Beamforming Scheme for MIMO Relay Based 5G and beyond Wireless Network

In this paper, in order to attain the maximum ergodic capacity and significantly increase the spectral efficiency of wireless communication systems, novel linear beamforming is proposed for dual-hop amplify-and-forward (AF) mul-ti-relay networks. The linear beamforming is designed based on the maximization of the signal-to-interference-plus-noise ratio (SINR) and signal-to-leakage-and-noise ratio (SLNR). The channel state information (CSI) is used in applying this new design to multi-relay (MR) nodes between the source and relays as well as relays and destination. The beamforming optimization problem is solved by using the Fukunaga-Koontz Transform (FKT). The scheme can achieve intra-node array and distributed gains by using multiple antennas and multi-relays (MRs). The performance of the proposed scheme demonstrates that by considering interference mitigation criteria the ergodic capacity at a significant level is improved as compared to the conventional techniques. Therefore, the proposed techniques based on the maximization of the signal-to-interference-plus-noise ratio (SINR) and signal-to-leakage-and-noise ratio (SLNR) relay processing outperform other conventional techniques in case of a multi-relay dual-hop network in terms of ergodic.

regularization parameter value causes the equivalent channel matrix to deviate from the diagonal matrix, causing interference and extra power expenditure throughout data streams [15] [16] [17]. Since, a specific amount of interference is allowed in the RZF technique [18], therefore with a non-zero regularization parameter value, the interference cannot be canceled completely [19].
In noise-limited scenarios, the MF beamforming technique is important to deliver better performance. However, the MF performance in interference-limited scenarios is poor [20]. Therefore, for both the scenarios, it is necessary to have the techniques that perform efficiently, in practical communication systems, cochannel interference as well as adjacent-channel interference is present [21], which should be included in the objective function of designing the beamforming for MRs. The designs based on the signal-to-interference-plus-noise ratio (SINR) maximization (SINR-Max) and signal-to-leakage-and-noise ratio (SLNR) maximization (SLNR-Max) criteria perhaps are the capable contender to overcome this problem. The techniques based on SINR-Max consider noise and interference and make the system perform better than the techniques used in [14] and [22] for relay receive beamforming. Nevertheless, the beamforming computational load has usually a large value, and to lower that value, efficient Fukunaga-Koontz Transform (FKT) can be used to design the relay receive beamforming based on SINR-Max [23] [24]. For MRs in a DH network, SLNR-Max is used which is based on downlink precoding [22].
However, this paper contributes to the design of relay receive beamforming based on SINR-Max using the FKT. It is worth mentioning that the scheme handles the noise and interference in both, the MR receives beamforming design and downlink precoding design. This novel relay processing design can achieve the distributed and intra-node array gain by controlling the interference at the reception of the relay nodes and intra-user interference because of the leakage at the destination. Intra-node array gain is achieved when multiple antennas are deployed at individual node of the network, whereas, the distributed array gain is obtained through various relay nodes connected in parallel [14]. The novelty of relaying scheme is in SINR-Max and SLNR-Max beamforming designs, which uses FKT for multiple AF relay nodes to obtain these types of gains. The proposed scheme can improve the enactment terms of ergodic capacity. It can make it possible to control interference among various antennas of the relays and at the destination node.

System Model
In this research, a dual-hop single user AF MR-based MIMO (DH-AF-MIMO) network is studied as presented in Figure 1. It consists of the transmit antennas at source '"N s ", the relay transmit and receiving antennas "N r ", and the destination antennas "N d ". Signal vector "s" is aired to AF relay nodes by the source. The transmission between the source and destination is not considered because of long-distance deep fading. The MR nodes were joined in parallel to help to Open Journal of Applied Sciences establish the communication between the source and destination. The source node first sends the information signal, processes it, and then forwards it to the destination by using MR nodes, which possesses multiple antennas at the individual relay. The relays with multiple antennas give better performance [25]. The mode of transmission of relay nodes is supposed to be the half-duplex mode. At the relay nodes, the channel knowledge of both channels. The channels are supposed to be impartial and uniformly distributed, experiencing the same Rayleigh flat fading effect.
The information signal transmission is distributed into two phases. In the first phase, the modulated signal vector "s" is transmitted to MR nodes by the source as The information signal at the k th relay node is as follows: where ,   T  T  T  T  1  2 r σ = noise variance at the relay node.
In the second stage, linear processing is performed through the AF relay nodes by the multiplication of a beamforming matrix " k F " of " r r N N × " dimension with the received signal vector " , r k s " and then forwarded to the destination. The network performance is improved by the beamforming matrix and the relay transmit power constraint is satisfied as: The transmitted signal by k th relays to the destination is shown as: where; k r = k th relay node transmit power Therefore, the condition of a power constraint for the precoded signal that is transmitted by AF relay terminals is given as: where; k ρ = power normalizing coefficient [26] This can also regulate the relay transmit power which is given as: After relay linear processing, the received signal is shown as: where;

Linear Beamforming for Multi-Relay Nodes
In relay receive beamforming, the cancellation of interference by the ZF technique will cost noise enhancement. Nevertheless, the SNR is maximized by minimizing the noise with the help of the MF beamforming technique but it does not take into consideration the interference cancellation. To deal with this issue, the SINR-Max criterion based on the relay receive beamforming is designed using the FKT. Therefore, the criterion like SINR-Max can provide a reconciliation between the noise and interference by eliminating the interference and minimizing the noise [27]. The issue of interference is faced because of the leakage signal from the desired signals that are forwarded by MR nodes at the designation. To deal with this issue of optimization, the SLNR-Max-based linear precoding technique is designed for MR downlink using the FKT as discussed in [24]. The relay processing technique based on SINR-Max and SLNR-Max for multiple AF relay nodes is proposed as an alternate technique to the conventional relay processing schemes.

SINR Maximization Based Beamforming for K Relays
In this section, SINR-Max based relay receive beamforming for multiple AF relays is designed and discussed using the FKT. For relay receivers, the beamforming vectors can be used in such a way that at k relay nodes, the beamforming can maximize the SINR. The interference is controlled by the beamforming between multiple antennas of MRs for the network as seen in Figure 1. " k H " represents the channel between the source and MR nodes i.e. . The channel matrix for K relay nodes is given as: where; c H represents the combined matrix.
For each relay receive antenna, the channel matrix is given as: In an MR system, the SINR, represented by " l k γ ", is obtained when the received signal power is divided by the indesired signal and noise power at k relays.
It is expressed as: It can also be written as: where, The numerator term in (9) is representing the desired signal, while the term in the denominator is representing the combination of interference and noise power at the l th receive antennas of k th relays. The vectors are developed independently, based on the vector-by-vector relay beamforming. Therefore, the antenna-wise SINR-Max beamforming at "k" relays is set as: where; k B = beamforming matrix for k relays

SLNR Based MR Downlink Precoding Design
As the interference caused by the signal leakage cannot be canceled by using conventional techniques like the RZF technique, which uses an adjustable parameter to control the interference. However, the interference is not canceled out completely by the non-zero value of the regularization parameter. Although, the leakage-based downlink precoding can show robustness against the interference between multiple antennas at the destination. In this design, the interference due to leakage and noise at the destination side is taken into account for vector by vector downlink precoder design as discussed in [23] and [24]. The proposed technique reduces the interference resulted caused by the signal leakage from the wanted signal among multiple antennas. Figure 1 illustrates the concept of the leakage signals from the desired signals, due to which interference is caused by other antennas. This design aims to reduce the interference that can help in improving the network ergodic capacity.
The channel matrix between the destination and MR nodes at the downlink of the given system is represented by the notation " k G ".
For j th antennas of k relay nodes to the destination, the channel matrix is given as: The relay precoder design is developed with the relay power constraint as: where, " j k F " is the k th RTP for j th receiving antennas.
The SLNR per antenna is obtained when the desired signal power is divided by the leakage signal and noise power and is given by: where; Here " j k F " represents the k th RTP matrix for j th receive antennas at the destination, which supports maximizing the SLNR.
For this objective function, different precoders are selected to maximize the effectiveness of the wanted signal analogous to the interference and noise due to the leakage. The multiplication of relay receive beamforming matrix from (11) and (16) gives:

Fukunaga-Koontz Transform (FKT) Based Relay Receive Beamforming Algorithm
For the selection of feature, Koontz and Fukunaga suggested a statistical method for high-dimensional data [23]. It was meant for a two-class reorganization problem i.e. set of vectors that represent two classes, concurrently the vectors that best represent one class will be the least representative one for the other class [28]. Let 1 Z and 2 Z be two data matrices, then The U and D matrices are used to build the transformation operator P , which is also termed as the FKT [29]. It is used to alter the data into the eigenspace and is given by: The same eigenvectors and eigenvalues are shared by 1 S and 2 S as these are transformed by using the same operator. If v is the eigenvector of 1 S with the eigenvalue 1 λ then, 1 [30].
( ) In (18), 1 S holds important information for the targeted class whereas, 2 S has more significant information for the background class. The training stage is completed after obtaining these two matrices.
The optimization problem of the relay receive beamforming for k number of relays is formulated to FKT as follows: And their sum is given as: The FKT factor can be calculated by using the facts of (21) and (22) [31]. It is important to note that, for a cluster of relay nodes, the computation of FKT is required only one time that reduces the computational load. The summary of the algorithm steps to compute the FKT factor for MR nodes is given in Table 1. Starting from step one to step two the FKT is computed, in step three and four beamforming is generated for the k th number of relays.
The received signal is given as:  (24) where; sd ρ = G GFH i = I GFs (Interference due to signal leakage) rk d = + z GFn n (Noise at the destination). According to [14], the filter used at the destination is based on QRD. The QRD operation of the equivalent channel sd G provides two output matrices Q and R , which are the m n × unitary and upper triangular matrices respectively.
It is given as The destination filter based on QRD is given as: The SINR is obtained when the transmitted signal is divided by the interfering signals and noise [32]. The SINR can be expressed as follows: where 2 , j j r are j th entries in the diagonal of the matrix " R ". Finally, the network ergodic capacity is given as:  (28) For the dual-hop multi-relay assisted network, the upper-bound capacity is given as: where, s P = total source transmit power.
1/2 = time-sharing factor (for signals of the receiving and forwarding process.

Simulation Methodology
In this section, the MCS is used to present the theoretical results of the proposed scheme. In all simulations, dimensionally uncorrelated MIMO channel matrices are developed between the source to the relay nodes and the relay nodes to the destination without loss of generality. These matrices are identically distributed, independent, and their entries are CG random variables with zero-mean components and unit-variance i.e.  The performance of a DH-MR-MIMO network is evaluated in terms of the ergodic capacity. From the source node, independent data streams are transmitted by using separate antennas having equal distribution power. The SNR of the S-R and R-D channels are given as The channel knowledge is considered at the relay terminals for S-R and R-D channels [14]. For the DH-MR-MIMO network, the upper-bound capacity is considered as a reference point [11].
The results from the MCS of the recommended beamforming technique for the DH-MR-network are balanced for 5000 independent channels to evaluate the performance of the suggested scheme. The performance of other available precoding methods that are discussed in [23], as well as ZF-ZF, MF-RZF, and MF-ZF techniques are evaluated that are explained in [13] [14] and [17] respectively. Table 2 represents the parameters used in the simulation process.

Result and Discussion
This section discusses the evaluation of the suggested and compared schemes. at each node and one relay between the source and destination.
The graph shows the results of the suggested and additional beamforming techniques. It is clear from the figure that at each SNR value, the recommended technique outperforms other techniques.
The regularization factor is used for the suggested scheme, which clearly shows that the MF-ZF technique is outperformed by the MF-RZF technique. When the value of the regularization parameter is reduced, then the scheme approaches the MF-ZF beamforming. Since the MF technique performs well at low SNR values, the MF-ZF technique outperforms the ZF-ZF technique only when the SNR values are low, although the interference is eliminated by the ZF beamforming that will cost the noise enhancement. The results clearly show that at low SNR values, the ZF-ZF scheme gives slow performance but it regains its performance at a high SNR value.
The plots of Figures 3-5 represent the efficiency of the suggested beamforming scheme at an increased number of relay nodes from one to six by keeping the Table 2. Parameters for simulation.

Parameters Value
InputRelay protocol Amplify-and-forward Network configuration DH-MR-MIMO system as shown in Figure 1 Antenna configurations at each node       Table 3 represents the capacity gained at 25 dB SNR by suggested and other techniques by keeping three antennas at each node and repeating the simulation process for various relay nodes such as 1, 3, and 6. The performance of the proposed beamforming technique is much improved as compared to the other techniques when applied to the MR-MIMO network. There is a linear increase in the capacity as the number of relay nodes increases.  The simulation results show that when SINR-Max is considered for beamforming, the design gives better performance alongside the inter-stream interference at     MR nodes. Whereas, the relay downlink provides unwanted signal reduction due to the signal leakage at the destination. Moreover, when the FKT is used in the proposed technique, it effectively solves the issue of optimization. It is clear from the FKT algorithm that the computational burden of beamforming is reduced because the transformation factor needs to be computed only one time for MRs.
However, when the number of antennas is increased at each terminal from three to four, the measured sum capacity using the proposed scheme is increased as compared to the MF beamforming at the relay receive side. Similarly, as the number of antennas rises to eight, the sum capacity also increases linearly. Based on the results and discussions mentioned above, it is concluded that the proposed technique for AF relay is more efficient as compared to other techniques. The performance of the whole system is enhanced in terms of the ergodic capacity by adding more relays due to the diversity order achieved by an additional number of relays. Moreover, the increasing number of antennas at individual nodes increases the capacity and decreases the number of relay nodes, which may result in complexity reduction.

Conclusions and Future Direction
A linear beamforming scheme has been proposed using the Fukunaga-Koontz Transform (FKT) to control the interference for amplify and forward multiple relay MIMO assisted dual-hop network, where the co-channel interference (CCI) was considered at relay receivers and interference at the destination node due to leakage signal. The performance of the proposed scheme demonstrates that by considering interference mitigation criteria the ergodic capacity at a significant level is improved as compared to the conventional techniques. Therefore, the proposed techniques based on the maximization of the signal-to-interference-plus-noise ratio (SINR) and signal-to-leakage-and-noise ratio (SLNR) relay processing outperform other conventional techniques in terms of ergodic capacity.
The results in this work provide a strong foundation for future work in the performance of wireless network. One area of the future work is to optimize the Performance of Massive MIMO systems, to limit inter-cell interference and to improve the use of the available frequency bands by covering cognitive radio and mobile to mobile communications(D2D), to guarantee a level of end-to-end quality of service in different mobile wireless environments. Another area is maturing enough beamforming algorithms in order to exploit Millimeter wave to its full potential. It requires improvement in the networks when personal base stations (BSs) and satellite connectivity can get merged into cellular communication.