Analysis of Compensation Network in a Correlated-based Channel using Angle of Arrivals

We explore combined effect of spatial correlation and mutual coupling matrix, and its subsequent effects on performance of multiple input multiple output (MIMO) systems After the decoupling process. We will also look at a correlation based stochastic channel model with the linear antenna arrays as the signal source. For the purpose of understanding, it is assumed that fading is correlated at both transmitter and receiver sides, in spite of the fact that the decoupling network enhances isolation between Receiving antenna array. In this paper, we model the transmit the antenna array in CST Microwave Studio, as a uniform linear Array with monopoles as antenna elements. On the receiving side, the scattering parameters of the coupled and decoupled monopole Array are measured in an anechoic chamber. The theoretical analysis and simulation results show the joint dependency of the system capacity on an angle of arrival (AoA) and antenna element spacing, with enhanced system performance at reduced AoAs with Increased antenna element separation. Consequently, essential benefits of MIMO system performance can be achieved with an efficient decoupling network while boosting the signal sources by adding further antenna elements. Keywords—Angle of arrival (AoA); channel correlation; decoupling network; mutual coupling; MIMO


INTRODUCTION
One of the challenges of MIMO antenna design is the task of enhancing the isolation between ports nearly located within restricted space in the mobile handset.This is because of the way the array elements have to be contained in a reduced volume, which brings about substantial pattern/spatial correlation and Strong mutual coupling effect between the elements.It is the common conclusion that mutual coupling influences the performance of antenna arrays, as the increase in correlation Restricts the channel capacity.Moreover, if mutual coupling is solid, a massive portion of the power fed into one port will be coupled to the other port rather than radiating to free space; consequently diminishing the signalto-noise ratio, radiation Sufficiency and channel capacity.Some of works have investigated the effect of mutual coupling on the performance of communication system [1]- [10].For this reason, building a successful decoupling technique to balance the performance degradation in MIMO antennas by mutual coupling effects has attracted the attention of the academic society recently.
In [11] researchers separates decoupling strategies into four classes: 1) Eigen-mode Decomposition Scheme: Its guideline is to diagonalize the scattering matrix of a compact array using 90  and or 180  [12]- [16].2).The Inserted Component Scheme: It works on the concept of inserting a section of transmission-line between the coupled antenna ports [17]- [21].3).Artificial Structure Decoupling Scheme: This method uses sub-wavelength EM structures such as electromagnetic band gap (EBG) structure [22], defected ground structures (DGS) [23], and magnetic meta-materials [24], [25].4).Coupled Resonator Decoupling Scheme: This method was proposed for the first time in 2014, and has the concept of decoupling pair of coupled elements using coupled resonators [11] and [26]- [29].
The above discussions focus on studying the influence of antenna separation on a set number of antennas and effects on The communication performance.The purpose of compensation or decoupling network, however, is to enhance the isolation between ports jointly located within restricted space in mobile handset.It is, therefore, reasonable to investigate the combined effect of spatial correlation and mutual coupling matrix on correlation-based stochastic channel coefficients, and subsequent effects on system capacity and transmit diversity After the decoupling process.To recognize user equipment (UE) channels and enhance channel estimation, the correlation channel model introduces angle of arrivals (AoAs).
For this reason, we investigate the system performance of a user equipment (UE) channels at different orientations for the uniform linear antenna arrays at diverse antenna separations, while increasing the signal sources by adding the further antenna elements.For the purpose of demonstrating the effectiveness of the research, we utilized a prototype of two-element compensation network with insertion losses between input and Output ports better than 11dB.Using the spatial correlation model [33] and incorporating the effects of mutual coupling matrix before and after the decoupling process, the results reveal different system performances for the user equipment (UE) channels at reduced AoAs and antenna physical separation while adding more elements.
The paper is organized as follows: Section II presents the formulation of operating matrix and the design of the compensation network.Part III focuses on the system model.Analytical results and discussions are presented in Section IV.Finally, we give concluding remarks in Section V.

II. OPERATING MATRIX AND DESIGN OF COMPENSATION NETWORK
The Operating pattern for two-element receiving array for the remittance network is expressed as [54] 12 12 1 2 1 1 Where 1 V and 2 V are the coupled voltages and the inputs to the network from the monopole terminals and the output voltages are

III. SYSTEM MODEL
In this paper, we examine the theoretical performance of MIMO system in the correlation-based stochastic channel Models with the decoupling network.It has been accounted for in [50] that the correlation-based stochastic channel models could be applied to cases that the user equipment (UE) with multiple antennas work at millimeter wave, in any case, we experiment the performance of the MIMO systems at 2.4 GHz.For the purpose of understanding, it is assumed fading is correlated at both transmitter and receiver sides, in spite of the fact that, the decoupling network enhances isolation between antenna arrays at the user equipment (UE).When the linear the antenna array is assumed, the steering matrix k R is expressed as [50], [51] ,1 ,2 ,D 1 ( ), ( ),..., ( ) Where d is the distance between the adjacent antennas, λ is the carrier wavelength and N the number of elements.
Incorporating mutual coupling the channel vector UE can be written as follows , 1, 2,..., )( ) Where, Where vectors a and b, are the complex envelopes of the inward-propagating and outward-propagating waves from the antenna elements respectively.In this paper, we model the transmit antenna array in CST Microwave Studio, as a uniform linear array with monopoles as antenna elements.For the receiving antenna array, the scattering parameters of the coupled and decoupled monopole array are measured in an anechoic chamber.The simulated channel is according to the channel model ( 1)-( 6) and the angle of arrival is between 0  and 360.
 For the purpose of demonstrating the effectiveness of the decoupling network, there are three different types of voltages listed in Table I.The last row in Table I is a ratio of the voltage obtained with monopole B to the voltage achieved with monopole A. It can be seen that the ratio of the compensated voltage is very close to the uncoupled voltages, demonstrating that the compensated voltages have successfully taken off from the coupling effect.

A. Fixed Number of Antennas-Traditional View
We investigate the effect of antenna spacing on performance according to coupling matrix model at the receiving side.For reasons of reference, first, we analyze the performance of the uncorrelated channel when the receiving antenna array are closely spaced with a separation of / 8. λ We do this for an angle of arrival at the receiving end as 360  for SNR of 10 dB, to illustrate the behavior of system performance regarding dependency between antenna spacing and average capacity.Figure 3 reveals that capacity of the decoupled receiving array is statistically better than that of the coupled receiving array.In order words, the results demonstrate the promising potentials of an efficient decoupling scheme in a correlated-based stochastic channel.However, system performance is restricted to antenna element spacing.With the decoupling network at the receiving end, therefore, results show the performance benefits that can be achieved by increasing the separation between antenna elements. .We repeat the process with increasing number of transmit antennas for AoAs Of 90  and 120  in figure 5 for 4 2

×
MIMO system.The graphs reveal that system performance at reduced AoAs with the increase antenna element separation outperformed that with increased AoA and reduced antenna separation.The results also demonstrate the dependency of channel capacity on an antenna separation.We note that reducing the distance between antenna elements affect system performance, however, the larger number of antenna elements at the signal source improves system performance.It is interesting to observe in Figure 5 that even though the channel is modeled with spatial correlation and mutual coupling at both ends, the performance for AoA of 60  at / 2 λ a uncorrelated Mutual coupling at SNR=10 dB.The result demonstrates the advantage of decoupling system in a correlated channel with reduced AoA

C. Transmit Diversity
For larger performance gain of almost 20 dB at error rate of  .However, a close observation in Figure 7 reveals an improvement in the BPSK performance.In spite of the fact that there was little change in the QPSK performance, we take note of that after an increase of 10 dB, the performance for coupled array with both modulations remains Nearly the same.In general, our analysis indicates a close match between QPSK and BPSK diversity performances under both conditions.We include theoretical performance based on the EMF method which outperformed the simulation results.Performance evaluation indicates the joint dependency of system capacity on the angle, angle of arrival and antenna separation.Results show that an important benefit of system performance can be achieved for reduced AoA with increase antenna element separation at the transmitter.Our analysis demonstrates the promising potentials when mutual coupling matrix is modeled with efficient Decoupling network for a compact antenna array.Further work can be carried out towards investigating the performance the behavior of rectangular and circular arrays with decoupling network for MIMO spatially correlated transmitters.

1 U and 2 U
, also known as the compensation voltages.The compensation network is designed using a power divider of unequal power-dividing ratio with no active circuit elements to minimize extra circuit noise and two ratrace couplers.The power divider has three transmission lines ( system's characteristic impedance, but unequal electrical Lengths φ , Ψ and θ[55].The electrical length φ can be defined as impedance.We fabricate the circuit by using the substrate FR4 with dielectric constant 4.8 at operating frequency of 2.4 GHz as shown in Figure1.The measured insertion losses between input and output ports of the decoupling network are shown in Figure2.

.
The mutual coupling matrix is defined as[51],[52] 1 ( are the antenna impedance, load impedance and mutual impedance respectively.For theoretical approximation of bilateral coupling (4) we assume that A Z and L z have a value of 50 Ω each.m z is calculated using the EMF method[7] using .dA. S-parameter Based Mutual CouplingRegarding scattering parameters the mutual coupling the Matrix in (5) of the linear array is expressed as[53] the S-parameter matrix of the antenna array.The voltage and current on the m the

Fig. 2 . 1 V and 2 V
Fig. 2. Measured insertion losses between input and output ports of the Decoupling Network IV.NUMERICAL RESULTS This section illustrates the analytical performance and results according to the modeling of mutual coupling matrix at the Receiving side.The simulation assumes a uniform linear array With monopoles as antenna elements at the source.The compact antenna array consists of two parallel monopoles operating at 2.4 GHz and placed on a metallic ground.The monopoles have the length of 30 mm, a radius of 0.5 mm and fixed element separation of / 8 λ .The S-parameters for the receiving array are determined in two different conditions.Firstly, the scattering parameters of the coupled monopole array are measured in order to determine the coupled voltages ( 1 V and 2 V ) and coupling matrix.Secondly, the monopole antennas in the array are connected to the decoupling network through equivalent length coaxial links, and scattering parameters of the output ports of the decoupling network are measured to determine the coupling matrix for the compensated voltages ( 1 U and 2 U ).

2 10 −
figure6 indicates no match between decoupled and coupled receive arrays for AoA = 360  .However, a close observation in Figure7reveals an improvement in the BPSK performance.In spite of the fact that there was little change in the QPSK performance, we take note of that after an increase of 10 dB, the performance for coupled array with both modulations remains Nearly the same.In general, our analysis indicates a close match between QPSK and BPSK diversity performances under both conditions.We include theoretical performance based on the EMF method which outperformed the simulation results.

Fig. 6 .
Fig. 6.Transmit diversity for decoupled and coupled array in correlated based stochastic model with linear array

Fig. 7 .
Fig. 7. Transmit diversity for decoupled and coupled array in correlatedbased stochastic model with the linear array