Finite Input Research Articles

A Unified Theory of Op-amp Sinusoidal Oscillators using Reactive π and T Networks in the Feedback Path

ABSTRACTA general theory of op-amp sinusoidal oscillators using reactive π and T networks in the feedback path is presented. A total of 12 such oscillators are investigated, 6 with the π configuration and another 6 with the T configuration, of three reactive elements in the feedback network. In each case, expressions are derived for the frequency of oscillation and the gain required of the op-amp, both of which, in general, are shown to depend upon the input and output resistances of the op-amp. One or both of these resistances can generally be ignored in most op-amp applications, but not for oscillators, thus creating problems for the students when they actually try to construct an op-amp oscillator in the laboratory. It is emphasised that with the π configuration, it is essential that the op-amp has a non-zero output resistance, while with the T configuration, the input resistance has to be finite. It is also pointed out that when the gain required is negative, a single op-amp circuit has to have a finite input resistance, irrespective of the configuration of the feedback network, while if the gain required is less than unity, the output resistance automatically arises.

RF low power subsampling architecture for wireless communication applications

With the increasing demands of wireless communication, flexible, complex, and diversified wireless communication applications are required. However, the difficulty of enabling new wireless communication applications is the lack of low power radio frequency (RF) transmission devices, especially the RF receiver. In order to alleviate this problem, an RF low power subsampling architecture for wireless communication applications is proposed in this paper. This subsampling architecture adopts a single-ended to differential configured balun low noise amplifier (balun-LNA), a subsampling mixer with high sampling ratio and a finite input response (FIR) filter and infinite impulse response (IIR) filter achieving frequency down-conversion, avoiding using high power-hungry blocks. Based on a subsampling theory, an optimum sampling frequency for the subsampling architecture is necessary to relax the complexity of the system. For the application of internet of things (IoT) wireless communication, the paper provides the implementation of the subsampling receiver solutions to get a tradeoff between power consumption, gain, noise, and sensitivity. It can achieve −85 dBm sensitivity for an amplitude shift keying (ASK) modulation at the data rate of 1 Mbps with the clock sampling frequency of 40 MHz. Finally, the theoretical analysis and simulation results show that the performance of the subsampling architecture has several advantages over others.

Power allocation for uplink SC‐FDMA systems with arbitrary input distribution

Existing power allocation schemes for single-carrier frequency division multiple access (SC-FDMA) systems are based on the assumption of Gaussian inputs. However, in practical systems, the inputs belong to a set of finite symbol alphabets. In this reported work the power allocation problem in the uplink SC-FDMA system with arbitrarily distributed finite power inputs is considered. An optimal solution to the problem is found by using the relationship between minimum mean-square error and mutual information. Simulation results show that solution allocates power in accordance to the modulation scheme employed and achieves significant power saving compared to schemes that assume Gaussian inputs.

Efficient Approximation of Quantum Channel Capacities

We propose an iterative method for approximating the capacity of classical-quantum channels with a discrete input alphabet and a finite dimensional output, possibly under additional constraints on the input distribution. Based on duality of convex programming, we derive explicit upper and lower bounds for the capacity. To provide an $\varepsilon$-close estimate to the capacity, the presented algorithm requires $O(\tfrac{(N \vee M) M^3 \log(N)^{1/2}}{\varepsilon})$, where $N$ denotes the input alphabet size and $M$ the output dimension. We then generalize the method for the task of approximating the capacity of classical-quantum channels with a bounded continuous input alphabet and a finite dimensional output. For channels with a finite dimensional quantum mechanical input and output, the idea of a universal encoder allows us to approximate the Holevo capacity using the same method. In particular, we show that the problem of approximating the Holevo capacity can be reduced to a multidimensional integration problem. For families of quantum channels fulfilling a certain assumption we show that the complexity to derive an $\varepsilon$-close solution to the Holevo capacity is subexponential or even polynomial in the problem size. We provide several examples to illustrate the performance of the approximation scheme in practice.

Analysis and Simple Circuit Design of Double Differential EMG Active Electrode.

In this paper we present an analysis of the voltage amplifier needed for double differential (DD) sEMG measurements and a novel, very simple circuit for implementing DD active electrodes. The three-input amplifier that standalone DD active electrodes require is inherently different from a differential amplifier, and general knowledge about its design is scarce in the literature. First, the figures of merit of the amplifier are defined through a decomposition of its input signal into three orthogonal modes. This analysis reveals a mode containing EMG crosstalk components that the DD electrode should reject. Then, the effect of finite input impedance is analyzed. Because there are three terminals, minimum bounds for interference rejection ratios due to electrode and input impedance unbalances with two degrees of freedom are obtained. Finally, a novel circuit design is presented, including only a quadruple operational amplifier and a few passive components. This design is nearly as simple as the branched electrode and much simpler than the three instrumentation amplifier design, while providing robust EMG crosstalk rejection and better input impedance using unity gain buffers for each electrode input. The interference rejection limits of this input stage are analyzed. An easily replicable implementation of the proposed circuit is described, together with a parameter design guideline to adjust it to specific needs. The electrode is compared with the established alternatives, and sample sEMG signals are obtained, acquired on different body locations with dry contacts, successfully rejecting interference sources.

An auxiliary model based least squares algorithm for a dual-rate state space system with time-delay using the data filtering

For dual-rate state space systems with time-delay, this paper combines the auxiliary model identification idea with the filtering technique, transforms the state space model into the identification model with different input and output sampling rates, and presents a filtering and auxiliary model based recursive least squares identification algorithm with finite measurement input–output data. Compared with the auxiliary model based recursive least squares algorithm, the proposed algorithm can generate more accurate parameter estimates and has a higher computational efficiency because the dimensions of its covariance matrices become small.

Simulation of the fracture behavior of Al6061 laser welded joints with the Rousselier model

Ductile fracture behavior of an aluminum laser beam welded joint is investigated experimentally and numerically. Based on the hardness test across the welded joints, the dimensions of different weld regions are fixed. Tensile tests of flat specimens extracted from the base material, from the fusion zone and from the heat affected zone are made. The mechanical properties of the different weld regions are used as finite element model input in the simulation work. Fracture toughness tests are performed on compact tension specimens with the initial crack located in the base material, and in the center of the fusion zone, respectively. The tensile test results of compact tension specimens are shown in the form of force vs. crack opening displacement and fracture resistance curves. Based on the numerical calibration of the Rousselier parameters on notched round specimens, the Rousselier model is used to investigate the crack propagation of the compact tension specimen. Good agreement between the numerical and experimental results is obtained from compact tension specimens with the initial crack located at different positions of the weld region.

Maximal capacity nonorthogonal pulse shape modulation

To improve spectral utilization of communication system, a novel nonorthogonal pulse shape modulation (NPSM) based on prolate spheroidal wave function (PSWF) is proposed. The modulation employs nonorthogonal PSWF pulses to transmit information and it shows a higher capacity than traditional orthogonal modulations. The NPSM capacity under the constraint of finite input alphabet, which is determined by parameters of PSWF pulse, is derived. An optimization model for maximal capacity of NPSM is constructed and an exhaustive self-adapting gradient search algorithm for the model is proposed. A practical NPSM scheme with the maximal capacity is obtained by this search algorithm and it is proved to be superior to orthogonal signaling in the capacity. Our theoretical analysis is validated by numerical simulations and practical tests, and the results show that NPSM outperforms orthogonal modulations in the capacity and has a lower Peak-to-Average Power Ratio.

Lower Bounds and Approximations for the Information Rate of the ISI Channel

We consider the discrete-time intersymbol interference (ISI) channel model, with additive Gaussian noise and fixed independent identically distributed inputs. In this setting, we investigate the expression put forth by Shamai and Laroia as a conjectured lower bound for the input–output mutual information after application of a minimum mean-square error decision-feedback equalizer receiver. A low-signal to noise ratio (SNR) expansion is used to prove that the conjectured bound does not hold under general conditions, and to characterize inputs for which it is particularly ill-suited. One such input is used to construct a counterexample, indicating that the Shamai–Laroia expression does not always bound even the achievable rate of the channel, thus excluding a natural relaxation of the original conjectured bound. However, this relaxed bound is then shown to hold for any finite entropy input and ISI channel, when the SNR is sufficiently high. We derive two conditions under which the relaxed bound holds, involving compound channel capacity and quasiconvexity arguments. Finally, new simple bounds for the achievable rate are proven, and compared with other known bounds. Information-estimation relations and estimation–theoretic bounds play a key role in establishing our results.

Nuclear spin noise in NMR revisited.

The theoretical shapes of nuclear spin-noise spectra in NMR are derived by considering a receiver circuit with finite preamplifier input impedance and a transmission line between the preamplifier and the probe. Using this model, it becomes possible to reproduce all observed experimental features: variation of the NMR resonance linewidth as a function of the transmission line phase, nuclear spin-noise signals appearing as a "bump" or as a "dip" superimposed on the average electronic noise level even for a spin system and probe at the same temperature, pure in-phase Lorentzian spin-noise signals exhibiting non-vanishing frequency shifts. Extensive comparisons to experimental measurements validate the model predictions, and define the conditions for obtaining pure in-phase Lorentzian-shape nuclear spin noise with a vanishing frequency shift, in other words, the conditions for simultaneously obtaining the spin-noise and frequency-shift tuning optima.

A General Formula for the Mismatch Capacity

The fundamental limits of channels with mismatched decoding are addressed. A general formula is established for the mismatch capacity of a general channel, defined as a sequence of conditional distributions with a general decoding metrics sequence. We deduce an identity between the Verdu–Han general channel capacity formula, and the mismatch capacity formula applied to maximum likelihood decoding metric. Furthermore, several upper bounds on the capacity are provided, and a simpler expression for a lower bound is derived for the case of a non-negative decoding metric. The general formula is specialized to the case of finite input and output alphabet channels with a type-dependent metric. The closely related problem of threshold mismatched decoding is also studied, and a general expression for the threshold mismatch capacity is obtained. As an example of threshold mismatch capacity, we state a general expression for the erasures-only capacity of the finite input and output alphabet channel. We observe that for every channel, there exists a (matched) threshold decoder, which is capacity achieving. In addition, necessary and sufficient conditions are stated for a channel to have a strong converse.

Linear Precoding Design for Mutual Information Maximization in Generalized Spatial Modulation With Finite Alphabet Inputs

In this letter, we develop a new precoding scheme that improves the performance of mutual information for generalized spatial modulation (GSM). First, the closed-form expression of the mutual information of the GSM with finite alphabet inputs is derived in order to update the precoder with regard to the mutual information. The joint precoding design problem to maximize the mutual information of the GSM is difficult to solve directly since it is a non-convex coupled problem. In order to solve this problem, we transform the GSM system into a virtual multiple-input multiple-output (MIMO) system, and then an extended ellipsoid algorithm is applied. Each precoder of the GSM can be solved using the common precoder of the virtual MIMO. The numerical results demonstrate that the proposed precoding scheme significantly enhances the performance in terms of the mutual information.

A Self-learning Robust Swing-up algorithm

A novel swing-up algorithm for an inverted pendulum under a restricted cart track length is introduced. The algorithm achieves the swing-up task by means of a control law that uses a finite input set. The algorithm neither knows nor uses values of cart and pendulum masses, or pendulum length. In the swing-up process, it self-learns a weight that is used in normalizing the energy injected to the pendulum. This weight makes it possible for the algorithm to determine the number of sampling periods needed to reach the upright equilibrium state. Also, by predicting the multi-step ahead cart position, it gives rise to a control law that keeps the cart within the track and makes the pendulum reach the neighbourhood of the upright equilibrium state in a smooth manner. The validity and robustness of the swing-up algorithm are verified through laboratory experiments.

The effect of finite duration inputs on the dynamics of a system: Proposing a new approach for cancer treatment

In this paper, a principal question regarding the effect of inputs on the characteristics of dynamic systems is discussed. Whether an input implemented only for a limited duration, can change the characteristics of a dynamic system such that the behavior of the free system, after eliminating the input, differs from that before acting the input? In this paper, it is shown that a limited time acted input is not able to change the dynamical properties of a system after its elimination. Regarding the proposed approach, a novel finite duration treatment method is developed for a tumor-immune system. The vaccine therapy is used to change the parameters of the system and the chemotherapy is applied for pushing the system to the domain of attraction of the healthy state. For optimal chemotherapy, an optimal control is used based on state-dependent Riccati equation (SDRE). It is shown that, in spite of eliminating the treatment (therapeutic inputs), the system approaches to healthy state conditions. The present analysis suggests that a proper treatment method must change the dynamics of the cancer instead of only reducing the population of cancer cells.

On renewal input state dependent working vacations queue with impatient customers

This paper studies the effect of balking and reneging in a finite buffer renewal input queue with multiple working vacations. Arriving customers balk with a probability and renege according to exponential distribution. As soon as the system becomes empty, the server leaves for a working vacation. During working vacations the server works at a different rate rather than completely stopping service. Service times during a service period, during a working vacation period and vacation times are assumed to be exponentially distributed with state dependent rates. Employing the supplementary variable and recursive techniques, the steady-state system length distributions at pre-arrival and arbitrary epochs have been derived. Some performance measures of the model and cost analysis through simulated annealing have been discussed. Finally, sensitivity analysis is carried out through some numerical experiments.

An Estimation of Achievable Rate for Digital Transmissions over MIMO Channels

Achievable rate (AR) is significant to communications. As to multi-input multi-output (MIMO) digital transmissions with finite alphabets inputs, which greatly improve the performance of communications, it seems rather difficult to calculate accurate AR. Here we propose an estimation of con-siderable accuracy and low complexity, based on Euclidean measure matrix for given channel states and constellations. The main contribution is explicit expression, non-constraints to MIMO schemes and channel states and constellations, and controllable estimating gap. Numerical results show that the proposition is able to achieve enough accurate AR computation. In addition the estimating gap given by theoretical deduction is well agreed.

Asymptotic Properties of Collective-Rearrangement Algorithms

We analyze asymptotic properties of collective-rearrangement algorithms being a class of dense packing algorithms. Traditionally, they transform finite systems of (possibly overlapping) particles into non-overlapping configurations by collective rearrangement of particles in finitely many steps. We consider the convergence of such algorithms for not necessarily finite input data, which means that the configuration of particles in any bounded sampling window remains unchanged after finitely many rearrangement steps. More precisely, we derive sufficient conditions implying the convergence of such algorithms when a stationary process of particles is used as input. We also provide numerical results and present an application in computational materials science.

Comparison of the Achievable Rates in OFDM and Single Carrier Modulation with I.I.D. Inputs

We compare the maximum achievable rates in single-carrier and OFDM modulation schemes, under the practical assumptions of i.i.d. finite alphabet inputs and linear ISI with additive Gaussian noise. We show that the Shamai-Laroia approximation serves as a bridge between the two rates: while it is well known that this approximation is often a lower bound on the single-carrier achievable rate, it is revealed to also essentially upper bound the OFDM achievable rate. We apply Information-Estimation relations in order to rigorously establish this result for both general input distributions and to sharpen it for commonly used PAM and QAM constellations. To this end, novel bounds on MMSE estimation of PAM inputs to a scalar Gaussian channel are derived, which may be of general interest. Our results show that, under reasonable assumptions, optimal single-carrier schemes may offer spectral efficiency significantly superior to that of OFDM, motivating further research of such systems.

Linear Precoding for the MIMO Multiple Access Channel With Finite Alphabet Inputs and Statistical CSI

In this paper, we investigate the design of linear precoders for the multiple-input multiple-output (MIMO) multiple access channel (MAC). We assume that statistical channel state information (CSI) is available at the transmitters and consider the problem under the practical finite alphabet input assumption. First, we derive an asymptotic (in the large system limit) expression for the weighted sum rate (WSR) of the MIMO MAC with finite alphabet inputs and Weichselberger's MIMO channel model. Subsequently, we obtain the optimal structures of the linear precoders of the users maximizing the asymptotic WSR and an iterative algorithm for determining the precoders. We show that the complexity of the proposed precoder design is significantly lower than that of MIMO MAC precoders designed for finite alphabet inputs and instantaneous CSI. Simulation results for finite alphabet signalling indicate that the proposed precoder achieves significant performance gains over existing precoder designs.

On Precoding for Constant <inline-formula> <tex-math notation="TeX">$K$</tex-math></inline-formula>-User MIMO Gaussian Interference Channel With Finite Constellation Inputs

This paper considers linear precoding for the constant channel-coefficient K-user MIMO Gaussian interference channel (MIMO GIC) where each transmitter-i (Tx-i) requires the sending of d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> independent complex symbols per channel use that take values from fixed finite constellations with uniform distribution to receiver-i (Rx-i) for i=1,2,..., K. We define the maximum rate achieved by Tx-i using any linear precoder as the signal-to-noise ratio (SNR) tends to infinity when the interference channel coefficients are zero to be the constellation constrained saturation capacity (CCSC) for Tx-i. We derive a high-SNR approximation for the rate achieved by Tx-i when interference is treated as noise and this rate is given by the mutual information between Tx-i and Rx-i, denoted as I[X <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> ;Y <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> ]. A set of necessary and sufficient conditions on the precoders under which [IX <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> ; Y <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> ] tends to CCSC for Tx-i is derived. Interestingly, the precoders designed for interference alignment (IA) satisfy these necessary and sufficient conditions. Furthermore, we propose gradient-ascent-based algorithms to optimize the sum rate achieved by precoding with finite constellation inputs and treating interference as noise. A simulation study using the proposed algorithms for a three-user MIMO GIC with two antennas at each node with d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> =1 for all i and with BPSK and QPSK inputs shows more than 0.1-b/s/Hz gain in the ergodic sum rate over that yielded by precoders obtained from some known IA algorithms at moderate SNRs.