We address the design and optimization of real-world-suitable hybrid precoders for multi-user wideband sub-terahertz (sub- THz) communications. We note that the conventional fully connected true-time delay (TTD)-based architecture is impractical because there is no room for the required large num-ber of analog signal combiners in the circuit board. Additionally, analog signal combiners incur significant signal power loss. These limitations are often overlooked in sub- THz research. To overcome these issues, we study a non-overlapping subarray architecture that eliminates the need for analog combiners. We extend the conventional single-user assumption by formulating an optimization problem to maximize the minimum data rate for simultaneously served users. This complex optimization problem is divided into two sub-problems. The first sub-problem aims to ensure a fair subarray allocation for all users and is solved via a continuous domain relaxation technique. The second sub-problem deals with practical TTD device constraints on range and resolution to maximize the sub array gain and is resolved by shifting to the phase domain. Our simulation results highlight significant performance gain for our real-world-ready TTD-based hybrid precoders.

To support a vast amount of Internet of Things (IoT) devices using massive multiple-input multiple-output (MIMO) systems simultaneously, due to the limited available resources, uplink orthogonal reference signals (ORSs) must be heavily reused for channel estimation. In this situation, the performance of massive MIMO systems can be seriously degraded due to the collision of ORSs. Random nonorthogonal reference signals (NORSs) can be considered to cope with this problem since they can be independently generated regardless of the number of IoT devices. However, as the number of IoT devices increases, RS contamination also increases. In this article, we consider applying random NORSs in massive MIMO to support a large amount of IoT devices. Generally, ORSs can deliver better spectral efficiency (SE) than NORSs. However, we show that the NORS scheme has higher fairness and lower outage probability. In addition, in the situation of massive IoT, the SE performance of the NORS scheme shows substantially similar to that of the ORS scheme. These results indicate that the NORS scheme has several advantages compared to the ORS scheme in the situation of massive IoT. We provide numerical analysis which reveals some useful characteristics of using NORSs for massive MIMO with massive IoT connectivity. Using these characteristics, we propose an algorithm that can significantly reduce the outage probability.

In this paper, we consider a sectorized Massive multiple-input multiple-output (MIMO) system to simultaneously support a large amount of Internet of things (IoT) devices. To implement low complexity and low latency IoT networks, it has been shown that the reuse of orthogonal uplink reference signal (RS) is quite effective. Sectorization can reduce the heavy RS reuse in the situation of massive IoT connectivity, and consequently reduce interference from RS contamination. However, inter-sector interference (ISI) can be another source that reduces performance. We investigate the characteristics of sectorized Massive MIMO with RS reuse, and compare the performance with the case of unsectorized Massive MIMO. We present theoretical closed-form expressions of spectral efficiency (SE) applying sectorized antenna systems in the situation of massive IoT connectivity. We show that, in the massive IoT connectivity situation, sectorized Massive MIMO can show better total SE performance than unsectorized Massive MIMO, while outage probability can be seriously increased due to nonuniform antenna patterns and ISI. We also show that the power control mechanism which has been applied to unsectorized RS reuse Massive MIMO also can be successfully applied to the sectorized RS reuse Massive MIMO.

Cell-free massive MIMO (CFmMIMO) is a promising paradigm to provide uniform coverage in future wireless networks. However, a fully connected CFmMIMO system where all the access points (APs) serve every user equipment (UE) makes it challenging to deploy and scale in real-time due to high computational complexity and increased signaling overhead. In this work, we study the problem of downlink power allocation in partially connected CFmMIMO (p-CFmMIMO) systems using maximal ratio transmission (MRT). We utilize the underlying geometry of the problem to propose a graph representation of the CFmMIMO system and develop a graph neural network (GNN) based power allocation strategy to maximize the minimum SINR in the system. We demonstrate that the proposed GNN model has excellent generalizability to deployment size, radio propagation morphologies, and per-AP serving density1. Our GNN can address the power allocation problem in the fully connected case, the partially connected case, and even the cellular case with magnitudes lower computational complexity compared to the conventional numerical solvers. Notably, we show that over a wide range of service scenarios, the model achieves a median spectral efficiency that is within 10% of the optimal second-order cone programming (SOCP) solution while requiring 100 times fewer FLOPS.

We investigate Cell-Free massive MIMO networks, where each access point (AP) is equipped with a hybrid transceiver, reducing the complexity and cost compared to a fully digital transceiver. Asymptotic approximations for the spectral efficiency are derived for uplink and downlink. Capitalizing on these expressions, a max-min problem is formulated enabling us to optimize the (i) analog beamformer at the APs and (ii) pilot assignment. Simulations show that the optimization of these variables substantially increases the minimum user throughput.

Beyond 5G wireless technology Cell-Free Massive MIMO (CFmMIMO) downlink relies on carefully designed pre-coders and power control to attain uniformly high rate coverage. Many such power control problems can be calculated via second order cone programming (SOCP). In practice, several order of magnitude faster numerical procedure is required because power control has to be rapidly updated to adapt to changing channel conditions. We propose a Graph Neural Network (GNN) based solution to replace SOCP. Specifically, we develop a GNN to obtain downlink max-min power control for a CFmMIMO with maximum ratio transmission (MRT) beamforming. We construct a graph representation of the problem that properly captures the dominant dependence relationship between access points (APs) and user equipments (UEs). We exploit a symmetry property, called permutation equivariance, to attain training simplicity and efficiency. Simulation results show the superiority of our approach in terms of computational complexity, scalability and generaliz-ability for different system sizes and deployment scenarios.

Cell-Free Massive Multiple-input Multiple-output (mMIMO) consists of many access points (APs) in a coverage area that jointly serve the users. These systems can significantly reduce the interference among the users compared to conventional MIMO networks and so enable higher data rates and a larger coverage area. However, Cell-Free mMIMO systems face multiple practical challenges such as the high complexity and power consumption of the APs’ analog front-ends. Motivated by prior works, we address these issues by considering a low complexity hybrid beamforming framework at the APs in which each AP has a limited number of RF-chains to reduce power consumption, and the analog combiner is designed only using the large-scale statistics of the channel to reduce the system’s complexity. We provide closed-form expressions for the signal to interference and noise ratio (SINR) of both uplink and downlink data transmission with accurate random matrix approximations. Also, based on the existing literature, we provide a power optimization algorithm that maximizes the minimum SINR of the users for uplink scenario. Through several simulations, we investigate the accuracy of the derived random matrix approximations, tradeoff between the 95% outage data rate and the number of RF-chains, and the impact of power optimization. We observe that the derived approximations accurately follow the exact simulations and that in uplink scenario while using MMSE combiner, power optimization does not improve the performance much.

Massive multiple-input–multiple-output (MIMO) systems can support a large number of Industrial Internet of Things (IIoT) devices using many service antennas that are equipped at a base station (BS). Even though massive MIMO can increase both spectral efficiency (SE) and energy efficiency (EE), to support numerous IIoT devices, a drastic amount of downlink power consumption can be required. We investigate the performance of downlink signal transmission for massive IIoT networks using massive MIMO, and propose a downlink signal transmission scheme that can significantly reduce the transmission power consumption with little SE loss. We consider a system in which the number of IIoT devices is much larger than the number of service antennas, and in order to simultaneously support a large number of IIoT devices, every orthogonal uplink reference signal (RS) may be reused by a few IIoT devices. In this situation, we derive simple SE approximations, and based on the approximation, a target data rate is determined. The target data rate is used to determine a target signal-to-interference and noise ratio (SINR) and the corresponding signal power. In addition, the SE approximation can be used as an upper bound and the corresponding signal power can be determined by setting an adjustable parameter, which is multiplied to the upper bound. The maximum allowable uplink/downlink signal power is predefined to prevent unexpected high-power requirements. The simulation results are provided to show the effectiveness of the proposed schemes.

Cell-Free Massive MIMO with MRT (Maximum-Ratio Transmission) has the advantage of decentralized beam-forming with the smallest front-haul overhead. Its downlink power control plays a dual role of fair power distribution among users and interference mitigation. It is well-known that finding the optimal max-min power control relies on SOCP (Second Order Cone Programming) feasibility bisection search, whose large computational delay is not suitable for practical implementation. In this paper, we devise a deep learning approach for finding a practical near-optimal power control. Specifically, we propose a convolutional neural network that takes as input the channel matrix of large-scale fading coefficients and outputs the total transmit power of each AP (access point). Using this information, the downlink power control for each user is then computed by a low-complexity convex program. Our approach requires to generate far fewer training examples than existing schemes. The reason is that we augment the training dataset with magnitudes larger number of artificial examples by exploiting the special structure of the problem. The resulting deep learning model not only provides a near-optimal solution to the original problem, but also generalizes well for problems with different number of users and different propagation morphologies, without the need to retrain it. Numerical simulations validate the near optimality of our solution with a significant reduction in computational burden.

We derive formulas and algorithms to numerically calculate SINRs and max-min power controls for Cell-Free Massive MIMO in LoS channels. We consider MR (maximum-ratio), ZF (zero-forcing), and optimal linear processing for both downlink and uplink. Unlike cellular Massive MIMO, users in cell-free are statistically similar, thus dropping or rescheduling users in cell-free is not necessary. Our simulation scenarios reveal that with max-min power control, downlink and uplink perform differently: downlink ZF is about 4 dB away from optimal while uplink ZF is substantially optimal. For the downlink, at 60 GHz, MR is less than 1 dB away from ZF, making conjugate beamforming a suitable precoding scheme. These formulas and algorithms can be readily used to simulate a Cell-Free Massive MIMO in LoS channels at different operating points, thereby provide useful insights for design and implementation of an efficient Cell-Free Massive MIMO wireless network.

We investigate the feasibility of using Massive MIMO to support URLLC in both coherence interval based and 3GPP compliant pilot settings. We consider grant-free uplink transmission with MMSE receiver and adopt 3GPP channel models. In the coherence interval based pilot setting, by extensive system level simulations, we find that using a Massive MIMO base station with 128 antennas and MMSE receiver, URLLC requirements can be achieved in Urban Macro (UMa) Non-Line of Sight (NLoS) with orthogonal pilots and Neyman-Pearson detector. However, in the 3GPP compliant pilot setting, even by using the covariance matrix of Physical Resource Block (PRB) subcarriers for active UE detection and channel estimation as well as open-loop power control, we find that URLLC requirements are still challenging to achieve due to the insufficient pilot length and pilot symbol location regulations in a PRB.

An Internet-of-Things (IoT) system supports a massive number of IoT devices wirelessly. We show how to use cell-free (CF) massive multiple input and multiple output (MIMO) to provide a scalable and energy-efficient IoT system. We employ optimal linear estimation with random pilots to acquire channel state information (CSI) for MIMO precoding and decoding. In the uplink (UL), we employ optimal linear decoder and utilize random matrix (RM) theory to obtain two accurate signal-to-interference plus noise ratio (SINR) approximations involving only large-scale fading coefficients. We derive several max–min type power control algorithms based on both exact SINR expression and RM approximations. Next we consider the power control problem for downlink (DL) transmission. To avoid solving a time-consuming quasiconcave problem that requires repeat tests for the feasibility of a second-order cone programming (SOCP) problem, we develop a neural network (NN) aided power control algorithm that results in 30 times reduction in computation time. This power control algorithm leads to scalable CF Massive MIMO networks in which the amount of computations conducted by each access point (AP) does not depend on the number of network APs. Both UL and DL power control algorithms allow visibly improve the system spectral efficiency (SE) and, more importantly, lead to multifold improvements in energy efficiency (EE), which is crucial for IoT networks.

We study internet of things (IoT) systems supported by cell-free (CF) massive MIMO (mMIMO) with optimal linear channel estimation. For the uplink, we consider optimal linear MIMO receiver and obtain an uplink SINR approximation involving only large-scale fading coefficients using random matrix (RM) theory. Using this approximation we design several max-min power control algorithms that incorporate power and rate weighting coefficients to achieve a target rate with high energy efficiency. For the downlink, we consider maximum ratio (MR) beamforming. Instead of solving a complex quasi-concave problem for downlink power control, we employ a neural network (NN) technique to obtain comparable power control with around 30 times reduction in computation time. For large networks we proposed a different NN based power control algorithm. This algorithm is sub-optimal, but its big advantage is that it is scalable.

Associating users with small cell access points using Gale-Shapley's “stable marriage matching” algorithm can deliver 100% to more than 400% increase for the 95% likely per user throughput than an ad hoc method used in current literature. Gale-Shapley association is fast (quadratic time) and does not depend on power controls employed, thus suitable for real world applications.

Recently, the first version of the fifth-generation (5G) new radio (NR) standard with massive multiple-input multiple-output (MIMO) has been finished by the 3rd Generation Partnership Project (3GPP), with initial deployments occurring in 2018. Despite the major advances in 5G, there are still many challenges remaining. 6G and beyond will require even higher data rates, lower latencies, better energy efficiency, and improved robustness.Multiple antenna technologies,which have played important roles in nearly all recent wireless standards, will be key to addressing these challenges. MIMO research continues to evolve, and new MIMO research topics such as enhanced massive MIMO techniques and array architectures hold much potential for 6G and beyond. Cell-free massive MIMO utilize a large number of distributed access points (APs) that jointly serve users in a coordinated fashion, using only local channel state information at each AP. While the performance of cell-free massive MIMO can be analyzed using a similar methodology as in cellular massive MIMO, the fundamental limits, signal processing, and resource allocation are substantially different. In order to reduce the hardware cost and energy consumption in millimeter wave (mmWave) massive MIMO systems, beamspace MIMO has been proposed to significantly reduce the number of required radio-frequency (RF) chains by using lens antenna arrays or phase shifters. Alternatively, the intelligent reflecting surface (IRS) concept involves electromagnetically controllable surfaces that can be integrated into large-scale infrastructure such as building walls, airports, and stadiums. There are active and partially passive forms of large intelligent surface (LIS), and variants with either large antenna spacing or continuous aperture. There are also some substantial differences between the new multiple antenna technologies and traditional MIMO systems, such as transceiver design and propagation models. This special issue aims to highlight recent research on multiple antenna technologies.

Multiple antenna technologies have attracted much research interest for several decades and have gradually made their way into mainstream communication systems. Two main benefits are adaptive beamforming gains and spatial multiplexing, leading to high data rates per user and per cell, especially when large antenna arrays are adopted. Since multiple antenna technology has become a key component of the fifth-generation (5G) networks, it is time for the research community to look for new multiple antenna technologies to meet the immensely higher data rate, reliability, and traffic demands in the beyond 5G era. Radically new approaches are required to achieve orders-of-magnitude improvements in these metrics. There will be large technical challenges, many of which are yet to be identified. In this paper, we survey three new multiple antenna technologies that can play key roles in beyond 5G networks: cell-free massive MIMO, beamspace massive MIMO, and intelligent reflecting surfaces. For each of these technologies, we present the fundamental motivation, key characteristics, recent technical progresses, and provide our perspectives for future research directions. The paper is not meant to be a survey/tutorial of a mature subject, but rather serve as a catalyst to encourage more research and experiments in these multiple antenna technologies.

Recently, the first version of the fifth-generation (5G) new radio (NR) standard with massive multiple-input multiple-output (MIMO) has been finished by the 3rd Generation Partnership Project (3GPP), with initial deployments occurring in 2018. Despite the major advances in 5G, there are still many challenges remaining. 6G and beyond will require even higher data rates, lower latencies, better energy efficiency, and improved robustness.Multiple antenna technologies,which have played important roles in nearly all recent wireless standards, will be key to addressing these challenges. MIMO research continues to evolve, and new MIMO research topics such as enhanced massive MIMO techniques and array architectures hold much potential for 6G and beyond. Cell-free massive MIMO utilize a large number of distributed access points (APs) that jointly serve users in a coordinated fashion, using only local channel state information at each AP. While the performance of cell-free massive MIMO can be analyzed using a similar methodology as in cellular massive MIMO, the fundamental limits, signal processing, and resource allocation are substantially different. In order to reduce the hardware cost and energy consumption in millimeter wave (mmWave) massive MIMO systems, beamspace MIMO has been proposed to significantly reduce the number of required radio-frequency (RF) chains by using lens antenna arrays or phase shifters. Alternatively, the intelligent reflecting surface (IRS) concept involves electromagnetically controllable surfaces that can be integrated into large-scale infrastructure such as building walls, airports, and stadiums. There are active and partially passive forms of large intelligent surface (LIS), and variants with either large antenna spacing or continuous aperture. There are also some substantial differences between the new multiple antenna technologies and traditional MIMO systems, such as transceiver design and propagation models. This special issue aims to highlight recent research on multiple antenna technologies.

Current outdoor mobile network infrastructure cannot support uplink intensive mobile applications such as connected vehicles that collect and upload large amount of real time data. Our investigation reveals that with maximum-ratio (MR) decoding, it is theoretically impossible to support such applications with cell-free Massive MIMO, and it requires a very large number of service antennas in single cell configuration, making it practically infeasible; but with zero-forcing (ZF) decoding, such applications can be easily supported by cell-free Massive MIMO with very moderate number of access points (AP's), and it requires a lot more service antennas in single cell configuration. Via the newly derived SINR expressions for cell-free Massive MIMO with ZF decoding we show that uplink power control is unnecessary, and that with 10 MHz effective bandwidth for uplink data transmission, in urban and suburban morphologies, on the 2 GHz band, 90/km2and 32/km2single antenna AP's are enough to support 18 autonomous vehicles respectively. In rural morphology, using 450 MHz band, only 2/km2single antenna AP's is enough.

We consider a multi-cell Massive MIMO system in a line-of-sight (LoS) propagation environment, for which each user is served by one base station, with no cooperation among the base stations. Each base station knows the channel between its service antennas and its users, and uses these channels for precoding and decoding. Under these assumptions we derive explicit downlink and uplink effective SINR formulas for maximum-ratio (MR) processing and zero-forcing (ZF) processing. We also derive formulas for power control to meet pre-determined SINR targets. A numerical example demonstrating the usage of the derived formulas is provided.

Cell-free Massive MIMO (Multiple Input Multiple Output) employs a large number of AP's (Access Points) that are distributed throughout the intended coverage area to simultaneously serve a much smaller number of user AT's (Access Terminals). Conjugate beamforming is the simplest precoding method for the downlink transmission, and allows decentralized precoding processing. Max-min power control maximizes the minimal effective SINR (Signal-to-Interference-plus-Noise Ratio) among all the active users, therefore provides a uniform throughput to all users. Cell- free Massive MIMO with conjugate beamforming precoding and max-min power control is naturally radiated energy efficient due to two facts: a well-known fact that with high probability at least one AP is nearby every user, and a surprising fact that, with max-min power control, a large portion of the AP's does not transmit with full power. We find that a cell-free Massive MIMO can deliver more than 80 Mb/joule in urban, and more than 40 Mb/joule in suburban and rural scenarios. We compare its energy efficiency and spectral efficiency with single cell Massive MIMO systems and demonstrate that in suburban and rural scenarios, cell-free systems can more than double the radiated energy efficiency and at the same time dramatically increase the 95% likely per user throughput, while in an urban scenario, the gain in radiated energy efficiency can be moderate at less than 50% with a comparable 95% likely per user throughput.

To apply cyber-physical system (CPS) technique in industrial internet, a wireless technology that is able to robustly maintain hyperconnectivity between a data center and distributed user entities and/or industrial Internet of Things devices is required. We investigate the feasibility of utilizing massive multiple-input multiple-output (MIMO) as such a wireless technology. We analyze the performance of a massive MIMO base station deployed at a data center to provide massive connectivity to a large number of devices. In addition, we discuss related research challenges for deploying massive MIMO in industrial internet applications of CPS, such as device scheduling and power control, energy efficient design and radio frequency energy transfer/harvesting, signaling techniques for drones and mobile robots, and applications of underwater industrial internet.

Under LoS (line-of-sight) propagation and the assumption of perfect CSI (channel state information), for either MR (maximum-ratio) or ZF (zero-forcing) precoding/decoding, one can readily obtain Massive MIMO (multi-input multi-output) per-user effective SINR for single-cell scenarios. LoS channels are typically less correlated than IID (independent and identically distributed) Rayleigh channels, but the maximum correlation for LoS is typically much greater than for IID Rayleigh. This motivates an investigation of the dependence of max-min SINR on the maximum channel correlation. Perron-Frobenius theory and the classical Fischer inequality are used to establish some rigorous and explicit upper bounds on the effective max-min SINR (signal to interference plus noise ratio) that depend on the maximum channel correlation. These upper bounds provide an accurate description of this dependence relationship, and readily facilitate system performance analyses and scheduler designs without simulations. In high channel correlation environment, ZF can perform substantially better than MR in the downlink but the opposite is true for the uplink.

By calculating the effective max-min SINR (signal- to-interference-plus-noise ratio) and the corresponding power controls explicitly, and selectively dropping a small number of mobiles based on a simple and effective algorithm, we demonstrate that for both downlink and uplink, employing maximum-ratio or zero-forcing linear pre-coding and de-coding, Massive MIMO with max- min power control performs comparably in LoS (Line-of-Sight) and iid (independent and identically distributed) Rayleigh fading propagation environments.

Massive MIMO relies on the asymptotic orthogonality of channel vectors to different users. For M service antennas, the expected correlation between a pair of channel vectors under line-of-sight (LoS) conditions decreases at least as fast as log(M)/M, while in independent and identically distributed (iid) Rayleigh fading, it decreases much slower at 1/√M, but the variance is higher under LoS. This signifies that typically channel vectors are more nearly orthogonal under LoS, but with a non-negligible probability, they can have an anomalously large correlation. A single-cell analysis discloses that Massive MIMO with max-min power control performs comparably under LoS and iid Rayleigh, when a simple algorithm is applied under LoS to drop a small number of high-correlation users from service.

Cell-free Massive multiple-input multiple-output (MIMO) comprises a large number of distributed low-cost low-power single antenna access points (APs) connected to a network controller. The number of AP antennas is significantly larger than the number of users. The system is not partitioned into cells and each user is served by all APs simultaneously. The simplest linear precoding schemes are conjugate beamforming and zero-forcing. Max-min power control provides equal throughput to all users and is considered in this paper. Surprisingly, under max-min power control, most APs are found to transmit at less than full power. The zero-forcing precoder significantly outperforms conjugate beamforming. For zero-forcing, a near-optimal power control algorithm is developed that is considerably simpler than exact max-min power control. An alternative to cell-free systems is small-cell operation in which each user is served by only one AP for which power optimization algorithms are also developed. Cell-free Massive MIMO is shown to provide five- to ten-fold improvement in 95%-likely per-user throughput over small-cell operation.

A Cell-Free Massive MIMO (multiple-input multiple-output) system comprises a very large number of distributed access points (APs), which simultaneously serve a much smaller number of users over the same time/frequency resources based on directly measured channel characteristics. The APs and users have only one antenna each. The APs acquire channel state information through time-division duplex operation and the reception of uplink pilot signals transmitted by the users. The APs perform multiplexing/de-multiplexing through conjugate beamforming on the downlink and matched filtering on the uplink. Closed-form expressions for individual user uplink and downlink throughputs lead to max-min power control algorithms. Max-min power control ensures uniformly good service throughout the area of coverage. A pilot assignment algorithm helps to mitigate the effects of pilot contamination, but power control is far more important in that regard. Cell-Free Massive MIMO has considerably improved performance with respect to a conventional small-cell scheme, whereby each user is served by a dedicated AP, in terms of both 95%-likely per-user throughput and immunity to shadow fading spatial correlation. Under uncorrelated shadow fading conditions, the cell-free scheme provides nearly fivefold improvement in 95%-likely per-user throughput over the small-cell scheme, and tenfold improvement when shadow fading is correlated.

A heterogeneous system of a Massive multiple- input-multiple-output (MIMO) macro cell with low power ancillary small cells can achieve higher spectral and energy efficiency than a Massive MIMO macro cell alone. The performance of such heterogeneous system is examined in this paper. A few small cells are used to enhance the spectral and energy efficiency of the overall system. Macro Massive MIMO base station uses a large number of antennas, which enables accurate nulling of small cell users to suppress the interference between macro cell and small cells. We derive analytical expressions for the capacity and signal-to- interference-plus-noise-ratio (SINR) lower bounds for both the downlink (DL) and uplink (UL) of the heterogeneous Massive MIMO system. Our simulation results show that nulling from macro cell Massive MIMO is essential for small cells' good and stable performance.

For a general multicell Massive MIMO network, we obtain easily verifiable conditions for the existence of power controls that meet given down-link and up-link per access terminal SINR requirements. Surprisingly, some loosely constructed sufficient conditions that guarantee the existence of power controls become necessary in the single cell case, whose “max-min” SINR problems are then easily solved.

We provide explicit formulas for the optimal number of antennas per base station to maximize the cell total energy efficiency of a power- controlled multi-cell Massive MIMO. Furthermore, we show that equipping the same number of antennas in each base station results in virtually no loss in energy efficiency due to the flatness of energy efficiency function. Conjugate beamforming compares very competitively with zero-forcing and in fact, due to the loss in effective array gain and the additional computational cost in zero-forcing, conjugate beamforming can achieve better energy efficiency when per user throughput demand is moderate. In single cell case, we provide explicit algebraic formulas for the optimal number of antennas and optimal radiated power when a target per user throughput is given.

Traditional macro-cellular wireless networks are not capable of delivering even throughputs to all the users due to large variations in slow fading and inter-cell and inter-user interferences, and the throughputs for cell edge users are necessarily sacrificed to achieve an acceptable level of cell spectral efficiency. We show that this is not the case for large-scale antenna systems (LSAS, also known as Massive MIMO). Specifically, we show that by means of its superior beamforming and frequency response flattening capabilities, simple noncooperative uplink and downlink power controls can be devised for an LSAS macro-cellular wireless network to provide intra-cell equalized, multi-Mbps throughputs to all users. Compared with current LTE, a 64-antenna LSAS can provide cell edge throughputs with at least a ten-fold increase in the uplink and a significant gain in the downlink, and at the same time provide a total spectral efficiency per cell that quintuples in the uplink and triples in the downlink.

Large-Scale Antenna Systems (LSAS) is a form of multi-user MIMO technology in which unprecedented numbers of antennas serve a significantly smaller number of autonomous terminals. We compare the two most prominent linear pre-coders, conjugate beamforming and zero-forcing, with respect to net spectral-efficiency and radiated energy-efficiency in a simplified single-cell scenario where propagation is governed by independent Rayleigh fading, and where channel-state information (CSI) acquisition and data transmission are both performed during a short coherence interval. An effective-noise analysis of the pre-coded forward channel yields explicit lower bounds on net capacity which account for CSI acquisition overhead and errors as well as the sub-optimality of the pre-coders. In turn the bounds generate trade-off curves between radiated energy-efficiency and net spectral-efficiency. For high spectral-efficiency and low energy-efficiency zero-forcing outperforms conjugate beamforming, while at low spectral-efficiency and high energy-efficiency the opposite holds. Surprisingly, in an optimized system, the total LSAS-critical computational burden of conjugate beamforming may be greater than that of zero-forcing. Conjugate beamforming may still be preferable to zero-forcing because of its greater robustness, and because conjugate beamforming lends itself to a de-centralized architecture and de-centralized signal processing.