Real Multipliers Research Articles

Demonstration of a low-complexity real-time FBMC transmitter for a spectral-efficiency IMDD system.

Filter bank multi-carriers (FBMC) have higher spectral efficiency, lower out-of-band spectrum leakage, and stronger ability to resist synchronization errors compared to orthogonal frequency-division multiplexing (OFDM), which has been widely considered as a promising solution for short-reach applications, such as passive optical networks. However, the traditional fast Fourier transform (FFT)-based FBMC scheme has quite high implementation complexity for high-speed optical communications. In this work, we proposed a low-complexity real-time FBMC transmitter scheme enabled by a single fully parallel pruned inverse FFT and simplified short prototype filter-based polyphase networks for a low-cost intensity-modulation and direct-detection (IMDD) system. Compared to the OFDM transmitter, the proposed FBMC one occupies a similar number of look-up tables and registers but saves 21% of real multipliers, reduces latency by 16.2%, and increases the data rate by 12.5%. The real-time FBMC/OFDM signals are generated with a field programmable gate array chip and 6-bit 30-GSa/s digital-to-analog converter and are experimentally demonstrated in an IMDD system. After a 20-km standard single-mode fiber transmission, the negligible power penalty can be achieved with the proposed FBMC transmitter scheme at the bit error rate of 3.8e-3 compared to the OFDM counterpart.

Linearly stable KAM tori for one dimensional forced Kirchhoff equations with refined Töplitz-Lipschitz property

We prove an abstract infinite dimensional KAM theorem, which could be applied to prove the existence and linear stability of small-amplitude quasi-periodic solutions for one dimensional forced Kirchhoff equations with Dirichlet boundary conditionsutt−(1+∫0π|ux|2dx)uxx+Mξu+ϵg(ω¯t,x)=0,u(t,0)=u(t,π)=0, where Mξ is a real Fourier multiplier, g(ω¯t,x)=−g(ω¯t,−x) is real analytic with forced Diophantine frequencies ω¯, ϵ is a small parameter. The proof is based on an improved Kuksin lemma and the off-diagonal decay together with the refined Töplitz-Lipschitz property of the forcing term.

Hardware Efficient and Chromatic Dispersion Tolerant Symbol-Rate Equalization Scheme for Short-Reach Coherent Transmission System

Chromatic dispersion enhanced spectrum aliasing, a nonlinear effect in the frequency domain, is theoretically analyzed under symbol-rate sampling conditions, and the relationship between its nonlinear strength and chromatic dispersion is investigated in detail. To address chromatic dispersion enhanced spectrum aliasing efficiently, a hardware efficient and chromatic dispersion tolerant equalization scheme is proposed to deal with inter-symbol-interference, chromatic dispersion, chromatic dispersion enhanced spectrum aliasing and phase noise simultaneously. Compared with the conventional T/2-spaced adaptive equalizer (AEQ) and symbol-rate AEQ, the proposed scheme can deal with large accumulated chromatic dispersion in a cost-efficient manner, which is extremely attractive for ultra-high baud rate and short-reach coherent optical interconnects. The experimental results also indicate that the proposed scheme can provide more than 3 dB received optical power sensitivity improvement over symbol-rate Sim-AEQ after 20 km fiber transmission links. With 7% FEC threshold, the proposed scheme with the same tap number can provide around 250 ps/nm and 90 ps/nm chromatic dispersion tolerance improvement over symbol-rate Sim-AEQ and conventional T/2-spaced equalization schemes, respectively. Additionally, compared with T/2-spaced 2 × 2 MIMO, the proposed scheme can also save around 50% real value multiplier because of the simplified equalization structure. Consequently, the proposed scheme with high chromatic dispersion tolerance and low complexity can be considered a promising DSP solution for ultra-capacity short-reach coherent optical interconnects such as datacenter interconnects and access applications.

Geographically Overlapping Real Estate Assets, Liquidity Spillovers, and Liquidity Multiplier Effects

Geographically Overlapping Real Estate Assets, Liquidity Spillovers, and Liquidity Multiplier Effects

Multiplier-Free Parallel Fixed-Point Adaptive Equalizer for Real-Time Digital Coherent Communication

Multiplier-free adaptive equalizers are significant for improving utilization, reducing costs, and ensuring robustness in real-time hardware implementation. In this letter, we demonstrate that using only one bit shift and one XOR operation to replace a real multiplier is a feasible and low-complexity way to obtain a multiplier-free parallel fixed-point adaptive equalizer (PFAEQ). The performances of the multiplier-free PFAEQ (MF-PFAEQ) are verified by a 112 Gbits/s polarization multiplexing quadrature phase shift keying (PM-QPSK) back-to-back experiment. It can be found that, under different parallels and different bit width of signals, MF-PFAEQ shows similar performances to traditional PFAEQ. Besides, in some cases, compared with the traditional PFAEQ, MF-PFAEQ also shows the similar convergent speed. In addition, according to the Quartus 15.0 synthesis, compared to traditional PFAEQ, the logic utilization and total registers of MF-PFAEQ reduce by 51.8% and 45.2%, respectively. This study is novel in using rather less shift operations to obtain a multiplier-free adaptive equalizer.

Quasi-Periodic Solution of Nonlinear Beam Equation on $${\mathbb T}^d$$ with Forced Frequencies

In this paper, we study the higher dimensional nonlinear beam equation under periodic boundary condition: utt+Δx2u+Mξu+f(ω¯t,u)=0,u=u(t,x),t∈R,x∈Td,d≥2where Mξ is a real Fourier multiplier, f=f(θ¯,u) is a real analytic function with respect to (θ¯,u), and f(θ¯,u)=O(|u|2). This equation can be viewed as an infinite dimensional nearly integrable Hamiltonian system. We establish an infinite dimensional KAM theorem, and apply it to this equation to prove that there exist a class of small amplitude quasi-periodic solutions corresponding to finite dimensional invariant tori.

Quasi-periodic solutions of fractional nonlinear Schrödinger equation systems

In this paper, the fractional nonlinear Schrödinger equation system with periodic boundary conditions is considered. I establish an abstract infinite-dimensional KAM theorem and apply it to fractional nonlinear Schrödinger equation system with real Fourier multiplier. By establishing a block diagonal normal form, we prove the existence of a class of Whitney smooth family of small-amplitude quasi-periodic solutions corresponding to finite-dimensional invariant tori of an associated infinite-dimensional dynamic system.

Reducible KAM tori for higher dimensional wave equations under nonlocal and forced perturbation

In this paper, we prove an infinite dimensional Kolmogorov-Arnold-Moser theorem. As an application, it is shown that there are many small-amplitude linearly-stable quasi-periodic solutions for higher dimensional wave equations with a real Fourier multiplier, which are under nonlocal and forced perturbations with a special structure in space and short range property.

New Design of Low Complexity Multipliers in DFT/IDFT

This paper presents a new design to implement DFT/IDFT using the two components of a sequence, which are even and odd component sequences to solve the complexity of complex multiplications and reduce the number of multipliers. The proposed two implementations reduce the number of real multipliers needed to compute the DFT. The first proposed design gives good results for N ≤ 512 as compared to conventional FFT algorithm, while the second scenario gives good results for N ≤ 1024 as compared to conventional FFT algorithm. The proposed design is performed directly from real and imaginary part equations of the DFT sequence X [k] without additional processing.

The Overshooting and Coordination of Monetary Policy and Financial Regulation in China: Money Multiplier Redux

From 2017 to 2018, to prevent the accumulating financial risks, the Chinese government used strict financial regulation and tight monetary policy to constrain the growth of the banking innovative businesses. It seems that there is no target conflict, however, the above policies resulted in a sharp drop of M2 growth, which drag down the economy growth further. I call this phenomenon as policy overshooting. I find the policy overshooting mechanism can be explained by money multiplier theory: Because there is a high required reserve ratio (RRR) for traditional deposit while none for innovative deposit, hence strict financial regulation will decrease the money multiplier growth. Combine with the decline in monetary base growth derive from the tight monetary policy, will lead to a sharp drop of M2 growth. To test this hypothesis, I calculate the exogenous monetary base growth and the correspondent real money multiplier growth. The former measures the monetary policy stance of the People’s Bank of China accurately. To solve the overshooting problem, I propose a new policy tool called differential reserve ratio based on money creation mechanism (DRRMCM), which set a low RRR on traditional deposit while a high RRR on innovative deposit. Then strict financial regulation will increase the money multiplier growth to offset the decline in monetary base growth due to the tight monetary policy. I call this phenomenon as policy coordination. At last, I give a discussion about how to use DRRMCM in practice.

Texas County Pilots Telehealth Crisis Response Program

The use of an iPad can extend the expertise of psychiatrists and other mental health professionals when Harris County deputies encounter situations that involve people with mental illness.

A KAM Theorem for Higher Dimensional Wave Equations Under Nonlocal Perturbation

In this paper, we prove an infinite dimensional KAM theorem. As an application, it is shown that there are many real-analytic small-amplitude linearly-stable quasi-periodic solutions for higher dimensional wave equation under nonlocal perturbation $$\begin{aligned} u_{tt}-\triangle u +M_\xi u +\left( \int _{\mathbb {T}^d} u^2 dx\right) u=0,\quad t\in \mathbb {R},\ x\in \mathbb {T}^d\ \end{aligned}$$where $$M_\xi $$ is a real Fourier multiplier.

Moduli of stability for heteroclinic cycles of periodic solutions

We consider $ C^2 $ vector fields in the three dimensional sphere with an attracting heteroclinic cycle between two periodic hyperbolic solutions with real Floquet multipliers. The proper basin of this attracting set exhibits historic behavior and from the asymptotic properties of its orbits we obtain a complete set of invariants under topological conjugacy in a neighborhood of the cycle. As expected, this set contains the periods of the orbits involved in the cycle, a combination of their angular speeds, the rates of expansion and contraction in linearizing neighborhoods of them, besides information regarding the transition maps and the transition times between these neighborhoods. We conclude with an application of this result to a class of cycles obtained by the lifting of an example of R. Bowen.

Adaptive predistortion algorithm based on the multilinear multiplier fusion

SummaryAiming at solving the problem of the insufficiency in the predistortion structure and low accuracy of the memory nonlinear power amplifier in the wireless communication system, an adaptive predistortion method for dual loop learning structure based on the fusion of multilinear multiplier model recognition is put forward. On the basis of the real number delay multilinear multiplier model, an improved quantum behaved optimization (QBO) algorithm is adopted in this method to carry out indirect learning structure off‐line training of the multilinear multiplier, so as to determine the model parameters as an initial value of the predistorter. And then, the least square method (LSM) algorithm is used to carry out direct learning structure on‐line micro adjustment of the parameters of the predistorter and to conduct fitting on the nonlinearity and memory effect of the power amplifier. The method has the advantages of simple structure, fast convergence, and high precision, which has avoided the local optimum. The experimental results show that the adjacent channel power in this scheme is improved by approximately 7 dB compared with that of the classical dual loop structure predistortion method, and the linearization performance of the amplifier has been significantly improved, thus its feasibility has been verified.

Complex Number Vedic Multiplier and its Implementation in a Filter

Complex numbers multiplication is a fundamental mathematical process in systems like digital signal processors (DSP). The main objective of complex number multiplication is to perform operations at lightning fast speed with less intake of power. In this paper, the best possible architecture is designed for a Real vedic multiplier based on the ancient Indian mathematical procedure known as URDHVA TIRYAKBHYAM SUTRA i.e. the structure of a MxM Vedic real multiplier architecture is developed. Then, a Vedic real multiplier solution of a complex multiplier is presented and its simulation results are obtained. The MxM Vedic real multiplier architecture, architecture of the Real Vedic multiplier solution for 32 x 32 bit complex numbers multiplication of complex multiplier and the architecture of a FIR filter has been code in Verilog and implementation is done through Modelsim 5.6 and Xilinx ISE 7.1 navigator.

Stabilizing torsion-free periodic orbits using method of harmonic oscillators

An odd number of real Floquet multipliers greater than unity prevents the classical time delayed feedback control from stabilizing torsion-free orbits of nonautonomous systems. This paper investigates this limitation in the context of the method of harmonic oscillators. This method aims to stabilize periodic orbits of dynamical systems through a proper coupling to a system of harmonic oscillators. The results show that the method of harmonics oscillators does not suffer from this limitation for a proper coupling condition. A practical approach of designing the coupling condition that allows stabilizing torsion-free orbits of nonautonomous systems is presented. The success of the proposed approach is demonstrated using numerical examples.

Geographically Overlapping Real Estate Assets, Liquidity Spillovers, and Liquidity Multiplier Effects

When liquidity providers for one asset obtain information from other asset prices, this may magnify the (upward or downward) comovement of asset liquidity. It also may yield an illiquidity multiplier. We empirically test the magnitude of this illiquidity multiplier for a sample of U.S. equity real estate investment trusts (REITs) using spatial autoregressive models. We find significant liquidity spillovers among REITs with geographically overlapping real estate holdings. Our findings suggest that the multiplier effect impacts neighboring REITs through cross-asset learning about firm fundamentals. This effect is stronger during market turmoil, after the Decimalization (a source of exogenous variation), and for REITs headquartered in MSAs with less information asymmetry.

A Serial Commutator Fast Fourier Transform Architecture for Real-Valued Signals

This brief presents a novel pipelined architecture to compute the fast Fourier transform of real input signals in a serial manner, i.e., one sample is processed per cycle. The proposed architecture, referred to as real-valued serial commutator, achieves full hardware utilization by mapping each stage of the fast Fourier transform (FFT) to a half-butterfly operation that operates on real input signals. Prior serial architectures to compute FFT of real signals only achieved 50% hardware utilization. Novel data-exchange and data-reordering circuits are also presented. The complete serial commutator architecture requires $\boldsymbol {2}\log _{\boldsymbol{2}}\boldsymbol{ N -2}$ real adders, $\log _{\boldsymbol{2}}\boldsymbol{ N -2}$ real multipliers, and $\boldsymbol {N+ 9}\log _{\boldsymbol{2}}\boldsymbol{ N - 19}$ real delay elements, where $\boldsymbol N$ represents the size of the FFT.

On the Stability of Periodic Motions of an Autonomous Hamiltonian System in a Critical Case of the Fourth-order Resonance

The problem of orbital stability of a periodic motion of an autonomous two-degreeof- freedom Hamiltonian system is studied. The linearized equations of perturbed motion always have two real multipliers equal to one, because of the autonomy and the Hamiltonian structure of the system. The other two multipliers are assumed to be complex conjugate numbers with absolute values equal to one, and the system has no resonances up to third order inclusive, but has a fourth-order resonance. It is believed that this case is the critical one for the resonance, when the solution of the stability problem requires considering terms higher than the fourth degree in the series expansion of the Hamiltonian of the perturbed motion. Using Lyapunov’s methods and KAM theory, sufficient conditions for stability and instability are obtained, which are represented in the form of inequalities depending on the coefficients of series expansion of the Hamiltonian up to the sixth degree inclusive.

Holomorphic last multipliers on complex manifolds

The goal of this paper is to study the theory of last multipliers in the framework of complex manifolds with a fixed holomorphic volume form. The motivation of our study is based on the equivalence between a holomorphic ODE system and an associated real ODE system and we are interested how we can relate holomorphic last multipliers with real last multipliers. Also, we consider some applications of our study for holomorphic gradient vector fields on holomorphic Riemannain manifolds as well as for holomorphic Hamiltonian vector fields and holomorphic Poisson bivector fields on holomorphic Poisson manifolds.