Performance Analysis of Large Intelligent Reflecting Surface Aided Moderate MIMO for 5G Communication

The recently completed 5G framework is the outcome of a few advanced technologies. Massive multiple input multiple output (MIMO), millimeter wave communication, and network densification are examples of these technologies. However, there are two disadvantages to this technology. (1) the lack of control over the wireless channel, and (2) the wireless interface’s excessive power consumption. The concept of re-configurable intelligent reflecting surface has emerged to answer the need for green and cost-effective future cellular networks. In this study, we’ll look at how using an intelligent reflecting surface (IRS) improve the performance of moderate MIMO communication in terms of the rate, SINR, energy efficiency and transmit power metrics. Despite the fact that the underlying issue is non-convexity, we use lagrangian dual transform and quadratic transform to change and rearrange the original issue. After that, active and passive beam forming improved alternatively using an alternating direction method of multiplier algorithm (ADMM). The IRS-aided system with a reasonable number of antennas at the access point (AP) outperforms the massive MIMO without IRS in terms of sum rate, SINR, energy efficiency and transmit power metrics.


Introduction
Through many creative developments, such as massive (MIMO), millimeter wave (mm wave) communication, and network densification, the fifth generation (5G) network standard promises to deliver enhanced bandwidth, accessibility, and incredibly low delay. Regardless of this advancement, providing services of consistent quality to clients in difficult propagation environments consumes a significant amount of power. The total network energy consumption, for instance, is related to the number of base stations (BS) and active antenna elements at each BS. Communication in the mm wave bands suffers from significant path/penetration losses. As a result of these issues, future cellular networks must be green and sustainable, with control over the propagation environment. The smart radio environment (SRE) is a new concept that fulfills this demand by changing the wireless propagation environment into an intelligent tun-able space that engages in radio frequency transmission from sender to receiver [1]. This concept can be realized by placing low-cost antenna arrays [2], smart reflect-arrays [3], and re-configurable meta-surfaces in the environment to passively shape intruding electromagnetic (EM) waves in the desired direction without producing additional radio signals.
Passive reflecting surfaces are used often in radar and satellite communications as the main structural element of traditional reflector arrays, but they are hardly ever employed in terrestrial wireless communication. This is due to the fact that conventional reflecting surfaces only have fixed phase shifters once they are manufactured, making it challenging to adapt them to the dynamics of wireless networks with time-varying channels. However, new developments in meta materials (such as meta surfaces) and RF micro electromechanical systems(MEMS) have made it possible to reconfigure reflecting surfaces, even via real-time regulating phase shifters [4]. To increase the strength of the received signal, the reflected signals can be added coherently at the intended receiver or destructively at the unintended receiver to prevent interference and improve security by carefully controlling the phase changes of every component at an IRS.
Furthermore, IRSs have other benefits, including lightweight, conformal geometry, and low profile, that make it simple to attach and detach them from surfaces like walls and ceilings. This gives them a high degree of flexibility and greater compatibility for use in real applications [5]. For instance, the signal strength and coverage of an access point (AP)/BS are expected to be greatly enhanced by putting IRSs on the walls that are in line-of-sight (LoS).
In addition to all these beneficial characteristics, an IRS has the ability to consume almost no energy because it excludes the power-consuming parts of traditional radio frequency chains. An IRS design typically only uses electrical circuitry with very low power that can be fueled by active control elements, passive meta material components, and energy-harvesting wireless modules [6]. These characteristics make IRSs an appealing plug-and-play technology for enhancing the functionality of upcoming communication networks. This paper will show the benefit of an intelligent reflecting surface in enhancing the performance of a moderate MIMO system.

Related Works
In [7], the comparative analysis of intelligent reflecting surfaces (IRS's) as well as amplify and forward (AF) relaying wireless networks considered, and it is demonstrated that IRS aided wireless systems has a higher spectral efficiency (SE) than the corresponding AF relaying wireless systems. In [8], a survey conducted on the IRS is presented. This encompasses IRSaided communications data rate and capacity assessments, deep learning-based design, power/ spectral optimization's, and reliability analysis. They also look into IRS deployments and how IRS's can be used for secure communications, terminal location, and other novel applications. In [9], it is investigated that the multi-user down-link MISO system, which is helped by the IRS. To optimize the WSR under the BS transmit power constraint, a hybrid active and passive beam forming issue is defined. An iterative solution based on the recently announced fractional programming methodology has been designed to solve this non convex issue. Three low-complexity algorithms are also offered to solve the problem. In [10], massive MIMO designs for milli meter wave (mm wave) communication is proposed. It is shown that properly locating the active receiving antennas for the intelligent surface significantly improves the spectral efficiency of RIS supported MIMO structures. Furthermore, they advocate for a power usage framework for RIS supported radio network that accounts for RIS effect imperfections, such as taper loss, spillover loss, phase shifter loss and aperture loss. In [11], the use of re-configurable intelligent surface (RIS) to enhance uplink beam formation gain in a massive MIMO system is investigated. It has also been demonstrated that IRS can improve network throughput. In [12], performance analysis of re-configurable intelligent surface (RIS) in multi-user MIMO systems was outlined. The capacity of both of the up link and down link channels has been discussed. In [13], after the concentrated weighted sum rate augmentation problem has been transformed to a manageable sub problem, the author presents an incremental alternate direction of multiplier (ADMM) calculation to up-date the beam former locally. In [14], it has been investigated that the problem of "capacity-maximization for MIMO IRS-assisted pointto-point communication, using joint IRS reflection coefficients". An alternative optimization strategy was proposed for frequency-flat channels, which provides a locally optimized solution by optimizing a single optimization variable ("the transmit co-variance matrix"). In [15], an IRS-assisted (MISO) remote framework was presented to consider where an IRS is sent to help a single radio wire client to receive the correspondence from the multiple receiving wire. So, the customer receives the channel directly from the AP at the same time, just as the IRS does. In [16], a twofold IRS-assisted multiple input multiple output (MIMO) communication framework for LOS channels is proposed. Advance the transmit co-variance network and the inactive beam forming grids of the two agreeable IRSs to investigate the limit amplification issue. In [17], the author offered three analytic approaches to play out the finding in a variety of settings with varying IRS's CSI requirements and computing complexities. In [18], the use of an IRS at the cell limit improved the cell-edge client execution of multi cell communication frameworks. They addressed the WSR augmentation problem by simplifying the passive shifts at the IRSs and active transmit precoding (TPC) lattices at the AP, while ensuring that each BS's power requirement and unit-modulus limitation at the IRS were met. In [19], the author devised as well as solved "a robust probabilistic constrained optimization problem for IRS-aided MISO communication systems in order to deal with inaccurate CSI estimates. The best beam forming vector there at BS as well as reflecting elements at the IRS are determined iteratively with the converging alternative optimization approach.

Down-Link Moderate MIMO System with IRS Support
We consider an intelligent reflecting surface (IRS) supported moderate MIMO communication framework as displayed in Fig. 1 in which there is a BS furnished with N transmitting antennas, M reflecting passive components serving K numerous antenna users each of has Q antenna components. Where, ((N >= 1, Q >= 1) indicate by S = [S 1 , … S k ] T ∈ C K.Q and 'the gaussian information images in which every component is a free arbitrary variable with zero mean and unit variance, likewise S k component image sent to the K th client. An IRS element is thought to be with Max elements on a level plane and May elements in an upward direction. (M = Max by May).
The smart controller also controlled the IRS unit, which arranges the reflecting modes for the IRS unit. Where w k ∈ C M * K is the matrix of linear transmit precoding (TPC) used by BS to send its information vector S k to the k th user. Also, base band channels crossing through BS to IRS, and those from IRS to the K th user, are denoted by G ∈ C N * M and h r,k ∈ C M * 1 in the order given. We assume that the BS has "perfect channel-state information (CSI)" [21] for all channels involved and all the channels are quasi-static flat-fading rayleigh. In likewise, we denote n ∈ F the RC of the n th reflection component, where F is the feasible set of RCs.
The BS transmits a signal that is given by: We consider the following assumption for the feasible set of RCs: [20] are the diagonal phase-shift lattice for the IRS, the combined incident signal's phase shift and amplitude reflection coefficient respectively. Now let's defined the total transmitted signal by: Where represents additive white Gaussian noise (AWGN) at the K th user receiver. Then by substituting (2.1) in to (2.2) we get

Problem Formulation
All signals from other users are treated as interference by the k th user. As a result, The major goal is to increase the WSR by creating the transmit beam forming matrix W at the BS and the phase shift matrix at the IRS together. The spectral efficiency (SE) (bits/ Hz) at user k is given by: And the sum rate is given by: Therefore, the WSR maximization problem is become

Beam Forming Design with Active and Passive Components
First, we have to make decouple the optimization of TPC matrix W and the phase shift matrix in to several tractable sub problems. So by using lagrangian dual transform we can address the logarithm problem in the objective function of (P1). Hence, we use the proposed lagrangian dual transform in [22] then (P1) becomes in the form: Where alpha refers to: is an extra vector introduced by the lagrangian dual transform. The WSR of problem (2.7) can be written as: Thus solving (2.7) is the same as solving (2.9) so, we provide a solution (2.9) by using an alternating iterative method that yields three alternating steps i.e., the auxiliary variable alpha, Active Beam Forming and Passive Beam Forming. So, in (Pl*) when w and hold fixed and setting The optimal alpha(k) is: Then for affixed alpha optimizing W and is reduced to: Here, Since, w and are related only to the SINR term the other variables in (2.9) will be ignored. Then we are going solve w by holding and solve by holding w respectively.

Active Beam Forming Scheme
Let us first optimize the ABF by fixing the PBF matrix. For problem 2.11 let denote the combined channel for user k by: Then the SINR in (2.4) becomes: So, by using 2.13 the primary function of problem 2.11 can be expressed as a function of w.
Substituting (2.13) in to (2.14) we get: Given this and enhancing w becomes: We not that (2.14) is a fractional programming problem with multiple ratios. As a result, by employing the quadratic transform proposed technique in [22] we can write (2.15) as: Where, is the additional variable introduced by using the quadratic transform. and (2.17) is a problem of biconvex enhancement. we can rewrite 2.17 as: The ADMM method is then used to solve problem (P2) perfectly [23]. Problem (P2) augmented 's lagrangian is: Then the variables can be updated incrementally by: The optimal solution of for problem (2.20a) is: This is obtained when w and hold fixed. The optimal solution of for problem (2.20b) is: This is obtained by setting: The optimal solution of w for problem (2.20c) is: This is obtained by setting: Where is the best dual variable to use in the transmit power constraint.

Passive Beam Forming Scheme
To find the optimal solution of we first rearrange some equations with some mathematical manipulation so, (2.15) can be re written as:

Where
To simplify let; Then we rewrite (2.19) as: Then using QT-we can write(2.25) as: Where 'r' is the auxiliary variable introduced by the lagrange multiplier-based quadratic transform, and setting the optimal 'r' is given by: Given 'r' the optimization of can be written as: Where Then, by removing the constant terms that are unrelated to , we can rewrite: Problem (2.29) is an example of a convex optimization problem. The lagrangian dual decomposition method can be used to solve (2.29). lagrange's dual of (2.29) can be expressed as [24]: where is the dual variable for the constraint and denotes the dual objective function given by: Where primary level vector with a one in the k th position and zeros everywhere else. Then by setting The optimal can be obtained as: Utilizing schur complement technique proposed in [25], the problem in (2.30) could be designed as a problem of semi definite programming(SDP). Where So, by solving (2.33) using CVX tool box we get the optimal value of .

Introduction
In this section, simulation results and corresponding analysis are presented following the algorithm analysis discussed in section 2. Simulation results are carried out to compare the performance of massive MIMO and IRS aided moderate MIMO systems.

Performance Metrics
Performance measures such as sum rate, SINR, energy efficiency and transmit power are used to analyze and validate the proposed system.

Sum Rate
One of the measures used to compare the performance of massive MIMO and IRS-assisted moderate MIMO communication systems is the user sum rate. So, to compare the network throughput achieved by the four techniques below, we present a numerical example: IRSassisted MIMO communication with and without the ADMM optimization algorithm and massive MIMO with MMSE and ZF beamforming algorithm without IRS. We assume the BS is installed with N = 70 antennas, K = 3 users, and the number of IRS elements varies between 8 and 80 with five number of points. Other important parameters are available in Table 1. Figure 2 illustrates the sum-rate performance of the three users characterized by various IRS element counts under the four schemes. Initially, it is noticed that the sum-rate performance of the IRS-assisted MIMO system is poorer than that of the massive MIMO system without IRS. Next, it is observed that under the optimal ADMM beamforming

Transmit Power
As shown in Fig. 3, the overall transmit power is reduced by using large intelligent reflecting surfaces. So, there is a significant power saving with IRS. For example, with 40 number of reflecting elements the transmitted power is 4.5 dBm and when we increase the number of IRS elements to 60 the transmitted power is dropped to 2 dBm and as we continually increase the number of reflecting elements to 160 the transmitted power will drop to around −11 dBm.

SINR
The other metrics used to compare massive MIMO and IRS-assisted moderate MIMO communication systems is SINR. So, we examine the network SINR achieved by the following three schemes:

Energy Efficiency
Another criterion used to compare the performance of IRS-aided moderate MIMO versus massive MIMO without the IRS is energy efficiency. As we can see in Fig

Conclusion
In this paper we have suggested the IRSs to enhance the performance of massive MIMO system. Specifically, to enhance the user rate, SINR, energy efficiency and lowering the overall transmit power at the access point are all goals. The IRS aided system does not have satisfactory result compared to massive MIMO system if it has not optimized by a proper beam forming algorithm. We have two different beamforming schemes the first is active beam forming at the AP, and the second is inactive reflecting beam forming at the IRS. So, we have proposed an ADMM algorithm to jointly optimize the two beam forming schemes. We demonstrated, using this solution, that the IRS-aided moderate MIMO system achieve higher user rate, SINRs, energy efficiency and low transmit power compared to its counterpart without IRS. Because of this, IRS aided MIMO has proven to be very effective in improving the efficiency of massive MIMO system.
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Fitsum Dessalegn Mekonnen is an assistant lecturer in Dilla University, Ethiopia, with 2 years of experience. Fitsum is an Electrical and Computer Engineer graduate major in communication engineering stream and now finalized his MSC education at Addis Ababa Science and technology university, Addis Ababa, Ethiopia. Fitsum is a powerful in the workplace and uses his positive attitude and tireless energy to encourage others to work hard and succeed.