Modulation Transfer from TDMA On-Off Bursting to FM Carriers in Memoryless Nonlinear Devices, Part II-Baseband Performance

When TDMA and FM carriers are commonly amplified by a memoryless device with nonlinear amplitude and phase characteristics, modulation transfer noise induced by the on-off bursting of the TDMA signals will be present at the FM carriers. In Part II of this paper, closed form expressions of the power spectra of the modulation transfer noise are derived for many special carrier configurations of interest. Numerical examples are also provided in terms of the signal-to-modulation transfer noise ratio, SNR, in the baseband of the FM carriers. It is shown how SNR varies as a function of TDMA burst levels, burst patterns, burst lengths, FM carrier levels, carrier sizes, and device nonlinearities and operating points. With these detailed analyses and numerical examples, insight can be gained into the mechanism of modulation transfer from TDMA on-off bursting to the FM signals. Results presented in this part of the paper should be useful for transmission systems planning and evaluation, and for TDMA burst scheduling.     

Third-order dispersion compensation using a phase modulator

Compensation of third-order dispersion in a fiber-optic transmission system using a phase modulator is studied both theoretically and experimentally. A sinusoidal signal is used as modulation function, where the amplitude and phase delay are optimized. The 2-ps input pulses (160-Gb/s compatible) were transmitted through a 626-km fiber link, where the characteristic oscillating tail was measured with a 1.6-ps resolution optical sampling system. When applying the phase modulation, the oscillating tail was significantly suppressed. The pulses were also used in a 160-Gb/s transmission experiment, where the eye diagrams were measured with the sampling system. Numerical simulations and practical experiments showed excellent agreement.     

基于AD9850多功能信号源的设计与实现

设计了一个以AT89S52为核心控制器件,直接控制两片DDS芯片AD9850,通过并行控制方式实现的正弦信号发生器,并且利用差动放大芯片AD830进行正弦信号幅值调节。该系统具有频率、相位可变,幅值可调,并且能够输出稳定的相位差和振幅调制的功能。     

Radio Signals with Large Relative Bandwidth for Over-the-Horizon Radar and Spread-Spectrum Communications

It is known that radio signals must have a small relative frequency bandwidth if structures and circuits resonating with sinusoidal functions are to be used for radiation and reception. This paper develops concepts showing that a small relative frequency bandwidth is also required for the use of amplitude or frequency modulation of sinusoidal radio carriers in the usual form. However, it is easy to modify the usual methods of amplitude and frequency modulation for signals with large relative frequency bandwidth. The primary application of such methods is for over-the-horizon radar and spread-spectrum communications in the short-wave region where the desired relative frequency bandwidths are neither small (in the order of 0.01 or less) nor close to 1.     

Cramer-Rao lower bounds for a damped sinusoidal process

The Cramer-Rao lower bounds (CRLBs) for the parameter estimators of a damped sinusoidal process are derived in this paper. Succinct matrix expressions for CRLB's of frequency, damping factor, amplitude, and initial phase are given for both scalar and vector processes. The relationships between the CRLBs of the characteristic parameters are established in the general multimode case. In particular, explicit, closed-form expressions for the single mode scalar/vector-damped/undamped cases are provided     

Theoretical analysis and performance of OFDM signals in nonlinearAWGN channels

Orthogonal frequency-division multiplexing (OFDM) baseband signals may be modeled by complex Gaussian processes with Rayleigh envelope distribution and uniform phase distribution, if the number of carriers is sufficiently large. The output correlation function of instantaneous nonlinear amplifiers and the signal-to-distortion ratio can be derived and expressed in an easy way. As a consequence, the output spectrum and the bit-error rate (BER) performance of OFDM systems in nonlinear additive white Gaussian noise channels are predictable both for uncompensated amplitude modulation/amplitude modulation (AM/AM) and amplitude modulation/pulse modulation (AM/PM) distortions and for ideal predistortion. The aim of this work is to obtain the analytical expressions for the output correlation function of a nonlinear device and for the BER performance. The results in closed-form solutions are derived for AM/AM and AM/PM curves approximated by Bessel series expansion and for the ideal predistortion case     

Nonlinear dynamics of a laser diode with optical feedback systemssubject to modulation

The nonlinear dynamic behavior of a direct frequency-modulated diode laser with strong optical feedback is examined and compared to a laser diode subject to electro-optically modulated, strong optical feedback. Direct modulation is achieved by sinusoidal modulation of the diode laser injection current. Electro-optic modulation is achieved by applying a sinusoidal voltage to an intracavity phase modulating element. The output state (characterized by the output power versus time, the intensity noise spectrum and the optical frequency spectrum) for both types of modulation is dependent on the ratio of the modulation frequency to the external cavity resonant frequency, and the modulation power. A number of distinct states are observed: conventional amplitude modulation (with FM spectra); multimode, low-noise amplitude modulation; multimode, high-noise amplitude modulation; periodic limit-cycle operation; quasi-periodicity; chaos; low-frequency fluctuations; and mode-locking. There are significant differences between the direct and electro-optic frequency-modulation cases. The onset of the dynamic instability is characterized as a noisy period-one oscillation for direct modulation and a low-frequency fluctuation for intracavity electro-optic modulation. Phase portraits produced experimentally with the use of a digital phosphor oscilloscope are shown to agree well with those constructed from output power versus time data. This represents an experimental method for examining the dynamics phase portraits in real-time     

Some effects of delay and modulation-index mismatch on cochannel FM interference

The baseband distortion resulting from the cochannel interference of two FM carriers nominally carrying the same modulation is considered. Such distortion was observed to plague VHF mobile telephone service in Phoenix, Ariz. This distortion arises when the landline audio delay and modulation indices of the two transmitters are not closely equalized. Both sinusoidal and Gaussian modulation age analyzed. Curves presented indicate that baseband distortion power as large as 20 percent of baseband signal power may occur for an RF carrier amplitude ratio of 0.7 and an unequalized delay of the order of 200 µs when the minimum rms transmitter phase deviation is 2 rad. Increasing the deviation to 4 rad reduces the distortion to the 5-percent range. The desirability of large index modulation in this context is thus apparent.     

Compensation of line-broadening factor in twin-stripe semiconductor lasers and improved modulation potential

A concept for a twin-stripe semiconductor laser is presented in which the simultaneous gain and refractive index variation induced by carriers injected into one stripe can be converted into either a pure amplitude or a pure frequency variation in the lasing supermode. Applications include high-frequency chirp-free amplitude modulation, reduced line width and pure phase modulation.     

Describing functions and oscillators

In this article the "Describing Function" technique is applied to the analysis and design of oscillators. It is shown that, with some simplifications of the expressions involved in the analysis, this technique allows one not only to quantify the amplitude but also to determine the degree of distortion of the generated sinusoidal signal. The advantage of the describing function is that it allows the inclusion of the nonlinear behavior of a system while maintaining the simplicity often associated with the linear system analysis. This will be demonstrated through an example presenting the analysis and design of a sinusoidal oscillator in the frequency domain. The method as such allows formulation of closed-form expressions for the amplitude and distortion levels in much the same way classical linear techniques are used     

The generalized discontinuous PWM scheme for three-phase voltage source inverters

This paper presents analytical techniques for the determination of the expressions for the modulation signals used in the carrier-based sinusoidal and generalized discontinuous pulse-width modulation schemes for two-level, three-phase voltage source inverters. The proposed modulation schemes are applicable to inverters generating balanced or unbalanced phase voltages. Some results presented in this paper analytically generalize the several expressions for the modulation signals already reported in the literature and new ones are set forth for generating unbalanced three-phase voltages. Confirmatory experimental and simulation results are provided to illustrate the analyses.     

Spectra of delta-sigma modulated inverters: an analytical treatment

Analytic expressions for the output voltage spectrum of an asynchronous delta (or delta-sigma) modulated inverter are reported and supported by experimental data. The analysis yields three functions that give the frequency, phase, and amplitude of each component of the spectrum. These functions are in terms of the sinusoidal reference waveform and the properties of the modulator. The method provides greater accuracy and computational efficiency than the numerical methods reported to date. The spectral components form pairs of sidebands around multiples of the average switching frequency. The functions detail the relationship between the number of significant sideband components and the depth of modulation and illustrate the spread-spectrum nature of delta modulation. Extensions to nonsinusoidal reference waveforms and to hysteresis current controllers are considered     

FM and AM mode locking of the homogeneous laser--Part I: Theory

A new general analysis for mode-locked operation of a homogeneously broadened laser with either internal phase (FM) or amplitude (AM) modulation is presented in this paper. In this analysis, a complex Gaussian pulse is followed through one pass around the laser cavity. Approximations are made to the line shape and modulation characteristics to keep the pulse Gaussian. After one round trip, a self-consistent solution is required. This yields simple analytic expressions for the pulse length, frequency chirp, and bandwidth of the mode-locked pulses. The analysis is further extended to include effects of detuning of the modulator, in which case analytical expressions are obtained for the phase shift of the pulse within the modulation cycle, the shift of the pulse spectrum off line center, the change in pulse length, and the change in power output. Numerical results for a typical Nd:YAG laser are given. In the case of the FM mode-locked laser it is found that there is a frequency chirp on the pulse and that this causes pulse compression and stretching when the modulator is detuned. Etalon effects and dispersion effects are also considered.     

Passive demodulation of optical interferometric sensors

Two techniques for passive (no-feedback) demodulation of signals from a remote two-beam interferometric sensor are discussed. Termed "synthetic heterodyne" and "quadrature recombination," both methods are based on forced sinusoidal modulation of phase within the interferometer. If the phase modulation is generated by linearly proportional frequency modulation of the laser light source, then the interferometer, deployed by means of optical fibers, can be a completely passive remote sensor, and an array of identical sensors can be operated from one light source. The former technique, proposed by Cole, Danver, and Bucaro permits standard FM demodulation. The latter technique, proposed by Cable and Green, employs arithmetic operations that are appropriate to digital implementation. Constraints on application of the technique, especially frequency distribution and amplitude of phase noise (out-of-band) versus signal amplitude (in-band), are analyzed and an implementation is proposed that is consistent with Contemporary analog-to-digital conversion technology.     

Performance analysis of dual-hop fixed-gain AF relaying systems with OSTBC over Nakagami-m fading channels

In this paper, we present outage probability and symbol error rate (SER) performance analyses of a dual-hop transmission using fixed-gain amplify-and-forward relaying in flat Nakagami-m fading channels. The system under consideration is equipped with multiple antennas at source and destination adopting orthogonal space-time block coding to provide transmit diversity and maximum ratio combining to provide receive diversity, respectively. For integer and half-integer m values, closed forms of exact outage probability and moment generating function (MGF) expressions are derived through cumulative distribution function (CDF) of the overall system signal-to-noise ratio. Closed-form exact SER expressions based on the overall CDF are obtained for binary phase shift keying, binary frequency shift keying and M-ary pulse amplitude modulation. Exact SER expressions based on the MGF method are also obtained for binary differential phase shift keying, M-ary phase shift keying and M-ary quadrature amplitude modulation. Moreover, the asymptotic diversity order analysis is performed through derivations of asymptotic outage probability and SER. Theoretical analyses are validated by Monte Carlo simulations showing perfect match between each other.     

Variance of least squares estimators for a damped sinusoidalprocess

The variance of least squares estimators for the parameter estimation of a damped sinusoidal process is analyzed, based on first-order perturbation. Analytical expressions for the variances of the frequency, damping factor, amplitude, and phase estimators are derived. Explicit expressions are given for both damped and undamped single-mode cases. The effect of mode separation on the accuracy is investigated through the two-mode case. The dependence of the variances on number of data points, model order, signal-to-noise ratio, and mode separation is investigated, both analytically and numerically, for practical applications. Extensive Monte Carlo simulation results are given to verify, enhance, and illustrate the analytical expressions     

A Comprehensive Study of a Hybrid Modulation Technique for the Neutral-Point-Clamped Converter

This paper presents a hybrid modulation technique for the three-level neutral-point-clamped converter. A modulation strategy, based on two modulation signals per phase, was presented previously. This strategy completely removes the low-frequency voltage oscillations that appear at the neutral point (NP) in some operation conditions. However, it also has a major drawback: it significantly increases the switching losses of the converter. The proposal in this paper combines such a modulation strategy with sinusoidal pulsewidth modulation (SPWM). The main characteristic of this hybrid modulation is the reduction in switching losses at the cost of some low-frequency voltage oscillations at the NP. The amplitude of these oscillations can be controlled by varying the combination of the two strategies. The performance of the hybrid modulation is analyzed and compared with the original strategies. Power losses and oscillation amplitudes on the dc-link capacitors are evaluated. Experimental results show how the hybrid modulation performs by balancing the dc-link capacitors.      

Signal Design and Detection in Presence of Nonlinear Phase Noise

In optical fiber transmission systems using inline amplifiers, the interaction of a signal and amplifier noise through the Kerr effect leads to nonlinear phase noise that can impair the detection of phase-modulated signals. We present analytical expressions for the maximum-likelihood (ML) decision boundaries and symbol-error rate (SER) for phase-shift keying and differential phase-shift keying systems with coherent and differentially coherent detection, respectively. The ML decision boundaries are in the form thetas(r) = c₂r² + c₁r + c₀, where thetas and r are the phase and the amplitude of the received signal, respectively. Using the expressions for the SER, we show that the impact of phase error from carrier synchronization is small, particularly for transoceanic links. For modulation formats such as 16-quadrature amplitude modulation, we propose various transmitter and receiver phase rotation strategies such that the ML detection is well approximated by using straight-line decision boundaries. The problem of signal constellation design for optimal SER performance is also studied for a system with four signal points.     

Power Spectra of Sinusoidal Amplitude-Modulated Binary Signals

Power spectra for binary phase-shift keyed (PSK) and frequency-shift keyed (FSK) signals with combined sinusoidal amplitude modulation by the bit rate clock are presented. Such signal formats have application in "burst" communication systems wherein reliable bit synchronization is provided with relative receiver simplicity. Effects of the clock amplitude modulation index and phase are considered, and corresponding power spectra are illustrated. Further, effects of the clock parameters on the rate of spectral rolloff are given and compared with those of conventional PSK and FSK spectra.