of the proposed scheme. The detailed values of parameters are listed in Table III [10], [23]. Numerical results on the performance of different schemes at the number of predefined RF beams NTBSS = 16, UPA AAs at the BS NAA = 4, and antenna elements in ULA AA on the train NR = 2 are shown in Fig. 3. Numerical results are consistent with the analysis presented in Section III-A. The proposed scheme achieves a good compromise among spectral efficiency, hardware cost, complexity, and flexibility. The BER difference between the proposed scheme and full digital dual beamforming (e.g., BER gap is 6.4% when distance is 400 m) is smaller than that between the proposed scheme and conventional SM (e.g., BER gap is 17% when distance is 400 m), as seen in Fig. 3(a), because the large path loss can be almost compensated by beamforming gain. SM is applied in digital domain of the proposed scheme, which leads to performance degradation compared to the full digital dual beamforming. The sum rate

CUI et al.: HYBRID SPATIAL MODULATION BEAMFORMING FOR MMWAVE RAILWAY COMMUNICATION SYSTEMS

9603

Fig. 3. Numerical results on the performance of different schemes. (a) Bit error rate comparison. (b) sum rate comparison.

gap between the proposed scheme and dual beamforming (e.g., 5 bit/s/Hz when distance is 400 m) is larger than the gap (e.g., 2 bit/s/Hz when distance is 400 m) between the proposed scheme and conventional SM, as seen in Fig. 3(b). The influences of NTBSS , NAA , and NR on BER performance are shown in Fig. 4. In the proposed scheme, a candidate beams’ set, which consists of a finite number of RF beams, is predefined in the service areas. Thus, the BER performance will be influenced and the fluctuation will occur due to the difference between the actual angle and the predefined angle of the selected beams, as seen in Fig. 4(a). For example, when the distance is 300 m, the BER is 0.603%, 0.007%, and 1.563% as the number of predefined RF beams is 6, 8, 10, respectively. It is apparent that the BER performance can be significantly improved by both NAA and NR with AA physical size constraint, as seen in Fig. 4(b) and (c). Moreover, the increased NR can provide more significant performance gain than NAA . For example, when the distance is 400 m, the BER of the proposed scheme is 9.8% as NAA = 8, and 0.6% as NR = 8, respectively. It results in a huge difference between them.

Fig. 4. Bit error rate of hybrid SM beamforming with different parameters. (a) Distance between BS and train d versus the number of predefined RF beams N TBSS . (b) Distance between BS and train d versus the number of AAs at BS N AA . (c) Distance between BS and train d versus the number of antenna elements on the train N R .

The influences of NTBSS , NAA , and NR on sum rate performance are shown in Fig. 5. The sum rate of the proposed scheme is not sensitive to NTBSS but to some extent is sensitive to both NAA and NR . It is also important to note that the performance improvement becomes smaller and smaller as NAA and NR increase. For example, when NR < 16, the sum rate increases

9604

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 65, NO. 12, DECEMBER 2016

B. Discussions As aforementioned in Section V-A, the BER increases and the sum rate decreases rapidly at mmWave frequency bands when the distance increases. It implies that the smaller service areas should be considered to guarantee the requirements of systems from an engineering implementation point of view. As a result, the reliability will be influenced due to high handover failure probability caused by frequent handover. Thus, some new network architectures (e.g., control and data signaling decoupled architecture) could be considered and applied in future HSR wireless communication systems. In the control and data signaling decoupled architecture, lower frequency bands are used to guarantee the reliability of the systems, while higher frequency bands are applied to enhance the performance of the systems [33], [34]. In the proposed scheme, beam tracking is turned into beam selection by using predefined RF beams’ set. Therefore, the complexity is reduced in the proposed scheme. However, in the proposed scheme, only a finite number of predefined RF beams are involved in the candidate beams’ set. It means that the BER will be influenced due to the difference between actual angles and predefined angles of the selected beams, especially when the train is not far away from the BS. Thus, the optimal numbers and directions of predefined RF beams should be investigated in our future work. In this paper, the large length of the train body is supposed, which makes it possible to deploy large scale antenna arrays on the train roof. However, the smaller and smaller gain is obtained as the number of antennas increases. Potential solutions should be explored to maximize the performance gain per antenna, such as high-rank LOS MIMO channels construction and optimal number of antennas (e.g., NR ). Moreover, we assume that channel estimation error can be almost well compensated in this paper. However, the impact of channel estimation error may also need to be evaluated. We are going to analyze the impact of performance degradation with imperfect CSI in the proposed scheme. In addition, the proposed scheme is analyzed and evaluated under the HSR scenario. It can also be extended to other intelligent transportation systems, such as vehicular communication systems (i.e., vehicle-to-roadside or vehicle-to-infrastructure). However, it is important to mention that the size of a car is much smaller than that of the train. As a result, few AAs can be mounted on the roof of a car. Furthermore, the random mobility characteristic of the car makes it difficult to predict the location, direction, and velocity. Fig. 5. Sum rate of hybrid SM beamforming with different parameters. (a) Distance between BS and train d versus the number of predefined RF beams N TBSS . (b) Distance between BS and train d versus the number of AAs at BS N AA . (c) Distance between BS and train d versus the number of antenna elements on the train N R .

linearly with NR . 0.214 bit/s/Hz gain is obtained by each antenna. When NR > 16, more and more antennas have smaller and smaller gain obtained by each antenna (e.g., 0.013 bit/s/Hz), as seen in Fig. 5(c).

VI. CONCLUSION For future 5G networks, higher frequency bands (e.g., mmWave) can be used to provide high data rates. The cellularnetworks-based HSR wireless communication systems will also need to be evolved to use higher frequency bands to support train-ground transmission. However, the characteristics of HSR propagation channels imply that multiple antenna gain is hardly to be achieved in this scenario. SM is a recently emerged multiple antenna technology, which activates only one of the transmit

CUI et al.: HYBRID SPATIAL MODULATION BEAMFORMING FOR MMWAVE RAILWAY COMMUNICATION SYSTEMS

antennas during transmission. The properties of SM make it a potential way for HSR wireless communication systems. In this paper, a hybrid SM beamforming scheme is proposed at mmWave frequency bands under the HSR scenario. Theoretical analysis and numerical results indicate that a good compromise can be achieved by the proposed scheme. Numerical results further show that the performance of the proposed scheme is not sensitive to the number of predefined RF beams, but it is to some extent sensitive to both AAs at BS and antenna elements in AA on the train. The challenges discussed in Section V-B will be our future work. REFERENCES [1] W. Roh et al., “Millimeter-wave beamforming as an enabling technology for 5G cellular communications: Theoretical feasibility and prototype results,” IEEE Commun. Mag., vol. 52, no. 2, pp. 106–113, Feb. 2014. [2] B. Ai et al., “Future railway services-oriented mobile communications network,” IEEE Commun. Mag., vol. 53, no. 10, pp. 78–85, Oct. 2015. [3] E. G. Larsson, O. Edfors, F. Tufvesson, and T. L. Marzetta, “Massive MIMO for next generation wireless systems,” IEEE Commun. Mag., vol. 52, no. 2, pp. 186–195, Feb. 2014. [4] F. Rusek et al., “Scaling up MIMO: Opportunities and challenges with very large arrays,” IEEE Signal Process. Mag., vol. 30, no. 1, pp. 40–60, Jan. 2013. [5] 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. 74–80, Feb. 2014. [6] B. H. Chen et al., “Channel characteristics in high-speed railway: A survey of channel propagation properties,” IEEE Veh. Technol. Mag., vol. 10, no. 2, pp. 67–78, Jun. 2015. [7] R. Y. Mesleh, H. Haas, S. Sinanovic, C. W. Ahn, and S. Yun, “Spatial modulation,” IEEE Trans. Veh. Technol., vol. 57, no. 4, pp. 2228–2241, Jul. 2008. [8] S. Wang, Y. Li, and J. Wang, “Multiuser detection in massive spatial modulation MIMO with low-resolution ADCs,” IEEE Trans. Wireless Commun., vol. 14, no. 4, pp. 2156–2168, Apr. 2015. [9] J. Zhang, Y. Wang, J. Zhang, and L. Ding, “Performance of spatial modulation with constant transmitted power under LOS and NLOS scenarios,” in Proc. IEEE Int. Conf. Commun., London, U.K., Jun. 2015, pp. 2750–2755. [10] Y. Cui and X. Fang, “Performance analysis of massive spatial modulation MIMO in high speed railway,” IEEE Trans. Veh. Technol., to be published, doi: 10.1109/TVT.2016.2518710. [11] M. Koca and H. Sari, “Performance of spatial modulation over correlated fading channels with channel estimation errors,” in Proc. IEEE Wireless Commun. Netw. Conf., Shanghai, China, Apr. 2013, pp. 3937–3942. [12] M. Koca and H. Sari, “Performance analysis of spatial modulation over correlated fading channels,” in Proc. IEEE Veh. Technol. Conf. Fall, Quebec City, Canada, Sep. 2012, pp. 1–5. [13] M. Di Renzo and H. Haas, “Space shift keying (SSK-) MIMO over correlated rician fading channels: Performance analysis and a new method for transmit-diversity,” IEEE Trans. Commun., vol. 59, no. 1, pp. 116–129, Jan. 2011. [14] C. Li, Y. Huang, M. Di Renzo, J. Wang, and Y. Cheng, “Low-complexity ML detection for spatial modulation MIMO with APSK constellation,” IEEE Trans. Veh. Technol., vol. 64, no. 9, pp. 4315–4321, Sep. 2015. [15] S. Wang, Y. Li, M. Zhao, and J. Wang, “Energy-efficient and lowcomplexity uplink transceiver for massive spatial modulation MIMO,” IEEE Trans. Veh. Technol., vol. 64, no. 10, pp. 4617–4632, Oct. 2015. [16] A. Garcia-Rodriguez and C. Masouros, “Low-complexity compressive sensing detection for spatial modulation in large-scale multiple access channels,” IEEE Trans. Commun., vol. 63, no. 7, pp. 2565–2579, Jul. 2015. [17] A. Younis et al., “Performance of spatial modulation using measured realworld channels,” in Proc. IEEE Veh. Technol. Conf. Fall, Las Vegas, NV, USA, Sep. 2013, pp. 1–5. [18] N. Serafimovski et al., “Practical implementation of spatial modulation,” IEEE Trans. Veh. Technol., vol. 62, no. 9, pp. 4511–4523, Nov. 2013. [19] J. Zhang, Y. Wang, L. Ding, and N. Zhang, “Bit error probability of spatial modulation over measured indoor channels,” IEEE Trans. Wireless Commun., vol. 13, no. 3, pp. 1380–1387, Mar. 2014.

9605

[20] Y. Fu et al., “A performance study of spatial modulation systems under vehicle-to-vehicle channel models,” in Proc. IEEE Veh. Technol. Conf. Spring, Seoul, South Korea, May 2014, pp. 1–5. [21] M. Zhang, X. Cheng, and L. Yang, “Differential spatial modulation in V2X,” in Proc. IEEE Eur. Conf. Antennas Propag., Lisbon, Portugal, Apr. 2015, pp. 1–5. [22] P. Yang, M. Di Renzo, Y. Xiao, S. Li, and L. Hanzo, “Design guidelines for spatial modulation,” IEEE Commun. Surveys Tut., vol. 17, no. 1, pp. 6–26, Mar. 2015. [23] T. Kim et al., “Tens of Gbps support with mmWave beamforming systems for next generation communications,” in Proc. IEEE Global Commun. Conf, Atlanta, GA, USA, Dec. 2013, pp. 3685–3690. [24] A. Alkhateeb, O. El Ayach, G. Leus, and R. W. Heath, “Hybrid precoding for millimeter wave cellular systems with partial channel knowledge,” in Proc. IEEE Inf. Theory Appl. Workshop, San Diego, CA, USA, Feb. 2013, pp. 1–5. [25] C. Kim, T. Kim, and J. Y. Seol, “Multi-beam transmission diversity with hybrid beamforming for MIMO-OFDM systems,” in Proc. IEEE Globecom Workshop, Atlanta, GA, USA, Dec. 2013, pp. 61–65. [26] C. Kim, J. Son, T. Kim, and J. Seol, “On the hybrid beamforming with shared array antenna for mmWave MIMO-OFDM systems,” in Proc. IEEE Wireless Commun. Netw. Conf., Istanbul, Turkey, April 2014, pp. 335–340. [27] O. E. Ayach, S. Rajagopal, S. Abu-Surra, Z. Pi, and R. W. Heath, “Spatially sparse precoding in millimeter wave MIMO systems,” IEEE Trans. Wireless Commun., vol. 13, no. 3, pp. 1499–1513, Mar. 2014. [28] A. Alkhateeb, G. Leus, and R. W. Heath, “Limited feedback hybrid precoding for multi-user millimeter wave systems,” IEEE Trans. Wireless Commun., vol. 14, no. 11, pp. 6481–6494, Nov. 2015. [29] N. Aboutorab, W. Hardjawana, and B. Vucetic, “A new iterative dopplerassisted channel estimation joint with parallel ICI cancellation for highmobility MIMO-OFDM systems,” IEEE Trans. Veh. Technol., vol. 61, no. 4, pp. 1577–1589, May 2012. [30] C. Jiao, Z. Zhang, H. Zhang, L. Zhu, and C. Zhong, “A sequential antennahopping scheme for high mobility MIMO communications,” in Proc. IEEE Int. Conf. Commun., London, U.K., Jun. 2015, pp. 4984–4989. [31] X. Ren, W. Chen, and M. X. Tao, “Position-Based compressed channel estimation and pilot design for high-mobility OFDM systems,” IEEE Trans. Veh. Technol., vol. 64, no. 5, pp. 1918–1929, May 2015. [32] M. Cheng and X. Fang, “Location information-assisted opportunistic beamforming in LTE system for high-speed railway,” EURASIP J. Wireless Commun. Netw., vol. 2012, no. 210, pp. 1–7, Jul. 2012. [33] L. Yan, X. Fang, and Y. Fang, “Control and data signaling decoupled architecture for railway wireless networks,” IEEE Wireless Commun., vol. 22, no. 1, pp. 103–111, Feb. 2015. [34] H. Song, X. Fang, and L. Yan, “Handover scheme for 5G C/U plane split heterogeneous network in high-speed railway,” IEEE Trans. Veh. Technol., vol. 63, no. 9, pp. 4633–4646, Nov. 2014. [35] J. Moreno, J. Riera, L. Haro, and C. Rodriguez, “A survey on future railway radio communications services: Challenges and opportunities,” IEEE Commun. Mag., vol. 53, no. 10, pp. 62–68, Oct. 2015. [36] J. Li, L. Tian, Y. Zhou, and J. Shi, “An adaptive handover trigger scheme for wireless communications on high speed rail,” in Proc. IEEE Int. Conf. Commun., Ottawa, ON, Canada, Jun. 2012, pp. 5185–5189. [37] X. Ren, M. Tao, and W. Chen, “Compressed channel estimation with position-based ICI elimination for high-mobility SIMO-OFDM systems,” IEEE Trans. Veh. Technol., vol. 65, no. 8, pp. 6204–6216, Aug. 2016. [38] R. He et al., “A measurement-based stochastic model for high-speed railway channels,” IEEE Trans. Intell. Transp. Syst., vol. 16, no. 3, pp. 1120–1135, Jun. 2015. [39] A. Ghazal, C. Wang, B. Ai, D. Yuan, and H. Haas, “A nonstationary wideband MIMO channel model for high-mobility intelligent transportation systems,” IEEE Trans. Intell. Transp. Syst., vol. 16, no. 2, pp. 885–897, Apr. 2015. [40] L. Liu, C. Tao, R. Sun, H. Chen, and Z. Lin, “Non-stationary channel characterization for high-speed railway under viaduct scenarios,” China Sci. Bull., vol. 59, no. 35, pp. 4988–4998, Dec. 2014. [41] L. Liu, C. Tao, R. Sun, H. Chen, and Z. Lin, “Markov chain based channel characterization for high speed railway in viaduct scenarios,” in Proc. IEEE Int. Conf. Commun., Sydney, NSW, Australia, Jun. 2014, pp. 5896– 5901. [42] M. Cheng, S. Yang, and X. Fang, “Adaptive antenna-activation based beamforming for large-scale MIMO communication systems of high speed railway,” China Commun., vol. 13, no. 9, pp. 12–23, Sep. 2016.

9606

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 65, NO. 12, DECEMBER 2016

[43] Y. Cui and X. Fang, “A massive MIMO-based adaptive multi-stream beamforming scheme for high-speed railway,” EURASIP J. Wireless Commun. Netw., vol. 2015, no. 259, pp. 1–8, Dec. 2015. [44] L. Zhu, F. R. Yu, B. Ning, and T. Tang, “Handoff performance improvements in MIMO-enabled communication-based train control systems,” IEEE Trans. Intell. Transp. Syst., vol. 13, no. 2, pp. 582–593, Jun. 2012. [45] L. Zhu, F. R. Yu, B. Ning, and T. Tang, “Cross-layer handoff design in MIMO-enabled WLANs for communication-based train control (CBTC) systems,” IEEE J. Sel. Areas Commun., vol. 30, no. 4, pp. 719–728, May 2012. [46] M. R. Akdeniz et al., “Millimeter wave channel modeling and cellular capacity evaluation,” IEEE J. Sel. Areas Commun., vol. 32, no. 6, pp. 1164–1179, Jun. 2014. [47] E. Telatar, “Capacity of multi-antenna Gaussian channels,” Eur. Trans. Telecommun., vol. 10, no. 6, pp. 585–595, Nov./Dec. 1999. [48] R. Rajashekar, K. V. S. Hari, and L. Hanzo, “Reduced-complexity ML detection and capacity-optimized training for spatial modulation systems,” IEEE Trans. Commun., vol. 62, no. 1, pp. 112–125, Jan. 2014. [49] J. Jeganathan, A. Ghrayeb, and L. Szczecinski, “Spatial modulation: Optimal detection and performance analysis,” IEEE Commun. Lett., vol. 12, no. 8, pp. 545–547, Aug. 2008. [50] J. G. Proakis and M. Salehi, Digital Communications, 5th ed. New York, NY, USA: McGraw-Hill, 2008. [51] M. Di Renzo and H. Haas, “Performance analysis of spatial modulation,” in Proc. 5th Int. ICST Conf. Commun. Netw. China, Beijing, China, Aug. 2010, pp. 1–7. [52] J. Kim and I. Kim, “Distributed antenna system-based millimeter-wave mobile broadband communication system for high speed trains,” in Proc. IEEE Int. Conf. ICT Convergence, Jeju, South Korea, Oct. 2013, pp. 218–222.

Xuming Fang (M’00–SM’16) received the B.E. degree in electrical engineering in 1984, the M.E. degree in computer engineering in 1989, and the Ph.D. degree in communication engineering in 1999, all from Southwest Jiaotong University, Chengdu, China. In September 1984, he was a Faculty Member in the Department of Electrical Engineering, Tongji University, Shanghai, China. He then joined the Key Laboratory of Information Coding and Transmission, School of Information Science and Technology, Southwest Jiaotong University, where he has been a Professor since 2001 and the Chair of the Department of Communication Engineering since 2006. He held visiting positions with the Institute of Railway Technology, Technical University Berlin, Berlin, Germany, in 1998 and 1999 and with the Center for Advanced Telecommunication Systems and Services, University of Texas at Dallas, Richardson, TX, USA, in 2000 and 2001. He has to his credit around 200 high-quality research papers in journals and conference publications. He is the author or the coauthor of five books and textbooks. His research interests include wireless broadband access control, radio resource management, multihop relay networks, and broadband wireless access for highspeed railways. Dr. Fang is an Editor of the IEEE TRANSACTION ON VEHICULAR TECHNOLOGY, Journal of Electronics and Information, and the Chair of the IEEE Vehicular Technology Society Chengdu Chapter.

Yaping Cui was born in Henan, China, in 1986. He received the B.E. degree from PLA Information Engineering University, in 2008, and the M.E. degree from Southwest Jiaotong University, Chengdu, China, in 2011, where he is currently working toward the Ph.D. degree with the Key Laboratory of Information Coding and Transmission. His research interests include millimeter wave communications, multiple antenna technologies, and smart antennas for high-speed railways.

Li Yan received the B.E. degree in communication engineering from Southwest Jiaotong University, Chengdu, China, where she is currently working toward the Ph.D. degree with the Key Laboratory of Information Coding and Transmission, School of Information Science and Technology. Her research interests include handover, network architecture, and reliable wireless communication for high-speed railways.