Channel Inversion Schemes with Compensation Network for Two-Element Compact Array in Multi-User MIMO

A R T I C L E I N F O A B S T R A C T Article history: Received: 01 March, 2017 Accepted: 04 April, 2017 Online: 15 April, 2017 In this paper, we investigate the performance of channel inversion schemes for interference cancellation with compensation network in multi-user MIMO broadcasting channel. To achieve good performance, mutual coupling between two-element compact arrays is characterized by the receiving mutual impedance method (RMIM) to formulate the compensation network-operating matrix. A prototype of two-element compensation network with an insertion loss between input and output ports better than 11 dB is fabricated. We demonstrate results to confirm that output voltages of decoupling network can effectively be removed off the coupling effect. A typical standard MIMO channel model is presented, and system performance is evaluated when coupling effects existed and after decoupling process. Bit error performance results also indicate the promising potentials of regularized channel inversion scheme with efficient decoupling scheme in massive MIMO system.


Introduction
The expanding interest for higher data rate, greater spectrum efficiency, larger average throughput and shorter latency by wireless systems has stimulated tremendous amount of research towards capacity enhancements of the communication links [1]. The main challenge in data transmission in broadcasting channel is interference cancellation, and channel inversion is one of the advanced technologies developed to confront the challenge. Channel Inversion (sometimes referred to as "zero-forcing (ZF) beamforming") can be viewed as a precoding strategy to undo the effects of a channel, and is one of the simplest modulation techniques for the multiuser channel [2]. This technique multiplies the vector signal to be transmitted by the inverse of the channel matrix and the result is an equalized channel to each user, and therefore, suppresses the co-channel interference [3]. It has the following advantages in the MIMO context: it is implementable with a non-iterative transmitter processing and unitary receiver processing [2], [4], and [5], therefore, no noise improvement happens at the receiver. Again, when the channel rank is restricted by the number of receiver antennas, receiver processing is not required, and the subsequent virtual channels correspond one-to-one with the receiver antennas.
Channel inversion has attracted tremendous amount of research, and is well investigated in light of the fact that it is suitable for multi-user MIMO downlink channels [6]- [11]. One noteworthy issue that should be tended to in connection to multi-user MIMO system is mutual coupling, and the development of a successful decoupling strategy to compensate the performance degradation in MIMO antennas. If mutual coupling is strong, a large portion of the power fed into one port will be coupled to the other port rather than radiating to free space; consequently diminishing the signal-to-noise ratio and restricting the channel capacity. Ref. [12] 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 /or180 [13]- [17].
It is clear at this point that decoupling techniques to balance the performance degradation by coupling are widely investigated. However, its coexistence with channel inversion needs further investigation, importantly, the effects of coupling matrix on the channel coefficients, and the resulting consequences on channel inversion interference cancellation schemes that are rarely accounted for or are studied in the signal processing or communication literature. We intend to investigate the system performance of channel inversion with decoupling network scheme in multi-user MIMO system by evaluating error performance of the coupled and decoupled antenna elements at the receiving end. This paper systematically presents the measurement of receiving mutual impedance of monopole array to formulate the decoupling network operating matrix and design. For illustration, coupling matrix under coupled and compensated voltages is determined and included in the multi-user MIMO system with channel inversion interference cancellation model for the broadcasting channel.
The purpose of decoupling network however is to enhance the isolation between ports closely located within restricted space in mobile handset. It is therefore reasonable to investigate the effect of mutual coupling matrix on channel coefficients, and subsequent effects on performance of channel inversion in MIMO system after decoupling process. For reasons of clarity, the contribution of this paper is to demonstrate the impacts of mutual coupling on channel inversion after the decoupling process. We do this by fabricating a two-element decoupling network to explore the effect of coupling matrix when incorporated in the MIMO system model with channel inversion algorithm. BER performance results also indicate the promising potentials of regularized channel inversion scheme with efficient decoupling scheme in massive MIMO system The outline of the paper is as follows: Section II presents channel inversion, coupling matrix, system and channel model. The theory of receiving mutual impedance to formulate coupling effect and to design the inserted component scheme are described in Section III. Section IV presents simulation results and discussions. Finally, we give concluding remarks in Section V.

System and Channel Model
In this paper, a standard MIMO channel of T transmitters and R receivers represented as a matrix H of dimension RT  is presented, where each of the entries t,r h is a zero-mean unitvariance complex-Gaussian fading gain. The received signal of each user can be represented as [31] t, 1 where r x is the signal sent from the th t antenna, and r n defined as a standard complex-Gaussian receiver noise seen at the th r user.
In a vector form, the receive signal is represented as We assume that the total transmit signal power 1   . The ergodic sum capacity of users with single receive antenna system in (bits/channel use) is expressed as [12], [13] H is the Hermitian transpose of H . We just consider impacts of mutual coupling and channel correlation of two-element compact array closely placed to each other due to the relatively limited space at the receiver. Hence, the channel o H is given by [32] denote the coupling matrix and spatial correlation matrix at the receiver respectively. The coupling matrix of the antenna array can be written as [33] 12 1 where A Z is the antenna impedance in isolation, I is identity matrix, T Z is the impedance of the receiver at each antenna element, chosen as the complex conjugate of A Z and 12 Z is the mutual impedance.

A. Plain and Regularized Channel Inversion Schemes
Recently, channel inversion has been introduced as one of transmission schemes for interference cancellation in multi-user multi input multi-output (MIMO) broadcasting channels. In the plain channel inversion (CI), data symbol is precoded with the pseudo-inverse of the channel prior to transmission; the precoded data symbol is calculated as As indicated by [31], the main drawback of this approach is the high power level required to cancel the small elements of H  (9) where  is the regularization parameter. Let the signal-tointerference noise ratio (SINR) be represented by [7]   2 1 2 2 then, the sum capacity for CI-R can be expressed as

A. Formulation for the Mutual Coupling Effect
Mutual coupling effect between two receiving monopoles for the study is characterized by receiving mutual impedance method (RMIM) described in [34]. The two parallel monopoles operating at 2. S and 11 S are measured utilizing the procedure in [34]. If  is complex and represents the square root of the transmitted power, the respective terminal voltages can be calculated as [35] (1) The voltage and current relationships can be expressed as (1) (2) 21 11 12 t V V Z I  (13) and 12 Z   (16) where ki t Z represents the mutual impedance between the kth and the ith antenna elements and L Z is the terminal impedance connected to the antennas.

B. Operating Matrix and Design of Compensation Network
Using (16), the operating matrix for two-element receiving array for the compensation network is expressed as 12 where 1 V and 2 V are the couple voltages and the inputs to the network from the monopole terminals and the output voltages are 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 rat-race couplers [37]. The even-mode circuit for the power divider is shown in Fig. 1, where 2 Y and 3 Y are the input admittances of the upper and lower branches respectively. In the odd-mode shown in Fig. 2, if 2 k is the power ratio, then 2 S kV  and 2 S V are the magnitude of voltage sources at the output ports of the divider circuit. We fabricate the circuit by using the substrate FR4 with dielectric constant 4.8 at operating frequency of 2.4 GHz as shown in Fig.  3. The measured insertion losses between input and output ports of the decoupling network are shown in Fig. 4.

Simulation Results and Discussion
For demonstrating the performance of channel inversion schemes with decoupling network in multi-user MIMO system effectively, coupling matrix of the decoupling network under two distinct conditions is determined in an anechoic chamber. In this work, the decoupling network has been fabricated using microstrip transmission-lines, the measured insertion loss between input and output ports are better than 11 dB. The scattering parameters of the coupled monopole array are measured to determine the coupled voltages ( 1 V and 2 V ) and coupling matrix.   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 ). These are incorporated into the channel inversion schemes of the multi-user MIMO broadcasting channel for performance evaluation. The BER performance of a multi-user MIMO system for plain and regularized channel inversion schemes are shown in the Fig. 5 and Fig. 6 respectively. It is clear that performance of the coupled voltages at different frequencies must incur losses to make practically identical results for the compensated voltages for the same bit error performance in both schemes due to the coupling phenomenon. under both conditions. As it can be seen, the regularized scheme accomplishes better performance than plain scheme, thanks to mitigating noise enhancement. Again, in Table I, the last row defines the ratio of the voltage obtained with monopole B to the voltage obtained with monopole A. Results confirm that the ratio of the compensated voltage is very close to the uncoupled voltages, demonstrating that the compensated voltages have successfully been removed off the coupling effect. It is a known fact that channel inversion provides effective interference cancellation in multi-user broadcasting channel, however, our analysis demonstrates that an efficient decoupling network with channel inversion schemes enhance system performance and demonstrated the lesser impacts of coupling on the compensated voltages in multi-user MIMO. This is because coupling matrix can have decorrelation effect on the channel coefficient and therefore improving the error performance of multi-user MIMO system.

Conclusion
In this paper, we demonstrate the effect of coupling matrix on channel coefficient, and the resulting consequences on channel inversion interference cancellation schemes in multi-user MIMO system. Our results confirm that the output of the decoupling network can adequately be removed off the coupling effect. In the event that coupling affects the performance of antenna arrays, our outcomes demonstrate an opposite case. This is because the lesser impacts of coupling on the compensated voltages also translated into an improved bit error performance, indicating the promising potentials of regularized channel inversion scheme with efficient decoupling scheme in multi-user MIMO system.