The paper studies the multi-user precoding problem as a non-convex optimization problem for wireless multiple input and multiple output (MIMO) systems. In our work, we approximate the target Spectral Efficiency function with a novel computationally simpler function. Then, we reduce the precoding problem to an unconstrained optimization task using a special differential projection method and solve it by the Quasi-Newton L-BFGS iterative procedure to achieve gains in capacity. We are testing the proposed approach in several scenarios generated using Quadriga -- open-source software for generating realistic radio channel impulse response. Our method shows monotonic improvement over heuristic methods with reasonable computation time. The proposed L-BFGS optimization scheme is novel in this area and shows a significant advantage over the standard approaches. Proposed method has a simple implementation and can be a good reference for other heuristic algorithms in this field.
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Modern wireless cellular networks use massive multiple-input multiple-output (MIMO) technology. This technology involves operations with an antenna array at a base station that simultaneously serves multiple mobile devices which also use multiple antennas on their side. For this, various precoding and detection techniques are used, allowing each user to receive the signal intended for him from the base station. There is an important class of linear precoding called Regularized Zero-Forcing (RZF). In this work, we propose Adaptive RZF (ARZF) with a special kind of regularization matrix with different coefficients for each layer of multi-antenna users. These regularization coefficients are defined by explicit formulas based on SVD decompositions of user channel matrices. We study the optimization problem, which is solved by the proposed algorithm, with the connection to other possible problem statements. We also compare the proposed algorithm with state-of-the-art linear precoding algorithms on simulations with the Quadriga channel model. The proposed approach provides a significant increase in quality with the same computation time as in the reference methods.
The strong interference suffered by users can be a severe problem in cache-enabled networks (CENs) due to the content-centric user association mechanism. To tackle this issue, multi-antenna technology may be employed for interference management. In this paper, we consider a user-centric interference nulling (IN) scheme in two-tier multi-user multi-antenna CEN, with a hybrid most-popular and random caching policy at macro base stations (MBSs) and small base stations (SBSs) to provide file diversity. All the interfering SBSs within the IN range of a user are requested to suppress the interference at this user using zero-forcing beamforming. Using stochastic geometry analysis techniques, we derive a tractable expression for the area spectral efficiency (ASE). A lower bound on the ASE is also obtained, with which we then consider ASE maximization, by optimizing the caching policy and IN coefficient. To solve the resultant mixed integer programming problem, we design an alternating optimization algorithm to minimize the lower bound of the ASE. Our numerical results demonstrate that the proposed caching policy yields performance that is close to the optimum, and it outperforms several existing baselines.
We consider the cache-aided multiple-input single-output (MISO) broadcast channel, which consists of a server with $L$ antennas and $K$ single-antenna users, where the server contains $N$ files of equal length and each user is equipped with a local cache of size $M$ files. Each user requests an arbitrary file from library. The objective is to design a coded caching scheme based on uncoded placement and one-shot linear delivery phases, to achieve the maximum worst-case sum Degree-of-Freedom (sum-DoF) with low subpacketization. Previously proposed schemes for this setting incurred either an exponential subpacketization order in $K$, or required specific conditions in the system parameters $L$, $K$, $M$ and $N$. In this paper, we propose a new combinatorial structure called multiple-antenna placement delivery array (MAPDA). Based on MAPDA and Latin square, the first proposed scheme achieves the sum-DoF $L+\frac{KM}{N}$ with the subpacketization of $K$ when $\frac{KM}{N}+L=K$. Subsequently, for the general case we propose a transformation approach to construct an MAPDA from any $g$-regular PDA (a class of PDA where each integer in the array occurs $g$ times) for the original shared-link coded caching problem. If the original PDA is the seminal coded caching scheme proposed by Maddah-Ali and Niesen, the resulting scheme can achieve the sum-DoF $L+\frac{KM}{N}$ with reduced subpacketization than the existing schemes.The work can be extended to the multiple independent single-antenna transmitters (servers) corresponding to the cache-aided interference channel proposed by Naderializadeh et al. and the scenario of transmitters equipped with multiple antennas.
In this paper, we investigate a cell-free massive MIMO system with both access points and user equipments equipped with multiple antennas over the Weichselberger Rayleigh fading channel. We study the uplink spectral efficiency (SE) based on a two-layer decoding structure with maximum ratio (MR) or local minimum mean-square error (MMSE) combining applied in the first layer and optimal large-scale fading decoding method implemented in the second layer, respectively. To maximize the weighted sum SE, an uplink precoding structure based on an Iteratively Weighted sum-MMSE (I-WMMSE) algorithm using only channel statistics is proposed. Furthermore, with MR combining applied in the first layer, we derive novel achievable SE expressions and optimal precoding structures in closed-form. Numerical results validate our proposed results and show that the I-WMMSE precoding can achieve excellent sum SE performance.
This paper studies the problem of online user grouping, scheduling and power allocation in beyond 5G cellular-based Internet of things networks. Due to the massive number of devices trying to be granted to the network, non-orthogonal multiple access method is adopted in order to accommodate multiple devices in the same radio resource block. Different from most previous works, the objective is to maximize the number of served devices while allocating their transmission powers such that their real-time requirements as well as their limited operating energy are respected. First, we formulate the general problem as a mixed integer non-linear program (MINLP) that can be transformed easily to MILP for some special cases. Second, we study its computational complexity by characterizing the NP-hardness of different special cases. Then, by dividing the problem into multiple NOMA grouping and scheduling subproblems, efficient online competitive algorithms are proposed. Further, we show how to use these online algorithms and combine their solutions in a reinforcement learning setting to obtain the power allocation and hence the global solution to the problem. Our analysis are supplemented by simulation results to illustrate the performance of the proposed algorithms with comparison to optimal and state-of-the-art methods.
Downlink precoding is considered for multi-path multi-user multi-input single-output (MU-MISO) channels where the base station uses orthogonal frequency-division multiplexing and low-resolution signaling. A quantized coordinate minimization (QCM) algorithm is proposed and its performance is compared to other precoding algorithms including squared infinity-norm relaxation (SQUID), multi-antenna greedy iterative quantization (MAGIQ), and maximum safety margin precoding. MAGIQ and QCM achieve the highest information rates and QCM has the lowest complexity measured in the number of multiplications. The information rates are computed for pilot-aided channel estimation and a blind detector that performs joint data and channel estimation. Bit error rates for a 5G low-density parity-check code confirm the information-theoretic calculations. Simulations with imperfect channel knowledge at the transmitter show that the performance of QCM and SQUID degrades in a similar fashion as zero-forcing precoding with high resolution quantizers.
A syntactic model is presented for the specification of finite-state synchronous digital logic systems with complex input/output interfaces, which control the flow of data between opaque computational elements, and for the composition of compatible systems to form closed-loop systems with no inputs or outputs. This model improves upon similar existing models with a novel approach to specifying input and output ports in a way which is uniform and symmetric. An automaton model is also presented for encoding arbitrary computational processes, and an algorithm is presented to generate an automaton representation of a closed-loop system. Using the automaton model, the problem of timing-agnostic verification of closed-loop systems against a desired behavioural specification, encoded as the similarity of closed-loop systems in terms of the set of computations performed, is shown to be decidable. The relationship between the models and real-world implementations of systems is discussed.
The multi-antenna coded caching problem, where the server having $L$ transmit antennas communicating to $K$ users through a wireless broadcast link, is addressed. In the problem setting, the server has a library of $N$ files, and each user is equipped with a dedicated cache of capacity $M$. The idea of extended placement delivery array (EPDA), an array which consists of a special symbol $\star$ and integers in a set $\{1,2,\dots,S\}$, is proposed to obtain a novel solution for the aforementioned multi-antenna coded caching problem. From a $(K,L,F,Z,S)$ EPDA, a multi-antenna coded caching scheme with $K$ users, and the server with $L$ transmit antennas, can be obtained in which the normalized memory $\frac{M}{N}=\frac{Z}{F}$, and the delivery time $T=\frac{S}{F}$. The placement delivery array (for single-antenna coded caching scheme) is a special class of EPDAs with $L=1$. For the multi-antenna coded caching schemes constructed from EPDAs, it is shown that the maximum possible Degree of Freedom (DoF) that can be achieved is $t+L$, where $t=\frac{KM}{N}$ is an integer. Furthermore, two constructions of EPDAs are proposed: a) $ K=t+L$, and b) $K=nt+(n-1)L, \hspace{0.1cm}L\geq t$, where $n\geq 2$ is an integer. In the resulting multi-antenna schemes from those EPDAs achieve the full DoF, while requiring a subpacketization number $\frac{K}{\text{gcd}(K,t,L)}$. This subpacketization number is less than that required by previously known schemes in the literature.
Interpretation of Deep Neural Networks (DNNs) training as an optimal control problem with nonlinear dynamical systems has received considerable attention recently, yet the algorithmic development remains relatively limited. In this work, we make an attempt along this line by reformulating the training procedure from the trajectory optimization perspective. We first show that most widely-used algorithms for training DNNs can be linked to the Differential Dynamic Programming (DDP), a celebrated second-order trajectory optimization algorithm rooted in the Approximate Dynamic Programming. In this vein, we propose a new variant of DDP that can accept batch optimization for training feedforward networks, while integrating naturally with the recent progress in curvature approximation. The resulting algorithm features layer-wise feedback policies which improve convergence rate and reduce sensitivity to hyper-parameter over existing methods. We show that the algorithm is competitive against state-ofthe-art first and second order methods. Our work opens up new avenues for principled algorithmic design built upon the optimal control theory.
In this paper, we study the optimal convergence rate for distributed convex optimization problems in networks. We model the communication restrictions imposed by the network as a set of affine constraints and provide optimal complexity bounds for four different setups, namely: the function $F(\xb) \triangleq \sum_{i=1}^{m}f_i(\xb)$ is strongly convex and smooth, either strongly convex or smooth or just convex. Our results show that Nesterov's accelerated gradient descent on the dual problem can be executed in a distributed manner and obtains the same optimal rates as in the centralized version of the problem (up to constant or logarithmic factors) with an additional cost related to the spectral gap of the interaction matrix. Finally, we discuss some extensions to the proposed setup such as proximal friendly functions, time-varying graphs, improvement of the condition numbers.
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