Error probabilities in binary angle modulation

Jain, P. C.

doi:10.1109/tit.1974.1055162

Cited by 14 publications

(11 citation statements)

References 12 publications

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“…The error probability expression of (26) is almost the same as that in [21,32] but with a different parameter of (27). The error probability of (26) is also similar to the cases when additive phase noise is independent to Gaussian noise [2,3,23,40,41]. The frequency depending SNR is originated from the dependence between the additional phase noise and the Gaussian noise [19,21,32,37].…”

Section: Exact Error Probabilitymentioning

confidence: 69%

“…Other than the projection of additive Gaussian noise to the phase, phase noises from other sources can be considered as multiplicative noise that adds directly to the phase of the received signal. When the local oscillator is not locked perfectly into the signal, the noisy reference gives additive phase noise [1,2]. Laser phase noise degrades coherent optical communication systems [3][4][5].…”

Section: Introductionmentioning

confidence: 99%

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Performance of DPSK Signals With Quadratic Phase Noise

2005

IEEE Trans. Commun.

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Nonlinear phase noise induced by the interaction of fiber Kerr effect and amplifier noises is a quadratic function of the electric field. When the dependence between the additive Gaussian noise and the quadratic phase noise is taking into account, the error probability for differential phase-shift keying (DPSK) signals is derived analytically. Depending on the number of fiber spans, the signal-to-noise ratio (SNR) penalty is increased by up to 0.23 dB due to the dependence between the Gaussian noise and the quadratic phase noise. 1 this paper, the additive phase noise is quadratic function of the electric field. When the electric field is contaminated with additive Gaussian noise, although the quadratic phase noise is uncorrelated with the linear phase noise, both non-Gaussian distributed, the phase noise weakly depends on the additive Gaussian noise.Differential phase-shift keying (DPSK) signals [6][7][8][9][10][11][12][13][14][15][16] have received renewed attention recently for long-haul or spectrally efficiency lightwave transmission systems. When optical amplifiers are used periodically to compensate the fiber loss, the interaction of optical amplifier noise and fiber Kerr effect induced nonlinear phase noise, often called Gordon-Mollenauer effect [17], or more precisely, nonlinear phase noise induced by self-phase modulation. Added directly into the signal phase, Gordon-Mollenauer effect is a quadratic function of the electric field and degrades DPSK signal [11,14,[17][18][19][20][21][22][23].Previous studies found the variance or the corresponding Q-factor of the quadratic phase noise [11,17,[24][25][26][27] or the spectral broadening of the signal [14,18,28]. Recently, quadratic phase noise is found to be non-Gaussian distributed both experimentally [20] and theoretically [29,30]. As non-Gaussian random variable, neither the variance nor Q-factor is sufficient to completely characterize the phase noise. The probability density of quadratic phase noise is found in [30] and used in [23] to evaluate the error probability of DPSK signal by assuming that quadratic phase noise and Gaussian noise are independent of each other. However, as shown in the simulation of [22,23], the dependence between Gaussian noise with quadratic phase noise increases the error probability.Using the distributed assumption of infinite number of fiber spans, the joint statistics of nonlinear phase noise and Gaussian noise is derived analytically by [19,21,31]. The characteristic function of nonlinear phase noise becomes a very simple expression with the distributed assumption [29]. The error probability of DPSK signal has been derived with [22] and without [21,32] the assumption that nonlinear phase noise is independent of the Gaussian noise. Based on the distributed assumption, it is found that the dependence between linear and nonlinear phase noise increases both the error probability and SNR penalty [21,32].The distributed assumption is very accurate when the number of fiber spans is larger than 32 [21,29]. For a typical fiber span...

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Section: Exact Error Probabilitymentioning

confidence: 69%

Section: Introductionmentioning

confidence: 99%

Performance of DPSK Signals With Quadratic Phase Noise

2005

IEEE Trans. Commun.

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“…When independent phase noises from different sources are summed together, the coefficients of the Fourier series of the overall probability density function are the product of the corresponding Fourier coefficients of each individual component. If the XPM-induced nonlinear phase noise is Gaussian distributed, the error probability of the DPSK signal is (18) The formulas of (17) and (18) are similar to that with noisy reference [36], laser phase noise [26], phase error [37], or laser phase noise together with phase error [38]. The terms within the summation of (18) are the product of that due to SPM-induced nonlinear phase noise [8] and laser phase noise [26].…”

Section: Error Probabilitymentioning

confidence: 99%

“…Fig. 2 also plots the error probability of (1/2) without nonlinear phase noise [7], [8], [36], [37].…”

Section: Error Probabilitymentioning

confidence: 99%

Error Probability of DPSK Signals With Cross-Phase Modulation Induced Nonlinear Phase Noise

2004

IEEE J. Select. Topics Quantum Electron.

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The error probability is derived analytically for differential phase-shift keying (DPSK) signals contaminated by both self-and cross-phase modulation (SPM and XPM)-induced nonlinear phase noise. XPM-induced nonlinear phase noise is modeled as Gaussian distributed phase noise. When fiber dispersion is compensated perfectly in each fiber span, XPM-induced nonlinear phase is summed coherently span after span and is the dominant nonlinear phase noise for typical wavelength-division-multiplexed (WDM) DPSK systems. For systems without or with XPM-suppressed dispersion compensation, SPM-induced nonlinear phase noise is usually the dominant nonlinear phase noise. With longer walkoff length, for the same mean nonlinear phase shift, 10-Gb/s systems are more sensitive to XPM-induced nonlinear phase noise than 40-Gb/s systems.

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“…It follows from(2),(8),(9) and(10) and the independence of c(t) and n(t) that where and is a random variable which depends on the symbol transmitted at time totd, say ad.It follows from that if to + (kl ) T S td < to + kT and T is small (actually, we need the result for T + 0 only) Thus for k = 0, ad is the same as a, and has only one value a(m)=2m-l-M(77) ad = a(m) if a, = a(m) For k > 0 ad has M equiprobable values, independent of a,, namely ad = 21l-M = a(l) , I = 1,2,. . .…”

mentioning

confidence: 99%

Error probability of m‐ary fsk with a limiter‐discriminator detector in satellite mobile channels

Korn

1991

Int. J. Satell. Commun.

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We derive formulae for the error probability of M-ary frequency shift keying with a limiter-discriminator detector in a satellite mobile channel, which includes as special cases the land mobile (Rayleigh) channel and the Gaussian channel. The received signal in this channel is composed of a specular signal, a diffuse signal and white Gaussian noise; hence the composite signal is fading with a Rician envelope. The error probability depends on the signal-to-noise ratio, the power ratio of the specular and diffuse components, the frequency deviation, the Doppler frequency, the maximum Doppler frequency, the time delay between diffuse and specular components, the autocorrelation of the diffuse component and the transfer function of the receive filter. Numerical results are presented as functions of the various parameters. Effects of the receive filter on the signal dependent components are neglected.KEY WORDS Frequency shift keying Limiter-discriminator detector Satellite mobile channel Rayleigh channel

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Error probabilities in binary angle modulation

Cited by 14 publications

References 12 publications

Performance of DPSK Signals With Quadratic Phase Noise

Performance of DPSK Signals With Quadratic Phase Noise

Error Probability of DPSK Signals With Cross-Phase Modulation Induced Nonlinear Phase Noise

Error probability of m‐ary fsk with a limiter‐discriminator detector in satellite mobile channels

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