Auxiliary Amplitude Research Articles

Holographic phase retrieval via Wirtinger flow: Cartesian form with auxiliary amplitude

We propose a new gradient method for holography, where a phase-only hologram is parameterized by not only the phase but also amplitude. The key idea of our approach is the formulation of a phase-only hologram using an auxiliary amplitude. We optimize the parameters using the so-called Wirtinger flow algorithm in the Cartesian domain, which is a gradient method defined on the basis of the Wirtinger calculus. At the early stage of optimization, each element of the hologram exists inside a complex circle, and it can take a large gradient while diverging from the origin. This characteristic contributes to accelerating the gradient descent. Meanwhile, at the final stage of optimization, each element evolves along a complex circle, similar to previous state-of-the-art gradient methods. The experimental results demonstrate that our method outperforms previous methods, primarily due to the optimization of the amplitude.

A new horizon of Few-Body Problems: Exact Coulomb treatment and the energy-momentum translation of the three-body Faddeev equation

We propose an off-shell Coulomb-like amplitude with an on-shell phase shift that is accurate to within 9-10 digits. The full Coulomb amplitude is separated into the leading and the auxiliary amplitudes using “the two-potential theory”. The leading amplitude reproduces most of the on- and off-shell parts, while the auxiliary amplitude contributes mainly to the off-shell part and minimally to the on-shell part. We then review the three-body calculation method developed during the last four decades. A reminder to a threshold behavior investigation method is pointed out based on the three-body Faddeev equation. We discuss the Efimov physics and some extensions, which are recovered from our predictions. The method may suggest a promising technique to resolve the existing discrepancies between current experimental and theoretical values.

Phase Retrieval via the Alternating Direction Method of Multipliers

We derive a phase retrieval algorithm using the alternating direction method of multipliers. For the cost function obtained from the maximum likelihood criterion, we introduce auxiliary amplitude and phase variables to avoid the absolute value operator and decouple the determination of the auxiliary phase variables from that of the auxiliary amplitude variables. As a result, a phase retrieval algorithm consisting only of two least-squares steps is derived. The performance of the proposed algorithm is investigated via numerical examples, as well as an application to flat-spectrum periodic unimodular sequence design.

Symbol rate identification for auxiliary amplitude modulation optical signal

In this paper, we creatively propose and demonstrate a method for symbol rate identification (SRI) of auxiliary amplitude modulation (AAM) optical signal based on asynchronous delay-tap sampling (ADTS) and average magnitude difference function (AMDF). The method can accurately estimate symbol rate and has large transmission impairments tolerance. Furthermore, it can be realized in the digital signal processor (DSP) with low logical resources because of multiplication-free. In order to improve the accuracy of SRI, the peak to valley ratio (PTVR) of AMDF is introduced into our method for blind chromatic dispersion (CD) compensation. The results of the numerical simulations show that the overall maximum SRI error is smaller 0.079% for return-to-zero (RZ) on-off keying (OOK), RZ differential phase-shift keying (DPSK), RZ differential quadrature phase-shift keying (DQPSK) and RZ 16-ary quadrature amplitude modulation (QAM) with 50% duty cycles.

Simultaneous optical signal to noise ratio and symbol rate estimation with blind chromatic dispersion compensation for auxiliary amplitude modulation optical signals

Based on the peak to valley ratio (PTVR) of the average magnitude difference function (AMDF), we present a novel optical signal to noise ratio (OSNR) and symbol rate (SR) estimation method for commonly used auxiliary amplitude modulations (AAMs). Moreover, it is demonstrated that the influence of chromatic dispersion (CD) on the method can be mitigated by maximizing the PTVR of the AMDF with additional tunable dispersion compensators. The results of simulations show that the OSNR estimation error can be kept within 0.8 dB in the wide OSNR range of (12, 32) dB, while the SR estimation error is below 0.079% for four widely used 10 Gsymbol/s AAM signals.

Improved symbol rate identification method for on–off keying and advanced modulation format signals based on asynchronous delayed sampling

Symbol rate identification (SRI) based on asynchronous delayed sampling is accurate, cost-effective and robust to impairments. For on–off keying (OOK) signals the symbol rate can be derived from the periodicity of the second-order autocorrelation function (ACF2) of the delay tap samples. But it is found that when applied this method to advanced modulation format signals with auxiliary amplitude modulation (AAM), incorrect results may be produced because AAM has significant impact on ACF2 periodicity, which makes the symbol period harder or even unable to be correctly identified. In this paper it is demonstrated that for these signals the first order autocorrelation function (ACF1) has stronger periodicity and can be used to replace ACF2 to produce more accurate and robust results. Utilizing the characteristics of the ACFs, an improved SRI method is proposed to accommodate both OOK and advanced modulation formant signals in a transparent manner. Furthermore it is proposed that by minimizing the peak to average ratio (PAPR) of the delay tap samples with an additional tunable dispersion compensator (TDC) the limited dispersion tolerance can be expanded to desired values.

Special type of three-phase oscillator using current gain control for amplitude stabilization

The main aim of this work is to demonstrate the use of electronically controlled second-generation current conveyor in providing electronic control to the condition of oscillation (CO) of a new active RC sinusoidal oscillator. Electronic control of the CO, which is independently set and does not affect the oscillation frequency, is enabled by the use of an auxiliary amplitude control loop to regulate the amplitude and provide very good total harmonic distortion performance. The proposed oscillator employs only one standard second-generation current conveyor, one electronically controlled second-generation current conveyor, five passive elements and is capable of providing three voltage outputs having phase shifts 45 and 90°, if specific design requirements are fulfilled. Similar simple types of oscillators do not provide such features. Non-ideal analysis of the circuit has also been carried out and the proposed oscillator has been verified by both PSpice simulations and experimental measurements using commercially available integrated circuits. Key words: Three-phase oscillator, special features, electronic control, electronically controllable current conveyor (ECCII), second generation current conveyor (CCII).

Propagation of modulated waves in a turbulent atmosphere. II. Correlation functions and frequency spectrum of fluctuations of the modulating-oscillation phase

An analysis is made of the statistical characteristics of the fluctuations of the phase transmitted along an optical communication line by auxiliary amplitude modulation. The method of smooth perturbations is used to calculate the spatial-temporal correlation functions as well as the frequency spectrum of fluctuations of the phase of the modulating oscillation. It is shown that the error in phase transmission behaves statistically exactly as the fluctuations of the phase of the carrier wave. The width of the frequency spectrum is of the order of v/L0.