Single-input Single-output Case Research Articles

Transmission Channel Characteristics of Relay Dual-Polarization MIMO System for Hypersonic Vehicles Under Plasma Sheath

The blackout problem caused by plasma sheath is a serious obstacle to the communication system of hypersonic vehicles. The uplink relay transmission method is an effective means of mitigating serious attenuation caused by plasma sheath. This paper proposes a Ka-band $2\times2$ dual-polarization multiple-input multiple-output (MIMO) scheme by adopting a left-/right-hand circular polarized antenna to increase channel capacity and signal quality. The relay dual-polarized MIMO channel model between the hypersonic vehicle and satellite is established by emphasizing the plasma sheath effect, especially the cross-polar coupling and polar correlation under plasma sheath. Useful numerical results on the relay dual-polarized MIMO ergodic channel capacity are analyzed. Thus, significant capacity gains with respect to the conventional single-input single-output case are illustrated based on this analysis. Simulation results show that the relay dual-polarized MIMO method can increase the channel ergodic capacity by 1.9–2 times under most circumstances, and the angle between the selected relay satellite and the vehicle normal direction should be minimal. This statistical channel model can be applied to the wireless communication system design and evaluation for hypersonic vehicles.

Positive realizations of nonlinear input–output discrete-time systems

The problem of realization of a positive nonlinear input–output discrete-time system as a positive state-space system is investigated. The input–output system is given by a difference equation of a higher order. A necessary and sufficient condition for existence of positive and regularly positively observable realization is provided. The state space variables of the realization are found as independent generators of some positive universe associated to the input–output system. Only the single-input single-output case is studied and all functions describing the systems and their properties are assumed to be continuous.

Explicit H∞ controllers for 1st to 3rd order single-input single-output systems with parameters

The purpose of this paper is to explicitly characterize H∞ controllers for single-input single-output (SISO) systems of order 1, 2 and 3 in terms of their coefficients considered as unknown parameters. In the SISO case, computing H∞ controllers requires to find the real positive definite solution of an algebraic Riccati equation. Due to the system parameters, no purely numerical method can be used to find such a solution, and thus parametric H∞ controllers. Using elimination techniques of zero-dimensional polynomial systems, we first give a parametrization of all the solutions of the algebraic Riccati equation associated with the H∞ control problem. Since the problem reduces to solving an univariate polynomial of degree less than or equal to 4, closed-form solutions are then obtained for the solutions of the algebraic Riccati equation by means of radicals. Using the concept of discriminant variety, we show that the maximal real root of this polynomial is always defined by the same closed-form expression, which yields the positive definite solution of the algebraic Riccati equation. Finally, we use the above results to explicitly compute the H∞ criteria γpt and H∞ controllers in terms of the system parameters and study them with respect to parameter variations.

Explicit H∞ controllers for 4th order single-input single-output systems with parameters and their application to the two mass-spring system with damping

The purpose of this paper is to explicitly characterize H∞ controllers for 4th order single-input single-output (SISO) systems in terms of their coefficients considered as unknown parameters. In the SISO case, computing H∞ controllers requires to find the real positive definite solution of an algebraic Riccati equation (ARE). Due to the system parameters, no purely numerical method can be used to find such a solution, and thus parametric H∞ controllers. Using elimination techniques for zero-dimensional polynomial systems, we first give a rational parametrization of all the solutions of the ARE. Then, as the problem reduces to solving polynomials of degree 4, closed-form solutions are obtained for all the solutions of this ARE by using expressions by radicals. Using the concept of discriminant variety, we then show that the maximal real root of one of these polynomials is encoded by two different closed-form expressions depending on the values of the system parameters, which yields to different positive definite solution of the ARE. The above results are then used to explicitly compute the H∞ criterion γopt and H∞ controllers in terms of the system parameters. Finally, we study in detail a particular system: the two-mass-spring system with damping. Due to the low number of parameters, we can plot the variations of γopt in function of the parameters, compute approximations of γopt at a working point, and derive the expression of a weight function of the parameters to set γopt to a desired value.

FxLMS versus H∞ Control for Broadband Acoustic Noise Attenuation in a Cavity

This paper deals with active noise control (ANC) in an enclosure on a broadband frequency range. It aims to compare two control strategies: (i) an adaptive control approach namely FxLMS control, (ii) a robust H∞ control, in the SISO (single input single output) case. Only feedback scheme is considered and disturbance sources are assumed to be unknown. For the aim of a fair comparison focusing on the same frequency range of attenuation, a new FxLMS algorithm with a weighting filter is proposed. Finally, achievable performances of each control are analyzed through simulation and experimental results driven on an instrumented setup.

Joint Beamforming and Power-Splitting Control in Downlink Cooperative SWIPT NOMA Systems

This paper investigates the application of simultaneous wireless information and power transfer (SWIPT) to cooperative non-orthogonal multiple access (NOMA). A new cooperative multiple-input single-output (MISO) SWIPT NOMA protocol is proposed, where a user with a strong channel condition acts as an energy-harvesting (EH) relay to help a user with a poor channel condition. The power splitting (PS) scheme is adopted at the EH relay. By jointly optimizing the PS ratio and the beamforming vectors, the design objective is to maximize the data rate of the "strong user" while satisfying the QoS requirement of the "weak user". It boils down to a challenging nonconvex problem. To resolve this issue, the semidefinite relaxation (SDR) technique is applied to relax the quadratic terms related with the beamformers, and then it is solved to its global optimality by two-dimensional exhaustive search. We prove the rank-one optimality, which establishes the equivalence between the relaxed problem and the original one. To further reduce the high complexity due to the exhaustive search, an iterative algorithm based on successive convex approximation (SCA) is proposed, which can at least attain its stationary point efficiently. In view of the potential application scenarios, e.g., IoT, the single-input single-output (SISO) case of the cooperative SWIPT NOMA system is also studied. The formulated problem is proved to be strictly unimodal with respect to the PS ratio. Hence, a golden section search (GSS) based algorithm with closed-form solution at each step is proposed to find the unique global optimal solution. It is worth pointing out that the SCA method can also converge to the optimal solution in SISO cases. In the numerical simulation, the proposed algorithm is numerically shown to converge within a few iterations, and the SWIPT-aided NOMA protocol outperforms the existing transmission protocols.

Joint Channel and Phase Noise Estimation in MIMO-OFDM Systems

The combination of multiple-input multiple-output (MIMO) techniques withorthogonal frequency division multiplexing (OFDM), MIMO-OFDM, is a promising way ofachieving high spectral efficiency in wireless communication systems. However, the performanceof MIMO-ODFM systems is highly degraded by radio frequency (RF) impairments such asphase noise. Similar to the single-input single-output (SISO) case, phase noise in MIMO-OFDMsystems results in a common phase error (CPE) and inter carrier interference (ICI). In this paperthe problem of joint channel and phase noise estimation in a system with multiple transmit andreceive antennas where each antenna is equipped with its own independent oscillator is tackled.The technique employed makes use of a novel placement of pilot carriers in the preamble anddata portion of the MIMO-OFDM frame. Numerical results using a 16 and 64 quadratureamplitude modulation QAM schemes are provided to illustrate the effectiveness of the proposedscheme for MIMO-OFDM systems.

Statistical modeling of the high altitude platform dual-polarized MIMO propagation channel

In order to investigate the benefit of multiple-input multiple-output (MIMO) technique applying to the high altitude platform (HAP), a 2×2 MIMO statistical model, which can accurately describe the channel between HAP and high-speed train, is presented. And dual polarization diversity is particularly considered. Based on first-order three-state Markov chain, the single-input single-output (SISO) channel, a subset of the MIMO channel is first established. The ray tracing approach applied to the digital relief model (DRM) which covers the railway between Xi'an and Zhengzhou is used to obtain the state probability vector and matrix of the state transition probability. The proposed model considers both Doppler shift and temporal correlation, and the polarization correlation and spatial correlation statistical properties of large-scale fading and small-scale fading are analyzed. Moreover, useful numerical results on the MIMO HAP channel outage capacity are provided based on which, significant capacity gains with respect to the conventional SISO case are illustrated. Such statistical channel model can be applied to the future wireless communication system between HAP and high-speed train.

Secrecy in MIMO Networks with No Eavesdropper CSIT

We consider two fundamental multi-user channel models: the multiple-input multiple-output (MIMO) wiretap channel with one helper (WTH) and the MIMO multiple access wiretap (MAC-WT) channel. In each case, the eavesdropper has $K$ antennas while the remaining terminals have $N$ antennas each. We consider a fast fading channel where the channel state information (CSI) of the legitimate receiver is available at the transmitters but no CSI at the transmitters (CSIT) is available for the eavesdropper’s channel. We determine the optimal sum secure degrees of freedom (s.d.o.f.) for each channel model for the regime $K\leq N$ , and show that in this regime, the MAC-WT channel reduces to the WTH in the absence of eavesdropper CSIT. For the regime $N\leq K\leq 2N$ , we obtain the optimal linear s.d.o.f., and show that the MAC-WT channel and the WTH have the same optimal s.d.o.f. when restricted to linear encoding strategies. In the absence of any such restrictions, we provide an upper bound for the sum s.d.o.f. of the MAC-WT channel in the regime $N\leq K\leq 2N$ . Our results show that unlike in the single-input single-output case, there is loss of s.d.o.f. for even the WTH due to lack of eavesdropper CSIT when $K\geq N$ .

On the Performance Gap between ML and Iterative Decoding of Finite-Length Turbo-Coded BICM in MIMO Systems

As real-time applications typically require short length code words, this paper analyzes the minimum achievable code word error rate of the given finite-length code words, namely, maximum likelihood (ML) decoding error probability. For coding schemes ML decoding is too complex, the key contribution of this paper is to analytically assess the performance gap between ML decoding and a practical decoding scheme. We analyze the combination of turbo codes and bit-interleaved coded-modulation that is a spectrally efficient coding scheme adopted in 3GPP long term evolution (LTE). In single-input single-output (SISO) systems, it was shown in the literature that turbo decoding delivers near-ML decoding performance. In this paper, we extend the analysis to a multi-input multi-output (MIMO) system. In contrast to the SISO case, the turbo principle-based iterative decoding scheme is subject to appreciable performance loss compared with the ML decoding, even in good MIMO channel conditions. For this reason, we further analyze potential reasons and examine possible improvements. By means of simulation, it is shown that convergence to a non-ML code word rather than non-convergence is the key reason for the observed performance loss in good channel conditions.

Power Allocation for a Downlink Non-Orthogonal Multiple Access System

This letter investigates power allocation for a downlink non-orthogonal multiple access system with a base station and two users. We first formulate an optimization problem for the single-input single-output (SISO) case in terms of power allocation between two users for maximizing the sum capacity under a total power constraint and a quality-of-service condition that the minimum rate requirement of each user is satisfied. Two closed-form solutions are subsequently derived. Then we extend the SISO solutions to a multiple-input multiple-output scenario. As compared to the optimal and the suboptimal approach presented in a recent work, the proposed schemes achieve close sum capacity performance with much lower computational complexity.

Diversity-Multiplexing Tradeoff for Log-Normal Fading Channels

Although there has been a growing interest on the study of diversity-multiplexing tradeoff (DMT), the existing works are mostly restricted to the outcomes reported for Rayleigh, Rician, and Nakagami fading channels. In this paper, we investigate the optimal tradeoff in the presence of log-normal fading, which provides an accurate model for indoor wireless, optical wireless, and ultra-wideband channels. We consider a multiple-input multiple-output (MIMO) log-normal channel, derive the outage probability expression, and then present the asymptotical DMT expression. It is shown that the asymptotical maximum diversity gain tends to infinity with logarithm of signal-to-noise ratio (SNR). To have further insight, we normalize the DMT with that of single-input single-output case and express the relative asymptotical DMT of the MIMO log-normal channel as a function of the number of transmit and receive antennas. We further study DMT for finite SNRs and demonstrate convergence to the asymptotical case. Extensive numerical results are provided to corroborate the analytical derivation.

Uncertain disturbances’ attenuation by homogeneous multi‐input multi‐output sliding mode control and its discretisation

Design of multi-input multi-output (MIMO) homogeneous sliding modes (HSMs) for uncertain dynamic systems is considered. The resulting closed-loop systems feature all well-known standard properties of single-input single-output (SISO) HSM systems. Introduction of robust exact differentiators produces homogeneous output-feedback controllers. The ultimate asymptotic accuracy of SISO HSM technique is proved to be preserved in the MIMO and SISO cases, if the discrete-time implementation is based on the one-step Euler integration.

Identification of High-Tech Motion Systems: An Active Vibration Isolation Benchmark

The benchmark Active Vibration Isolation System (AVIS) in this paper is a complex high-tech industrial system used in vibration and motion control applications. The system is complex in the sense of high order exible dynamics and multiple inputs and outputs. The aim of this benchmark is to compare difierent black box, linear time invariant system identification algorithms. Difierent large data sets are provided, enabling the use of both frequency domain and time domain identification approaches. The idea of the benchmark is to investigate both model accuracy and numerical reliability of the computational steps. Several reference solutions are provided, which demonstrate the challenging aspects of this benchmark already in the singleinput single-output case. The benchmark data and additional info are available on the website of Tom Oomen.

Symbol Error Rate for Nonblind Adaptive Equalizers Applicable for the SIMO and FGn Case

A nonzero residual intersymbol interference (ISI) causes the symbol error rate (SER) to increase where the achievable SER may not answer any more on the system’s requirements. Recently, a closed-form approximated expression was derived by the same author for the residual ISI obtained by nonblind adaptive equalizers for the single-input single-output (SISO) case. Up to now, there does not exist a closed-form expression for the residual ISI obtained by nonblind adaptive equalizers for the single-input multiple-output (SIMO) case. Furthermore, there does not exist a closed-form expression for the SER valid for the SISO or SIMO case that takes into account the residual ISI obtained by nonblind adaptive equalizers and is valid for fractional Gaussian noise (fGn) input where the Hurst exponent is in the region of0.5≤H<1. In this paper, we derive a closed-form approximated expression for the residual ISI obtained by nonblind adaptive equalizers for the SIMO case (where SISO is a special case of SIMO), valid for fGn input where the Hurst exponent is in the region of0.5≤H<1. Based on this new expression for the residual ISI, a closed-form approximated expression is obtained for the SER valid for the SIMO and fGn case.

도플러 대역폭이 채널 추정의 성능에 미치는 영향

본 연구에서는 도플러 대역폭이 채널 사운딩에 미치는 영향을 고려한다. 이를 위해 먼저 수학적인 공식을 전개한 후에 단순한 상관기와 MMSE를 비교한다. 시간 변화의 영향을 평가하기 위하여 MMSE와 상관기의 성능은 SISO 환경하에서 다양한 도플러 대역폭 값을 적용하여 분석한다. 시뮬레이션 결과를 통하여 <TEX>$f_dT$</TEX> 값이 증가할수록 MMSE와 상관기의 성능은 더 열화되며 MMSE의 성능은 상관기에 비해 향상됨을 보인다 또한 정확한 채널 정보가 알려져 있지 않을 경우의 성능 열화에 대해서도 고려한다. 채널 정보의 부정확도가 낮을 경우에는 여전히MMSE의 성능이 좋지만 채널 정보의 부정확성이 커질수록 상관기의 성능이 더 좋아짐을 보인다. 본 연구는 기존에 직관적으로 시행해 왔던 MMSE와 성관기의 성능 분석을 위한 시뮬레이션에 추가적으로 수학적인 접근법을 제공하여 그 응용분야를 넓혀 갈 수 있음을 보인다. In this work, we consider the effect of doppler bandwidth on the performance of channel sounding. We develop the mathematical formulation of the problem and compare the MMSE channel estimator to the simple correlator. Examples of the performance of the MMSE and correlator estimators are presented for the single-input single-output (SISO) case with various values of Doppler bandwidth to assess the impact of time variation. The results show that as the <TEX>$f_dT$</TEX> product increases the performance of both the MMSE and correlator estimates gets worse, and that the performance of the MMSE estimator improves relative to the correlator.We also consider case that the exact statistics of the channel are unknown It is shown that when the mismatch is not too large, the MMSE estimator with mismatch still does better than the simple correlator, but if the mismatch is large, then the correlator can do better.

Capacity Pre-Log of Noncoherent SIMO Channels Via Hironaka's Theorem

We find the capacity pre-log of a temporally correlated Rayleigh block-fading single-input multiple-output (SIMO) channel in the noncoherent setting. It is well known that for block-length L and rank of the channel covariance matrix equal to Q, the capacity pre-log in the single-input single-output (SISO) case is given by 1-Q/L. Here, Q/L can be interpreted as the pre-log penalty incurred by channel uncertainty. Our main result reveals that, by adding only one receive antenna, this penalty can be reduced to 1/L and can, hence, be made to vanish for the block-length L→∞, even if Q/L remains constant as L→∞. Intuitively, even though the SISO channels between the transmit antenna and the two receive antennas are statistically independent, the transmit signal induces enough statistical dependence between the corresponding receive signals for the second receive antenna to be able to resolve the uncertainty associated with the first receive antenna's channel and thereby make the overall system appear coherent. The proof of our main theorem is based on a deep result from algebraic geometry known as Hironaka's Theorem on the Resolution of Singularities.

The Generalized Degrees of Freedom Region of the MIMO Interference Channel and Its Achievability

The generalized degrees of freedom (GDoF) region of the MIMO Gaussian interference channel (IC) is obtained for the general case of an arbitrary number of antennas at each node and where the signal-to-noise ratios (SNRs) and interference-to-noise ratios vary with arbitrary exponents to a nominal SNR. The GDoF-optimal coding scheme involves message splitting and partial interference decoding and consists of linear Gaussian superposition coding of the private and common submessages that can be seen as jointly performing signal-space and signal-level interference alignment. The admissible degree of freedom (DoF)-splits between the private and common messages are also specified. A study of the GDoF region reveals various insights through the joint dependence of optimal interference management techniques at high SNR on the SNR exponents and the numbers of antennas at the four terminals. For instance, it reveals that, unlike in the scalar IC, treating interference as noise is not always GDoF-optimal even in the very weak interference regime. Moreover, while the DoF-optimal strategy that relies just on transmit/receive zero-forcing beamforming and time sharing is not GDoF optimal (and thus has an unbounded gap to capacity), the precise characterization of the very strong interference regime-where single-user DoF performance can be achieved simultaneously for both users-depends on the relative numbers of antennas at the four terminals and thus deviates from what it is in the single-input single-output case. For asymmetric numbers of antennas at the four nodes, the shape of the symmetric GDoF curve can be a “distorted W” curve to the extent that for certain multiple-input multiple-output ICs it is a “V” curve.

Control System Synthesis: A Factorization Approach, Part II

Abstract This book introduces the so-called factorization to the synthesis of feedback controllers for linear control systems. The key to this approach is to view the multi-input, multi-output (MIMO) plant for which one wishes to design a controller as a matrix over the fraction field F associated with a commutative ring with identity, denoted by R, which also has no divisors of zero. In this setting, the set of single-input, single-output (SISO) stable control systems is precisely the ring R, while the set of stable MIMO control systems is the set of matrices whose elements all belong to R. The set of unstable, meaning not necessarily stable, control systems is then taken to be the field of fractions F associated with R in the SISO case, and the set of matrices with elements in F in the MIMO case. The central notion introduced in the book is that, in most situations of practical interest, every matrix P whose elements belong to F can be factored as a ratio of two matrices N,D whose ...

The Secrecy Capacity Region of the Gaussian MIMO Multi-Receiver Wiretap Channel

In this paper, we consider the Gaussian multiple-input multiple-output (MIMO) multi-receiver wiretap channel in which a transmitter wants to have confidential communication with an arbitrary number of users in the presence of an external eavesdropper. We derive the secrecy capacity region of this channel for the most general case. We first show that even for the single-input single-output (SISO) case, existing converse techniques for the Gaussian scalar broadcast channel cannot be extended to this secrecy context, to emphasize the need for a new proof technique. Our new proof technique makes use of the relationships between the minimum-mean-square-error and the mutual information, and equivalently, the relationships between the Fisher information and the differential entropy. Using the intuition gained from the converse proof of the SISO channel, we first prove the secrecy capacity region of the degraded MIMO channel, in which all receivers have the same number of antennas, and the noise covariance matrices can be arranged according to a positive semi-definite order. We then generalize this result to the aligned case, in which all receivers have the same number of antennas; however, there is no order among the noise covariance matrices. We accomplish this task by using the channel enhancement technique. Finally, we find the secrecy capacity region of the general MIMO channel by using some limiting arguments on the secrecy capacity region of the aligned MIMO channel. We show that the capacity achieving coding scheme is a variant of dirty-paper coding with Gaussian signals.