The phase of a vector perturbed by Gaussian noise anddifferentially coherent receivers

Some results are presented regarding the asymptotic distribution of the phase of a vector perturbed by Gaussian noise. It is shown that for large signal-to-noise ratio, the asymptotic distribution of the phase is of the Tikhonov type. This framework is then used for the synthesis of differentially coherent receiver structures, one for M -ary phase-shift keying (MPSK) and the other for minimum-shift keying (MSK). The first structure bridges the performance gap between coherent and differentially coherent demodulation of MPSK. The MSK receiver uses matched filtering with differential demodulation     

Distribution of phase angle between two Rayleigh vectors perturbed by Gaussian noise

Two general, closed form expressions for the distribution of the phase angle between two vectors in fast Rayleigh fading and Gaussian noise are derived. These general expressions include the effect of fading as well as noise correlation and, in special cases, reduce to several previously published formulas. The convenience when applying these new formulas to evaluate the error performance of DPSK and FSK systems is highlighted.<>     

PLL performance of DS-CDMA systems in the presence of phase noise,multiuser interference, and additive Gaussian noise

The performance of decision-directed phase-locked loops (PLL) for use in direct-sequence code-division multiple-access (DS-CDMA) systems is investigated in the presence of phase noise, multiuser interference, and additive white Gaussian noise (AWGN). A unified and accurate analysis of the effect of these sources of noise on the PLL is carried out based on a nonlinear model (the Fokker-Planck method) since a linear analysis yields a large deviation between analytical results and actual performance at low signal-to-noise ratios (SNR). After describing the implementation of the PLL, the steady-state probability density function (PDF) of the phase estimator error in a first-order loop is derived. It is shown that a tradeoff exists between the effect due to the phase noise, the magnitude of the multiuser interference, and the AWGN as a function of loop bandwidth. The optimal loop bandwidth minimizing the impact of these sources of noise on the PLL and the requirements on the frequency uncertainty of the carrier source for a required accuracy of the phase estimator are detailed. Numerical results of the variance of the phase estimator error are discussed for Gold codes     

Performance of CDMA with differential detection in the presence of phase noise and multiuser interference

Phase noise can be a major source of performance degradation in low-cost, low-bit-rate digital systems operating in the millimeter wavelength band. The use of code-division multiple access (CDMA) for several new applications is envisaged, and the study of the effects of phase noise shows that even CDMA systems exhibit a performance degradation comparable to that of standard modulation formats. The use of CDMA with a differential modulation at the chip level improves the system performance with a simpler demodulator at the expense of the enhancement of multiuser interference. In this paper we propose a new approach to CDMA modulation, and a possible solution is suggested to obtain a tradeoff between the performance degradation due to the phase noise and to the multiuser interference.     

Error probability due to Gaussian noise and near-end crosstalk

The error probability is calculated of a baseband digital system operating on multipair cable subject to Gaussian noise and near-end crosstalk from a number of interfering plesiochronous digital systems carrying a.m.i.-coded random binary signals.     

Envelope probability density function of the sum of signal, noise and interference

A new closed-form expression of the envelope probability density function for the sum of signal, Gaussian noise and c.w. interference is found.     

Error probability of 2DPSK with phase noise

A simple tight upper bound on the BEP of 2DPSK over the AWGN channel with phase noise in the received signal is obtained. The phase is modeled as a Gaussian random process which is slowly varying compared to the bit rate so that a piecewise-constant approximation can be made. The bound is verified by computer simulations, and it provides good estimates of the error probability. It shows that for high SNR the error probability decreases as the reciprocal of the square-root of the SNR. The results are applicable in particular to heterodyne optical communications     

Phase derivative distribution of signal and Gaussian noise sum

Characteristic function and integral function of the phase derivative distribution of harmonic signal and narrowband Gaussian noise sum are obtained for the case when the signal’s central frequency coincides with the central frequency of noise spectrum. It is shown that the power series for the distribution density of the phase derivative is determined by odd moments of the envelope.     

Intermodulation interference probability distribution in mobile radiocommunication systems

The problem of mobile radio system outage in the presence of two signal third order intermodulation interferences is presented. The probability that the desired signal level exceeds the interference level by a predetermined value is defined, computed and graphically illustrated. For all signals the superposition of lognormal and Rayleigh distributions is assumed.<>     

Distribution of the phase angle between two vectors perturbed byGaussian noise II

The Case I, Case II, and Case III distributions for the phase angle between two vectors perturbed by Gaussian noise are restated in terms of integrals with integrands containing only exponentials. Added to these are a Case IV distribution in which one of the vectors is noise free; and Case V, Case VI, and Case VII distributions for the instantaneous radian frequency that results when the time between the two vectors goes to zero. In addition, existing and new forms for the probability density functions corresponding to each of the distributions are given. The results are applied to digital FM with a limiter/discriminator receiver to easily obtain the bit error probability without coding and the corresponding probability density function needed in a Chernoff bound approach to study the bit error probability with coding     

Bit error probability of phase-coherent communication systems in the presence of noise and interference

The signal, interference and noise are applied at the input to the phase-coherent communication receiver and an expression for the bit error probability is derived. Error curves are calculated for the case when the reference carrier is not ideal. The reference carrier is extracted by the first order loop.<>     

Performance ofM-ary PSK systems in Gaussian noise and intersymbol interference

A useful method is presented for the evaluation of the error probability ofM-ary phase-shift-keyed systems with Gaussian noise and intersymbol interference. By regarding a portion of the intersymbol interference as an equivalent Gaussian noise, this method suggests first calculating the probability of error caused by the combined effects of the Gaussian noise and the equivalent noise. Necessary correction terms are then added to the calculation to take into account the fact that the intersymbol interference is actually non-Gaussian. It is shown that with this method any desired accuracy can be theoretically achieved in the evaluation of the probability of error. This method has been programmed for numerical computations. Some examples are also given for illustrative purposes.     

Evolution of the probability density functions of Gaussian ASE noise in zero-memory nonlinear fiber

The propagation of Gaussian amplified emission noise in nonlinear optical fiber with negligible dispersion is considered. It is well known that fiber Kerr nonlinearity causes a nonlinear phase noise, also known as the Gordon–Mollenauer effect. In this paper, we examine the effect of the Kerr nonlinearity on the probability density functions of the Gaussian noise quadratures. This can lead to large deviations from the Gaussian statistics of the amplified spontaneous emission noise. Analytical statistics of the noise quadratures at the output of nonlinear fiber with negligible dispersion are derived and compared with numerical simulations. The statistics of the noise squared envelope are also presented and, based on these results, the influence of Kerr nonlinearity on the direct detection and coherent detection amplitude modulated links is discussed.     

Design of binary bandlimited signals imbedded in colored Gaussian noise and intersymbol interference

This paper considers the design of binary bandlimited receiver signals as well as the design of the receiver filter for signal immunity to intersymbol interference and additive colored Gaussian noise. The design problem is treated in the frequency domain. The maximum probability of error is minimized by choosing signals with zero intersymbol interference. When transmission is below the Nyquist rate, bandlimited signals with gradual cutoff are designed. Other waveforms, with intersymbol interference but possessing no sequences of unbounded amplitude, are also investigated. Examples are given demonstrating the application of the theory.     

On the error probability of decision-feedback differential detection

We give a tight approximation for the bit-error rate (BER) of decision-feedback differential detection (DF-DD). The influence of error propagation is modeled by a Markov chain. A simple state reduction method is proposed to limit computational complexity. Our results show that error propagation strongly depends on the chosen feedback filter. In particular, the popular assumption that error propagation increases BER by a factor of two is not always justified.     

Bit-error probability for optimum combining of binary signals in the presence of interference and noise

We derive an exact bit-error probability (BEP) expression for coherent detection of binary signals with optimum combining in wireless systems in the presence of multiple cochannel interferers and thermal noise. A flat Rayleigh fading environment with space diversity, uncorrelated equal-power interferers, and additive white Gaussian noise is considered. The approach is to use the chain rule of conditional expectation together with the joint probability density function (pdf) of the eigenvalues of the interference correlation matrix. This joint pdf is related to the Vandermonde determinant. Let N/sub A/ denote the number of antennas and N/sub I/ the number of interferers. We consider both the cases of an overloaded system, in which N/sub I//spl ges/N/sub A/, and an underloaded system, in which N/sub I/相似文献   

Calculation of bit-error probability for a lightwave system withoptical amplifiers and post-detection Gaussian noise

The author's previously published results (ibid., vol.8, p.1816-23, 1990) which dealt with the bit-error probability of a lightwave communication system whose noise contribution was exclusively attributed to spontaneous emission noise of optical amplifiers are extended. The earlier theory was based on an NRZ (nonreturn-to-zero) modulation format with zero signal power assigned to logical zeros. The extension is based on the same mathematical technique but includes Gaussian noise originating after the signal has been converted to an electrical current. This noise could be thermal noise, shot noise, or a combination of both. It is no longer assumed that the pulse representing a logical one fills its time slot completely. Now, the optical pulses can be much shorter than the bit period (solitons), the power level of logical zeros need not vanish, and the thermal noise of the postdetection electronic circuit is taken into account     

On probability distributions for filtered white noise

When white noise generated by an underlying Poisson process is filtered by any member of a large class of stable (not necessarily linear nor stationary) filters, the first-order probability distributions of the filter output is infinitely divisible. The Kolmogorov canonical form for the characteristic function is displayed and related to the parameters of the white noise and of the filter. In certain linear stationary cases, cubclasses of the infinitely divisible distributions are identified. An invariance property of the bilateral exponential distribution is demonstrated.