Massive OAM-MIMO transmission scheme for 5G networks and beyond

The combination of orbital angular momentum (OAM) and massive multiple-input multiple-output (MIMO) brings the possibility of almost inﬁnite transmission capability, which may be applied in the coming 5th generation networks and beyond. In this study, a uniform line array (ULA)-based massive OAM-MIMO scheme in a multipath scene is presented. The cumulative phase of OAM carriers and multiple reference coordinate systems relative to each transmitting antenna are used to describe the OAM-MIMO wireless channel model theoretically. The performance indices of interest including capacity, energy efﬁciency, and capacity gain are numerically investigated in detail. The results indicate that the presented ULA-based massive OAM-MIMO scheme performs better overall than a conventional MIMO scheme via enhancing the OAM multiplexing intensity, and multi-fold capacity gain can be obtained especially in the low signal-to-noise rate communications.


INTRODUCTION
The 5th generation (5G) networks and beyond are characterised by the unprecedented traffic volumes, with very different usage scenarios, huge throughput per device, and high spectrum efficiency [1]. To meet the 1000 times growth of wireless traffic, a number of key technologies were proposed, such as communication in the higher spectrum (mmWave and visible light) [2,3], ultra-dense networks [4], sparse code multiple access [5], massive multiple-input multiple-output (MIMO) [6], and orbital angular momentum (OAM) multiplexing [7]. Next-generation networks that integrate these technologies, for example, the combination of OAM and massive MIMO [8], are expected to hold the explosive growth of transmission and access.
OAM is indeed a new degree of freedom for multiple access [9]. Its huge potential in capacity enhancement has been verified in free-space optical communication [10], fibre communication [11], and mmWave communication [12] and so forth. In terms of wireless communications in lower frequencies, the first report on OAM generation via a uniform circular array (UCA) was presented in 2007 [13]. Then, many strategies for the radio OAM generation were published, including the spi-This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. © 2021 The Authors. IET Communications published by John Wiley & Sons Ltd on behalf of The Institution of Engineering and Technology ral phase plate [14], multi-arm spiral patch [15], metasurfaces [16], helical paraboloid antenna [17], annular patch antenna [18], dielectric resonator antenna [19], and so on. Another important issue is the detection and decomposition of OAM carriers, which now can be dealt with by using the entire or partial received wavefront information [20][21][22]. Powerful algorithms, for example, convolutional neural network, deployed in digital signal processer are able to provide reliable assistance for the OAM detection [23,24]. The generation and decomposition of wireless OAM carriers make it possible for the OAM-based communications in low frequencies. As a typical example, [14] shows a 32 Gbps wireless transmission rate by employing eight OAM channels. Based on these progresses, the natural next step thought by researchers is the combination of OAM and other transmission technologies like massive MIMO, namely, OAM-MIMO [8,[25][26][27], to meet the 10-100 times growth of capacity demand from 2020 to 2030 [28].
As the basis of channel matrix-based performance analysis, OAM-MIMO systems are so far mainly configured by UCA [29][30][31][32][33][34], uniform line array (ULA) [35][36][37][38], and uniform rectangular array (URA) [39]. System models of OAM-MIMO in the cases of line-of-sight (LoS) [40][41][42], non-LoS (NLoS) FIGURE 1 Uniform line array (ULA)-based massive orbital angular momentum and multiple-input multiple-output (OAM-MIMO) system in the multipath scene [38,43,44], alignment [29,45] and misalignment [33,34,44] were preliminarily analysed, which show many positive results about OAM-MIMO increasing the spectrum efficiency. However, UCA is often used as an OAM generator rather than a suitable OAM multiplexer in lots of existed reports, and such conduct misses the possible benefits of OAM multiplexing technology since only an OAM carrier works per time slot [32,41,45]. In addition, the spatial geometric phase that is merely relative to a single coordinate system of the UCAs or ULAs is misused to build the channel model in these reported OAM-MIMO systems [29,35,46]. Such a premise ignores the extreme spatial dependence of OAM fields and thus misleads the researchers to some extent.
In this study, we consider a ULA-based massive OAM-MIMO scheme in a multipath scene for future 5G applications and beyond. In our scheme, OAM antennas that are capable of producing OAM carriers independently are employed as the transmitting antennas. So the ULA is just a preferred style of OAM multiplexer in this work. In addition, the cumulative phase of OAM carriers in relation to each pair of transmitting/receiving antennas is used to replace the above-mentioned spatial geometric phase in our channel model. Then, system performances in terms of capacity, energy efficiency, and transmission gain are analysed to show some positive results on OAM enhancing the performance indices of conventional MIMO systems.

SYSTEM MODEL
The proposed ULA-based wireless massive OAM-MIMO system in a simple multipath scene is shown in Figure 1. Two ULAs are placed in parallel above the reflector with a height of h. The number of transmitting and receiving antenna are N and M , respectively. denotes the space between adjacent antennas in the ULAs, D is the distance between the facing ULAs, d mn and d ′ mn correspond to the path length from the n-th transmitting antenna T n and its image T ′ n to the m-th receiving antenna R m . L n = l 1 , … , l j , … , l Q means all OAM carriers produced by T n | n≤N . Here, l j stands for the topological charge of j-th OAM carrier generated by T n | n≤N ; Q is the total number of OAM carriers generated by T n | n≤N , which can be viewed as the criteria of OAM multiplexing intensity. OAM fields reverse their polarisation state when they encounter the reflector. Thus, the topological charge of reflective OAM wave produced by T n | N <n≤2N is −L 2N −n+1 . The coordinate systemo ′ − x ′ y ′ z ′ for the wireless OAM-MIMO system is set at the first transmitting antenna T 1 , while the reference coordinate system o − xyz is set at T n to describe correctly the OAM carriers generated by T n . The transformation between o ′ − x ′ y ′ z ′ and o − xyz can be known from the below.
The normalised channel response between arbitrary transmitting/receiving antenna pair T n − R m can be written as where k = 2 ∕ is the wavenumber, the wavelength, and the antenna gain. h MIMO mn = ( ∕4 d mn )e − jkd mn represents the transfer function in the conventional MIMO system. h OAM mn = (e jl 1 mn + ⋯ + e jl Q mn )∕ √ Q means the normalised channel response of OAM multiplexing operation. mn denotes the cumulative phase of the l-labelled OAM carrier when it arrives at R m from T n and can be calculated by where mn is the initial phase defined as the azimuth difference between T n − R m . Note that the initial phase is independent of topological charge l and propagation distance D. It depends entirely on the relative location relationship of T n − R m . Because of this feature, the initial phase can also be named as the spatial geometric phase, which is easily found in many articles [29,46]. Considering the arrangement of parallel ULAs in our model, the initial phase can be determined by Formula (4) is obtained by the rule that mn equals to zero once the projection of R m falls on the half axis of x ≥ 0; otherwise, mn takes . This is because the projection of R m will absolutely fall on the x-axis. There are no exceptions in the proposed system model.
The second term in formula (3) represents the propagation phase klD when the carrier arrives at R m from T n . It implies that different OAM carriers possess unique propagation phase. Besides, the propagation distance also affects the propagation phase. So the physical meaning of Formula (3) can be explained as both the spatial relationship and propagation effect contribute to the cumulative phase.
If we substitute Formulas (3) into (2), the transfer function between arbitrary receiving-transmitting pairs R m − T n in the ULA-based OAM-MIMO system can be obtained as Channel matrix of the ULA-based OAM-MIMO wireless transmission system now can be calculated clearly by using Formula (5). Thanks to the existence of the reflective pathd ′ mn , the dimensions of channel matrix for an M × N system is indeed M × 2N , which can be written as where h mn with n ≤ N and N < n ≤ 2N denote the transfer function from the direct path d mn and the reflective path d ′ mn , respectively. To determine the channel matrix H, the involved path length can be performed by the following formulas: and

CAPACITY AND ENERGY EFFICIENCY
When the transmitter knows channel state information, the total transmitting power will be allocated to all active transmitting antennas by the water-filling principle to pursue a higher system capacity [35]. The corresponding capacity for this case is where is the rank of channel matrix; k is the singular value of channel matrix obtained by the singular value decomposition algorithm; n is the variance of noise; p k is the sub-power allocated to the k-th transmitting antenna. For the convenience of subsequent discussions, the capacity gain of the proposed ULA-based massive OAM-MIMO scheme over the conventional MIMO scheme is defined as and snr j = P j ∕ 2 n are the signal-to-noise rate (SNR). It can be known from Formulas (9) and (10)  Similar to Formula (10), the capacity gain of multipath channel against the LoS channel is defined by The energy consumption of arbitrary transmitting antenna T n consists of two parts: The transmission power and the ohmic loss. The average transmission power and average ohmic loss of active transmitting antennas are represented by P t and P c , respectively. Then the energy efficiency of the ULA-based massive OAM-MIMO system can be performed by where B is the bandwidth, is the average efficiency of power amplifiers, N t is the amount of the active transmitting antennas, C (N t P t ) is the capacity brought by the total transmission power of N t P t . The gain of energy efficiency in the ULA-based massive OAM-MIMO scheme over the conventional MIMO scheme is defined as Meanwhile, the gain of energy efficiency in the multipath channel against the LoS channel is defined by

RESULTS AND DISCUSSIONS
The joint of OAM multiplexing technology in massive MIMO scheme will significantly affect the transmission performance of the wireless communication systems. To observe this, the main simulation parameters are set as listed in Table 1. The total transmitting power for all Q-setting system keeps the same. Of special note is that Q = 0 means OAM multiplexing technology is not included in the system and, therefore, represents the conventional massive MIMO system. Figure 2 shows how the capacity and energy efficiency of the proposed ULA-based massive OAM-MIMO system vary with the SNR over -40 to 40 dB in the multipath scene. As predicted by Shannon theorem, capacity and energy efficiency of the proposed ULA-based OAM-MIMO communication system is up to the SNR. More importantly, higher OAM multiplexing intensity (i.e. the larger Q value), leads to higher system capacity as well as energy efficiency. This observation intuitively shows that OAM multiplexing technology does bring improvements to transmission performances. Figure 3 shows the capacity gains of the proposed OAM-MIMO system with varying Q over a conventional MIMO system, that is, G OAM −MIMO and, therefore, omitted here for brevity. It can be known from Figure 3(a) that OAM multiplexing technology brings multiplicative capacity gain, especially in the low SNR scenes. For all Q > 1 cases, the capacity gain decreases and is always larger than 1 as SNR increases (or Q decreases). It indi- cates that OAM-MIMO has better anti-noise performance than MIMO. This phenomenon can be theoretically explained as follows. i and j will dominate Formula (10) in the low SNR circumstances; thus, 2 where ∝ means 'positive correlation', and F (Q) = e jl 1 ( mn +k⋅l 1 ⋅D) + ⋯ + e jl Q ( mn +k⋅l Q ⋅D) ∕ √ Q. Figure 4 shows the curve of |F (Q)| against Q, which reveals why G OAM −MIMO MIMO ∝ Qin low SNR circumstances. Figure 3(b) is the detailed comparison between Q = 0 and Q = 1. It can be observed that OAM-MIMO performs at most 0.5% worse and 0.4% better than MIMO when the number of involved sub-channels is same. The possible reason is that the spatial dependency of OAM signals results in additional reliability expenditure. LoS and ignored because of the linear relationship between system capacity and energy efficiency. As can be seen from Equation (6), the channel matrix for the multipath scene is larger than that for the LoS scene, which means the rank of former is larger than or equal to that of latter. So as shown in Figure 5, in terms of capacity or energy efficiency, OAM-MIMO systems perform better in the multipath scene than in the LoS scene. Also note that in Figure 5, the relative capacity gain G Mp LoS decreases with the Q or SNR increases. This indicates that higher Q and SNR are not good to enhance G Mp LoS , though they really bring higher capacity and energy efficiency.
Considering the distance D between two facing ULAs as the variable, Figure 6 shows the capacity of OAM-MIMO system with different Q setting in multipath scene. The main simulation parameters are same with Table 1, while the remaining are set as follows: SNR = 20 dB in Figure 6(a) and -10 dB in Figure 6(b), D = 100λ ∼ 150,000 λ, and B = 20MHz. In order to facilitate comparative observation, the illustration in Figure 6(b) shows the curves in a smaller range, that is, D = 100λ : 10,000λ. It can be seen that the capacity of the 128 × 128 ULA-based OAM-MIMO system deceases as the propagation distance D increases. Such a process occurs in small fluctuations in high SNR (Figure 6(a)) and is smooth in low SNR scenes (Figure 6(b)). The OAM multiplexing intensity (marked by Q), by comparison with D, has a much smaller effect on the system capacity. Similar results can also be found in the curves of energy efficiency according to extra simulations. This reveals that D is the more important parameter than Q in OAM-MIMO systems. Figure 7 depicts the capacity gain of OAM-MIMO system with different Q setting in the multipath scene over LoS scene, namely, G Mp LoS , versus the propagation distance D. As far as the high SNR circumstances are concerned (Figure 7(a)), G Mp LoS slightly decreases as the value of Q rises. Meanwhile, the capacity  Another principal parameter for OAM-MIMO systems is the array dimension, that is, M × N . We here consider a square array configuration featured as N × N for convenience. Major parameters in this simulation are the same with Table 1, while SNR = -20 dB, and N ranges from 10 to 510. Figure 8 shows the capacity and energy efficiency versus array dimension N of the ULA-based OAM-MIMO system with varying OAM multiplexing intensity Q. Obviously, the more transmitting/receiving antennas are deployed, the higher transmission performance can be acquired. This is consistent with the general MIMO theory [48]. Another positive result is that higher OAM multiplexing intensity Q leads to higher capacity and energy efficiency, though such enhancement effect gradually decreases as Q increases. Figure 9 shows the capacity gain versus array dimension N × N with SNR = -20 dB, in which Figure 9  Other array parameters like h and also affect the transmission performances by changing the singular values of the channel matrix. To observe the effects of h and on the capacity gain, we set them as the independent variables, respectively, in the following simulations, with the simulation parameters listed in Table 1 , corresponding to SNR = -10 dB and SNR = 20 dB. In comparison, larger capacity gain and more general trends are found in the low SNR circumstances (Figure 10(a)), while smaller capacity gain and more fluctuations appear at high SNR scenes (Figure 10 All parameters of interest and their effects on the transmission performances of the proposed ULA-based massive OAM-MIMO system are listed in Table 2 for a brief review, where '+', '-', '∧', '∨' and 'w' represent, respectively, the features of monotonically increasing, monotonically decreasing, convex, lower convex, and uneven as the corresponding parameter increases progressively. Note that an approximate global optimum may occur in the former four cases, while only some local optimal solutions appear in the 'w' case. In the actual environment, the optimisation of all major parameters should weigh different indices for which Table 2 offers a reference of value.

CONCLUSION
In summary, we proposed a ULA-based massive OAM-MIMO scheme for future 5G networks and beyond. The wireless channel model is analysed theoretically based on the cumulative phase of OAM carriers and multiple reference coordinate systems associated with each transmitting antenna. The effects of major parameters including SNR, the distance between ULAs D, the array dimension N , the height of ULAs h, the space between adjacent antennas , and the OAM multiplexing intensity Q on the transmission indices are investigated numerically in detail. Both the cases of multipath and LoS are calculated and discussed. The simulation results reveal that OAM-MIMO scheme performs much better than conventional MIMO scheme in terms of capacity, energy efficiency, and multiplicative capacity gain can be obtained by enhancing the OAM multiplexing intensity Q, especially in the low SNR wireless communications.