Resource Allocation in Collocated Massive MIMO for 5G and Beyond

Massive multiuser multiple-input multiple-output (MIMO) systems have been recently introduced as a promising technology for the next generation of wireless networks. It has been proven that linear precoders/detectors such as maximum ratio transmitting/maximum ratio combining (MRT/MRC), zero forcing (ZF), and linear minimum mean square error (LMMSE) on the downlink (DL)/uplink (UL) transmission can provide near optimal performance in such systems. Acquiring channel state information (CSI) at the transmitter as well as the receiver is one of the challenges in multiuser massive MIMO that can affect the network performance. Any data transmission in multiuser massive MIMO systems starts with the user transmitting UL pilots. The base station (BS) then uses the MMSE estimation method to accurately estimate the CSI from the pilot sequences. Since the UL and DL channels are reciprocal in time division duplex (TDD) mode, the BS employs the obtained CSI to precode the data symbols prior to DL transmission. The users also need the CSI knowledge to accurately decode the DL signals. Beamforming training (BT) scheme is one of the methods that is proposed in the literature to provide the CSI knowledge for the users. In this scheme, the BS precodes and transmits a pilot sequence to the users such that each user can estimate its effective channel coefficients. Developing an optimal resource distribution method that enhances the system performance is another challenging issue in multiuser massive MIMO. As mentioned earlier, CSI acquisition is one of the requirements of multiuser massive MIMO, and UL pilot transmission is the common method to achieve that. Conventionally, equal powers have been considered for the pilot transmission phase and data transmission phase. However, it can be shown that the performance of the system under this method of power distribution is not optimal. Therefore, to further improve the performance of multiuser massive MIMO technology, especially in cases where the antenna elements are not well separated and the propagational dispersion is low, optimal resource allocation is required. Hence, the main objective of this M.A.Sc. thesis is to develop an optimal resource allocation among pilot and data symbols to maximize the spectral efficiency, assuming different receivers such as MRC, ZF, and LMMSE are employed at the BS. Since the calculation of spectral efficiency using the lower bound on the achievable rate is computationally very intensive, we first obtain closed-form expressions for the achievable UL rate of users, assuming the angular domain in the physical channel model is divided into a finite number of separate directions. An approximate expression for spectral efficiency is then developed using the aforementioned closed-form rates. Finally, we propose a resource allocation scheme in which the pilot power, data power, and training duration are optimally chosen in order to maximize the spectral efficiency in a given total power budget. Extensive simulations are conducted in MATLAB and the results are presented that illustrate the notable improvement in the achievable spectral efficiency through the proposed power allocation scheme. Moreover, the results show that the performance of the proposed method is much superior when the number of channel directions or the number of antennas at BS increases. Furthermore, while the advantage of the proposed method is more notable in the case of ZF and LMMSE receivers, it still outperforms the equal power allocation method for the MRC receiver in terms of spectral efficiency

Power allocation and user selection in multi-cell: multi-user massive MIMO systems

Submitted in fulfilment of the academic requirements for the degree of Master of Science (Msc) in Engineering, in the School of Electrical and Information Engineering (EIE), Faculty of Engineering and the Built Environment, at the University of the Witwatersrand, Johannesburg, South Africa, 2017The benefits of massive Multiple-Input Multiple-Output (MIMO) systems have made it a solution for future wireless networking demands. The increase in the number of base station antennas in massive MIMO systems results in an increase in capacity. The throughput increases linearly with an increase in number of antennas. To reap all the benefits of massive MIMO, resources should be allocated optimally amongst users. A lot of factors have to be taken into consideration in resource allocation in multi-cell massive MIMO systems (e.g. intra-cell, inter-cell interference, large scale fading etc.) This dissertation investigates user selection and power allocation algorithms in multi-cell massive MIMO systems. The focus is on designing algorithms that maximizes a particular cell of interest’s sum rate capacity taking into consideration the interference from other cells. To maximize the sum-rate capacity there is need to optimally allocate power and select the optimal number of users who should be scheduled. Global interference coordination has very high complexity and is infeasible in large networks. This dissertation extends previous work and proposes suboptimal per cell resource allocation models that are feasible in practice. The interference is introduced when non-orthogonal pilots are used for channel estimation, resulting in pilot contamination. Resource allocation values from interfering cells are unknown in per cell resource allocation models, hence the inter-cell interference has to be modelled. To tackle the problem sum-rate expressions are derived to enable power allocation and user selection algorithm analysis. The dissertation proposes three different approaches for solving resource allocation problems in multi-cell multi-user massive MIMO systems for a particular cell of interest. The first approach proposes a branch and bound algorithm (BnB algorithm) which models the inter-cell interference in terms of the intra-cell interference by assuming that the statistical properties of the intra-cell interference in the cell of interest are the same as in the other interfering cells. The inter-cell interference is therefore expressed in terms of the intra-cell interference multiplied by a correction factor. The correction factor takes into consideration pilot sequences used in the interfering cells in relation to pilot sequences used in the cell of interest and large scale fading between the users in the interfering cells and the users in the cell of interest. The resource allocation problem is modelled as a mixed integer programming problem. The problem is NP-hard and cannot be solved in polynomial time. To solve the problem it is converted into a convex optimization problem by relaxing the user selection constraint. Dual decomposition is used to solve the problem. In the second approach (two stage algorithm) a mathematical model is proposed for maximum user scheduling in each cell. The scheduled users are then optimally allocated power using the multilevel water filling approach. Finally a hybrid algorithm is proposed which combines the two approaches described above. Generally in the hybrid algorithm the cell of interest allocates resources in the interfering cells using the two stage algorithm to obtain near optimal resource allocation values. The cell of interest then uses these near optimal values to perform its own resource allocation using the BnB algorithm. The two stage algorithm is chosen for resource allocation in the interfering cells because it has a much lower complexity compared to the BnB algorithm. The BnB algorithm is chosen for resource allocation in the cell of interest because it gives higher sum rate in a sum rate maximization problem than the two stage algorithm. Performance analysis and evaluation of the developed algorithms have been presented mainly through extensive simulations. The designed algorithms have also been compared to existing solutions. In general the presented results demonstrate that the proposed algorithms perform better than the existing solutions.XL201

Energy-Efficient Pilot-Data Power Control in MU-MIMO Communication Systems

Multiple-input multiple-output (MIMO) antenna system is considered as a core technology for wireless communication. To reap the benefits of MIMO at a greater scale, massive MIMO with very large antenna arrays deployed at base station (BS) has recently become the forefront in wireless communication research. Till present, the design and analysis of large-scale MIMO systems is a fairly new subject. On the other hand, excessive power usage in MIMO networks is a crucial issue for mobile operators and the explosive growth of wireless services contributes largely to the worldwide carbon footprint. As such, significant efforts have been devoted to improve the spectral efficiency (SE) as well as energy efficiency (EE) of MIMO communication systems over the past decade, resulting in many energy efficient techniques such as power allocation. This thesis investigates novel energy-efficient pilot-data power control strategies which can be used in both conventional MIMO and massive MIMO communication systems. The new pilot-data power control algorithms are developed based ontwo optimization frameworks: one aims to minimize the total transmit power while satisfying per-user signal-interference-plus-noise ratio (SINR) and power constraints; the other aims to maximize the total EE, which is defined as the ratio of the total SE to the transmit power, under individual user power constraints. The proposed novel pilot-data power allocation schemes also take into account the maximum-ratio combining (MRC) and zero-forcing (ZF) detectors in the uplink together with maximum-ratio transmission (MRT) and ZF precoder in the downlink. Considering that a direct use of such SINR expressions in the power control schemeswould lead to a very difficult optimization problem which is not mathematically tractable, we first investigatethe statistical SINR lower bounds for multi-cell multi-user MIMO (MU-MIMO)communication systemsunder minimum mean square error (MMSE) channel estimation. These lower bounds of the per-user average SINRs are used to replace the true SINRs to simplify the power allocation optimization problems. Such relaxation of the original average SINR yields a simplified problem and leads to a suboptimal solution. Then, based on the derived average SINR lower bounds, two novel energy efficient pilot-data power control problems are formulatedwithin the first optimization framework,aiming to minimize the total transmit power budget subject to the per-user SINR requirement and power consumption constraint in multi-cell MU-MIMO systems. For the EE-optimal power allocation problems with MRT precoder and MRC detector, it is revealed that such minimization problems can be converted to a standard geometric programming (GP) procedure which can be further converted to a convex optimization problem. For the pilot-data power control scheme with ZF precoder and ZF detector, geometric inequality is used to approximate the original non-convex optimization to GP problem. The very large number of BS station situation is also discussed by assuming infinite antennas at BS. Numerical results validate the tightness of the derived SINR lower bounds and the advantages of the proposed energy efficient power allocation schemes. Next, two pilot and data power control schemes are developed based on the second power allocation optimization framework to jointly maximize the total EE for both uplink and downlink transmissions in multi-cell MU-MIMO systems under per-user and BS power constraints. The original power control problems are simplified to equivalent convex problems based on the derived SINR lower bounds along with the Dinkelbach's method and the FrankWolfe (FW) iteration. By assuming infinite antennas at BS, the pilot-data power control in massive MIMO case is also discussed. The performance of the proposed pilot-data power allocation schemes based on the two frameworks, namely total transmit power minimization and total EE maximization, are evaluated and compared with the SE maximization scheme. Furthermore, we investigate the pilot-data power allocation for EE communications in single-cell MU-MIMO systems with circuit power consumption in consideration. The pilot and data power allocation schemes are proposed to minimize the total weighted uplink and downlink transmit power as well as processing circuit power consumption while meeting the per-user SINR and BS power consumption constraints. In our proposed schemes, both fixed and flexible numbers of BS antennas are investigated. For the fixed number of BS antennas case, the non-convex optimization problems are converted to a general GP problem to facilitate the solution. An iterative algorithm is proposed to solve the EE-optimal power control problems in the flexible number of BS antennas casebased on the partial convexity of both the cost function and the constraints. It is shown that the convergence of the proposed iterative algorithm is guaranteed due to the fact that each iteration follows convex optimization

Spectral Efficiency Maximization of a Massive Multiuser MIMO System via Appropriate Power Allocation

Massive multiuser multiple-input multiple-output (MU-MIMO) systems are being considered for the next generation wireless networks in view of their ability to increase both the spectral and energy efficiencies. For such systems, linear detectors such as zero-forcing (ZF) and maximum-ratio combining (MRC) detectors on the uplink (UL) transmission have been shown to provide near optimal performance. As well, linear precoders such as ZF and maximum-ratio transmission (MRT) precoders on the downlink (DL) transmission offer lower complexity along with a near optimal performance in these systems. One of the most challenging problems in massive MU-MIMO systems is obtaining the channel state information (CSI) at the transmitter as well as the receiver. In such systems, the base station (BS) obtains CSI using pilot sequences, which are transmitted by the users. Due to the channel reciprocity between the UL and DL channels in the time-division duplex (TDD) mode, BS employs CSI obtained to precode the data symbols in DL transmission. To accurately decode the received symbols in the DL transmission, the users also need to acquire CSI. In view of this, a beamforming training (BT) scheme has been proposed in the literature to obtain the estimates of CSI at each user. In this scheme, BS transmits a short pilot sequence to the users in a way such that each user estimates the effective channel gain. Conventionally, the power of the pilot symbols has been considered equal to the power of data symbols for all the users. In this thesis, we pose and answer a basic question about the operation of a base station: How much the spectral efficiency could be improved if the transmit power allocated to the pilot and data symbols of each user are chosen in some optimal fashion? In answering this question and in order to maximize the spectral efficiency for a given total energy budget, some methods of power allocation are proposed. First, we derive a closed-form approximate expression for the achievable downlink rate for the maximum ratio transmission precoder based on small-scale fading in order to evaluate the spectral efficiency in the BT scheme. Then, we propose three methods of power allocation in order to maximize the spectral efficiency for a given total power budget among the users. In the first proposed method, we allocate equal pilot power as well as equal data power for all users in order to maximize the spectral efficiency. In the second proposed method, we allow for the allocation of different data powers among the users, whereas the pilot power for each user is kept the same and is specified. In the third method, we optimally allocate equal pilot power and a different data power for each user in such a way that the spectral efficiency is maximized. Numerical results are obtained showing that all the three proposed methods are superior to the existing methods in terms of spectral efficiency. In addition, they also show that the third proposed method of power allocation outperforms the other two proposed methods in terms of the spectral efficiency. Next, we derive a closed-form approximate expression for the achievable downlink rate for the maximum ratio transmission precoder based on large-scale fading in order to evaluate the spectral efficiency in the BT scheme. Then, we propose four methods of power allocation in order to maximize the spectral efficiency for a given total power budget among the users. In the first method, power is allocated among the pilot and data symbols in such a way that the pilot power as well as the data power for each user is the same. In the second method, power is allocated among the data symbols of the various users, whereas the pilot power for each user is the same and is specified. In this method, the data power for each user is optimally determined to maximize the spectral efficiency. In the third method, power is allocated among the pilot and data symbols of the various users, whereas the pilot power for each user is the same but determined. In this method, the same pilot power along with the various data powers is optimized to maximize the spectral efficiency. Finally, in the fourth method, power is allocated optimally among each of the pilot and data symbols of the various users so as to maximize the spectral efficiency. Numerical results are obtained showing that the performance of the first proposed method is approximately the same as that of the conventional approach. In addition, they also show that the second, third and fourth methods of power allocation yield similar performance in terms of spectral efficiency, and that the spectral efficiency of these methods is much superior to that of the first method or of the conventional method. Finally, we investigate the spectral efficiency of massive MU-MIMO systems on an UL transmission with a very large number of antennas at the base station serving single-antenna users. A practical physical channel model is proposed by dividing the angular domain into a finite number of distinct directions. A lower bound on the achievable rate of the uplink data transmission is derived using a linear detector for each user and employed in defining the spectral efficiency. The lower bound obtained is further modified for the maximum-ratio combining and zero-forcing receivers. A power control scheme based on the large-scale fading is also proposed to maximize the spectral efficiency under the peak power constraint. Experiments are conducted to evaluate the lower bounds obtained and the performance of the proposed method. The numerical results show that the proposed power control method provides a spectral efficiency which is the same as that of the maximum power criterion using the ZF receiver. Further, the proposed method provides a spectral efficiency that is higher than that provided by the maximum power criterion using the MRC receiver