Dual-Cross-Polarized Antenna Decoupling for 43 GHz Planar Massive MIMO in Full Duplex Single Channel Communications

Massive Multiple Input Multiple Output (MIMO) and Full Duplex Single Channel (FDSC) at mm-Wave are key technology of future advanced wireless communications. Selfinterference is the main problem in this technique because big number of antennas. This paper proposes dual-cross-polarized configuration to reduce self-interference between antennas. We conduct some computer simulations to design the antenna and to verify self-interference effect of the designed antenna. Computer simulation shows that the proposed design has lower Envelope Correlation Coefficient (ECC). This result is achieved because dual-cross-polarized technique can reduce coupling between antennas. We found that bit-error-rate (BER) performances of the proposed antenna is better than single polarized antenna indicating that the designed antenna is well design to reduce self-interference effect between antennas. Keywords—Massive MIMO; dual polarized; mm-Wave; coupling; self-interference; full duplex single channel


I. INTRODUCTION
FDSC on massive MIMO at mm-Wave offers better performance compared to conventional communications using FDD or TDD on Single Input Single Output (SISO).Massive MIMO provides high degree of diversity [1]- [3] and FDSC simultaneously which transmit and receive signals in same frequency and time [4]- [8].Combination of FDSC and massive MIMO is excepted having benefits from both techniques.
Self-interference is the main problem of implementing FDSC on massive MIMO.It caused by duplexer's leakage and coupling matrix between antennas.Coupling matrix between antennas become greater with increasing number of antennas.Low coupling is needed to reduce amount of self-interference.Dual-cross-polarized antenna [9], [10] and sectoral antenna [11] are two main methods to achieve low coupling.
Sectoring antenna is potentially the most suitable configuration in base station.Low coupling is achieved by make low intersection between antennas' radiation pattern by sectoring antenna which has high gain.Each sector only served by partial number of antennas, there antennas usually formed as array to achieve high gain.Previous research in [11] use this method for dual band massive MIMO antenna at 28 and 38 GHz.
Planar antenna is the most common antenna for high frequency application.Dual polarized method can be easily applied in planar antenna to minimize coupling effect.It has been shown in [10], [12] that dual polarized in planar configuration can reduce coupling and improve isolation between antennas.These research has been done in low number of antennas and lower frequency.More massive number of antennas in mm-Wave has been evaluated in [9], [13].Another technique to improve antenna isolation using absorptive shielding has been proposed in [14].This technique is not suitable for massive MIMO becuase of high number of antenna.This paper proposed dual polarized antenna decoupling for FDSC evaluated at 43 GHz.This technique can reduce self-interference by reducing coupling between antennas.4×4 planar array MIMO at 43 GHz is used as basic model with single polarized and dual polarized configuration.These antennas are tested in simulation system considering self-interference with and without S-parameter matrix based self-interference cancellation.
Antenna design is presented in Section II starting from single element to full 16 elements MIMO antenna with both single polarized and dual polarized configurations.Simulation model of self-interference is explained in Section III.Antennas are evaluated by ECC and BER performance in Section IV and V, respectively.Finally, conclusion is pretested in Section VI.

II. ANTENNA DESIGN
Basic model of antenna design in microstrip planar antenna with circular disk proximity coupled.This model is chosen due to its flexibility.Both single polarized and dual polarized model are extended from this basic model.Design process is started with single antenna model using basic model.This basic single antenna then extended into single cluster composed from four single antennas.Finally, final antenna for both single polarized and dual polarized configurations are formed by duplicating single cluster of antenna model.This clustering method is chosen to simplify design process.

A. Single Antenna Design
Single antenna is formed as basic model of MIMO array.
Stepping of design is started by this single antenna model.Single antenna is modeled and optimized in order to get its best performance.The performance can be measured by return loss because antenna works at certain value of return loss.Each single antenna is designed as circular disk proximity coupled antenna as shown in Figs.1(a) and 1(b).Rogers RT-5880 with h = 0.127 mm is used as substrate's material with permittivity r = 2.2.
Basic formula in [15] has simplified as with where h is depth or height of substrate in cm, f is antenna's resonance frequency, and r is substrate's relative permittivity.
Antenna is design and optimized at 43 GHz resonant frequency and 50 Ω reference impedance.The result is antenna's width W = L = λ = 6.98 mm, length of feed l f = W/2 = 3, 49 mm, width of feed w f = 0.70 mm, and disk radius r = 1.30mm.
Single antenna model has unidirectional radiation pattern with 7.456 dBi gain with total efficiency of -0.1933 dB as shown in Fig. 2. Formed planar massive MIMO antenna by using this single antenna is also unidirectional.This configuration is suitable for single sector sectoral massive MIMO base station as in [11].

B. Clustering
Clustering method is chosen in order to simplify the design process.A single cluster of each configuration are shown in Fig. 3 using a wavelength spacing between antennas' center horizontally and vertically.Polarization variation is set by different direction of feeding.
Single antenna is set as basis of single cluster using dimensional parameter from Section II-A.This model then optimized to get the best performance in a single cluster.It assured antenna's performance in smaller number of antennas before final model is formed.There is an assumption that significant change only happened in 1 to 4 elements expansion.

C. Final Model of The Antenna
Different feeding is applied to each configuration to get different polarization characteristic.Single polarized antenna is fed with same direction as shown in Fig. 4(a).Dual polarized antenna is fed with cross direction as shown in Fig. 4(b).It is made by extend single cluster to form full 16 elements MIMO antenna.
Designed antenna has 8 sectors in total shown in Fig. 5(a).Each sector has total 16 antennas with 4 × 4 planar configuration.Antennas are numbered for each single element from lefttop to bottom right.This numbering is used to identify each single antenna.Antennas numbering is shown in Fig. 5

(b).
Clustering is applied for 4 near antennas, for example antenna 1, 2, 5, and 6 are in the same cluster.There are 4 clusters composed massive MIMO antenna for each configuration.

III. SIMULATION MODEL
There are three parts explained in this section.First part is self-interference model.Quasi-Orthogonal Space Time Block Code (QOSTBC) for full rate massive MIMO is explained in second part of this section.Last part explains self-interference management for massive MIMO FDSC.

A. Self-Interference
Self-Interference is the main problem in FDSC as described in [4]- [8], [16].Self-interference is interference part caused by the node itself.In this case, self-interference caused by duplexer's leakage and coupling between antennas.It can be modeled as where y is received signal, x is transmitted information signal, w is transmitted self-interference signal, and n 0 is Additive White Gaussian Noise (AWGN).This model is shown in Fig. 6.Self-interference is caused by S and L I with and There are two types of QOSTBC proposed in [17], [18].Extended-Alamouti QOSTBC has pattern of with each of A and B is Alamouti coded signal.If A is Alamouti coded signal of x 1 and x 2 , If B is Alamouti coded signal of x 3 and x 4 , EA-QOSTBC for 4 coded signal by substituting (7) and ( 8) to ( 6) is Another popular typr of QOSTBC is ABBA QOSBC.In ABBA QOSTBC, ABBA QOSTBC by substituting ( 7) and ( 8) to (10) is These pattern of EA-QOSTBC and ABBA QOSTBC can be repeated until 2 n × 2 n matrix is formed with n is number of coded signals or symbols.In this research, we consider ABBA QOSTBC due to its simplicity.

C. Equivalent Virtual Channel Matrix (EVCM)
EVCM take advantages of mathematical property by transform coded signals into coded channel matrix [18] It can simplify simulation and MIMO decoding process by assuming relatively same response of channel in a single period of coded signals.
Let say there is received signal vector for one receive antenna is T is equivalent additive noise where N C is length of STBC in time domain.For two antennas case using Alamouti SBTC, Conjugating second row of ( 14), which equivalent with .

D. Self-Interference Management
There are some methods to manage effect of selfinterference.In this paper, these methods are categorized into four main methods.All of these methods are focused on reducing or cancelling self-interference in the systems.These four main methods are receiving-transmitting power control, antenna decoupling, isolated duplexer, and cancellation by selfinterference cancellation matrix.
Receiving-transmitting power control are focusing on reducing self-interference signal power ratio defined as for node, base station, or user i. P T x−i and P T x−i are transmitted power and received power on node, base station, or user i.In node i, it is evaluated using (3) by where pow(z) represents power of z.Effect of self-interference is decreasing if α can be reduced.
Antenna decoupling are focusing on value of on (3).If this part can be reduced close to zero, receive signal equation become If S is reduced, effect if Sw in (3) also reduced.This decoupling is realized by modifying S-Parameter of the antenna by some antenna design technique.
Isolated duplexer works by using near-perfect duplexer with leakage near to zero.Assuming duplexer's leakage can be eliminated, receive signal equation become which left Sw as self-interference part.Effect of L I w is reduced if duplexer's leakage is reduced.
Cancellation by self-interference cancellation matrix works by reducing receive signal (3) by Assuming S and L I can be predicted, this self-interference cancellation matrix can be formed.
Each of self-interference managements method have its challenge.In this research, we assume linear deviation on antenna decoupling.Received signal is with deviated scattering parameter S is default-mean scattering parameter, k is normally distributed value with zero mean and σ deviation, and I is identity matrix.Self-interference cancellation matrix is using mean value in (22).

IV. ENVELOPE CORRELATION COEFFICIENT OF ANTENNA MODEL
In this section, both single polarized and dual polarized configuration are evaluated by ECC.This coefficient represents correlation between antennas.ECC can be calculated from antenna's scattering parameter using [19], [20] ) with i and j are antenna's index number where i = j.These ECC show independency between antennas.If two antennas are completely independent, ECC value is 0. If these antennas are completely dependent, ECC value is 1.Requirement for diversity is set at ECC less than 0.5.

(c) maximum
There are 120 pairs of ECC for 16 elements antenna.It is simplified to only presents minimum, average, and maximum value of ECC as representations.These statistical value contain range and mean of all ECC values.Fig. 7 shows minimum, average, and maximum value of ECC.Lower ECC is shown by dual polarized configuration.ECC value also has impact on diversity gain.This relation is presented in [21] by Lower ECC means greater diversity gain at related pair of antennas.Dual polarized configuration also provides polarization diversity.Theoretically, dual polarized configuration has better performance on diversity compared to single polarized configuration.Both of single polarized and dual polarized configurations has ECC lower than 0.5.It means diversity can be effectively applied on both configurations.Average ECC of both configurations are lower than 10 −3 which is very small.Antennas correlation is neglected because of very low ECC.
There are two main focuses on lowering ECC.The most popular technique is by reducing coupling between antennas.This coupling is presented by s ij = s ji with i = j .It mainly can be reached by making orthogonal radiation pattern or polarization.These orthogonality represents relation between related antennas.Designing low return loss antennas also can reduce correlation between antennas.

A. Various α without Deviation
Dual polarized configuration has lower coupling compared to single polarized configuration as shown in Fig. 8.The highest coupling on single polarized and dual polarized configuration is -22.98 dB and -29.29 dB, respectively.The highest return loss on single polarized and dual polarized configuration is -17.18 dB and -17.58 dB, respectively.In this case, lower ECC on dual polarized configuration is more caused by lower coupling rather than lower return loss.

V. SYSTEM PERFORMANCE ON FULL DUPLEX SINGLE CHANNEL
System performances are tested on 16 × 16 MIMO configuration.Correlation between antennas are neglected because the values of ECC in center frequency are below 10 −3 .Several self-interference signal power ratio is applied.Full rate QOSTBC with 16 antennas is applied with EVCM representation.
Both single polarized and dual polarized configurations are tested using S-parameter of antennas from antenna simulation.These values at magnitude representation are presented in Fig. 8.These values are used as in the systems simulation.Experiment results are classified into three categories: good, bad, and very bad.System is classified as good if there is no error floor in the simulation result.Bad classification is made for system with error floor.If total error or flat BER is happened, result is classified as very bad.
System performance of both single polarized and dual polarized configurations are shown in Fig. 9.It has been shown that dual polarized configuration has better performance than single polarized configuration.Lower BER at the same selfinterference signal power ratio and SNR has been achieved by dual polarized configuration.
There is critical range at α of 20dB until 35dB for single polarized configuration and 25dB until 40dB for dual polarized configuration.Performance change drastically in critical range region from good to very bad.Critical range of dual polarized configuration is at the larger α compared to single polarized configuration.This critical range shows that dual polarized configuration has better stability by changing of α.

A. Deviated S-Parameter
Based on simulation result without deviation, α = 30dB is taken for simulation with deviated S because of its critical range.Both of single polarized and dual polarized are classified as bad in this research's classification.
Results of simulation with self-interference cancellation at α = 30 dB are presented in Fig. 10.It has been shown that the result of single polarized and dual polarized configuration are relatively similar.It is because self-interference cancellation cancels the self-interference from other antennas.We also found that higher deviation of S-parameter leads to higher error because the deviation makes error on self-interference cancellation using basic (constant) S-parameter.

VI. CONCLUSION
We have proposed dual-cross-polarized antenna decoupling for 43 GHz Planar Massive MIMO in Full Duplex Single Channel Communications.We designed dual-cross polarized antenna such that coupling between antennas can be reduced using different polarization for nearby antenna.The results confirmed that the proposed antenna reduces coupling by average of 37.83% at 43 GHz, reduces ECC by average of 89.69% at 43 GHz, and provide lower BER in self-interference environment compared to single polarized antenna configuration.