Output signal-to-noise ratios of FM correlation systems

An analysis is presented on the output signal-to-noise ratios for the FM correlation systems having an FM detector in each input channel of a conventional correlator. The input consists of a frequency-modulated signal combined additively with stationary narrow-band Gaussian random noise. A general expression is derived for the output signal-to-noise ratio. A detailed calculation is made for the output signal-to-noise ratios when each input signal is a carrier frequency-modulated by a Gaussian random process and the integrating filter is of RC low pass. The dependence of the output signal-to-noise ratios on several parameters is discussed.     

A Universal Microwave Photonic Receiving Channel

Main characteristics of a model of the microwave photonic receiving channel with optical heterodyning have been numerically simulated and experimentally investigated. The transducer is based on a twoarm (signal and reference) balanced circuit with a continuous wave laser, amplitude modulators, narrow-band optical filters, and a photodetector. The possibility of implementation of the receiving channel with a signal-to-noise ratio of up to 60–70 dB, a carrier frequency of up to 40 GHz and more, and a detection bandwidth of up to 1 GHz is demonstrated. It is shown that semiconductor lasers without outer stabilizing cavities can be used in an optical pumping source by means of compensation of the laser frequency noise. It has been found, that if the modulator working point corresponds to the optical carrier frequency suppression mode, the noise characteristics of the detector can be maintained without application of narrow-band optical filters.     

Amplitude modulation with a noise carrier

Consider an ideal amplitude modulation system in which the usual sinusoidal carrier is replaced by a narrow band of random noise, of midband frequency f0and half-bandwidth B; the spectral density and the total power of the output noise of this system are determined. An optical system of this type would use an incoherent spectral line as a carrier, rather than the coherent output of an optical maser. Considerable improvement is obtained by shifting a baseband modulating signal to a frequency band much lower in frequency than f0but much higher than B, before modulating the noise carrier. In an optical system this translated modulating signal might lie in the microwave region. Even so W, the bandwidth of the modulation, must be very small compared to B to attain a high output signal-to-noise ratio.     

A New Carrier Recovery Technique for Vestigial-Sideband (VSB) Data Systems

In this concise paper we have developed a new carrier recovery system for vestigial sideband amplitude modulation (VSB-AM) data sets. Neither dc restoration nor extra bandwidth is required for the proposed system. A pilot tone is transmitted at the carrier frequency and the phase jitter is derived from the quadrature chnnnel. "Artificial" phase jitter which is introduced by the data signal can be eliminated by properly shaping the transmitted signal. We have also shown that even in the presence of channel distortion and white Gaussian noise, the proposed system can faithfully track up to 60-Hz phase jitter.     

Analog communication over randomly-time-varying channels

The problem of analog communication over a randomly-time-varying channel is considered. An analog source generates a message which is assumed to be a sample function from a Gaussian random process. The message is passed through a linear realizable system before modulation. (This corresponds to the pre-emphasis network in FM.) The output of this system is the modulating signal for a no-memory modulator which, in general, will be nonlinear. The modulated signal is transmitted over a time-varying channel We restrict ourselves to Gaussian multiplicative channels. At the channel output, noise is added. The specific problem of interest is to find the optimum estimate of the message. The principle results are: begin{enumeratge} item An integral equation whose solution is the optimum estimate. item A feedback demodulator whose output is the optimum estimate over a certain range of signal-to-noise ratios. item A proof that the optimum demodulator corresponds to a joint channel and message estimator. This result is the continuous analog of the estimator-correlator result in digital systems. Some related problems and possible extensions are discussed briefly. end{enumerate}     

Cramer-Rao bounds in the parametric estimation of fadingradiotransmission channels

The context of this paper is parameter estimation for linearly modulated digital data signals observed on a frequency-flat time-selective fading channel affected by additive white Gaussian noise. The aim is the derivation of Cramer-Rao lower bounds for the joint estimation of all those channel parameters that impact signal detection, namely, carrier phase, carrier frequency offset (Doppler shift), frequency rate of change (Doppler rate), signal amplitude, fading power, and Gaussian noise power. Time-selective frequency-flat fading is modeled as a low-pass autoregressive multiplicative distortion process. In particular, the important case of “slow” fading, with the multiplicative process remaining constant over the whole data burst, is specifically discussed. Asymptotic expressions of the bounds, valid for a large observed sample or for high signal-to-noise ratio (SNR), are also derived in closed form. A few charts with numerical results are finally reported to highlight the dependence of the bounds on channel status (SNR, fading bandwidth, etc.)     

On the channel capacity for constant envelope signals witheffective bandwidth constraint

The problem of the optimization of the information rate with an assigned cost function is addressed. In the case of a constant envelope channel with a prescribed effective bandwidth as a cost function, an expression of the channel capacity is derived in the presence of Gaussian noise for large values of signal-to-noise ratio. The analysis of the optimum source statistics has also shown that the source signal is Gaussian, and therefore its autocorrelation function and power spectral density have been determined in terms of the required channel capacity     

GMSK with differential phase detection in the satellite mobilechannel

A formula is derived for the error probability of partial-response continuous-phase modulation (which contains Gaussian minimum shift keying (GMSK) as a special case) with N-b (N=1, 2) differential phase detection (DPD) for the satellite mobile channel, which contains as special cases the Gaussian and Rayleigh channels. In the satellite mobile channel, the input signal is the sum of a direct component, a diffuse component, and white Gaussian noise. The receiver is either with or without decision feedback, and the decision region is optimized for 2-b DPD to minimize the error probability. The error probability for GMSK is computed as a function of signal-to-noise ratio and other system or channel parameters (Doppler frequency, Gaussian filter bandwidth, ratio of powers in the direct and diffuse signal components, etc.). It is shown that decision feedback is more effective for GMSK with narrow bandwidth. The 2-b DPD is superior to the 1-b DPD for low Doppler frequencies and signal-to-noise ratios. For practical vehicle velocities and bit rates, a 2-b DPD with decision feedback outperforms all other analyzed schemes when the signal-to-noise ratio is low     

Approximate band-pass limiter envelope distributions

An approximate distribution is computed for the envelope of sine wave plus noise after passage through a wide-band filter, limiter, and narrow-band filter. It is shown that as the input bandwidth to the limiter increases, the output envelope distribution converges to the usual sine wave in noise envelope distribution, without limiting, but with a definite1.04db loss. First-order correction terms are supplied which make it possible to compute first-order statistics for the output envelope when the output signal-to-noise ratio is on the order of one.     

高斯白噪声经过线性系统后等效带宽特性研究

以随机信号经过线性系统理论为基础,研究了加性高斯白噪声经过滤波器后的带宽特性、等效带宽特性以及两者的关系,推导了以低通滤波器为例的线性系统的带宽和等效带宽公式。分析结果表明,等效带宽是说明线性系统滤波能力的一个重要参数,简单的使用带宽参数代替噪声等效带宽参数将使线性系统输出噪声功率的计算值增加,从而导致系统输出信噪比偏低,影响系统抗噪或滤波性能的评价。     

A double-sampling pseudo-two-path bandpass ΔΣ modulator

A double-sampling pseudo-two-path bandpass ΔΣ modulator is proposed. This modulator has an output rate equal to twice the clock rate, uses n/2 operational amplifiers (op-amps) for an nth-older noise transfer function, and has reduced clock feedthrough in the signal path band. The required clocks can be simpler to implement than the conventional pseudo-two-path techniques. The measured signal-to-noise ratio and dynamic range of the fourth-order double-sampling pseudo-two-path bandpass ΔΣ modulator in a 30-kHz bandwidth at a center frequency of 2.5 MHz (at a clock frequency of 5 MHz) are 62 and 68 dB, respectively     

Phase-noise effects on turbo trellis-coded over M-ary coherent channels

The effect of the phase noise on the performance of bandwidth-efficient coded modulation is studied. To this end, the average mutual information (AMI) for specific constellations such as 8-phase-shift keying and 16-quadrature amplitude modulation is calculated in the presence of carrier phase error caused by imperfect carrier tracking over an additive white Gaussian noise channel. The AMI not only quantifies the effect of the phase noise from an information-theoretic viewpoint, but also serves as an estimate for a permissible amount of the phase noise for a given signal-to-noise ratio. The bit-error rate (BER) performance of a near-optimal turbo trellis-coded modulation scheme is then investigated over such a channel. For this purpose, an optimal branch metric which best fits the channel characteristics is derived. Furthermore, simple branch metrics (referred to as suboptimal, simplified, and Gaussian metrics) are derived, which may offer the tradeoff between BER performance and computational complexity. Numerical analysis shows that a near-optimal coded-modulation scheme renders a transmission system more robust against phase noise than is the case with a conventional trellis-coded modulation scheme.     

Performance Optimization of High Order QAM in Presence of Phase Noise and AWGN: Application to a Decision Directed Frequency Synchronization System

The paper presents an analysis of the impact of Local Oscillators (LO) phase noise on the performance of digital transmission systems. Using an efficient phase noise model, we study degradations induced by phase noise and Additive White Gaussian Noise (AWGN) on a carrier recovery system combined to high order Quadrature Amplitude Modulations (QAM). Simulation results show that an optimum trade-off between AWGN and phase noise robustness for the loop bandwidth can be determined. In order to compare simulated and analytical performance, a new general expression of the bit error probability is developped for square QAM in the presence of phase noise over Gaussian channel. Furthermore, novel decision areas related to Quadrature Amplitude Modulations are determined in order to improve the performance of the carrier recovery algorithm in the presence of phase noise and frequency offset.     

The mean value of derivative of phase modulus of the harmonic signal and Gaussian noise sum

The expression for mean value of derivative of phase modulus of the signal and narrow-band Gaussian noise sum, when signal’s frequency does not coincide with center frequency of noise, is obtained. The derivative of phase is a quotient of random functions and sum envelope.     

Some criteria for frequency domain design of signals imbedded in Gaussian noise

The design of time-limited binary signals imbedded in colored Gaussian noise resulting from passing white noise through a channel of known transfer function is investigated. It is shown that, for a class of channels whose magnitude characteristic is expressible as the ratio of polynomials with the numerator divisible by and of lower or the same degree as the denominator, the output noise kernel (correlation function) and its inverse will have Fourier transforms which are reciprocals of each other. The above assumption results in an expression for probability of error which is independent of the received waveform and depends solely on the transmitter signal-to-noise ratio. The additional freedom of design afforded by the above enables one to impose further restrictions in the form of energy concentration in the frequency domain on the received signal without deterioration of system performance. Some such bandwidth constraints and their associated optimum signal designs are considered in this paper.     

On the use of a suppression filter for CDMA overlay

This paper is concerned with a direct-sequence code-division multiple-access (DS-CDMA) system operating over a Rayleigh fading channel and sharing a common spectrum with a narrow-band waveform. A suppression filter at the receiver is employed to reduce the narrow-band interference. We evaluate the average up-link bit error rate (BER) performance and investigate how the performance is influenced by various parameters, such as the number of taps of the suppression filter, the number of multiple-access users, the ratio of narrow-band interference bandwidth to the spread-spectrum bandwidth, the interference power to signal power ratio, the ratio of the offset of the interference carrier frequency from the spread-spectrum carrier frequency to the half spread-spectrum signal bandwidth, and so on     

Analysis of stability condition for LDPC codes and optimizing degree sequences over mixed channel

Under the circumstance that white Gaussian noise and random erasures exist all at once,the stability condition for LDPC codes over mixed channel was proposed.And it was proved that a good degree sequence of LDPC codes was not optimized over mixed channel.It can also be proved by simulation.The random particle swarm optimization (RPSO) and simulated annealing (SA) algorithm were combined to find some capacity-approaching degree sequences over mixed channel with different erasure probabilities.The threshold of signal-to-noise ratio improves 1.615 9 dB than that of the classical degree sequences calculated by Gaussian approximation over mixed channel.These degree sequences are optimal for optical recording and frequency-hopping communication with narrow-band interference.     

Enhancement of optical receiver sensitivities by amplification of the carrier

The amplification before detection of the carrier of a modulated optical signal by a narrow-band quantum amplifier enhances the signal-to-noise ratio, particularly when the signal wave-front is distorted. A further improvement is obtained by using a combination of wide-band and narrow-band quantum amplifiers. The practical application of these schemes requires a degenerate regenerative ring-type amplifier capable of amplifying arbitrary transverse field configurations. Experiments show that such an amplifier with a gain of 24 dB and a bandwidth of 1 MHz is feasible. The incident beam axis can be displaced by as much as ten times the beam-waist radius without losing more than 4 dB in gain. Frequency modulation may be converted into amplitude modulation by the phase shift introduced in the carrier.     

Coherent extraction of signals from turbulent noise

This paper reports the results of some theoretical and experimental studies of the extraction of signals from convecting and decaying fluid dynamic turbulent noise employing an analog correlation receiver. In addition, it presents an extension of the theory of correlator analysis for finite observation times to the case of a linear time-varying delay. Detailed study of the mean and variance of the output signal from a correlation receiver permits a prediction of the gain in signal-to-noise ratio in the receiver and its dependence upon various fluid dynamic fluctuation, signal, and correlator parameters. The gain in signal-to-noise ratio for periodic and Gaussian random signals in extraction from turbulent noise is found to depend upon 1) a ratio of correlation lengths involving several statistical properties of the turbulence obtained from a model of the space-time correlations, 2) a ratio of a characteristic signal frequency to a characteristic frequency of the turbulence and 3) a time bandwidth product associated with the effective finite averaging time of the correlator and a characteristic frequency of the convolution of the signal and noise spectra. Experimental studies in a subsonic wind tunnel employing acoustic signals are in good agreement with theoretical predictions of the gain in signal-to-noise ratio. Some receiver design considerations emerge from the analysis. Of special interest are the influence of linear scanning and ranging and the finite lifetime of the turbulence on the required averaging process.     

On the effects of a spacecraft subcarrier unbalanced modulator

This paper presents mathematical models with associated analysis of the deleterious effects which a spacecraft's subcarrier unbalanced modulator has on the performance of a phase-modulated residual carrier communications link. The undesired spectral components produced by the phase and amplitude imbalances in the subcarrier modulator can cause (1) potential interference to the carrier tracking and (2) degradation in the telemetry bit signal-to-noise ratio (SNR). A suitable model for the unbalanced modulator is developed and the threshold levels of undesired components that fall into the carrier tracking loop are determined. The distribution of the carrier phase error caused by the additive White Gaussian noise (AWGN) and undesired component at the residual RF carrier is derived for the limiting cases. Further, this paper analyses the telemetry bit signal-to-noise ratio degradations due to undesirable spectral components as well as the carrier tracking phase error induced by phase and amplitude imbalances. Numerical results which indicate the sensitivity of the carrier tracking loop and the telemetry symbol-error rate (SER) to various parameters of the models are also provided as a tool in the design of the subcarrier balanced modulator.