Distribution of the Phase Angle Between Two Vectors Perturbed by Gaussian Noise

Pawula, R.; Rice, Stephen A.; Roberts, J. H.

doi:10.1109/tcom.1982.1095662

Cited by 407 publications

(118 citation statements)

References 13 publications

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“…The difference in required OSNR when moving from 4-level to 8-level modulation, is at around 6.5 dB in both the cases of single and dual polarization systems, which is close to the theoretical value of 6.3 dB for DQPSK and D8PSK perturbed by Gaussian white noise [8].…”

Section: Simulation Results and Discussionsupporting

confidence: 79%

Analysis of non-linear impairments in 40 Gbaud PM DQPSK and D8PSK transmission

Chughtai

Forzati

Mårtensson

et al. 2010

2010 12th International Conference on Transparent Optical Networks

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Section: Simulation Results and Discussionsupporting

confidence: 79%

Analysis of non-linear impairments in 40 Gbaud PM DQPSK and D8PSK transmission

Chughtai

Forzati

Mårtensson

et al. 2010

2010 12th International Conference on Transparent Optical Networks

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“…Alternatively, we substitute (21) into (8), and the SEP for MPSK becomes (23) (24) Note in (24) that, since the ordered physical branches are no longer independent, direct use of the methods given in [21] and [22] requires an -fold nested integration for the expectation operation in (23). This is alleviated using the virtual branch technique by substituting (21) into (20) as (25) Exploiting the fact that 's are independent, (25) becomes (26) where is the th element of . The powerfulness of the virtual branch technique is apparent by observing that the expectation operation in (23) no longer requires an -fold nested integration.…”

Section: ) Sep For Mpsk With Gdcmentioning

confidence: 99%

Virtual branch analysis of symbol error probability for hybrid selection/maximal-ratio combining in Rayleigh fading

Win

Winters

2001

IEEE Trans. Commun.

249

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Abstract-In this paper, we derive analytical expressions for the symbol error probability (SEP) for a hybrid selection/maximalratio combining (H-S/MRC) diversity system in multipath-fading wireless environments. With H-S/MRC, out of diversity branches are selected and combined using maximal-ratio combining (MRC). We consider coherent detection of -ary phase-shift keying (MPSK) and quadrature amplitude modulation (MQAM) using H-S/MRC for the case of independent Rayleigh fading with equal signal-to-noise ratio averaged over the fading. The proposed problem is made analytically tractable by transforming the ordered physical diversity branches, which are correlated, into independent and identically distributed (i.i.d.) "virtual branches," which results in a simple derivation of the SEP for arbitrary and . We further obtain a canonical structure for the SEP of H-S/MRC as a weighted sum of the elementary SEP's, which are the SEP's using MRC with i.i.d. diversity branches in Rayleigh fading, or equivalently the SEP's of the nondiversity (single-branch) system in Nakagami fading, whose closed-form expressions are well-known. We present numerical examples illustrating that H-S/MRC, even with , can achieve performance close to that of -branch MRC.Index Terms-Diversity combining, error probability, fading channel, maximal ratio combining, selection diversity, virtual branch technique.

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“…The pdf of the correlated phase difference modulo [−π, π), given in [93,94], is adopted to derive the pdf of the output phase of an FM receiver. Under very high SNRs, the probability of the phase difference lying either on [−2π, −π) or (π, 2π] is small, so the approximation by taking a modulus of [−π, π) is acceptable.…”

Section: Besides These Investigations For General Values Of the Fm Rementioning

confidence: 99%

“…When K is large, say, K > 8dB, the phase difference pdf can be approximated by the pdf of phase difference modulo [−π, π) [93],…”

Section: Pdf Of the Phase Differencementioning

confidence: 99%

Absolute phase in mobile channels

Ren¹,

Vaughan²

2011

Wireless Communications

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Radio channels are usually modeled as a well‐defined Rice process. The statistics of its wrapped phase (i.e., phase values in [−π,π)), such as the mean, variance, and probability density function (pdf), are known. The absolute phase, i.e., the accumulated phase change over an observation interval, is considered here as a new channel variable. Its use for channel characterization can extend to cognitively track users. However, there is very little knowledge about the statistics of the absolute phase. In fact, the known, associated effects of the absolute phase, such as various click noise contributions, are not consistently treated or interpreted in the literature. The definitions of absolute phase, based on both unwrapping and on other methods previously discussed for FM receivers, lay a basis for analysis of the mean, variance, and pdf of the absolute phase for a well‐defined Rice process. The conditions are identified for approximate pdf models to hold, and it is noted that pdfs for the absolute phase for small or medium Rice factor and small observation interval are open problems. Simulations are used to support the analysis and discussion. Copyright © 2009 John Wiley & Sons, Ltd.

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Distribution of the Phase Angle Between Two Vectors Perturbed by Gaussian Noise

Cited by 407 publications

References 13 publications

Analysis of non-linear impairments in 40 Gbaud PM DQPSK and D8PSK transmission

Analysis of non-linear impairments in 40 Gbaud PM DQPSK and D8PSK transmission

Virtual branch analysis of symbol error probability for hybrid selection/maximal-ratio combining in Rayleigh fading

Absolute phase in mobile channels

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