1. Introduction
In recent years, the data traffic increases mainly driven by the popularity of various smart devices with heavy data usage such as internet access and video streaming services. To handle these tremendous mobile data traffic, two major 5G technologies are currently being intensely investigated: small cell and massive multiple-input multiple-output (MIMO) system. Small cell increases the system capacity by decreasing cell sizes to increase the number of line-of-sight (LOS) between transmitter (Tx) and receiver (Rx). Another key technology is massive MIMO system. Massive MIMO system comprises hundreds of antenna elements that create the sharp beams and increase the transmit diversity at Tx. Therefore, channel characteristics of both small cell and massive MIMO system are found to have high cross polarization discrimination (XPD) with lower angular spread (AS) [1] and its channel statistics over the array is changed due to its large size of the array [1],[2].
Polarization division multiple access (PDMA) using dual-polarized antennas in high XPD could increase data rate by almost double via vertically and horizontally polarized channels. Consequently, the physical array size of the PDMA with dual-polarized MIMO system can be cut in half while dual-polarized antenna supports the same degree of freedom compared to two spatially separated the single-polarized antennas. However, polarization mismatch is occurred by the random handset orientation where the use of conventional single-polarized antenna receiving the signal by only one polarization results in the power loss at the Rx. The upper bound of capacity loss due to polarization mismatch is known to be 2 bit/s/Hz [3]. To minimize capacity loss by polarization mismatch, dual-polarized antenna should be equipped at a Rx to receive signals by both vertically and horizontally polarized antennas. Therefore, it is clear that dual-polarized antenna can be the potential antenna structure for future massive MIMO system to overcome limitation of physical array size and polarization mismatching.
The several dual-polarized MIMO channel models have been proposed in previous literatures. Performance evaluation of dual-polarized MIMO system with 3rd generation partnership project (3GPP) dual-polarized MIMO channel is achieved through mixed vertically and horizontally polarized signals at mobile station (MS) [4]. The polarization diversity under Rayleigh fading environment is analyzed in [5]. The performance analysis of PDMA with polarization filtering detection is achieved where two data signals are transmitted via vertically and horizontally polarized antenna elements to different MSs at the same time [6]. However, previous PDMA technique is lack of spatial diversity at BS since only one dual-polarized antenna is installed at BS.
Afterwards, more advanced space-polarization division multiple access (SPDMA) for dual-polarized frequency division duplexing (FDD) MIMO system is introduced in [7]. The SPDMA is an extension technique of space division multiple access (SDMA) which achieves the diversity gains not only by spatial domain but also by polarization domain. This paper concludes that SPDMA outperforms conventional SDMA for the same size of array when MS fully exploiting the multiple access in both space and polarization domains.
Previously dual-polarized MIMO channel is suggested based on Ricean fading channel to evaluate performance of SPDMA in [7]. However, the realistic geometry parameters such as AS, path delay, and antenna gains would be required to evaluate the practical performance of SPDMA. Hence, geometry-based dual-polarized MIMO spatial channel model (SCM) is proposed to evaluate practical performance of SPDMA. To the best of our knowledge, this is the first study that addresses the practical performance of SPDMA through dual-polarized MIMO SCM in TDD system.
The rest of the paper is organized as follows. In section 2, description of the proposed dual-polarized SCM is presented. In section 3, SPDMA and its multi-MS scheduling algorithm are described. In section 4, performance evaluation of SPDMA is achieved compare to SDMA via two simulation scenarios; same number of antenna elements and identical array size of SDMA. Finally, section 5 summarizes the key simulation results and future extension.
2. Dual-Polarized MIMO SCM
2.1 Fundamental Concept of Proposed Dual-polarized MIMO SCM
To analyze the performance of SPDMA by downlink system-level simulation, the dual-polarized MIMO channel coefficient is proposed which considers independent vertical to vertical (VV), horizontal to vertical (VH), vertical to horizontal (HV), and horizontal to horizontal (HH) channel polarizations between a dual-polarized Tx and Rx.
The proposed dual-polarized MIMO SCM consists of S/2 co-located dual-polarized antennas (total S antenna elements) at base station (BS) and U/2 co-located dual-polarized antennas (total U antenna elements) at MS. Then, downlink received signal of the kth MS can be written as
where Hk denotes the U×S dual-polarized MIMO channel matrix of the kth MS, x is U×1 transmitted signal vector with power constraint ε[‖x‖2]≤P, and zk denotes the U×1 additive complex Gaussian noise at MS. The channel configuration of 2×2 dual-polarized MIMO at kth MS, Hk, is presented in Fig. 1 as the simplest example.
Fig. 1.2×2 dual-polarized MIMO channel
Basically, 2×2 matrix consists of four independent propagation channels between dual-polarized Tx and Rx antennas can be represented by
where each element is defined as follows.
hVV: vertical transmit and vertical receive polarization
hHV: vertical transmit and horizontal receive polarization
hVH: horizontal transmit and vertical receive polarization
hHH: horizontal transmit and horizontal receive polarization
2.2 Dual-polarized MIMO SCM
The proposed dual-polarized MIMO SCM is a geometry-based channel model that describes multipath directions of the arrival and departure angles, path delays, AS, and antenna gains between BS and MS.
As shown in Fig. 2, BS and MS are equipped with ±45˚slanted dual-polarized antennas. BS is consists of spatially separated dual-polarized antennas and equispaced at interval of on x-axis.
Fig. 2.Geometries and parameters of the proposed dual-polarized MIMO SCM
The channel matrix of proposed dual-polarized MIMO SCM is composed by U/2 co-located dual-polarized transmitting antennas (U total antenna elements) at BS and S/2 co-located dual-polarized receiving antennas (S total antenna elements) at MS. Then, (u,s)th dual-polarized MIMO channel composed of nth multipath (n = 1,…, N) and each of the N multipath component is comprised of M subpaths. Proposed dual-polarized MIMO channel is generated by N=6 and M=20 which is recommended by 3GPP [8]. The proposed dual-polarized MIMO channel between BS and MS at time t can be represented by Hu,s,n(t) as equation (3)
where
where VV, HV, VH, and HH represent independent propagation channels between dual-polarized Tx and Rx as shown as Fig. 1. Moreover, βAoD and βAoA denote angle phase due to BS and MS respectively. ψAoA represents Doppler shift term at MS and notations are listed in Table 1.
Table 1.Dual-polarized MIMO SCM notations
The first matrix of equation (3) represents independent VV, VH, HV, and HH propagation channels between Tx and Rx including XPD. XPD represents the ratio of the co-polarized to the cross-polarized average power at a Rx as follows
where XPD quantifies the extent of the polarization mismatching and simulation results in section 4 show how XPD values affect the performance of proposed MIMO systems.
The proposed channel matrix notation is indicated by the number of Rx×Tx antenna elements. Consequently, 2×2 dual-polarized MIMO channel can be extended to 2×4 dual-polarized MIMO channel by adding another 2×2 dual-polarized channel beside reference 2×2 dual-polarized MIMO channel matrix. For example, 2×4 dual-polarized MIMO SCM represents two spatially separated dual-polarized antennas at BS and one dual-polarized antenna at MS. Then, 2×4 dual-polarized MIMO channel matrix can be expressed as
where hu,s,Pu,Ps denotes the propagation channels from the sth Tx antenna element with Ps polarization to the uth Rx antenna element with Pu polarization. Furthermore, the first and second column indexes (s=1 and 2) represent the first co-located dual-polarized antenna and the third and fourth column indexes (s=3 and 4) represent the second co-located dual-polarized antenna at BS.
2.3 Single-polarized MIMO SCM
Proposed single-polarized MIMO channel matrix can be represented by vertical single-polarized antennas at BS and one co-located dual-polarized antenna at MS. Thus, the channel coefficients are simply obtained by extracting the odd column indexes from the proposed dual-polarized MIMO channel matrix. For instance, 2×4 single-polarized MIMO channel matrix, H2×4,single-pol., can be expressed by vertical single-polarized antenna terms from 2×8 channel matrix, H2×8,dual-pol., as follows
Similarly, 2×2 single-polarized MIMO channel matrix can be written by two odd column indexes as follows
In section 4, the performance of SPDMA and SDMA are evaluated by proposed dual- and single-polarized MIMO SCMs respectively.
3. MRT-based SPDMA
3.1 SPDMA vs SDMA
The concept of conventional SDMA is utilization of spatial domain by spatial multiplexing and this technique makes it possible to increase the performance by serving different MSs simultaneously in spatial domain. Afterwards, SPDMA and its codebook are proposed for dual-polarized MIMO system in [7]. As mentioned before, SPDMA is the extended technique of SDMA with extra polarization utilization while SDMA serves signals in spatial domain only. Since MRT transmit signals by along the strongest eigenmode at BS and transmitted signals are combined by maximal ratio combing at MS, SPDMA enables to maximize the performance for high XPD by transmitting two different data signals via two orthogonally polarized propagation channels.
Fig. 3 (a) and (b) represent the basic idea of signal transmission of SPDMA and SDMA respectively.
Fig. 3.Transmit configuration of (a) SPDMA and (b) SDMA
As shown as Fig. 3 (a), two signals can be transmitted by one co-located dual-polarized antenna since SPDMA utilizes not only by space domain but also by polarization domain. Therefore, dual-polarized MIMO system with SPDMA able to achieve same degrees of freedom by the same number of antenna elements but half array size compare to spatially separated single-polarized MIMO system with SDMA.
3.2 Proposed Multi-MS Scheduling Algorithm
The data symbols for the selected S MSs from total K MSs are linearly precoded by maximum ratio transmission (MRT) and transmitted signal vector can be represented as follows
where F = [f1 f2 ⋯ fS] is the S×S precoding matrix where fk is the S×1 precoding vector for the kth MS among selected S MSs and b = [b1 b2 ⋯ bS]T is the S×1 transmit symbol vector where bk is the transmit symbol for the kth MS among the selected S MSs.
ㅠThen achievable rate of the kth MS by MMSE receiver can be written as
where Hk denotes U×S dual-polarized MIMO channel of the kth MS and I represents S×S identity matrix respectively. The precoding vector of MRT of the kth MS is denoted by fk obtained as
where SVD represents the singular value decomposition. Uk, Σk, and Vk represent S×S complex unitary matrix, S×U rectangular diagonal matrix, and U×U complex unitary matrix of the kth MS, respectively.
To evaluate the performance of proposed simulation scenarios, multi-MS selection algorithm is proposed to achieve the maximum throughput with optimal MS selections in the sector. The proposed MS selection algorithm is specified as follows.
where γk denotes SINR and represents historical average SINR of kth MS to achieve proportional fair scheduling which avoids starvation for MS on bad channel conditions [8]. O represents the universal set of MSs. Stx, C, and Cmax represent the number of Tx antenna elements, throughput, and the maximum throughput of the kth MS, respectively.
According to proposed Algorithm 1, the throughput is obtained by add a MS candidate in subset Gopt. until the maximum throughput is achieved. The proposed MS selection algorithm is applied to obtain the maximum sector throughput from simulation scenarios with optimal MS selections.
3.3 TDD Operations
In traditional FDD systems, channel state information (CSI) is estimated by training pilot symbols at Rx and sent to Tx through the feedback channel. Since the pilot symbols for each transmit antenna is allocated to different time or frequency resource for the exact estimation of CSI, the FDD system with the very large number of antennas is not affordable for CSI estimation due to its dramatically increased CSI information and result in requirement of extremely large amount of radio resources. On the other hand, time division duplexing (TDD) would be more reliable technique to estimate CSI of massive MIMO system where training signal is not required and alternatively requires the channel reciprocity between forward and reverse channels. Thus, the perfect CSI and TDD system is assumed to evaluate proposed dual-polarized MIMO system with SPDMA technique.
4. Performance evaluation
4.1 Simulation Scenarios
To analyze the performance of SPDMA with dual-polarized MIMO system, the sector throughput of 4Tx/2Rx SPDMA, 4Tx/2Rx and 2Tx/2Rx SDMA are evaluated as shown in Fig. 4. 4Tx/2Rx and 2Tx/2Rx SDMA represent the same number of antenna elements and identical array size as proposed 4Tx/2Rx SPDMA. Furthermore, the sector throughput of 8Tx/2Rx SPDMA, 8Tx/2Rx SDMA, and 4Tx/2Rx SDMA are evaluated to investigate the effect of increased number of antenna elements at BS.
Fig. 4.Simulation scenarios of (a) 4Tx/2Rx SPDMA, (b) 4Tx/2Rx SDMA, and (c) 2Tx/2Rx SDMA
Aforementioned, each MS consists of one dual-polarized antenna since MMSE receiver able to decide whether MS receives one strongest signal or two combined signals after SINR calculations. Then proposed MS selection algorithm will determine best MS combinations to achieve maximum throughputs in sector. For instance, some MS will prefer to receive one strongest signals and the other MSs will prefer to receive two signals depend on channel conditions at the same time. Furthermore, MS is assumed as one co-located dual-polarized antenna for all simulation scenarios to achieve fair comparison of the performances.
Important simulation parameters are shown in Table 2. Simulation scenarios of urban macro are adapted by 3GPP [9] and evaluation of proposed simulation models are followed by [10].
Table 2.Simulation parameters
4.2 Simulation Results
In this subsection, the comparative simulation results of proposed systems are presented. Fig. 5 and Fig. 6 show the sector throughput of 4Tx/2Rx SPDMA, 2Tx/2Rx SDMA, and 4Tx/2Rx SDMA of AS 8˚ and 15˚ respectively as a function of the number of MSs.
Fig. 5.Throughput comparison of 4Tx/2Rx SDMA, 4Tx/2Rx SPDMA, and 2Tx/2Rx SDMA for urban macro with AS 8˚
Fig. 6.Throughput comparison of 4Tx/2Rx SDMA, 4Tx/2Rx SPDMA, and 2Tx/2Rx SDMA for urban macro with AS 15˚
As shown in Fig. 5 and Fig. 6, the sector throughput of 4Tx/2Rx SDMA is always slightly higher than that of 4Tx/2Rx SPDMA for every simulation results due to its less interferences between antenna elements. Nevertheless, it is notable that the proposed 4Tx/2Rx SPDMA performs very close to conventional 4Tx/2Rx SDMA by half-size array and has almost 1.6 times higher throughput gain over 2Tx/2Rx SDMA for identical array size. This is remarkable simulation results since the physical size of antenna arrays is a major obstacle to implement BS with a large number of antennas.
Fig. 7 and Fig. 8 show the sector throughput of 8Tx/2Rx SPDMA, 8Tx/2Rx SDMA, and 4Tx/2Rx SDMA of AS 8˚ and 15˚ respectively as a function of number of MS. As shown as Fig. 7 and Fig. 8, 8Tx/2Rx SDMA outperforms 8Tx/2Rx SPDMA with wider throughput gaps compared to simulation result of 4Tx/2Rx SPDMA and 4Tx/2Rx SDMA. This is because more interference arises between co-located two orthogonal antennas for larger dual-polarized antenna array. However, 8Tx/2Rx SPDMA outperforms 1.6 higher than 8Tx/2Rx SDMA. Furthermore, as shown in Fig. 5~8, the overall sector throughput of urban macro with AS 8˚ outperforms urban macro with AS 15˚ because of lower level of intra-stream interference are generated for lower angle of AS.
Fig. 7.Throughput comparison of 8Tx/2Rx SPDMA, 8Tx/2Rx SDMA, and 4Tx/2Rx SDMA for urban macro with AS 8˚
Fig. 8.Throughput comparison of 8Tx/2Rx SPDMA, 8Tx/2Rx SDMA, and 4Tx/2Rx SDMA for urban macro with AS 15˚
Additionally, simulation results from Fig. 5~8 show that sector throughput is significantly dependent on the level of XPD which affects level of antenna correlations and interference between vertically and horizontally polarized antennas at MS. The sector throughput is higher for lower XPD value when small number of MSs are existed in sector since each MS prefers to receive two uncorrelated signals simultaneously instead of receiving highly correlated two signals simultaneously. This is because lower XPD leads lower antenna correlation and interferences between vertically and horizontally polarized antennas at MS but higher XPD leads higher antenna correlation and interferences between two orthogonally polarized antennas. Therefore, each MS prefers to receive two different signals with lower correlation and interferences when small number of MSs are exist in sector.
On the other hand, sector throughput is increased for higher value of XPD as the number of MSs are increased in sector. This is because dual-polarized antennas at BS prefer to transmit two independent signals to different MSs simultaneously with high directivity (high XPD) since large number of MSs increase the probability of find MS with high directivity among MS candidates in sector. In other words, dual-polarized antenna at MS prefer to select and receive only one strongest signal with high directivity instead of receiving two signals since intra-interferences occurs when two signals are received by MS.
5. Conclusions
In this paper, SPDMA with MRT for dual-polarized MIMO system is proposed. The comparative study are conducted on SDMA and SPDMA by dual- and single-polarized MIMO systems respectively.
Simulation results show that how XPD values affect the performances of SPDMA and SDMA as the number of MS are increased. SPDMA with dual-polarized antenna MIMO system outperforms almost 1.6 times higher than SDMA with single-polarized MIMO system for identical array size. This simulation results indicate that dual-polarized MIMO system with SPDMA could be the key technology to utilize XPD and array size of massive MIMO system could be reduced by half compare to conventional single-polarized MIMO system with SDMA.
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