1

Communication
Mode Selection Method Suitable for Dual Circular Polarized OAM
Transmission
Kazunori YURI, Non-Member, Naoki HONMA and Kentaro MURATA, Member, IEEE

Abstract—This paper proposes an analog orbital angularmomentum (OAM) transmission method based on dual circularpolarization (CP), where the low-gain modes are excluded forenhancing the achievable data-rate. Two sequential arrays, eachof which has four circular microstrip antennas with dual CP,
are used at both transmitter and receiver sides, and face eachother. A discrete Fourier transform (DFT) feed network is used atboth sides to realize quasi-eigenmode transmission, where mode
orthogonalization is achieved by using just an analog circuit;digital interference cancellation is not used. The key idea ofthe proposed method is its mode selection technique, whichsimply choses some of the highest modes and distributes all
available power to the chosen modes equally. An analysis showsthat this method increases the achievable rate by 2 bits/s/Hz
compared to short-range multiple input and multiple output (SRMIMO) when the number of the ports at each side is 8 and the
distance between transmitter and receiver antennas is 10λ0 (λ0is wavelength in vacuum) or more. Also, it is found that theachievable rate of the proposed scheme is asymptotic to that of
SR-MIMO with water-filling.
Index Terms—discrete Fourier transforms (DFT), eigenmodetransmission, orbital angular momentum (OAM), dual circularpolarized wave, microstrip antenna

I. I NTRODUCTION
Recently, due to the spread of the Internet, demands forhigher data-rates continue to grow, even in wireless communication services. Orbital angular momentum (OAM) is attracting significant attention because it can, where the transmitterand receiver antennas are in line of sight (LOS), enhancethe data-rate just by increasing the number of the modes,[1] [2] [3]. The OAM scheme using array antennas can berecognized as a kind of short-range (SR) multiple-input andmultiple-output (MIMO) communication [4] [5]. A key featureof OAM is the way in which it generates modes, that is, thegenerated field distribution rotates moment by moment. Thisfeature makes the fixed analog mode generator applicable to
OAM transmission because the excitation weight can be easily
generated by using a discrete Fourier transform (DFT) feed
network [6] [7] [8]. In the analog OAM transmission scheme,
the channel between the transmitter and receiver antennas isorthogonalized by the fixed analog feed network, and the signals are transmitted in parallel without any digital interference
cancellation. In addition, we use the dual-circular polarizations
to improve the data-rate [9] [10] [11]. If the channels of thedual-circular polarizations are completely isolated, i.e., there
Kazunori YURI and Naoki HONMA are with the graduate schoolof Arts and Science, Iwate University, Morioka, 020-8551 Japan.(email:g0317155@iwate-u.ac.jp )Kentaro MURATA is with National Defense Academy, Yokosuka 239-0811,
Japan.

Fig. 1. OAM transmission scheme using circular array antennas.

is no interference between two polarizations, the data-rate canbe simply doubled.
However, the gain of the all parallel channels is not
identical, and some of the modes suffer from the serious
degradation of the channel gain. Furthermore, the imperfectchannels created by displacement of the antennas cause intermode interference and this deteriorates the data-rate. Thisdrawback cannot be overcome, even by increasing the numberof antennas.
This paper proposes a simple mode selection scheme suitable for OAM transmission with a fixed analog feed network. Several of the lowest gain channels are excluded from
OAM transmission, and all transmission power is equallydistributed to the remaining modes. This simple proceduresignificantly improves the transmission efficiency and intermode interference. Numerical simulations are performed toverify the performance of the proposed scheme, where dualcircular polarized microstrip arrays are used at both transmitterand receiver sides. In the remainder of this paper, basic explanations of OAM with array antennas and DFT feed networks
are presented for better understanding of the proposed scheme.
Also, numerical results are shown to demonstrate the validityof the proposed scheme.

II. T HEORY
A. Analog OAM transmission
This section reviews the basic idea of the analog OAM
transmission method [8] for easier understanding of themethod proposed in the next section. Figure 1 shows thesystem model of OAM transmission using array antennas. The
transmitter and receiver antennas are identical in number and2face each other. Channel matrix H is given by
h1,1 h1,2 . . . h1,N h2,1 h2,2 . . . h2,N 
H =  .
..
.. 
..
 ..
.
.
. 
=

hN,1

a1,1
a1,N

 ..
 .

hN,2
a1,2
a1,1
..
.

a1,2

...

. . . hN,N

...
a1,N
. . . a1,N −1 ..  ,
..
.
. 
a1,N
a1,1

(1)

= C.

(3)

The nth column vector (n is a positive integer up to N ) of
W N is given by,
wn 1

...

wnN −1

T,

where {·}T is transposition. wn is defined by,−j2π(n − 1).
wn = exp
N

(4)

(5)

wn is the rotation factor. For example, when N is 4, W 4 isexpressed as,
 0
e
1
e0
W4 = 

2 e0
e0

0

e

−j π
2

−jπ

e

e
e−jπ
3π
e−j 2

e

0

e0
e−jπ

OUT.2

IN. 2
0

IN.3

IN.2
IN.4

180 deg
hybridcouplers

180 deg
hybridcouplers

OUT.1

180 deg
hybridcouplers

OUT.2

PS

180 deg
hybridcouplers

IN. 2
0

IN. 3
0

Unit : rad
OUT. 1
OUT. 2
OUT. 3
OUT. 4

IN. 1
0
0
0
0

OUT.3

OUT.4
IN. 4
0

0

(2)

= WH
N HW N1
wn 0
wn = √
N

IN.2

Fig. 2. 180 degree hybrid coupler.
IN.1

where W N is a unitary DFT matrix whose number of elements
is N ; {·}H is complex conjugate transposition. C becomes a
diagonal matrix, which is written as C = diag(c1 , · · · , cN ),where ck is a complex number corresponding to the complex
amplitude of the isolated path.
By multiplying the weights, W N and W H
N , on transmitterand receiver sides, respectively, the resulting channel matrix,
H ′ , is diagonalized as,
H′

OUT.1

Unit : rad IN. 1
OUT. 10
OUT. 20where N is the number of transmitting and receiving antenna
elements. H becomes a cyclic matrix due to this configuration.
Note that the channel is assumed to be ideal, i.e. the remainderof this section assumes the perfect cyclic matrix. In this case,
the DFT matrix is completely equivalent to the eigenvector
matrix of H. Similar to singular value decomposition, thechannel can be decomposed as,
H = W N CW H
N,

IN.1

e

0



−j 3π
2 

e
.
e−jπ 
π
e−j 2

(6)

A feed network, which can generate the weight W N , isdefined as an DFT feed network in this paper. This DFT
feed network can be realized by combining 180 degree hybrid
couplers that are considered as the analog components. Figure
2 shows the 180 degree hybrid coupler and its transmission
characteristics. The 180 degree hybrid coupler equally distributes the input power to both output ports, and the output

Fig. 3. DFT feed network (N = 4).

signals of IN.1 and IN.2 ports are in-phase and anti-phase,respectively. This hybrid circuit can be easily realized by usinga rat-race circuit etc.
Figure 3 shows its DFT weight couplers and its transmission
characteristics, where N is 4. Four hybrids are combined, anda − π2 phase shifter (PS) is used as well. This configuration
generates OAM weight. For example, when the signal is input
to IN.1, the phase difference among the four output ports is 0.
When the signal is input to IN.2, the phase differences between
adjacent output ports are π2 . Note that this circuit also equallydistributes the power at any input ports among all output
ports. Although the structure of the DFT network may becomecomplex when realized, a broadband network can be realized
without an excessive increase in hardware cost because thethere are many techniques for realizing broadband hybrids,
for example, see [12] and [13]. This is a key advantageof the analog technique over digital signal processing; thecomputation complexity of the latter is proportional to thesignal bandwidth and so tends be excessive.
B. Proposed method
In this study, we use dual circular polarized waves andthe mode selection technique. At first, we describe how dual
circular polarization (CP) is incorporated into OAM transmission. The dual circular polarized waves are generated using
dual-port microstrip antennas and 90 degree hybrid couplers.
Figure 4 presents a dual-port microstrip antenna. The 90
degree hybrid couplers also distributes the input power equally,
and the phase difference among the output ports is π2 . By
using both input ports of the hybrid, both right hand (RH)
and left hand (LH) CP are simultaneously radiated; this is awell-known technique for generating dual CP. By using thistechnique, the number of the available modes can be doubled
without using digital processing.

3

that the maximum rate is achieved when all available poweris equally distributed to all remaining modes. The easiest way
to evaluate the achievable rate with several excluded modes is
explained as follows. The modes are classified by using (11)as,Ground plate
Feed ports

Patch antenna

Fig. 4. Dual-port antenna.

X sel
The transmitter and receiver are assumed to have identicalcircular array antennas, where each array element comprises
the antennas shown in Fig. 4, and the two array antennas faceeach other straight on. This configuration yields channel matrix
H, and the channel observed through the 90 degree hybrid at
both sides of the array antennas is expressed as,Hc==

W H HW 90

 90
hRR
hRL
co
x
,
hLR
hLL
x
co

(7)

LL
where hRR
co and hco is the channel matrix of RHCP and LHCP,
are the channel matrices ofand hLR
respectively, and hRLxxcross CP. W 90 is defined as,
1
I
W 90 = √
2 w90


w90
,
I

(8)

U H H cU M
 MRR
C co C RL
x
,
C LL
C LR
co
x

(9)

where I is an N × N identity matrix and w90 are diagonalπmatrices that contain e−j 2 . By multiplying the weights as per(3), the channel through the weight matrices is expressed as,
H OAM

=
=

where U M is expressed as

WN
UM =
0

0
WN



,

(10)

where M expresses the number of ports at each side of
the array, U M is a unitary matrix, and W N is definedin (6). Since N represents the total number of modes foreach polarization, M = 2N is satisfied. Note that N = 4
is assumed due to the antenna configuration dealt with in
LL
this simulation study. Ideally, C RR
co and C co are complex
diagonal matrices, but imperfect antenna arrangements yieldnon-diagonal components that cause inter-stream interference.
Ideally, C RL
and C LRare zero matrices, but they becomexx
non-zero matrices due to inter-polarization leakage in the
RLchannel matrices hLR
x and hx . This also causes inter-stream
interference. While the non-diagonal components of H OAM
cause inter-stream interference, it can be reduced by accurate
antenna arrangement and antenna elements with high crosspolarization discrimination (XPD).
Next, we will describe the mode selection method. The
diagonal elements of H OAM are given as,diag(H OAM ) = (hOAM11 , hOAM22 , · · · , hOAMmm ),(11)

where hOAMmm represents the element of matrix H OAM ,and the amplitude of the diagonal components shown in (11)corresponds to the gain of the mode. The key idea of the mode
selection proposal is excluding the weakest L modes, such={k| |hOAMkk | > |hOAMll |(l ∈/ X sel )}, (12)where l ∈/ X sel corresponds to the excluded mode index. The
SINR of k-th mode (k ∈ X sel ) is calculated by
γ(k) =


P0 
M −L

X

P0
|hOAMkk |2
M −L!

i∈X sel|hOAMki |2− |hOAMkk |2, (13)+ σn2

where P0 represents the total transmitting power and σn2
represents the noise power. From equation (13), the achievablerate of the proposed method is given by,X
log2 (1 + γ(k)).
(14)
Cprop. =k∈X selThe mode selection method determines the number of excluded modes based on the receiving gain and interference
among the modes. The proposed method determines the number of excluded modes by the following steps.
1) The gains of modes and interference power among allmodes are observed.
2) The relation between the number of the excluded modes,
L, and achievable rate is verified, where the weakest
L modes are excluded, and all available power is distributed equally to the remaining modes.
3) L with the maximum rate is identified from the resultsof step 2).
Note that, dual circular polarized waves are used to increase
the number of streams and optimization of mode number isperformed by considering all available modes.
One example is a backhaul network for cellular basestations. The distance is much longer than the aperture widthand is always constant after base-station installation. The
system can constantly use the ports corresponding to the mode
selected by this method, but the number of available modes
may be limited. In that case, the initial computation is needed,
but the cost incurred by selection is almost negligible. Anotherpractical example is the application to vehicle platooning forself-driving cars. The vehicles may share a lot of information,e.g. the video images for collision avoidance systems andthe status of the vehicle (speed, acceleration, brake). In thisapplication, the relative distances to the neighboring vehicle
are mostly constant over short periods, but the distance mayvary depending to the situation, such as the road and traffic
conditions. The distance can be several wavelengths (microwave band), and the propagation environment is completelyline-of-sight. This means that OAM transmission is quite
suitable for this scenario. In that case, a table of modes selected
for inter-vehicle distance can be prepared beforehand.

4

Level [dB]

0
-20
-40
-60
-80

Fig. 5. System model.

Others2.3

2.47
Freqency [GHz]2.6

Fig. 7. S-parameter of the antenna

#6

#4

#2

#8
#5

Desired Pol. (phi=0)
Desired Pol. (phi=90)
Cross Pol. (phi=0)
Cross Pol. (phi=90)z-axis#1x-axisFig. 6. Antenna model.

III. N UMERICAL A NALYSIS
A. Analysis condition
As described in II, OAM weight multiplication can berealized by an analog circuit. Since the feasibility of the analog
DFT feed network was well studied in [5], this paper verifies
the performance of OAM transmission with an ideal feed
network. Focusing on the ideal feed network yields a simple
evaluation of the ultimate performance of the OAM antennaconfiguration.
Figure 5 shows a system model. Transmitter and receiverantennas have a circular array arrangement with plane symmetry; the dual-port circular elements face each other. D isthe distance between transmitter and receiver side antennas.
Each antenna is connected via a 90 degree hybrid coupler tothe DFT feed network.
Figure 6 shows the antennas dealt with in this paper. The
permittivity and permeability of the antenna substrate are taken
to be identical to that of vacuum for simplicity. Total antenna
size is 2λ0 × 2λ0 (λ0 : wavelength in a vacuum). Antenna
separation on the same side is λ0 . Frequency used is 2.47125
GHz. θ and φ are defined as shown Fig. 6.
Figure 7 plots the S-parameter from port 1 to port 1 ∼ 8.
Since the antenna in this paper has point symmetry at theantenna center, we describe only the S-parameter from port 1
to the others. Note that Sk1 represents the S-parameter fromport 1 to port k. The curves show that the designed antenna
array has fairly good performance at the operation frequency
in terms of reflection and coupling; both are lower than -20
dB at the operation frequency (2.47125 GHz).
Figure 8 shows the actual gain of desired and cross polarizedcomponents for a single antenna element and axial ratio(AR) for a single antenna element. This result shows thatthe maximum level of the desired polarized waves is 9.9 dBi
at θ = 0◦ . Moreover, the half-power width is 80 degrees.
Maximum level of XPD is 33 dB at θ = 0◦ . In addition, AR

10
0
-10
-20
-30
-40
-50
-60
-180

40
30
20
10
-90

0

Elevation angle ,90

Axial Ratio [dB]y-axisAR (phi=0)
AR (phi=90)
50

Actual gain [dBic]

#7

#3

0
180

[deg]

Fig. 8. Actual gain and axial ratio as functions of the elevation angle.

at θ = 0◦ is 0.15 dB. The angular range of the AR values
under 3 dB runs from −60◦ ≤ θ ≤ 50◦ . From Fig. 8, it
is necessary to lower the isolation level in order to improve
the XPD since the isolation level in the front direction of theantenna element is almost equal to the XPD.
Figure 9 shows the radiation patterns yielded by the proposed method.
Four OAM modes are realized for both polarizations. The
RHCP and LHCP are simultaneously realized by setting ±90
degree phase difference to dual-ports at each microstrip antenna. From this figure, OAM mode 0 with RHCP and LHCP
has maximum gain on the z-axis. The maximum gain is 13 dBi
at θ = 0◦ , and this OAM mode for both CPs is understood asa main mode. On the other hand, the other modes do not havemaximum gains on the z-axis direction. The maximum gain
of OAM modes ±1 (both polarizations) is 5.5 dBi at θ = 20◦ .
In addition, OAM mode 2 with RHCP and LHCP has 8 dBi
maximum gain at θ = 35◦ .
B. Analysis results
Figure 10 plots achievable rate versus SNR for 8 × 8 SRMIMO, SR-MIMO with WF, and the proposed method. In thisstudy, the channel capacity of SR-MIMO, C, is given by,


P0
H
H
H
(15)
C = log2 det I M +
OAM
OAM ,
M σn2

where I M is an M × M identity matrix. Total transmitting
power, P0 , is -10dBm and noise level, σn2 , is -50 dBm.
For the proposed method, the number of excluded modes isAchievable rate [Bits/s/Hz]

5

70
60
50
40
SR-MIMO
30
+WF
20
10
0
20
30

Prop.
SR-MIMO䠄8 streams䠅

40
SNR [dB]

50

60

SR-MIMO+WF
SR-MIMO
Prop.
OAM (8 streams)

110
Antenna distance, D /100

Fig. 11. Achievable rate versus antenna distance, D.

The number of exclued modes

Achievable rate [Bits/s/Hz]

Fig. 9. Radiation pattern with OAM mode and CP. The notes above thepattern represent the index number of the excited port in the DFT matrix, e.g.
IN.1 R corresponds to the port1 in Fig. 3 for RHCP.

80
70
60
50
40
30
20
10
0

7
6
5
4
3
2
1
0

Prop.
WF
1

10
Antenna distance, D /100

Fig. 12. The number of excluded modes, L, versus distance, D.
Fig. 10. Achievable rate versus SNR.

determined by finding the value of L that yields the maximum
achievable rate. The achievable rate of OAM is given in (14)when the number of excluded modes is 0. From this figure,the difference in the curves is less than 0.5 bits/s/Hz in therange of 20 to 40 dB. However, a clear difference exists above
50 dB. In addition, SR-MIMO has greater achievable rate thanthe proposed method at high SNR values because the level ofinterference is greater than the noise power.
Figure 11 plots achievable rate versus D. In this figure,
SNR is 40 dB. The results reveal that the performance of the
proposed method asymptotically approaches that of SR-MIMO
with WF as D increases. SR-MIMO has lower performance
than the proposed method at D = 7λ0 . When D = 100λ0 , theproposed method has double the performance of SR-MIMO.
Therefore, the proposed method works well even when D islarger than about 10λ0 .
Figure 12 shows how the number of excluded modeschanges with D for WF and proposed method. From thisresult, the number of excluded modes increases with D. In thearea of 1λ0 to 7λ0 , the number of excluded modes is 0.These
results reveal that the proposed method is not effective if the
distance is extremely short. This technique can be used when
the distance is comparable to or longer than the aperture width.
Moreover, the number is 6 for D above 20λ0 . These results
are almost same as the results yielded by WF. This is because
arrays sufficiently distant from each other suffer from modedegeneration, i.e. only single eigen-paths can be observed
due to the strong LOS environment. Since this scheme uses
dual CP, only a fundamental mode generating a single beamremains for each polarization.
Next, the impact of non-ideal environments on the per-formance of the proposed method is studied. Essentially, theproposed method only works in LOS environments because thecyclic channel matrix cannot be realized in non-LOS (NLOS)
environments. Nevertheless, the array displacement from theideal location will affect the performance as well, even in LOS
environments.
Figure 13 shows the simulation model; either of the arrays
move from x = 0 to 10λ0 , where ∆x is the displacement
distance in the x-axis direction. By analyzing this model, theperformance of the proposed method is evaluated when thechannel matrix is not a perfect cyclic matrix.
Figure 14 plots achievable rate versus the displacement
distance, ∆x, for SR-MIMO with 8 streams, SR-MIMO
with WF, proposed method, and OAM transmission with 8
streams. This result reveals that the achievable rate with OAM
transmission with 8 streams rapidly decreases in the range
0 ≤ ∆x ≤ 1.5λ0 . This indicates that the OAM mode isgreatly affected by non-ideal antenna arrangement, and theinterference among modes is increased due to the imperfectchannel. On the other hand, the proposed method yields better
performance even if the channel is not ideal. This means thatmode selection is also effective in alleviating the inter-mode
interference created by imperfect channels. In this case, theproposed method improves the achievable rate by 10 bits/s/Hz
at ∆x = 1.5λ0 compared to the OAM transmission method
using 8 streams.
Figure 15 plots the number of excluded modes versus ∆x
for SR-MIMO with WF and proposed method. From thisresult, the number of excluded modes of the proposed method
is generally 6. This means that the proposed method uses theremaining 2 OAM modes that correspond to RHCP and LHCP
fundamental modes.

The number of exclued modes

6

7
6
5
4
3
2
1
0

Prop.

WF

0

2

4
6
Offset distance,

8

10

Fig. 15. The number of excluded modes versus ∆x.
Fig. 13. The simulation model for non-ideal arrangement.
IN.1_R
IN.2_R
IN.3_R
IN.4_R

SR-MIMO+WF
SR-MIMO
Prop.
OAM (8 streams)

25
20
15
10

-10
Level [dB]

Achievable rate [Bits/s/Hz]0IN.1_L
IN.2_L
IN.3_L
IN.4_L

-20
-30
-40

5

-50
0

0
0

2

4
6
Offset distance,

8

10

Fig. 14. Achievable rate versus ∆x.

Figure 16 plots mode gain versus ∆x. Note that the mode
gain is defined by diag(H OAM ) in (11). This result reveals
that there is a crossover of the first (IN.2 R/L) and second(IN.1 R/L) mode curves around ∆x = 3λ0 for both polarizations. This is because the first mode pattern has its gain
maximum in the front direction while the second mode pattern
has its gain maximum in the oblique direction.
IV. C ONCLUSION
This paper has proposed a mode selection scheme to improve the achievable rate for OAM transmission over fixedanalog OAM networks. Also, this study has dealt with optimizing the design of arrays consisting of dual circular polarized
microstrip antennas, which are suitable for OAM transmission.
Analyses showed that the achievable rate of this scheme
approached that of SR-MIMO with WF at antenna separation
distances, D, larger than 10λ0 . The proposed method offers
twice the performance of SR-MIMO at D = 100λ0 . These
results confirm that the proposed method is a practical way
of increasing the achievable rate for OAM transmission overfixed analog DFT networks.
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