Spectral Efficiency and Energy Efficiency Tradeoff in Massive MIMO Downlink Transmission with Statistical CSIT

As a key technology for future wireless networks, massive multiple-input multiple-output (MIMO) can significantly improve the energy efficiency (EE) and spectral efficiency (SE), and the performance is highly dependant on the degree of the available channel state information (CSI). While most existing works on massive MIMO focused on the case where the instantaneous CSI at the transmitter (CSIT) is available, it is usually not an easy task to obtain precise instantaneous CSIT. In this paper, we investigate EE-SE tradeoff in single-cell massive MIMO downlink transmission with statistical CSIT. To this end, we aim to optimize the system resource efficiency (RE), which is capable of striking an EE-SE balance. We first figure out a closed-form solution for the eigenvectors of the optimal transmit covariance matrices of different user terminals, which indicates that beam domain is in favor of performing RE optimal transmission in massive MIMO downlink. Based on this insight, the RE optimization precoding design is reduced to a real-valued power allocation problem. Exploiting the techniques of sequential optimization and random matrix theory, we further propose a low-complexity suboptimal two-layer water-filling-structured power allocation algorithm. Numerical results illustrate the effectiveness and near-optimal performance of the proposed statistical CSI aided RE optimization approach.Comment: Typos corrected. 14 pages, 7 figures. Accepted for publication on IEEE Transactions on Signal Processing. arXiv admin note: text overlap with arXiv:2002.0488

Practical Sparse Matrices in C++ with Hybrid Storage and Template-Based Expression Optimisation

Despite the importance of sparse matrices in numerous fields of science, software implementations remain difficult to use for non-expert users, generally requiring the understanding of underlying details of the chosen sparse matrix storage format. In addition, to achieve good performance, several formats may need to be used in one program, requiring explicit selection and conversion between the formats. This can be both tedious and error-prone, especially for non-expert users. Motivated by these issues, we present a user-friendly and open-source sparse matrix class for the C++ language, with a high-level application programming interface deliberately similar to the widely used MATLAB language. This facilitates prototyping directly in C++ and aids the conversion of research code into production environments. The class internally uses two main approaches to achieve efficient execution: (i) a hybrid storage framework, which automatically and seamlessly switches between three underlying storage formats (compressed sparse column, Red-Black tree, coordinate list) depending on which format is best suited and/or available for specific operations, and (ii) a template-based meta-programming framework to automatically detect and optimise execution of common expression patterns. Empirical evaluations on large sparse matrices with various densities of non-zero elements demonstrate the advantages of the hybrid storage framework and the expression optimisation mechanism.Comment: extended and revised version of an earlier conference paper arXiv:1805.0338

Practical Sparse Matrices in C++ with Hybrid Storage and Template-Based Expression Optimisation

Despite the importance of sparse matrices in numerous fields of science, software implementations remain difficult to use for non-expert users, generally requiring the understanding of underlying details of the chosen sparse matrix storage format. In addition, to achieve good performance, several formats may need to be used in one program, requiring explicit selection and conversion between the formats. This can be both tedious and error-prone, especially for non-expert users. Motivated by these issues, we present a user-friendly and open-source sparse matrix class for the C++ language, with a high-level application programming interface deliberately similar to the widely used MATLAB language. This facilitates prototyping directly in C++ and aids the conversion of research code into production environments. The class internally uses two main approaches to achieve efficient execution: (i) a hybrid storage framework, which automatically and seamlessly switches between three underlying storage formats (compressed sparse column, Red-Black tree, coordinate list) depending on which format is best suited and/or available for specific operations, and (ii) a template-based meta-programming framework to automatically detect and optimise execution of common expression patterns. Empirical evaluations on large sparse matrices with various densities of non-zero elements demonstrate the advantages of the hybrid storage framework and the expression optimisation mechanism.Comment: extended and revised version of an earlier conference paper arXiv:1805.0338

Efficient provision of public goods with endogenous redistribution

We study a continuous and balanced mechanism that is capable of implementing in Nash equilibrium all the Pareto-efficient individually rational allocations for an economy with public goods. The Government chooses a set of weights directly related to the Lindahl prices corresponding to the Pareto-efficient allocation it wants to implement. The mechanism then guarantees that initial endowments are re-allocated so that the chosen vector of Lindahl prices is indeed a Lindahl equilibrium, and implements the corresponding Lindahl allocation. Previously known mechanisms that implement the Lindahl correspondence do not allow the Government to choose which point on the Pareto frontier should be implemented, unless it can also redistribute initial endowments in the appropriate way. By contrast, in our case the Government directly controls the distribution of welfare in the economy. Finally, besides being balanced and continuous, our mechanism is `simple'. Each agent has to declare a desired increase in the amount of public good, and a vector of redistributive transfers of initial endowments (across other agents).

Robust Monotonic Optimization Framework for Multicell MISO Systems

The performance of multiuser systems is both difficult to measure fairly and to optimize. Most resource allocation problems are non-convex and NP-hard, even under simplifying assumptions such as perfect channel knowledge, homogeneous channel properties among users, and simple power constraints. We establish a general optimization framework that systematically solves these problems to global optimality. The proposed branch-reduce-and-bound (BRB) algorithm handles general multicell downlink systems with single-antenna users, multiantenna transmitters, arbitrary quadratic power constraints, and robustness to channel uncertainty. A robust fairness-profile optimization (RFO) problem is solved at each iteration, which is a quasi-convex problem and a novel generalization of max-min fairness. The BRB algorithm is computationally costly, but it shows better convergence than the previously proposed outer polyblock approximation algorithm. Our framework is suitable for computing benchmarks in general multicell systems with or without channel uncertainty. We illustrate this by deriving and evaluating a zero-forcing solution to the general problem.Comment: Published in IEEE Transactions on Signal Processing, 16 pages, 9 figures, 2 table