A. Related Works
In 2011, Xu et al. [1] have considered the adaptively adjusting system parameters that were composed of mode, transmit power and bandwidth for maximizing the “Bits per- Joule” energy efficiency (BPJ-EE) having imperfect CSIT in the case of downlink MIMO systems. The mode was described as the transmission strategy choice such as the active user number, active receive/transmit antenna number, Block Diagonalization (BD), or Singular Value Decomposition (SVD). Initially, for every dedicated mode, transmit power as well as the optimal bandwidth were derived with appropriate capacity estimation schemes. An ergodic capacity-oriented mode switching scheme offered insights under the provided scenarios.
In 2012, Heliot et al. [2] have introduced a new tradeoff that offered better accuracy for several antenna configurations and SE values. The EE gain associated with the MIMO was analytically assessed over SISO system for two distinct forms of Power Consumption Models (PCMs) such as more realistic PCM and theoretical PCM. The more realistic PCM considered the amplifier inefficiency and fixed consumed power. The EE gain rises with the antenna count and SE that in turn described MIMO as a better EE enabler. With consideration of the realistic PCM, the EE gain was small and minimizes with the transmit antenna count.
In 2013, Onireti et al. [3] have investigated the tradeoff among SE and EE for the downlink and uplink of the Distributed MIMO system with consideration of distinct forms of PCMs. Moreover, accurate and generic high and low SE approximations were derived for several Radio Access Units (RAUs). DMIMO was much energy efficient in both the realistic and idealistic PCMs for cell edge users. Quoc et al. [4] have derived the lower capacity bounds for “Minimum Mean Square Error (MMSE) detection, Zero Forcing (ZF), and Maximum Ratio Combining (MRC)” detection. The MRC receiver was worse than the MMSE and ZF. It enhanced the EE and SE with magnitude orders than the single-antenna system. Nguyen et al. [5] have considered the transmission of data in a Full Duplex (FD) MU MIMO system, in which the communication between the BS and multiple users occurs bidirectionally in the UpLink (UL) and DownLink (DL) channels on the similar system resources. It was not practical because of the Self-Interference (SI) among receive and transmit antennas. The recent approaches revealed that SI permitted for the FD transmission. The low complexity designs were developed for the EE and SE maximization and their performance was evaluated in a numerical manner. Ketonen et al. [8] have considered the channel estimation algorithms along with their implementations in the case of mobile receivers. The performance was enhanced by the "Decision Directed (DD) Space Alternating Generalized Expectation maximization (SAGE)". The channel was also estimated by the MMSE filtering among the pilot symbols. The latency issues as well as the complexity reduction were also defined in the architectural design.
In 2014, Bi et al. [6] have addressed an EE selection algorithm on the basis of convex optimization for the massive MIMO wireless communication systems. The EE was maximized by jointly optimizing servable Mobile Terminals (MTs), transmit antenna subset, and transmit antenna count with consideration of the larger channel capacity compared to a specific threshold. Better performance was achieved when differentiated with the no antenna selection.
In 2015, Xuan and Chan [7] have learnt the capacity characteristics of Signal-to-Leakage-and-Noise Ratio Precoding Scheme (SLNR-PS). The capacity bounds were derived when the BS antenna count was large. A tradeoff was described among SE and EE for the purpose of equal power allocation. Additionally, the EE optimization problem was considered under both the maximum QoS and transmits power constraints. This optimization problem was handled by the EE power allocation strategy. Xin et al. [9] have analyzed the characteristics of massive MIMO cellular systems having pilot contamination. The area EE was attained with consideration of a practical power consumption method. The theoretical outcomes examined few parameters like “count of symbols, count of users, and count of antennas at the BS” and it was found that the channel remained constant everywhere. Zhang et al. [10] have addressed a multi-pair amplify-and-forward two-way relay channel. Here, the information was exchanged by several full-duplex users via a full-duplex relay. The EE was enhanced by four typical power scaling techniques on the basis of the ZF reception/ZF transmission and MRC/MRT. The asymptotic EE and SE were quantified for the introduced power scaling techniques. The loop interference was minimized by the transmit power reduction. The inter user interference as well as the inter pair interference was also eradicated in vast antenna count.
Patcharamaneepakorn et al. [12] have learned the Generalized Spatial Modulation (Gen-SM) techniques in MU-MIMO for EE and high throughput approach in the case of 5G wireless network. A detection algorithm was suggested on the basis of linear processing approaches. The achievable sum rates were approximated by a general framework having linear detection. It also investigated the probability of antenna combination detection. It also enabled an implicit tradeoff among EE and SE. Tang et al. [13] have analyzed the fundamental EE-SE relationship having a practical power method with consideration of the consumption of power because of the active transmit antenna count and admitted user count. The description of active transmits antenna set, and optimal admitted user set was considered to be non-convex. The EE-SE tradeoff for a single carrier problem was analyzed by the transmit antenna set and fixed admitted user set. The optimal tradeoff was further explored by the antenna and the user selection techniques. Sun et al. [16] have described the fading MIMO channels with the help of statistical CSI, and the potential gains of MIMO NOMA strategy were explored with respect to EE and ergodic capacity. The maximization problem of the ergodic capacity was initially studied for the MIMO NOMA systems. The optimal input covariance structure was derived for the ergodic capacity maximization. In the case of EE maximization, the optimization problem was defined under the minimum rate constraint as well as the total transmit power constraint. The optimal power allocation associated with the EE design was also labelled. The computation complexity was further minimized by introducing a suboptimal closed form solution and near-optimal solution. Chun and Ho [18] have described the MIMO system with consideration of the SM on the basis of Rayleigh fading channel transmission having known channel correlations and large scale fading loss. The observation was impacted by the configurations and transmission mechanisms. The transmission mode selection was developed by a framework for the optimal EE or SE. It conformed to the error rate and transmission needs with less complexity. A closed form error rate approximation was also described. The problems could be handled through naive exhaustive search technique. The complexity was also minimized through lookup tables. The framework was evaluated using the computer simulations. Liu et al. [19] have analyzed the tradeoff among EE and SE for the massive MIMO. The SE and EE were optimized in terms of the transmit power count and transmit antenna count. The two algorithms proposed were the Normal Boundary Intersection Particle Swarm Optimization (NBI-PSO) and Weighted Sum PSO (WS-PSO). The NBI-PSO offered many evenly distributed solutions. Li et al. [20] have analyzed the achievable rate of FD having massive MIMO. The BS utilized imperfect CSI that was attained from linear receiver and transmitter, non-ideal hardware, and received pilots like MRC/MRT or ZF for processing the signals. The approximate closed form expressions investigated the impact of the hardware imperfection as well as antenna count on the SI that was considered as the bottleneck of FD. Two non-convex power allocation optimization problems were described for the EE and SE maximization such as the fractional programming approach and sequential convex approximation approach. Two iterative algorithms were also introduced with accurate local convergence.
In 2016, Chen et al. [11] have labelled a relay-aided massive MIMO. On the basis of the theoretical outcomes, the impacts of few system parameters like “transmit power of Relay Station (RS), transmit power at the BS, and antenna count at the BS” were analyzed for obtaining the tradeoff among EE and SE through the power control. Two optimization techniques were also introduced such as alternate optimization and 1-D searching. The outcomes tested the efficiency of the two techniques. Hao et al. [14] have analyzed the tradeoff among SE and EE. Here, power coordination as well as user association was considered in a joint fashion. An efficient algorithm was addressed. Higher rate fairness was attained than several algorithms. Tsz et al. [15] have considered the EE-SE maximization of a multi-cell, multi-relay, MU system, in which the entire network nodes were joined with multi-antenna transceivers. A set of transmission protocols were conceived for the potentially excessive interference on the basis of the Interference Alignment (IA). The full-IA eradicated the entire Intra Cell Interference (ICI) and various cell interference with the help of the Receie Beam Forming Matrices (RxBFMs). The partial IA empties the ICI. The conflict of finding the power control variables and optimal SMCs was transformed into a convex optimization form with chosen transformations and relaxations. It was computed distributively with the help of sub gradient and classic dual decomposition techniques. Byung Moo Lee [32] has analyzed the possibility of enhancing the EE of massive MIMO -OFDM systems that was subjected to the battery-lessened IoT networks. The EE enhancement was much significant one. Few efficient techniques were classified for the consideration. The UL reference signal was considered for the UL aspect. The UL RS power reduction increased the possibility of channel estimation error. The usage of RF energy transfer was considered with the help of Unmanned Aerial Vehicles (UAVs) for expanding the operating time of battery-lessened IoT devices.
In 2017, He et al. [17] have proposed a spatially dynamic power control solution for reducing the D2D-to-cellular and cellular-to-D2D interference. It involved maximum transmit power and no D2D links. The EE and SE were evaluated using an analytical technique. Hence, the exact SE expressions were derived that quantified the effects of key system parameters like D2D density and massive MIMO antennas. The necessary conditions were offered for attaining the anticipated SE. It reduced the interference among the D2D and cellular tier. Xu et al. [21] have addressed a multi pair massive MIMO relay network, in which the relay was equipped with vast antenna count and driven by few count of Radio Frequency (RF) chains. Some of the user pairs were scheduled for the simultaneous transmission. A hybrid signal processing strategy was proposed for DL and UL network transmissions. The analytical expressions of EE and SE were derived in terms of the RF chain count under imperfect channel estimation. The transmit power associated with the relay and user were scaled down by handling an asymptotically unvaried SE. It was revealed that EE was a quasi-concave function in terms of the RF chain count and thus admitted a unique globally optimal choice of the RF chain count.
Hao et al. [22] have developed a framework for learning the tradeoff among SE and EE in massive MIMO enabled heterogeneous networks with consideration of the backhaul capacity constraint. It jointly optimized the activated antenna count, power coordination, spectrum allocation, and user association that was defined as a multi objective optimization problem for the SE and EE maximization. It was transformed into single objective optimization problem by the weighted Tchebycheff technique that needed extra computational complexity for attaining the optimum. Therefore, a low-complexity efficient algorithm was proposed on the basis of primal decomposition, in which spectrum allocation problem, user association problem, antenna count optimization problem, and the power coordination problem were solved separately. It fast converged among various iterations. Yang et al. [23] have analyzed the EE and SE for a massive MIMO system. Here, the information was exchanged through a relay station that was considered with vast scale antennas. It was considered that imperfect CSI was present, and MRT/MRC beamforming was used at the relay station. With consideration of the scaled or constant transmit pilot sequence power, the asymptotic EE and SE were quantified, where the RS and transmit power was scaled down when the relay antenna count became infinity. Additionally, a closed form SE expression was achieved in an approximate manner. Wang et al. [24] have addressed a MU-FD massive MIMO system. The CSI was considered imperfect, and it did not attain instantaneous Loop Interference (LI) CSI channel. Based on the less complexity DL precoding and UL beamforming approaches, the asymptototic expressions associated with the SINR of DL and UL were derived when the antenna count of the BS attained infinity. The Power Allocation (PA) scenarios were developed for the sum SE and EE maximization having the maximum power constraint at the users and BS. It was better than the HD counterpart. Qiang et al. [34] have analyzed the EE-SE tradeoff problem in the case of downlink large-scale MIMO systems. It was considered as Pareto optimal set-oriented multiple objective optimization problem in terms of the available antenna count and transmit power at the BS. It could also be maximized by the optimization of available antenna count and transmit power in the DL large scale MIMO systems. Kashi and Abolhassani [36] have introduced a Cognitive Radio Network (CRN), in which the BS and primary BS were equipped with vast antenna count. Here, imperfect as well as the perfect CSI were addressed in a separate manner. Additionally, the effect of pilot contamination was also analyzed. The minimum antenna count attained a particular SE in the closed form expression.
In 2018, Verenzuela et al. [25] have described the UL of a massive MIMO with the help of MRC detection and the Superimposed Pilot (SP) and Regular Pilot (RP) was compared with respect to EE and SE. The closed form achievable rates were derived under BS deployment in a randomly practical format. The RP achieved better EE and SE in the areas of practical scenarios. Huang et al. [26] have studied MU-DL beamforming in massive MIMO systems for Resource Efficiency (RE) maximization that was described as a weighted combination of SE and EE. It contained much flexibility in handling the balance among EE and SE. Initially, a DL-UL duality was analyzed for maximizing the RE. The duality handled the RE or EE beamforming optimization problem. An optimization algorithm was proposed for realizing the EE and SE MU beamforming having statistical or instantaneous CSI. It attained better performance asymptotically, but with lesser complexity.
Tan et al. [27] have analyzed the DL achievable EE and SE of massive MIMO for the consideration of hybrid architectures on the basis of phase shifters, in which the BS contained accurate CSI and baseband processing was accomplished for the ZF precoding. An approximated upper bound was derived using the ideal phase shifters. The total achievable SE enhanced with the SNR, user count, and BS antenna count. The achievable SE could be enhanced by improving the phase shifter bits and antenna count as well as optimal SNR maximized the achievable EE. Ribeiro et al. [28] have analyzed the EE of quantized hybrid transmitters that in turn was equipped with a partially/fully joined phase shifting network. It consisted of passive/active phase shifters and it was compared to the quantized digital precoders. A quantized SU-MIMO was developed on the basis of an additive quantization noise approximation with consideration of the loss models and realistic power consumption for evaluating the EE and SE of the transmit precoding techniques. The partially connected hybrid precoders were more effective. The active phase shifters offered larger data rates and superior EE was maintained by the passive phase shifters. Xuan and Chan [29] have derived tractable bound expressions on SE for MIMO system. These bounds were tight and exact values were approached when the BS antenna count was large. The impacts of the channel estimation quality as well as the system parameters involving the training length transmit power, and BS antenna count was investigated in an explicit manner. The optimum EE was attained by an alternating optimization algorithm. The training length and the optimal transmit power could attain high EE.
Moghadam et al. [30] have studied the characteristics of a MIMO in the availability of non linear Power Amplifiers (PAs). Initially, a statistical method was proposed for the transmitted signal and the spatial direction was shaped using the beamforming filter. The effect of nonlinear PAs should not be eradicated even in the case of large antenna regime. The tradeoff was analyzed among EE and SE. Enhancing the level of transmit power was much effective with respect to EE. When the transmit power was increased, the analog beamforming resulted in higher EE and SE than the hybrid and digital beamforming strategies. Sharma et al. [31] have considered two-way Amplify-and-Forward (AF) relaying, in which the information was exchanged by the FD user pairs through a shared FD massive MIMO relay. The non-convex EE metric was maximized by considering it as a Pseudo Concave (PC) problem that was handled with the help of classic Dinkelbach technique. It also characterized the inter-user interference and self loop regimes. Sharma et al. [33] have considered a hybrid massive MIMO AF relay having fewer RF chains when compared with the antennas. The ZF processing was considered at the relay and the asymptotic EE and SE expressions were derived in an analytical manner with the relay antenna count attaining infinity. Liu et al. [35] have proposed a new technique for tight holding of massive MIMO having ZF beamforming under Imperfect Reciprocity Calibration (IRC). Depending on the analytical outcomes, key insights were described for modelling the practical system in three ways such as the SE loss bound, SE saturation region, and interference power scaling rule. The optimal EE loss was much sensitive to the IRC while considering a typical transmits power value range. Cao et al. [37] have proposed the performance of UL-SE in massive MIMO. The MRC receiver was utilized at the BS for the two channel estimation techniques. The initial technique was dependent on Least Minimum MSE (LMMSE). The second technique was dependent on Line-of-Sight (LOS). The corresponding analytical expressions were also provided. The data rate associated with the LOS technique was linear with the BS antenna count. The spatial correlation might increase or decrease the rate.
Chen et al. [38] have considered the performance and QoS needs of users and learned the EE PA and joint user association problem. The optimization problem was difficult to handle directly because of its non-convex and mixed-integer features. The real problem was decomposed into power allocation and user association sub-problem. In the final step, a sub optimal solution was attained with the help of a less complexity iterative algorithm. It offloaded the BS traffic in a very efficient manner. The system EE was enhanced than the user association schemes. Zheng and Gharavi [42] have analyzed the tradeoff among mobile and static communication scenarios through closed form expressions. The computational complexity was minimized that activated the RF chains for the channel condition and MIMO system. Specific RF chain count must be activated for the EE maximization at high SNRs that was distinct from the optimal configuration for the SE maximization. A simple analog beamforming with one RF chain was optimal for EE and SE. The beamforming gain was efficiently attained among high speed mobile devices. Fan and Zhang [47] have optimized and analyzed the EE of MU-MIMO in DL multi cell networks. Initially, the SE was analyzed using vast BS antenna count with the help of ZF and MRT precoders in DL cellular networks. The BS antenna count was vast. Next, the EE definition and the analytical SE outcome were utilized for attaining the EE expression. The EE maximization was achieved using iterative optimization algorithms. The analytical outcomes were accurate when the CSI was present at the transmitter. Hei et al. [49] have concentrated on the tradeoff optimization among SE and EE in MU massive MIMO systems with respect to the transmit power and transmit antenna count. The Pareto optimal front was achieved by the multi-objective adaptive Genetic Algorithm (GA) for enhancing the convergence speed. It maintained better performance on the benchmark functions with respect to the adopted performance metrics. Bhandari and Jadhav [51] have developed new channel estimation technique for handling the ISI problem. The ISI could lead to bad performance. It was joined with Independent Component Analysis (ICA), thus known as Hybrid ICA (HICA) for the ISI effect minimization. It also claimed the reliability and scalability. The performance metrics considered here were the SE, Bit Error Rate (BER), computational costs, and Peak to Average Power Ratio (PAPR).
In 2019, Ding et al. [39] have analyzed EE and SE of hybrid precoding in massive MIMO. An approximation expression was derived with consideration of the quantization noise. The performance was identical to the full digital precoding. Zhou et al. [40] have labelled a crucial parameter for adjusting the SE-EE preference. The final problems were shown in complicated forms. Initially, required variations must be made and then the feasible algorithms could be modelled. The associated convergence analysis computation complexity was also described. Distinct network parameters were analyzed for various traditional mechanisms and advocated mechanisms. Ngozichukwuka et al. [41] have initially diverse the exploration of array response vectors. The joint optimization was decoupled over the combiners and hybrid precoders. The identification step associated with the Orthogonal MP (OMP) was revised for choosing the accurate column indices. The sparse solution was refined iteratively that needed only some iterations. It attained better SE with minimized iteration count. Saatlou et al. [43] have handled the problem of SE maximization in a MU-MIMO DL system, in which a BS was equipped with vast antenna count. The accuracy as well as the computational simplicity was tested via the simulations. It attained the SE of massive MIMO with the beamforming training scheme and optimal resource allocation scheme. Gong et al. [44] have analyzed the EE of MIMO AF relaying networks that relied on the imperfect CSI. The relay jointly optimized the relay beamforming matrices and source covariance by EE maximization under multiplicative or additive destination CSI errors. It also derived the optimal channel diagonalizing structure. It has the capability to attain the locally optimal solution. The channel diagonalizing structure was optimal for the multiple relay beamforming matrices and source covariance matrix. Li et al. [45] have analyzed the EE maximization problem of distributed massive systems that were considered to be non convex. A PA algorithm was introduced with sequential convex approximation and fractional programming. The optimization problem was solved over a lengthier interval. It converged to the Karush Kuhn Tucker points. The simulation outcomes revealed the efficiency of the suggested algorithm and derived expression accuracy. Better conclusions were arrived among distinct antenna deployments and beamforming schemes.
Bashar et al. [46] have considered a cell-free massive MIMO-UL. A closed form expression with consideration of the SE was derived by the impacts of quantization distortion and channel estimation error. The maximization problem associated with EE was identified using throughput requirement, backhaul capacity, and per-user power constraints. The PA problem was converted into Geometric Programming (GP) problem by the heuristic sub-optimal scheme and Successive Convex Approximation (SCA). An iterative algorithm handled every sub problem in an alternate manner. Salh et al. [48] have analyzed the tradeoff among SE and EE for DL massive MIMO in terms of the PA problem. The maximum tradeoff among SE and EE could be attained on the basis of the optimal transmit PA when the BS count for the SE value was more. Ghosh et al. [50] have treated the cognitive femtocell BS as secondary BS for attaining a channel with the help of auction game having utility function. The spectrum was allocated to the femtocell BS by the spectrum manager on the basis of maximum pricing value. It minimized the active antenna count that in turn decreased the consumption of energy. It also enhanced the SE and SINR MIMO CRN-oriented techniques and traditional CRN. Qian et al. [55] have studied a HD Decode-and-Forward (DF) massive MIMO relaying system, where the information’s were exchanged via a massive MIMO relay. The ZFT/ZFR was considered at the relay. Initially, the large scale approximations of the sum SE were learned. Three particular power scaling laws were also concentrated for learning the tradeoff among transmit power and relay. It also concentrated on scaling the transmit power with the relay antenna count for maintaining a finite SE performance. A practical power consumption method was considered for analyzing the EE and the effect of interplay among the EE performance as well as the power scaling laws was also described. The system fairness was considered through the SE maximization.
In 2020, You et al. [52] have analyzed SE-EE tradeoff in single cell massive MIMO-DL transmission having statistical CSI at the transmitter side. The system RE was optimized that has the capability to strike an SE-EE balance. A closed form solution was considered for the eigen vectors of distinct user terminals that represented the beam domain in MIMO-DL. The RE optimization model was minimized to a real-valued PA problem. The approaches of random matrix theory and sequential optimization theory by developing a water filling structured PA algorithm. Hong et al. [53] have addressed a new PA algorithm for the EE and SE maximization of MIMO under QoS constraints. One of the major factors for guaranteeing the QoS was the delay outage. The effect of delay outage was considered using Effective Capacity (EC). The effective EE formulated an effective EE and Effective Capacity (EC) maximization that was called as the adaptive PA problem. The Lagrangian technique handled the problem of optimization and also developed an optimal PA algorithm. Ataeeshojai et al. [54] have modelled a "green, highly energy-efficient cellular heterogeneous network (HetNet)" with the benefits of MIMO and small cell deployment. The users were served by multiple-antenna small cells. The consumption of circuit energy was assumed to be critical. This was labelled by developing radio resource block assignment algorithm and EE antenna selection and a single RF structure were assumed for the massive MIMO. It also formulated the PA optimization problem and EE beamforming design problem in terms of fronthaul capacity, transmit power budget of BS, and QoS needs of users. The problem was handled by the Dinkelbach technique. Nguyen et al. [56] have formulated a comprehensive and new optimization problem for the EE and SE maximization, where the Access Point (AP) selection, AP-UE association, and power control were optimized jointly under a realistic power consumption method that in turn produced difficult mixed-integer nonconvex programming class. An effective technique was proposed through the exploitation of a strong coupling among continuous and binary variables that in turn created much tractable problem. Two complexity transmission models were developed on the basis of ZF. The impacts of pilot contamination were lessened by a new heap-oriented pilot assignment algorithm. It needed only minimum execution time. Mandawaria et al. [57] have considered a massive MIMO system, in which the users were served by the BS through multiple relays with the help of NOMA. These two artifacts were valid for arbitrary BS antenna count. The relay powers and the Bs were allocated jointly for the weighted sum EE and global EE optimization that were considered as fractional functions of the optimization variables. These two optimizations developed two new transformations. The additional power usage was avoided when an optimal value was achieved. Ali et al. [58] have derived approximate and new mathematical expressions of the SE lower bound of a massive MIMO. Three antenna scheduling algorithms were considered distance-oriented, random, and semi-orthogonal user scheduling algorithms, in which the antennas were chosen on the basis of maximum SNR having scheduled users. The impact of the changes of transmitting radius, number of antennas, and SNR was also investigated. The outcomes were identical to the identical factor variation.
Satyanarayana Murthy Nimmagadda [59] has implemented a massive MIMO model with consideration of the EE and SE. The optimal solutions were generated for the PA as well as the beamforming vectors. The EE and SE were maximum via the resource efficiency metric method. The complex optimization problems were solved by these algorithms under distinct applications in terms of good convergence rate and also offered superior tradeoff among the EE and SE in massive MIMO technology. Sun et al. [60] have constructed a mathematical optimization method with consideration of the fairness problem so that the SE was optimized for the entire users. An attention-oriented CNN was developed for enhancing the SE. The CNN minimized the network parameter count and floating point operations. The experiments were performed from three aspects such as computational performance, PA performance, and fair antenna PA. The heat maps having distinct interference thresholds described the fair allocation for the entire users.
B. Chronological Review
The chronological review considering the gathered 60 works from the years 2011 to 2020 is given in pictorial format as in Fig. 2. Here, 1.6% of the works are gathered from the year 2011, 2012, and 2014. 6.67% of the works are gathered from the year 2013 and 2016. 15% of the works are collected from the year 2015. 11.67% of the works are collected from the year 2017. 25% of the works is gathered from the year 2018. 16.67% of the works are collected from the year 2019. 13.33% of the works are collected from the year 2020. Hence, it is clear that maximum of the works was gathered from the year 2018.