Masaaki Nagahara

Massive overloaded MIMO signal detection via convex optimization with proximal splitting

In this paper, we propose signal detection schemes for massive overloaded multiple-input multiple-output (MIMO) systems, where the number of receive antennas is less than that of transmitted streams. Using the idea of the sum-of-absolute-value (SOAV) optimization, we formulate the signal detection as a convex optimization problem, which can be solved via a fast algorithm based on Douglas-Rachford splitting. To improve the performance, we also propose an iterative approach to solve the optimization problem with weighting parameters update in a cost function. Simulation results show that the proposed scheme can achieve much better bit error rate (BER) performance than conventional schemes, especially in large-scale overloaded MIMO systems.

Characterization of maximum hands-off control

Abstract Maximum hands-off control aims to maximize the length of time over which zero actuator values are applied to a system when executing specified control tasks. To tackle such problems, recent literature has investigated optimal control problems which penalize the size of the support of the control function and thereby lead to desired sparsity properties. This article gives the exact set of necessary conditions for a maximum hands-off optimal control problem using an L 0 -norm, and also provides sufficient conditions for the optimality of such controls. Numerical example illustrates that adopting an L 0 cost leads to a sparse control, whereas an L 1 -relaxation in singular problems leads to a non-sparse solution.

Discrete-Valued Control of Linear Time-Invariant Systems by Sum-of-Absolute-Values Optimization

In this paper, we propose a new design method of discrete-valued control for continuous-time linear time-invariant systems based on sum-of-absolute-values (SOAV) optimization. We first formulate the discrete-valued control design as a finite-horizon SOAV optimal control, which is an extended version of

Symbol Detection for Faster-Than-Nyquist Signaling by Sum-of-Absolute-Values Optimization

{\mathbb{L}^{1}}

Discrete-time Hands-off Control by Sparse Optimization

optimal control. We then give simple conditions that guarantee the existence, discreteness, and uniqueness of the SOAV optimal control. Also, we show that the value function is continuous, by which we prove the stability of infinite-horizon model predictive SOAV control systems. We provide a fast algorithm for the SOAV optimization based on the alternating direction method of multipliers (ADMM), which has an important advantage in real-time control computation. A simulation result shows the effectiveness of the proposed method.

Tracking of signals beyond the Nyquist frequency

In this letter, we propose a new symbol detection method in faster-than-Nyquist signaling for effective data transmission. Based on the frame theory, the symbol detection problem is described as underdetermined linear equations on a finite alphabet. While the problem is itself NP (nondeterministic polynomial-time) hard, we propose convex relaxation using the sum-of-absolute-values optimization, which can be efficiently solved by proximal splitting. Simulation results are shown to illustrate the effectiveness of the proposed method compared to a recent ℓ∞-based (ellinfinity-based) method.

Maximum hands-off control without normality assumption

Maximum hands-off control is a control mechanism that maximizes the length of the time duration on which the control is exactly zero. Such a control is important for energy-aware control applications, since it can stop actuators for a long duration and hence the control system needs much less fuel or electric power. In this article, we formulate the maximum hands-off control for linear discrete-time plants by sparse optimization based on the ℓ1 norm. For this optimization problem, we derive an efficient algorithm based on the alternating direction method of multipliers (ADMM). We also give a model predictive control formulation, which leads to a robust control system based on a state feedback mechanism. Simulation results are included to illustrate the effectiveness of the proposed control method.

Sampled-data design of interpolators using the cutting-plane method

This paper studies the problem of tracking or disturbance rejection for sampled-data control systems, where the tracking signal can have frequency components higher than the Nyquist frequency. In view of the well-known sampling theorem, one recognizes that any high-frequency components may be detected only as an alias in the low base band, and hence it is impossible to recover or detect such frequency components. This paper examines the basic underlying assumption, and shows that this assumption depends crucially on the underlying analog model. We show that it is indeed possible to recover such high-frequency signals, and also that, by introducing multirate signal processing techniques, it is possible to track or reject such frequency components. Detailed analysis of multirate closed-loop systems and zeros and poles are given. It is shown via examples that tracking of high-frequency signals beyond the Nyquist frequency can be achieved with satisfactory accuracy.

Rate-distortion analysis of Delta-Sigma modulators

Maximum hands-off control is a control that has the minimum L0 norm among all feasible controls. It is known that the maximum hands-off (or L0-optimal) control problem is equivalent to the L1-optimal control under the assumption of normality. In this article, we analyze the maximum hands-off control for linear time-invariant systems without the normality assumption. For this purpose, we introduce the Lp-optimal control with 0 <; p <; 1, which is a natural relaxation of the L0 problem. By using this, we investigate the existence and the bang-off-bang property (i.e. the control takes values of ±1 and 0) of the maximum hands-off control. We then describe a general relation between the maximum hands-off control and the L1-optimal control. We also prove the continuity and convexity property of the value function, which plays an important role to prove the stability when the (finite-horizon) control is extended to model predictive control.

Simultaneous rejection of signals below and above the nyquist frequency

This paper presents a practically efficient method for designing an interpolator that minimizes the L/sup 2/-induced norm of the error system between the interpolator and a time-delay. The method is based on the so-called cutting-plane method for nondifferentiable convex optimization. The advantage of the proposed method is that it can solve design problems of practical size with a reasonable amount of computation. Numerical examples show the effectiveness of the proposed method in comparison with the conventional ones.