We study downlink (DL) channel estimation in a multi-cell Massive multiple-input multiple-output (MIMO) system operating in a time-division duplex. The users must know their effective channel gains to decode their received DL data signals. A common approach is to use the mean value as the estimate, motivated by channel hardening, but this is associated with a substantial performance loss in non-isotropic scattering environments. We propose two novel estimation methods. The first method is model-aided and utilizes asymptotic arguments to identify a connection between the effective channel gain and the average received power during a coherence block. The second one is a deep-learning-based approach that uses a neural network to identify a mapping between the available information and the effective channel gain. We compare the proposed methods against other benchmarks in terms of normalized mean-squared error and spectral efficiency (SE). The proposed methods provide substantial improvements, with the learning-based solution being the best of the considered estimators.

A large-scale distributed antenna system that serves the users by coherent joint transmission is called Cell-free Massive MIMO (multiple input multiple output). For a given user set, only a subset of the access points (APs) is likely needed to satisfy the users' performance demands. To find a flexible and energy-efficient implementation, we minimize the total power consumption at the APs in the downlink, considering both the hardware and transmit powers, where APs can be turned off. Even though this is a non-convex optimization problem, a globally optimal solution is obtained by solving a mixed-integer second-order cone program. We also propose a low-complexity algorithm that exploits group-sparsity in the problem formulation. Numerical results manifest that our optimization framework can greatly reduce the power consumption compared to keeping all APs turned on and only minimizing the transmit powers.

This paper considers the sum spectral efficiency (SE) optimization problem in multi-cell Massive MIMO systems with a varying number of active users. This is formulated as a joint pilot and data power control problem. Since the problem is non-convex, we first derive a novel iterative algorithm that obtains a stationary point in polynomial time. To enable real-time implementation, we also develop a deep learning solution. The proposed neural network, PowerNet, only uses the large-scale fading information to predict both the pilot and data powers. The main novelty is that we exploit the problem structure to design a single neural network that can handle a dynamically varying number of active users; hence, PowerNet is simultaneously approximating many different power control functions with varying number inputs and outputs. This is not the case in prior works and thus makes PowerNet an important step towards a practically useful solution. Numerical results demonstrate that PowerNet only loses 2% in sum SE, compared to the iterative algorithm, in a nine-cell system with up to 90 active users per in each coherence interval, and the runtime was only 0.03 ms on a graphics processing unit (GPU). When good data labels are selected for the training phase, PowerNet can yield better sum SE than by solving the optimization problem with one initial point.

Massive MIMO (multiple-input multiple-output) is considered as an heir of the multi-user MIMO technology and it has gained lots of attention from both academia and industry since the last decade. By equipping base stations (BSs) with hundreds of antennas in a compact array or a distributed manner, this new technology can provide very large multiplexing gains by serving many users on the same time-frequency resources and thereby bring significant improvements in spectral efficiency (SE) and energy efficiency (EE) over the current wireless networks. The transmit power, pilot training, and spatial transmission resources need to be allocated properly to the users to achieve the highest possible performance. This is called resource allocation and can be formulated as design utility optimization problems. If the resource allocation in Massive MIMO is optimized, the technology can handle the exponential growth in both wireless data traffic and number of wireless devices, which cannot be done by the current cellular network technology.

In this thesis, we focus on the five different resource allocation aspects in Massive MIMO communications: The first part of the thesis studies if power control and advanced coordinated multipoint (CoMP) techniques are able to bring substantial gains to multi-cell Massive MIMO systems compared to the systems without using CoMP. More specifically, we consider a network topology with no cell boundary where the BSs can collaborate to serve the users in the considered coverage area. We focus on a downlink (DL) scenario in which each BS transmits different data signals to each user. This scenario does not require phase synchronization between BSs and therefore has the same backhaul requirements as conventional Massive MIMO systems, where each user is preassigned to only one BS. The scenario where all BSs are phase synchronized to send the same data is also included for comparison. We solve a total transmit power minimization problem in order to observe how much power Massive MIMO BSs consume to provide the requested quality of service (QoS) of each user. A max-min fairness optimization is also solved to provide every user with the same maximum QoS regardless of the propagation conditions.

The second part of the thesis considers a joint pilot design and uplink (UL) power control problem in multi-cell Massive MIMO. The main motivation for this work is that the pilot assignment and pilot power allocation is momentous in Massive MIMO since the BSs are supposed to construct linear detection and precoding vectors from the channel estimates. Pilot contamination between pilot-sharing users leads to more interference during data transmission. The pilot design is more difficult if the pilot signals are reused frequently in space, as in Massive MIMO, which leads to greater pilot contamination effects. Related works have only studied either the pilot assignment or the pilot power control, but not the joint optimization. Furthermore, the pilot assignment is usually formulated as a combinatorial problem leading to prohibitive computational complexity. Therefore, in the second part of this thesis, a new pilot design is proposed to overcome such challenges by treating the pilot signals as continuous optimization variables. We use those pilot signals to solve different max-min fairness optimization problems with either ideal hardware or hardware impairments.

The third part of this thesis studies a two-layer decoding method that mitigates inter-cell interference in multi-cell Massive MIMO systems. In layer one, each BS estimates the channels to intra-cell users and uses the estimates for local decoding within the cell. This is followed by a second decoding layer where the BSs cooperate to mitigate inter-cell interference. An UL achievable SE expression is computed for arbitrary two-layer decoding schemes, while a closed form expression is obtained for correlated Rayleigh fading channels, maximum-ratio combining (MRC), and largescale fading decoding (LSFD) in the second layer. We formulate a sum SE maximization problem with both the data power and LSFD vectors as optimization variables. Since the problem is non-convex, we develop an algorithm based on the weighted minimum mean square error (MMSE) approach to obtain a stationary point with low computational complexity.

Motivated by recent successes of deep learning in predicting the solution to an optimization problem with low runtime, the fourth part of this thesis investigates the use of deep learning for power control optimization in Massive MIMO. We formulate the joint data and pilot power optimization for maximum sum SE in multi-cell Massive MIMO systems, which is a non-convex problem. We propose a new optimization algorithm, inspired by the weighted MMSE approach, to obtain a stationary point in polynomial time. We then use this algorithm together with deep learning to train a convolutional neural network to perform the joint data and pilot power control in sub-millisecond runtime. The solution is suitable for online optimization.

Finally, the fifth part of this thesis considers a large-scale distributed antenna system that serves the users by coherent joint transmission called Cell-free Massive MIMO. For a given user set, only a subset of the access points (APs) is likely needed to satisfy the users' performance demands. To find a flexible and energy-efficient implementation, we minimize the total power consumption at the APs in the DL, considering both the hardware consumed and transmit powers, where APs can be turned off to reduce the former part. Even though this is a nonconvex optimization problem, a globally optimal solution is obtained by solving a mixed-integer second-order cone program (SOCP). We also propose low-complexity algorithms that exploit group-sparsity or received power strength in the problem formulation.

Massive multiple-input–multiple-output (MIMO) systems can suffer from coherent intercell interference due to the phenomenon of pilot contamination. This paper investigates a two-layer decoding method that mitigates both coherent and non-coherent interference in multi-cell Massive MIMO. To this end, each base station (BS) first estimates the channels to intra-cell users using either minimum mean-squared error (MMSE) or element-wise MMSE estimation based on uplink pilots. The estimates are used for local decoding on each BS followed by a second decoding layer where the BSs cooperate to mitigate inter-cell interference. An uplink achievable spectral efficiency (SE) expression is computed for arbitrary two-layer decoding schemes. A closed form expression is then obtained for correlated Rayleigh fading, maximum-ratio combining, and the proposed large-scale fading decoding (LSFD) in the second layer. We also formulate a sum SE maximization problem with both the data power and LSFD vectors as optimization variables. Since this is an NP-hard problem, we develop a low-complexity algorithm based on the weighted MMSE approach to obtain a local optimum. The numerical results show that both data power control and LSFD improve the sum SE performance over single-layer decoding multi-cell Massive MIMO systems.

This paper investigates the joint data and pilot power optimization for maximum sum spectral efficiency (SE) in multi-cell Massive MIMO systems, which is a non-convex problem. We first propose a new optimization algorithm, inspired by the weighted minimum mean square error (MMSE) approach, to obtain a stationary point in polynomial time. We then use this algorithm together with deep learning to train a convolutional neural network to perform the joint data and pilot power control in sub-millisecond runtime, making it suitable for online optimization in real multi-cell Massive MIMO systems. The numerical result demonstrates that the solution obtained by the neural network is 1% less than the stationary point for four-cell systems, while the sum SE loss is 2% in a nine-cell system.

This paper studies a two-layer decoding method that mitigates inter-cell interference in multi-cell Massive MIMO systems. In layer one, each base station (BS) estimates the channels to intra-cell users and uses the estimates for local decoding on each BS, followed by a second decoding layer where the BSs cooperate to mitigate inter-cell interference. An uplink achievable spectral efficiency (SE) expression is computed for arbitrary two-layer decoding schemes, while a closed-form expression is obtained for correlated Rayleigh fading channels, maximum-ratio combining (MRC), and large-scale fading decoding (LSFD) in the second layer. We formulate a non-convex sum SE maximization problem with both the data power and LSFD vectors as optimization variables and develop an algorithm based on the weighted MMSE (minimum mean square error) approach to obtain a stationary point with low computational complexity.

In this paper, we address the pilot contamination problem in multi-cell massive MIMO systems. Particularly, we propose a pilot design scheme that simultaneously minimizes the channel estimation errors of all base stations (BSs) and the total pilot power consumption of all users subject to the transmit power constraint for every user in the network. We decompose the proposed non-convex problem into distributed optimization problems to be solved at each BS, assuming the knowledge of pilot signals of the other BSs. Then, we introduce a successive optimization approach to cast each distributed optimization problem into a convex linear matrix inequality form. Simulation results confirm that the proposed approach significantly reduces pilot power while maintain the same level of channel estimation error as a recent work in [1].

In this letter, we introduce a novel pilot designapproach that minimizes the total mean square errors of theminimum mean square error estimators of all base stations (BSs)subject to the transmit power constraints of individual users inthe network, while tackling the pilot contamination in multicellmassive MIMO systems. First, we decompose the originalnon-convex problem into distributed optimization sub-problemsat individual BSs, where each BS can optimize its own pilotsignals given the knowledge of pilot signals from the remainingBSs. We then introduce a successive optimization approach totransform each optimization sub-problem into a linear matrixinequality form, which is convex and can be solved by availableoptimization packages. Simulation results confirm the fast convergenceof the proposed approach and prevails a benchmarkscheme in terms of providing higher accuracy.

This paper compares centralized and distributed methods to solve the power minimization problem with quality-of-service (QoS) constraints in the downlink (DL) of multi-cell Massive multiple-input multiple-output (MIMO) systems. In particular, we study the computational complexity, number of parameters that need to be exchanged between base stations (BSs), and the convergence of iterative implementations. Although a distributed implementation based on dual decomposition (which only requires statistical channel knowledge at each BS) typically converges to the global optimum after a few iterations, many parameters need to be exchanged to reach convergence.