Arbitrary Modulation Research Articles

DPSK Modulation With a Dual-Drive Silicon Photonic Loop-Mirror Modulator

A loop-mirror modulator (LMM) combines a Mach-Zehnder modulator with an integrated loop mirror. Differential phase shift keying modulation for the LMM with dual-drive traveling wave electrodes is investigated. We show analytically that when operated with the proper bias conditions, the LMM can achieve the arbitrary phase and amplitude modulation. We demonstrate experimentally an error-free transmission at 10 Gb/s.

Counting submodules of a module over a noetherian commutative ring

We count the number of submodules of an arbitrary module over a countable noetherian commutative ring. We give, along the way, various characterizations of minimax modules, as well as a structural description of meager modules, which are defined as those that do not have the square of a simple module as subquotient. We deduce in particular a characterization of uniserial modules over commutative noetherian rings.

Representations of the small nonstandard quantum groups

In this paper, we study the representations of a class of small nonstandard quantum group over which the isomorphism classes of all indecomposable modules are classified, and the decomposition formulas of the tensor product of arbitrary indecomposable modules and simple (or projective) modules are established. The projective class rings and Grothendieck rings of are also characterized.

Low-complexity carrier phase recovery based on principal component analysis for square-QAM modulation formats.

We propose, numerically analyze and experimentally demonstrate a low-complexity, modulation-order independent, non-data-aided (NDA), feed-forward carrier phase recovery (CPR) algorithm. The proposed algorithm enables synchronous decoding of arbitrary square-quadrature amplitude modulation (QAM) constellations and it is suitable for a realistic hardware implementation based on block-wise parallel processing. The proposed method is based on principal component analysis (PCA) and it outperforms the well-known and widely used blind phase search (BPS) algorithm at low signal-to-noise ratio (SNR) values, showing much lower cycle slip rate (CSR) both numerically and experimentally. For operation at higher SNR values, a hybrid two-stage implementation combining the proposed method and BPS is also proposed and their performance are investigated benchmarking them against the two-stage BPS (2S-BPS). The complexity of the proposed simple and hybrid methods are evaluated against 2S-BPS and computational complexity savings of 92% and 40% are expected for the simple and hybrid methods, respectively.

Extending OCaml's 'open'

We propose a harmonious extension of OCaml's 'open' construct. OCaml's existing construct 'open M' imports the names exported by the module 'M' into the current scope. At present 'M' is required to be the path to a module. We propose extending 'open' to instead accept an arbitrary module expression, making it possible to succinctly address a number of existing scope-related difficulties that arise when writing OCaml programs.

On the Gaudin model of type G2

We derive a number of results related to the Gaudin model associated to the simple Lie algebra of type G2. We compute explicit formulas for solutions of the Bethe ansatz equations associated to the tensor product of an arbitrary finite-dimensional irreducible module and the vector representation. We use this result to show that the Bethe ansatz is complete in any tensor product where all but one factor are vector representations and the evaluation parameters are generic. We show that the points of the spectrum of the Gaudin model in type G2 are in a bijective correspondence with self-self-dual spaces of polynomials. We study the set of all self-self-dual spaces — the self-self-dual Grassmannian. We establish a stratification of the self-self-dual Grassmannian with the strata labeled by unordered sets of dominant integral weights and unordered sets of nonnegative integers, satisfying certain explicit conditions. We describe closures of the strata in terms of representation theory.

Injective stabilization of additive functors, I. Preliminaries

This paper is the first one in a series of three dealing with the concept of injective stabilization of the tensor product and its applications. Its primary goal is to collect known facts and establish a basic operational calculus that will be used in the subsequent parts. This is done in greater generality than is necessary for the stated goal. Several results of independent interest are also established. They include, among other things, connections with satellites, an explicit construction of the stabilization of a finitely presented functor, various exactness properties of the injectively stable functors, a construction, from a functor and a short exact sequence, of a doubly-infinite exact sequence by splicing the injective stabilization of the functor and its derived functors. When specialized to the tensor product with a finitely presented module, the injective stabilization with coefficients in the ring is isomorphic to the 1-torsion functor. The Auslander-Reiten formula is extended to a more general formula, which holds for arbitrary (i.e., not necessarily finite) modules over arbitrary associative rings with identity. Weakening of the assumptions in the theorems of Eilenberg and Watts leads to characterizations of the requisite zeroth derived functors.The subsequent papers, provide applications of the developed techniques. Part II deals with new notions of torsion module and cotorsion module of a module. This is done for arbitrary modules over arbitrary rings. Part III introduces a new concept, called the asymptotic stabilization of the tensor product. The result is closely related to different variants of stable homology (these are generalizations of Tate homology to arbitrary rings). A comparison transformation from Vogel homology to the asymptotic stabilization of the tensor product is constructed and shown to be epic.

Visible achromatic super-oscillatory metasurfaces for sub-diffraction focusing.

Conventional optical lenses enable precise foci but suffer from the diffraction limit due to the cutoff of spatial frequencies. Development of a super-oscillatory phenomenon offers an alternative approach to realize far-field sub-diffraction focusing. However, most super-oscillatory lenses exhibit a strong dependence on incident wavelengths, resulting in a narrow-band working frequency due to a fragile super-oscillatory field. Here, for the first time, achromatic super-oscillatory metasurfaces (ASOMs) are proposed to simultaneously steer optical fields at visible wavelengths of 473 nm, 532 nm and 632.8 nm and to achieve focusing at the same axial position with a resolution beyond the diffraction limit. These metasurface-based devices provide dispersionless phase profiles so that the material dispersion can be neglected in the optimization process. In addition, the design strategy can effectively circumvent the axial chromatic aberration observed in previously demonstrated metasurfaces. Constructed ASOMs are further verified numerically and simulated results for one ASOM with spot sizes of 0.706, 0.722 and 0.750 times the diffraction limit at the preset plane are consistent with the designs. Furthermore, benefiting from flexible and arbitrary phase modulations of the metasurface, the proposed method gives more freedom for a design of a super-oscillatory field and enables a lightweight, low-cost and compact optical element to replace the bulky doublet/triplet lens in a conventional optical system.

Relations between endomorphism rings, injectivity, surjectivity and uniserial modules

For a right module [Formula: see text] over a ring [Formula: see text], we consider the set [Formula: see text] of all the endomorphisms [Formula: see text] that are not injective and the set [Formula: see text] of all the endomorphisms [Formula: see text] that are not surjective. We prove that when [Formula: see text] is a uniserial module, then [Formula: see text] is a left chain domain and [Formula: see text] is a right chain domain. The technique we make use of to prove this can be applied to arbitrary modules [Formula: see text], not-necessarily uniserial. When the endomorphisms [Formula: see text] are not in [Formula: see text] (not in [Formula: see text]), then left (right) divisibility in [Formula: see text] corresponds to inclusion in the lattice [Formula: see text] of all submodules of [Formula: see text]. This allows to study factorizations of injective (surjective, respectively) endomorphisms of [Formula: see text] analyzing finite chains in the partially ordered set [Formula: see text].

Photonic generation of multi-frequency dual-chirp microwave waveform with multiplying bandwidth

Abstract A photonic approach to generate dual-chirp microwave waveform with multi-carrier frequencies and multiplying bandwidth is proposed and demonstrated by using a dual-polarization Mach-Zehnder modulator (DPol-MZM) and balanced detection. In the approach, the DPol-MZM driven by a baseband waveform modulates the injected optical signal to generate optical broad-spectra sidebands. After heterodyne in balanced photodetector (BPD), multi-frequency dual-chirp microwave waveform can be generated. The proposed generator allows the injected optical signal with arbitrary intensity modulation format. The key features of the approach are the multi-carrier frequencies generation ability and the bandwidth multiplying operation. The proposed approach is verified by simulation. Dual-chirp signal with four-carrier frequencies is generated by employing optical frequency comb (OFC) with five comb lines. Auto-correlations of the generated signals show good pulse compression ratio and high peak-to-sidelobe ratio. The maximum frequency number of the system is analyzed, and the maximum power ratio is also investigated.

Spatial Spin-Wave Modulator for Quantum-Memory-Assisted Adaptive Measurements

Utilization of the spatial degree of freedom vastly enhances informational capacity of light at the cost of stringent requirements on the processing devices. Multi-mode quantum memories constitute a viable candidate for quantum and classical information processing; however, full utilization of the assets of high-dimensionality requires a flexible processing technique. We employ a spatially varying ac-Stark effect to perform arbitrary 1D phase modulation of a coherent spin-wave state stored in a wavevector-multiplexed quantum memory. A far-field and an interferometric near-field characterizations of the introduced phase profiles are presented. Additionally, coherence between temporally separated partial readouts of a single coherent spin-wave state is demonstrated, offering possible applications in adaptive measurements via conditional spin-wave modulation.

Electrically Reconfigurable Micromirror Array for Direct Spatial Light Modulation of Terahertz Waves over a Bandwidth Wider Than 1\u2009THz

We report the design, fabrication and experimental investigation of a spectrally wide-band terahertz spatial light modulator (THz-SLM) based on an array of 768 actuatable mirrors with each having a length of 220 μm and a width of 100 μm. A mirror length of several hundred micrometers is required to reduce diffraction from individual mirrors at terahertz frequencies and to increase the pixel-to-pixel modulation contrast of the THz-SLM. By means of spatially selective actuation, we used the mirror array as reconfigurable grating to spatially modulate terahertz waves in a frequency range from 0.97 THz to 2.28 THz. Over the entire frequency band, the modulation contrast was higher than 50% with a peak modulation contrast of 87% at 1.38 THz. For spatial light modulation, almost arbitrary spatial pixel sizes can be realized by grouping of mirrors that are collectively switched as a pixel. For fabrication of the actuatable mirrors, we exploited the intrinsic residual stress in chrome-copper-chrome multi-layers that forces the mirrors into an upstanding position at an inclination angle of 35°. By applying a bias voltage of 37 V, the mirrors were pulled down to the substrate. By hysteretic switching, we were able to spatially modulate terahertz radiation at arbitrary pixel modulation patterns.

Capacity and Achievable Rate Regions for Linear Network Coding Over Ring Alphabets

The rate of a network code is the ratio of the block size of the network’s messages to that of its edge codewords. We compare the linear capacities and achievable rate regions of networks using finite field alphabets to the more general cases of arbitrary ring and module alphabets. For non-commutative rings, two-sided linearity is allowed. Specifically, we prove the following for directed acyclic networks. First, the linear rate region and the linear capacity of any network over a finite field depend only on the characteristic of the field. Furthermore, any two fields with different characteristics yield different linear capacities for at least one network. Second, whenever the characteristic of a given finite field divides the size of a given finite ring, each network’s linear rate region over the ring is contained in its linear rate region over the field. Thus, any network’s linear capacity over a field is at least its linear capacity over any other ring of the same size. An analogous result also holds for linear network codes over module alphabets. Third, whenever the characteristic of a given finite field does not divide the size of a given finite ring, there is some network whose linear capacity over the ring is strictly greater than its linear capacity over the field. Thus, for any finite field, there always exist rings over which some networks have higher linear capacities than over the field.

Mathematical model of the process of tabular’s implementation of the operation algebraic multiplication in the residues class

Based on the properties of the class of residues in the article, a mathematical model of the process of tabular implementation of modular multiplication was synthesized, for both positive and negative numerical ranges of information processing by means of integer information processing. This model is recommended for practical application in the development of methods and algorithms for rapid processing of cryptographic information. Finding ways to simplify the structure of the table operating device integer information processing has led to the need to improve the mathematical model, methods and algorithms for modular operations, which increase the efficiency of the use of table arithmetic in the class of residues. A feature of the implementation of this model is the possibility of reducing the number of equipment operating device integer information by reducing the (50-70)% of logical elements "And" in the nodes of the table permanent storage device, directly implement the operation of modular multiplication by arbitrary mi module residual class. This is possible by using the symmetry properties of the aibi (mod mi) implementation table of the modular multiplication operation.

Differential Homological Algebra and General Relativity

In 1916, F.S. Macaulay developed specific localization techniques for dealing with “unmixed polynomial ideals” in commutative algebra, transforming them into what he called “inverse systems” of partial differential equations. In 1970, D.C. Spencer and coworkers studied the formal theory of such systems, using methods of homological algebra that were giving rise to “differential homological algebra”, replacing unmixed polynomial ideals by “pure differential modules”. The use of “differential extension modules” and “differential double duality” is essential for such a purpose. In particular, 0-pure differential modules are torsion-free and admit an “absolute parametrization” by means of arbitrary potential like functions. In 2012, we have been able to extend this result to arbitrary pure differential modules, introducing a “relative parametrization” where the potentials should satisfy compatible “differential constraints”. We recently noticed that General Relativity is just a way to parametrize the Cauchy stress equations by means of the formal adjoint of the Ricci operator in order to obtain a “minimum parametrization” by adding sufficiently many compatible differential constraints, exactly like the Lorenz condition in electromagnetism. In order to make this difficult paper rather self-contained, these unusual purely mathematical results are illustrated by many explicit examples, two of them dealing with contact transformations, and even strengthening the comments we recently provided on the mathematical foundations of General Relativity and Gauge Theory. They also bring additional doubts on the origin and existence of gravitational waves.

A Standard-Cell-Based All-Digital PWM Modulator With High Resolution and Spread- Spectrum Capability

The use of digital pulse-width modulators (DPWMs) as controllers for dc–dc converters is becoming more and more popular, due to the lower sensitivity to process variations, programmability, and easiness to translate complex control algorithm in digital architecture. DPWMs require high resolution to avoid limit cycling. Moreover, especially in high-frequency switching power converters, the reduction of the electromagnetic interference (EMI) is of primary importance. A novel DPWM circuit is proposed in this paper. The circuit uses only standard cells, easing portability to new technological nodes. The DPWM includes a coarse delay stage, based on an enhanced counter-based architecture, which is able to modulate both the frequency and duty cycle. As a result, the proposed DPWM supports spread-spectrum modulation, with arbitrary modulation law, to reduce the EMI. The DPWM also includes a fine delay stage that employs digitally controlled NAND-based delay lines with excellent linearity and resolution. A measurement unit is used to compensate at run time, the process, voltage, and temperature variations. The circuit has been fabricated in low-cost UMC 130-nm CMOS technology and is fit in a 44-pin package. The chip can generate spread-spectrum pulse-width waveforms up to 10 MHz. Measurement of the conducted EMI in buck dc–dc converter is reported in this paper.

A digital receiver signal strength detector for multi-standard low-IF receivers

Abstract. This paper presents a receiver signal strength detector based on a discrete Fourier transform implementation. The energy detection algorithm has been designed and measured using a custom multi-standard transceiver ASIC with a low-IF receiver at 0.5, 1 and 2 MHz IF. The proposed implementation directly processes the single bit ΔΣ modulator data and features a clear channel assessment for arbitrary modulation schemes without energy consuming demodulation. Continuous monitoring of the derivative of the RSSI takes advantage of faster coefficient convergence for higher power levels and reduces computation time. A dynamic range of 65 dB has been achieved in FPGA based measurements with a linearity error of less than 1.2 dB. Furthermore, synthesis results for an on-chip implementation for an 130 nm RF CMOS technology show an overall power consumption of 1.5 mW during calculation.

Photonic generation of microwave binary digital modulation signal with format agility and parameter tunability

Abstract A method for photonic generation of arbitrary microwave binary digital modulation signal based on polarization switch is proposed and investigated. A polarization modulator is utilized to switch the direction of a linearly-polarized optical signal between two orthogonal axes. Then, a polarization-dependent modulation structure is employed to modulate an external RF signal to the two optical carriers with different polarization directions respectively. The modulation structure consists of a polarization beam splitter, two parallel placed dual-drive Mach–Zehnder modulators and an optical combiner. By adjusting the parameters of the two modulators, different optical sidebands can be obtained in two polarization directions. After optical-to-electrical conversion, a microwave amplitude shift keying (ASK), frequency shift keying (FSK) or phase shift keying (PSK) signal can be achieved. The modulation format, bit-rate and carrier frequency of the generated signal can be tuned independently and flexibly. A simulation is demonstrated to verify the proposed scheme, a 2-Gbit/s 40-GHz ASK signal, a 2-Gbit/s FSK signal with carrier frequencies of 20 and 40 GHz, and a 2-Gbit/s 20-GHz PSK signal are obtained. The scheme has good tunability.

Non-Coherent Spatial Modulation and Optimal Multi-Ring APSK Constellation Design

A non-coherent spatial modulation scheme assuming no channel state information (CSI) at the receiver is proposed in this letter. Different from the differential spatial modulation, in which the difference between the previous information block and the current information block is employed, the proposed scheme only utilizes the estimation of the previous transmission block to eliminate the restriction of CSI. Moreover, a generalized multi-ring amplitude phase shift keying (APSK) constellation with arbitrary modulation order of PSK on each circle is used in the scheme, and the optimal one is found through the design method proposed in this letter. Simulation results show that, at the same spectral efficiency, the proposed scheme with optimal constellation outperforms the scheme with traditional PSK, QAM, and existing APSK in Rayleigh fading channel.

Embedding MATLAB Optimizers in SIMSIDES for the High-Level Design of <inline-formula> <tex-math notation="LaTeX">$\Sigma \Delta$ </tex-math> </inline-formula> Modulators

This brief shows how to combine SIMSIDES, a SIMULINK-based time-domain behavioral simulator, with different optimization engines available in MATLAB for the automated high-level design of sigma-delta ( ${\Sigma \Delta }$ ) modulators. To this purpose, an updated version of SIMSIDES has been developed, which includes a user-friendly interface that links the simulator with the optimizers, and guides designers through the main steps required to set the design variables, constraints and select the most suitable algorithm to maximize the performance of an arbitrary modulator topology for a given set of specifications. Several examples and results of the optimization procedure are shown to illustrate the benefits of the presented tool for the high-level synthesis of ${\Sigma \Delta }$ modulators.