Mode Division Multiplexing Communication Using ... - IEEE Xplore

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 16, NO. 2, FEBRUARY 2017

Mode Division Multiplexing Communication Using Microwave Orbital Angular Momentum: An Experimental Study Weite Zhang, Shilie Zheng, Xiaonan Hui, Ruofan Dong, Xiaofeng Jin, Hao Chi, and Xianmin Zhang Abstract— Mode division multiplexing (MDM) using orbital angular momentum (OAM) is a recently developed physical layer transmission technique, which has obtained intensive interest among optics, millimeter-wave, and radio frequency due to its capability to enhance communication capacity while retaining an ultra-low receiver complexity. In this paper, the system model based on OAM-MDM is mathematically analyzed and it is theoretically concluded that such system architecture can bring a vast reduction in receiver complexity without capacity penalty compared with conventional line-of-sight multiple-inmultiple-out systems under the same physical constraint. Furthermore, a 4×4 OAM-MDM communication experiment adopting a pair of easily realized Cassegrain reflector antennas capable of multiplexing/demultiplexing four orthogonal OAM modes of l = −3, −2, +2, and +3 is carried out at a microwave frequency of 10 GHz. The experimental results show high spectral efficiency as well as low receiver complexity. Index Terms— Mode division multiplexing (MDM), orbital angular momentum (OAM), low receiver complexity, high spectral efficiency, microwave communication.

I. I NTRODUCTION URING the last decade, spatial division multiplexing (SDM) using conventional multiple-in-multipleout (MIMO) technique which exploit multiple-antenna at either the transmitter, the receiver, or both, to increase the data rates without additional spectrum utilization for wireless communication systems has received an upsurge of research interest both in academic and industry [1]. Recently, another solution to SDM using a set of mutually orthogonal spatial modes, known as mode division multiplexing (MDM), has been proposed, in which each spatially overlapping and coaxially propagating mode at the same carrier frequency can carry an independent data stream, thereby increasing the capacity and spectral efficiency linearly with the number of modes used. There are many different types of orthogonal modal basis sets which would be potential candidates for MDM systems, one of which is orbital angular momentum (OAM) modes [2], [3].

D

Manuscript received July 4, 2016; revised October 17, 2016 and December 5, 2016; accepted December 20, 2016. Date of publication December 26, 2016; date of current version February 9, 2017. This work was supported by the National Basic Research Program of China (973 Program) under Grant 2014CB340005 and in part by the National Natural Science Foundation of China under Grant 61371030 and Grant 61571391. The associate editor coordinating the review of this paper and approving it for publication was M. Uysal. The authors are with the College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310027, China (e-mail: [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/TWC.2016.2645199

Different from the spin angular momentum (SAM) determining the polarization states of electromagnetic (EM) field, OAM indicates the spatial distribution of EM field, namely, the helical phase front of e− j lϕ , in which ϕ is the transverse azimuthal angle and l is the OAM mode number, being an arbitrary integer [4]. Due to the helical phase structure, an OAM-carrying wave (for non-zero l) has a doughnut-shape radiation pattern with a phase undefined area at the pattern centre where the intensity of EM field vanishes. From the viewpoint of channel spatial multiplexing in a line-of-sight (LOS) scenario, solely taking the achievable capacity into consideration, an OAM-MDM system would be equivalent to conventional MIMO system with the same transceiver aperture size of D [5], [6], which means that for 2 a transmission distance below the Rayleigh distance of 2D λ , λ being wavelength of the operating frequency, both OAMMDM and LOS MIMO system would achieve a near maximum capacity gain compared to a single-in-single-out (SISO) system. However, in spite of the equivalent capacity gain, the practical implementations of these two SDM systems are totally different, giving rise to several crucial OAM-aided advantages compared with conventional LOS MIMO solutions. In MIMO, communication systems suffer from high inter-channel interference (ICI) which is imposed by simultaneously transmitting multiple data streams and an algorithm via digital signal processing (DSP) for counter-acting the ICI is required at receiver [7], [8]. While in OAM-MDM, a set of mutually orthogonal spatial modes, namely the coaxially propagating OAM-carrying waves with different mode numbers, are exploited, the mode multiplexing/demultiplexing is simply realized by the OAM-antennas with phase-shift network (PSN) which are passive devices [9]–[16]. Therefore, receiver ICI would be completely circumvented in an OAM-MDM system, resulting in a vast reduction in receiver computational complexity (CC). Additionally, the stringent inter-antenna synchronization which represents the baseline assumption of space-time and delay-diversity encoded methods could be avoided by introducing OAM mode as data carrier. Motivated by the distinguishable features above, OAM-MDM has become a fundamentally new physical layer transmission technique, which can also be combined with the conventional multiplexing in time, polarization, and frequency to achieve a communication system of high data rates as well as a low receiver CC, in optics [17]–[21], millimeter-wave (mm-wave) [22]–[24] and radio frequency (RF) [11], [13], [25], [26]. Especially, mm-wave OAM-MDM technologies would have potential

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ZHANG et al.: MODE DIVISION MULTIPLEXING COMMUNICATION USING MICROWAVE ORBITAL ANGULAR MOMENTUM

applications in various areas, such as short-range backhaul links with virtually unlimited bandwidth and data centre where large bandwidth links between large-scale computer clusters are required, with a low system-implementation complexity [23], [27]–[29]. The rest of the paper is organized as follows: In Section 2, a general system model based on OAM-MDM is described and compared with conventional LOS MIMO system mainly through the analysis of channel characteristic, receiver CC and communication capacity. In Section 3, a 4 × 4 OAM-MDM link operated at a microwave frequency of 10 GHz is experimentally demonstrated to quadruple the spectral efficiency while keeping a low receiver CC. To our best knowledge, it is the first experiment report adopting one pair of identical OAM-antennas with simply structured PSN to realize simultaneously multiplexing/demultiplexing of no less than four OAM modes. Finally, a brief conclusion is drawn in Section 4. II. OAM-MDM C OMMUNICATION C OMPARED W ITH C ONVENTIONAL LOS-MIMO S OLUTION A. Channel Characteristic We commence by the OAM-carrying field radiated from the widely adopted uniform circular array (UCA) because such system is simple but sufficient enough to study the general characteristics of OAM-MDM communication systems [2], [3]. The electric field at a receiving point of (ρ, ϕ, z) in cylindrical coordinates can be described as √ k Dρ α0 j l 2 2 e− j k ρ +z e− j lϕ Jl El (ρ, ϕ, z) = 2 2 2 2 ρ +z 2 ρ +z = Al (ρ, z) e− j lϕ

(1)

where l is the OAM mode number; α0 contains all relevant constants associated with transmitting antenna configuration; k is wave number of the carrier frequency; D is the transmitter aperture size; Jl (x) is the Bessel function of the first kind of order l; and ρ, ϕ, and z correspond to the radial position, the transverse azimuthal angle, and the transmission distance, respectively, in cylindrical coordinates. Consider any two OAM-carrying waves with mode numbers of l1 and l2 , respectively, El1 (ρ, ϕ, z) = Al1 (ρ, z) e− j l1 ϕ (2) El2 (ρ, ϕ, z) = Al2 (ρ, z) e− j l2 ϕ The inter-modal orthogonality can be simply proved by 2π 0

0 if l1 = l2 El1 El∗2 dϕ = ∗ Al1 Al2 if l1 = l2

(3)

which theoretically indicates that OAM-carrying waves with different mode numbers are mutually orthogonal and can be used as independent carriers for simultaneously transmitting multiple spatially overlapped data streams without inducing ICI at receiver. Fig. 1 depicts a paradigm of a free-space wireless communication based on OAM-MDM, in which a pair of

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Fig. 1. A general system model for a N × N OAM-MDM wireless communication system using N different OAM modes. xi and yi correspond to the transmitted and received complex symbol in OAM channel of li , respectively, i = 1, 2, · · · , N − 1, N .

identical OAM-antennas capable of simultaneously multiplexing/demultiplexing N coaxially propagating OAM-carrying waves with different mode numbers of li , i = 1, 2, · · · , and N, are installed at the transmitter and receiver end, respectively; x i corresponds to the complex M-QAM modulated symbol carried by OAM mode of li ; and yi is the received complex symbol from OAM mode of li . Due to the inter-modal orthogonality described in Eq. (3), the channel matrix of such an N × N OAM-MDM system would be ⎤ ⎡ h 11 0 ··· 0 ⎢ 0 h 22 · · · 0 ⎥ ⎥ ⎢ HOAM = ⎢ . (4) . .. ⎥ .. .. ⎣ .. . . ⎦ 0

0

···

h N×N

N×N

where HOAM ∈ C N×N is a diagonal matrix with its i th diagonal element denoted as h ii , indicating the transmission gain of the i th OAM channel of li . Consider typical OAM antennas with a continuous receiver aperture, for example the OAM generation by the plane/spiral phase plate and the helicoidal parabolic antenna, given an aperture size of D, the channel response of h ii can be calculated by h ii =

Eli (e

(e− j li ϕ )∗

) d S

D/2

− j li ϕ ∗

=D

= 2π

Ali (ρ, z)ρdρ

(5)

0

denotes the OAM mode demultiplexing realwhere ized by passive PSN at the receiver OAM-antenna, (·)∗ being the conjugation operation. Based on Eq. (5), we show in Fig. 2 the free-space transmission gain, namely, |h ii |2 , for OAM channels of |li | = 0, 1, 2, 3 and 4, respectively, as a function of the transmission distance z ranging from 0.1 to 100 times the Rayleigh distance 2 (z R = 2D λ ) with D set to 20λ. As anticipated, the transmission gain of OAM channel li asymptotically tends to straight lines with slope of −20(|li | + 1), satisfying an attenuation of ( 4πλ z )2(|li |+1) , in far-field [30], [31], which would be attributed to the doughnut radiation pattern of OAM-carrying wave and more obvious divergence of the OAM-carrying wave with a larger mode number, approximately linear |li |-scaling [32].

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Fig. 2. Calculated free-space transmission gain of |h ii |2 for OAM channels of |li | = 0, 1, 2, 3 and 4, respectively, as a function of the transmission distance 2 of z ranging from 0.1 to 100 times the Rayleigh distance of z R = 2D λ , D = 20λ being the transceiver aperture and λ being the wavelength of the operating frequency.

When it occurs to conventional LOS MIMO architecture with the same physical resource constraints, namely, the same transceiver aperture size of D and the same antenna elements of N in transmitter and receiver end, the free-space channel response from the mth transmitter element to the nth receiver − j kdnm [33], in which β0 contains all element would be β0 ednm relevant constants; k is wave number corresponding to the carrier frequency; and dnm is the transmission distance between the two antenna elements. In spite of the mutual coupling between the elements, the channel matrix of N × N MIMO system can be modeled as ⎡ − j kd11 ⎤ − j kd e e− j kd12 · · · e d1N1N d11 d12 ⎢ − j kd21 − j kd2N ⎥ e− j kd22 ⎢ e · · · e d2N ⎥ ⎢ d21 ⎥ d22 HMIMO = β0 ⎢ . (6) ⎥ .. .. .. ⎢ . ⎥ . . . . ⎣ ⎦ e− j kd N1 e− j kd N2 e− j kd N N · · · d N1 d N2 dN N

Fig. 3. Two typical system models of MIMO wireless communications. (a) and (b) are the uniform linear array (ULA) and the uniform circular array (UCA), respectively. D is the transceiver aperture, dnm is the transmission distance from mth transmitter element to the nth receiver element, and ϕ0 is a relative array rotation angle. 2

With D = 20λ and z R = 2D λ = 400λ, we obtain ICImin = −0.97 dB for a small transmission distance of z = 0.1z R . Obviously, for a larger transmission distance of z D, the ICImin would further increase and tend to 0 dB, for instance, z = z R leading to ICImin = −0.02 dB. B. Receiver Complexity The receiver CC is the total number of complex operations, including additions, multiplications, and divisions, used in the symbol recover processing at receiver. In simple mathematical term, the signal model of the above two N × N SDM system would both be y = Hx + n

N×N

which is different from the channel matrix of an OAM-MDM system described in Eq. (4), and all the elements of HMIMO ∈ C N×N are non-zero and depend on the relative positions of the transmitter and receiver elements. Hence, the LOS MIMO system will suffer from high ICI and the channel equalization algorithm via digital signal processing is necessary at receiver end for cancelling the ICI. In order to have a quantitative approximation of ICI for the LOS MIMO system, two typical kinds of system models, namely, the uniform linear array (ULA) and UCA, are considered, as shown in Fig. 3a and 3b, respectively. Either in ULA or UCA, without loss of generality, assuming that the transmitter array is in the the (x,y)-plane (for ULA, it is on the x-axis) and the receiver array is also in the (x,y)-plane while having a relative rotation angle of ϕ0 . Both the transmitter and receiver array have their centers located at the origin and the distance between the centers of the two arrays is z. Without loss of generality, assuming ϕ0 = 0, the minimum ICI, in either ULA or UCA based system model, would be 2 to the maximum d 2 , defined as the ratio of the minimum dnm nm namely, 2 D z2 = −10log10 1 + ICImin (dB) = 10log10 2 2 z +D z (7)

(8)

where x ∈ C N×1 is the complex transmitted vector; y ∈ C N×1 is the complex received vector; n ∈ C N×1 is the complex additive white Gaussian noise vector at the receiver; and H ∈ C N×N is the complex channel matrix which would be either HOAM or HMIMO . Consider the linear zero-forcing as a decoding technique for simplified analysis, the symbol recover processing at receiver would be described as ˆ −1 y xˆ = H

(9)

ˆ ∈ C N×N is equivalent channel matrix constructed where H at receiver, (·)−1 is the matrix inverse operation, and xˆ is the estimated complex transmitted vector. Therefore, one matrix reversion and one matrix multiplication are required. In conventional MIMO system with the channel matrix defined in Eq. (6), the first matrix reversion would need 2N 3 +3N 2 −5N 6

−5N complex multiplications, 2N +3N complex 6 N(N+1) additions, and complex divisions, respectively (using 2 Gaussian Elimination [34], [35]). The second matrix multiplication would take N 2 complex multiplications and N (N − 1) complex additions, respectively. Consequently, the total number of complex operations would be 3

CCMIMO =

4N 3 + 21N 2 − 13N 6

2

(10)


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UCA relating the input OAM mode of l, l = 0, 1, · · · , N − 1, (m−1)l and the output feeding √1 e− j 2π N for mth antenna, m = N 1, 2, · · · , N, functions as the discrete Fourier transform (DFT) matrix of T ∈ C N×N [2]. The (n, m)th entry of T would be

Fig. 4. Estimated receiver CC of a N × N OAM-MDM and a conventional N × N LOS MIMO system. CC: the total number of the complex operations in the symbol recover processing at receiver.

(m−1)(n−1) 1 N (12) t (n, m) = √ e− j 2π N On the other hand, the PSN2 for helical phase compensation and OAM mode demultiplexing at the receiver end can be characterized as the inverse discrete Fourier transform (IDFT) matrix T H ∈ C N×N where (·) H being the matrix conjugate transpose operation [2]. Note that the total number of the antenna elements in a UCA would limit the OAM modes that can be generated or received due to discrete sampling. For an input OAM mode of |l| > N2 , the actually excited OAM mode would be negative and equal to (l − N) [5]. Therefore, from the inputs of PSN1 to the outputs of PSN2 , the channel matrix HOAM in the OAM-MDM system can be

HOAM = T H HMIMO T

Fig. 5. System models for the UCA-based OAM-MDM and LOS MIMO communications. xl /yl : the complex transmitted/received vector to be transmitted/received in the N OAM channel, l = 1, 2, · · · , N ; PSN1 /PSN2 : the phase-shift networking (PSN) in the transmitter/receiver end for OAM modes multiplexing/demultiplexing; H: the matrix characterizing the wireless propagation channel.

While for an OAM-MDM system with a channel characteristic given in Eq. (4), it only requires N complex divisions for the first matrix inversion and N complex multiplications for the second matrix multiplication. As a result, the total number of complex operations would reduced to CCOAM = 2N

(11)

In Fig. 4, the receiver CC of OAM-MDM and conventional LOS MIMO system is compared based on Eq. (10) and Eq. (11). As anticipated, for N = 1, both these two SDM systems are reduced to a SISO system and they are equivalent to each other. While with N increasing, it is seen that the receiver CC of MIMO system is far larger than that of 2 OAM-MDM system, approximately, CCMIMO being 2N3 times of CCOAM for large N. Apparently, with the help of OAM-MDM technique, a vast reduction in CC which can be CC OAM is achieved for any N > 1. defined as 1 − CC MIMO C. Communication Capacity To achieve a fair comparison of the communication capacity, a scenario where the UCA-based OAM-MDM and LOS MIMO system with the same physical sources including the total number of transmitter/receiver antennas of N and the transmitter/receiver aperture size of D, is considered. Fig. 5 plots the system models of these two kinds of UCA-based communications. Different from the MIMO system, OAM-MDM communication would have an additional PSN attached to the transmitter/receiver UCA for OAM modes multiplexing/demultiplexing. The PSN1 in the transmitter

(13)

where HMIMO is the free-space wireless channel response of the UCA-based LOS MIMO system and is given in Eq. (6). As dnm only depends on the difference of (n − m), HMIMO is a circulant matrix [36] and can be diagonalized by the N × N unitary DFT and IDFT matrix [5], [37], HMIMO = T T H

(14)

where = di ag {λ1 , λ2 , · · · , λ N } ∈ C N×N is a diagonal matrix containing the eigenvalues of the channel matrix. Due to T H T = I N where I N is a N ×N identity matrix, substituting Eq. (14) to Eq. (13), we obtain HOAM =

(15)

According to Eq. (14) and (15), we can simply conclude that HOAM is equivalent to HMIMO due to their same eigenvalues. The nth diagonal element λn , corresponding to the transmission response of the nth subchannel in the LOS MIMO system or the OAM channel of l = n − 1 in the OAM-MDM, can be expressed as

N

β e− j krm1 − j 2π nm

0 N λn = e (16)

4π

rm1 m=1

from which we note that the integration in Eq. (5) for the OAM antennas with continuous aperture is replaced by the discrete summation when it comes to UCA-based antenna. Nonetheless, the linear |l|-scaling propagation characteristic still remains. According to Eq. (16), the information-theoretic limit to the capacity, measured in bit/s/Hz, for these two SDM system would be [38] M Pk (17) log2 1 + λ2k 2 SE = σ k=1

λ2k

where is the squares of the singular values of the channel matrix, HOAM or HMIMO , being the transmission gain of the corresponding subchannel, Pk is the power transmitted in the

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Fig. 7. (a) Measured near-field results including the phase and normalized intensity distributions of the generated OAM waves of l = −2, and −3, respectively. (b) Corresponding simulating near-field results to verify the measured results. Fig. 6. Singular values of the channel matrix, either HOAM or HMIMO , in the UCA-based system for different transmission distance z of 0.2, 0.4, 0.8, 2 1.0 and 10.0 times the Rayleigh distance of z R = 2D λ , respectively, D = 20λ being the transceiver aperture and λ being the operating wavelength. Note that λn would correspond to the transmission response of the nth subchannel in the LOS MIMO system or the OAM channel of l = n − 1 in the OAM-MDM.

mth subchannel of the channel matrix, and σ 2 is the noise variance in each receiver element. Given a fixed receiver noise variance σ 2 as well as a fixed total transmission power M Pk , the capacity is determined by M, the number of P= k=1

independent and available spatially multiplexed subchannels, and by λ2k , the gains of the subchannels. Consider the channel matrices given in Eq. (14) and Eq. (15) with N = 30, Fig. 6 shows the equivalent singular values calculated from the channel matrix, either HOAM or HMIMO , for different transmission distances z of 0.2, 0.4, 0.8, 1.0, and 10.0 times the Rayleigh distance z R , respectively. Note that λn = λ N−n , calculating λn , n ≤ N2 , is enough. The transceiver aperture D is 20λ. It is seen that there exists a large number of independent and available subchannels for the cases of z/z R = 0.2 and 0.4, while the number of independent and available subchannels become much smaller as the transmission distance z further increases to near or above z R . Therefore, it is reasonable that a near theoretical maximum capacity gain with respect to that of a SISO system is able to be obtained at a transmission distance below z R while the performance degrades at larger distances, which, undoubtedly, would be an unavoidable physical limit of any SDM-based system in a LOS free-space propagation environment [5], [6], [39], [40]. Actually, at an ultra-large transmission distance z, only one subchannel, being the OAM channel of l = 0 in the OAM-MDM system, is useful for communication, seen in the case of z/z R = 10.0, and the only gain available is the array gain. Obviously, in the OAM-MDM case which can be regarded as a hardware-realized MIMO system, the OAM modes multiplexing/ demultiplexing is simply realized by the phaseshift networks attached to transmitter/receiver end, leading to a reduction in CC in the OAM-MDM system. While in the LOS MIMO case which can be viewed as a softwarerealized MIMO system, the multiplexing/demultiplexing is achieved by the pre-/post-proccessing via DSP. In addition, the OAM multiplexing is sensitive to the antenna placement [41], and, consequently, the inter-antenna misalignment would induce a severe system performance degeneration. While this

can be avoided in the LOS MIMO system adopting the software scheme to achieve the reconfigurability. Therefore, for practical multiplexed communications, an appropriate trade-off between these two methods should be made to achieve a cost-effective solution. III. F OUR -OAM-M ODE MDM E XPERIMENT To experimentally demonstrate an OAM-MDM link, two OAM-antennas capable of simultaneously multiplexing/ demultiplxing multiple OAM modes are required. To achieve this, a pair of identical Cassegrain antennas operated at 10 GHz with the parabolic reflector aperture D of 600 mm, therefore, 2 D = 20λ and z R = 2D λ = 24 meters, is adopted in our experiment and they are placed on the transmitter-receiver LOS of 10 meters, z/z R ≈ 0.42. Each of the Cassegrain antennas is fed by two concentrically stacked radiators based on the traveling-wave ring-slot structure [42] with each radiator connected by a commercial 90◦ hybrid coupler as an easily realized PSN for generating or receiving OAM modes of ±l. Thus, a four-OAM-mode antenna capable of simultaneous generation and reception of four OAM-carrying waves is constructed. The Cassegrain antenna and the metallic radiator are both manufactured by the computerized-numerical-control machine. In this experiment, the utilized mode numbers are l = −3, −2, +2, and +3, respectively. Typical examples of the measured near-field results including the phase and intensity distributions of the OAM-carrying waves of l = −2, and −3, respectively, are presented in Fig. 7. More details about the design of the four-OAM-mode antenna can be found in [43]. A. Experimental Setup Fig. 8a gives the block diagram of the whole link, and the outdoor experimental setup of the communication system is presented in Fig. 8b. In the transmitter part, employing the orthogonal-frequency-division-multiplexing (OFDM) technique with 64 subcarriers, four independent M-QAM modulated baseband signals with a bandwidth of 40 MHz at the intermediate frequency (IF) of 800 MHz are generated by the software-defined-radio (SDR, Microsoft Research, Sora-MIMO) platform and fed to four IF ports of the mixers, respectively. Then, a 9.2 GHz continuous-wave (CW) signal is divided into four paths and fed to four local oscillator (LO) ports of the mixers, respectively, to achieve a carrier frequency of 10 GHz. Followed by passing through the power amplifiers (PAs) and the band-pass filters (BPFs), the four data


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TABLE I L INK B UDGET AND T OTAL M ODAL C ROSSTALK OF THE 4 × 4 OAM-MDM-L INK

Fig. 8. 4 × 4 OAM-MDM experimental setup with a LOS transmission distance of near 10 m. The used OAM modes are l = −3, −2, +2, and +3, respectively, the transceiver aperture size is 0.6 m, and the operating frequency is 10 GHz. (a) The schematic diagram of the 4 × 4 OAM-MDM link. (b) The outdoor experimental setup of the communication link. SDR: software-defined-radio, IF: intermediate frequency, LO: local oscillator, BPF: band-pass filter, PA: power amplifier, Tx/Rx: transmitter/receiver, LNA: low noise amplifier.

streams are fed to the four exciting ports of the transmitter antenna and modulated onto four independent OAM channels of l = −3, −2, +2, and +3, respectively. After near 10 m spree-space transmission, the four coaxially propagating data streams are demultiplexed by the receiver antenna. Then, amplified by the low noise amplifiers (LNAs) and down converted to the IF signals, four received signals are fed to the SDR platform where a second amplifying and down conversion is performed to get the digital baseband signals. Finally, the transmitted M-QAM signals are recovered adopting the linear zero-forcing and, further, the received constellations as well as raw bit-error rates (BER) performances are evaluated. B. Link Budget To characterize the link budget as well as evaluate the intermodal crosstalk of the established 4 × 4 OAM-MDM link, a 10 GHz continuous-wave signal is fed to one exciting port of the transmitter antenna and transmitted over the corresponding OAM channel while keeping all the other three channels off. Accordingly, the received power for each OAM channel is recorded at the receiver antenna after near 10 meters freespace transmission. Repeating the above measurements for all the four transmitting channels with a same feeding power of 0 dBm, a 4 × 4 power transfer matrix would be obtained and shown in Table I, from which the total crosstalk is calculated by adding the power from all other channels and dividing it by the received power of the transmitted OAM channel. For example, to calculate the crosstalk of channel l = +2, the total received power from channel l = −2, ±3 is measured and divided by the received power of channel P =2 . It is seen that the orthogonality between l = +2, namely, Pll=2 the generated OAM modes in the designed OAM-MDM system is experimentally verified as the diagonal elements of

Fig. 9. The autocorrelation with a time lag of 16 samples of the received baseband signal from the OAM channel l = +2 at a receiving SNR of 18 dB.

the measured power transfer matrix are far larger, 11.2 dB, than non-diagonal elements, and the total crosstalk of the each OAM mode is near or below −10 dB. The crosstalk would be attributed to several practical factors including imperfect OAM-carrying waves generation and inter-antenna misalignment [41], [43]. In Table I, it is noted that the transmission gains of OAM channels of |l| = 3 is near 3 dB smaller than that of OAM channels of |l| = 2, while in Fig. 2, the receiving power difference is near 10 dB for the same transmission distance, which would be mainly attributed to the different transmitting/receiving efficiency of the OAM mode of |l| = 2 and |l| = 3 caused by the antenna manufacture error and the mismatching between the separated components for constructing the dual-ring-slot radiator. To circumvent the receiving power imbalance at receiver and keep an approximately same receiving signal-to-noise ratio (SNR) for all four OAM modes, the receiving gains for the OAM channels of |l| = 3, able to be set by the SDR platform, is 3 dB higher than that for OAM modes of |l| = 2. This configuration is applied to the following 4 × 4 OAM-MDM experiment. C. Experimental Results of 4/16/32-QAM Transmission Before the data transmission, it is necessary to test the stability of the wireless propagation channel. Therefore, all the four OAM channels are turned on with the receiving SNR set as 18 dB and 50 simultaneously transmitted data frames used for the channel estimation. The pseudo-noise (PN) sequence based preambles are added at the start of each frame for synchronization. Fig. 9 shows the autocorrelation

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Fig. 11. Frequency spectrum of the received signal from OAM channel of l = +2 at a receiving SNR of 18 dB in the 4-QAM transmission.

Fig. 10. Normalized magnitude of the estimated channel matrix calculated from the 50 received signal frames. (a)-(d) correspond to the receiving OAM channels of l = +2, -2, +3, and -3, respectively.

with a time lag of 16 samples of the received baseband signal from the OAM channel of l = +2, in which the power difference between the synchronization section and the noise section is obvious guaranteeing the successful peak detection of the begin of the data section. For each frame, the channel matrix is estimated by employing the pilot-symbolaided channel estimation algorithm [44], [45]. In Fig. 10, the normalized magnitude of the estimated channel matrix is plotted. As is anticipated, |h ii |, i = 1, 2, 3, and 4, indicating the transmission gain of the OAM channel of l = +2, −2, +3, and −3, respectively, almost keeps in a stable level near to 1. Additionally, the estimated ICI defined as |h i j |, i = j , indicating the inter-OAM-channel interference, is much small than the OAM channel gain of h ii , which is consistent to the results given in Table I. As is shown in Table I, the total OAM modal crosstalk of each OAM channel is near or below a level of −10 dB, which is sufficient for establishing a reliable 4-QAM transmission link if the receiving SNR is large enough [16], [25], [46]–[49]. ˆ 4−QAM ∈ C4×4 constructed at The equivalent channel matrix H receiver for transmitted symbol retrieving would be a diagonal matrix, described as ⎤ ⎡ˆ h 11 0 0 0 ⎢ hˆ 22 0 0 ⎥ ⎥ ˆ 4−QAM = ⎢ 0 (18) H ⎣ 0 ˆ 0 ⎦ 0 h 33 0 0 0 hˆ 44 where hˆ ii corresponds to the estimated transmission gain of OAM mode of li , [l1 , l2 , l3 , l4 ] = [+2, −2, +3, −3]. Therefore, the algorithm for counter-acting the ICI at receiver is completely avoided in this case and a theoretical reduction in CC of near 91.1% compared with the corresponding LOS MIMO system, indicated in Fig. 4 at N = 4, is achieved. To analyze the spectral efficiency of the whole link, the typical of the frequency spectrum received from the OAM channel of l = +2 at a receiving SNR of 18 dB is shown in Fig. 11. The spectrum is obtained by applying the fast Fourier transformation (FFT) to the sampled baseband signal from

Fig. 12. 4-QAM transmission case with a spectral efficiency of 7.5 bit/s/Hz. (a) The typically received constellations with the measured error vector magnitude (EVM) at a receiving SNR of 18 dB for four OAM channels with sparse channel equalization. (b) The measured raw BER curves for four OAM channels with sparse channel equalization. (c) The measured raw BER curves for four OAM channels with full channel equalization.

the outputs of the 16-bit analog-to-digital converter (ADC) in the SDR platform. As is often done in the OFDM-MIMO experimental systems, the center subcarrier of the OFDM symbol is left blank to avoid the direct-current (DC) effect. Moreover, two leftmost subcarriers and one rightmost subcarrier of the OFDM symbol are left blank to circumvent the possible spectral overlap. Accordingly, the achieved spectrum efficiency of the 4-QAM transmission would be 7.5 bit/s/Hz (2 bits per symbol × 4 OAM modes × 60 64 ). Fig. 12a shows the typically received constellations with the measured error vector magnitude (EVM) at a receiving SNR of 18 dB for four OAM channels of l = −3, −2, +2, and +3, respectively, in the 4 × 4 OAM-MDM experiment. Fig. 12b gives the measured raw BER curves for the four OAM channels as a function of receiving SNR. It is seen that all the four OAM channels are able to reach a raw BER far below 3.8 × 10−3 , which is a level allowing extremely low block error rates through the application of efficient forward error correction (FEC) codes [50], indicating the robustness of the established communication link. Obviously, there exists an approximation in Eq. (18) for sparse channel equalization where the small inter-channel crosstalk indicated in Table I is considered as zero, which, however, would lead to a performance degradation in the OAM link compared to the conventional MIMO link with full channel equalization where all the elements in the estimated channel matrix are applied for data recover. To have a quantity analysis of the degradation, the measured raw BER curves as a function of receiving SNR for the four OAM channels with full channel equalization are measured and plotted in Fig. 12c. It is seen that the BER performance for the four OAM channels are slightly enhanced, and all have a similar


BER performance because the inter-channel crosstalk is nearly cancelled and only thermal noise is effective. Consequently, in practical wireless communications, it would be concluded that OAM communications with low computing complexity would suffer a little bit penalty in system performance compared to conventional MIMO communications, which can be caused by some common factors, such as, imperfect OAM modes generating/receiving and inter-antenna misalignment, in an OAM-multiplexing communication link [41], [43]. To use much more efficient digital modulation formats for higher spectral efficiency, 16/32-QAM transmissions are evaluated. Theoretically, these enhanced transmissions can be realized without receiver ICI cancelling if sufficient intermodal isolations are achieved, namely, the channel matrix remains to be a diagonal matrix. However, due to our realistic experimental conditions including imperfect OAM waves generation as well as antenna misalignment, we would seen that not all the inter-modal isolations indicated in Table I can support such enhanced modulations. For instance, an inter-modal isolation of 32.7 dB would be enough for 32-QAM transmission without the need of inter-acting of ICI at receiver, while an isolation of 11.2 dB would not be enough. There would exist an isolation level L 16/32−QAM above which an inter-modal isolation would be sufficient to guarantee a reliable BER performance for 16/32-QAM transmissions if the receiving SNR is large enough [46]–[48] and inter-modal isolations smaller than L 16/32−QAM should be considered in ˆ 16/32−QAM constructed the equivalent channel matrixes of H ˆ 16/32−QAM would no longer be at receiver. Consequently, H a diagonal matrix but a sparse matrix, leading to a relatively modest reduction in CC [51], [52]. In our experimental realization, we typically choose L 16−QAM = 15 dB for 16-QAM transmission while L 32−QAM = 20 dB for 32-QAM transmission. According to the measured inter-modal isolation which can be derived from Table I, the equivalent channel matrixes constructed at receiver for 16/32-QAM transmission are characterized in Eq. (19), and Eq. (20), respectively, ⎤ ⎡ˆ h 11 0 hˆ 13 0 ⎢ hˆ 22 0 hˆ 24 ⎥ ⎥ ˆ 16−QAM = ⎢ 0 (19) H ⎣ hˆ 31 ˆ 0 h 33 0 ⎦ 0 hˆ 42 0 hˆ 44

ˆ 32−QAM H

⎡ˆ h 11 ⎢ 0 =⎢ ⎣ hˆ 31 0

hˆ 12 hˆ 22 0 hˆ 42

hˆ 13 0 ˆh 33 0

⎤ 0 hˆ 24 ⎥ ⎥ hˆ 34 ⎦ hˆ 44

(20)

where hˆ i j corresponds to the estimated channel response from the transmitting OAM channel of l j to the receiving OAM channel of li . Fig. 13a and 13b show the typically received spectrums from the OAM channel of l = +2 at a receiving SNR of 23 dB and 26 dB for the 16-QAM and 32-QAM transmission, respectively. With a same frame structure of the 4-QAM transmission, the achieved spectrum efficiency of 16-QAM

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Fig. 13. Typically received frequency spectrum from the OAM channel of l = +2 at a receiving SNR of 23 dB and 26 dB in the 16-QAM and 32-QAM transmission experiment, respectively.

Fig. 14. Measured raw BER curves as a function of the receiving SNR for four OAM channels of l = −3, −2, +2, and +3, respectively. The achieved spectral efficiency of 16-QAM and 32-QAM transmissions is 15 bit/s/Hz and 18.75 bit/s/Hz, respectively. (a) and (b) for 16-QAM and 32QAM transmission with sparse channel equalization, respectively. (c) and (d) for 16-QAM and 32-QAM transmission with full channel equalization, respectively.

and 32-QAM transmission is 15 bit/s/Hz and 18.75 bit/s/Hz, respectively. Fig. 14a and 14b shows the measured raw BER curves for 16-QAM and 32-QAM transmission with sparse channel equalization, respectively. It is seen that four OAM channels all get a BER much low than the FEC-limit for both 16-QAM and 32-QAM transmission when the receiving SNR is sufficient. Fig. 14c and 14d shows the measured raw BER curves for 16-QAM and 32-QAM transmission with full channel equalization, respectively. The result trends are similar to the case of 4-QAM transmission and a bit performance degradation is also caused owing to the approximation in the sparse channel equalization. However, this degradation undoubtedly would be reduced to a large extent with the help of the fast development of high-performance multi-OAMmode antennas with better inter-modal isolation [9]–[16]. Fig. 15a shows the typical received constellations with the measured EVM of 16-QAM transmission at a receiving SNR of 23 dB for four OAM channels. While Fig. 15b plots the received constellations of 32-QAM transmission at a receiving SNR of 26 dB.

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instance, high security communication [53], [54], radar imaging [55], [56], and motion detection [57], [58], which, undoubtedly, would pave the way to a much wider utilization of OAM-MDM techniques. R EFERENCES

Fig. 15. Typically received constellations with the measured EVM for four OAM channels of l = −3, −2, +2, and +3, respectively. (a) for 16-QAM transmission at a receiving SNR of 23 dB; and (b) for 32-QAM transmission at a receiving SNR of 26 dB.

Fig. 16. Theoretical and experimental reduction in receiver CC for 4-QAM, 16-QAM, and 32-QAM transmission, respectively, compared with a conventional 4 × 4 LOS MIMO system. CC: the total number of the complex operations in the symbol recover processing.

Theoretically, we are able to obtain a vast reduction in receiver CC of near 91.1% in a 4 × 4 OAM-MDM system for all kinds of M-QAM modulation formats as is calculated in Fig. 4 at N = 4. However, in the realistic communication experiment, due to the imperfect inter-modal isolation, a slightly modest reduction in CC is achieved for high order M-QAM modulations including those of M = 16 and 32. Based on the equivalent channel matrixes constructed for data recover processing at receiver characterized in Eq. (19) and Eq. (20), we calculated the receiver CC of 16-QAM and 32-QAM transmission are 30 and 49, respectively (using Gaussian Elimination [34], [35]). As is shown in Fig. 16, the experimental achieved reduction in CC of 4-QAM, 16-QAM, and 32-QAM transmissions in the 4 × 4 OAM-MDM experiment are 91.1%, 66.7%, and 45.6%, respectively, compared with a conventional 4 × 4 LOS MIMO system. IV. C ONCLUSION In this paper, a general characteristics of OAM-MDM system is mathematically analyzed compared with conventional LOS MIMO solutions. Further, a multiplexed microwave communication experiment using four OAM modes is carried out to quadruple the spectral efficiency while retaining a very low receiver CC, indicating that OAM-MDM can be a promising candidate for high-capacity and low-complexity LOS MIMO implementations. Although research on OAM is still a young-born field, recent achievements based on OAM-MDM have shown many significant applications, for

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Weite Zhang received the B.S. degree in electronics science and technology from the Zhejiang University of Technology, Hangzhou, China, in 2014. He is currently pursuing the M.S. degree with the Department of Information Science and Electronic Engineering, Zhejiang University, where his research interests include microwave antennas and devices for orbital angular momentum generation, high spectrum and energy efficiency wireless communication systems, and motion detection radar using electromagnetic vortices.

Shilie Zheng received the B.S. and M.S. degrees in materials science and the Ph.D. degree in physical electronics and optoelectronics from Zhejiang University, Hangzhou, China, in 1995, 1998, and 2003, respectively. In 1998, she joined the Department of Information Science and Electronic Engineering, Zhejiang University, where she was appointed as an Associate Professor in 2005. Her current research interests include microwave photonics, twisted radio waves and applications, electrooptic detection, and fiber-optic sensors.

Xiaonan Hui received the B.S. degree from Northeastern University, Shenyang, China, in 2012. He is currently pursuing the M.S. degree in electronic science and technology with Zhejiang University, Hangzhou, China. His research interests include optical orbital angular momentum, millimeter wave vortices, and distributed fiber sensors.

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Ruofan Dong received the B.S. degree in electronic science and technology from the Huazhong University of Science and Technology, Wuhan, China, in 2015. He is currently pursuing the M.S. degree in electronic science and technology with Zhejiang University, Hangzhou, China. His research interests include twisted radio waves and applications, and millimeter wave communication.

Xiaofeng Jin received the B.S. degree in optical engineering from the Huazhong University of Science and Technology, Wuhan, China, in 1990, the M.S. degree in underwater acousto-electronics engineering from the China Ship Building Institute in 1993, and the Ph.D. degree in optical engineering from Zhejiang University, Hangzhou, China, in 1996. In 1999, he was appointed as an Associate Professor with the Department of Information and Electronic Engineering, Zhejiang University, and a Full Professor in 2006. His current research interests include microwave photonics, photonic circuits, components and modules, and smart sensing systems.

Hao Chi received the B.S. degree in applied physics from Xian Jiaotong University, Xian, China, in 1994, and the M.S. degree in optical engineering and the Ph.D. degree in electronics from Zhejiang University, Hangzhou, China, in 1997 and 2011, respectively. From 2000 to 2001, he spent a halfyear at The Hong Kong Polytechnic University, Hong Kong, as a Research Assistant. From 2001 to 2003, he was a Post-Doctoral Fellow with Shanghai Jiaotong University, Shanghai, China. From 2006 to 2008, he was a Visiting Professor with the Microwave Photonics Research Laboratory, University of Ottawa, ON, Canada. He joined the Department of Information Science and Electronic Engineering, Zhejiang University, in 2003, where he is currently a Full Professor. His research interests include optical communications and networking, microwave photonics, fiber-optic sensors, and optical signal processing. Xianmin Zhang received the B.S. and Ph.D. degrees in physical electronics and optoelectronics from Zhejiang University, Hangzhou, China, in 1987 and 1992, respectively. He was appointed as an Associate Professor of Information and Electronic Engineering with Zhejiang University in 1994 and a Full Professor in 1999. He was a Research Fellow with the University of Tokyo, Tokyo, Japan, from 1996 to 1997, and Hokkaido University, Sapporo, Japan, from 1997 to 1998. In 2007, he spent two months with the Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA, as a Visiting Research Fellow. He is currently the Chair with the Department of Information Science and Electronic Engineering, Zhejiang University. His research interests include microwave photonics, and electromagnetic wave theory and applications.