Distribution of the phase angle between two vectors perturbed by Gaussian 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.

[1]  Marvin K. Simon.  A simple evaluation of DPSK error probability performance in the presence of bit timing error , 1994, IEEE Trans. Commun..

[2]  Tjeng Thiang Tjhung,et al.  Distribution of phase angle between two Rayleigh vectors perturbed by Gaussian noise , 1992 .

[3]  Mohamed-Slim Alouini,et al.  Exponential-type bounds on the generalized Marcum Q-function with application to error probability analysis over fading channels , 2000, IEEE Trans. Commun..

[4]  Pil Lee.  Computation of the Bit Error Rate of Coherent M-ary PSK with Gray Code Bit Mapping , 1986, IEEE Trans. Commun..

[5]  R. F. Pawula,et al.  On the Theory of Error Rates for Narrow-Band Digital FM , 1981, IEEE Trans. Commun..

[6]  Mohamed-Slim Alouini,et al.  A unified approach to the probability of error for noncoherent and differentially coherent modulations over generalized fading channels , 1998, IEEE Trans. Commun..

[7]  R. Pawula,et al.  The Effects of Noise Correlation and Power Imbalance on Terrestrial and Satellite DPSK Channels , 1983, IEEE Trans. Commun..

[8]  Marvin K. Simon.  Double Symbol Error Rates for Differential Detection of Narrow-Band FM , 1985, IEEE Trans. Commun..

[9]  Marvin Kenneth Simon.  Digital Communication Techniques , 1994 .

[10]  Seymour Stein,et al.  Distribution of instantaneous frequency for signal plus noise , 1964, IEEE Trans. Inf. Theory.

[11]  M. Simon,et al.  Differential Versus Limiter - Discriminator Detection of Narrow-Band FM , 1983, IEEE Transactions on Communications.

[12]  Mohamed-Slim Alouini,et al.  A unified approach to the performance analysis of digital communication over generalized fading channels , 1998, Proc. IEEE.

[13]  Marvin K. Simon.  The Impact of Mismatch on the Performance of Coded Narrow-Band FM with Limiter/Discriminator Detection , 1983, IEEE Trans. Commun..

[14]  Robert F. Pawula.  Digital FM double errors , 2001, IEEE Trans. Veh. Technol..

[15]  Robert F. Pawula.  Generic error probabilities , 1999, IEEE Trans. Commun..

[16]  Distribution of phase difference between two Nakagami faded signals perturbed by Gaussian noise , 1995 .

[17]  Sandeep Chennakeshu,et al.  Error rates for Rayleigh fading multichannel reception of MPSK signals , 1995, IEEE Trans. Commun..

[18]  S. Rice,et al.  Distribution of the Phase Angle Between Two Vectors Perturbed by Gaussian Noise , 1982, IEEE Trans. Commun..

[19]  Robert F. Pawula.  Improved performance of coded digital FM , 1999, IEEE Trans. Commun..

[20]  Israel Korn,et al.  Relation between bit and symbol error probabilities for DPSK and FSK with differential phase detection , 1994, IEEE Trans. Commun..

[21]  Tjeng Thiang Tjhung,et al.  Error Performance Analysis for Narrow-Band Duobinary FM with Discriminator Detection , 1985, IEEE Trans. Commun..

[22]  Robert F. Pawula.  A new formula for MDPSK symbol error probability , 1998, IEEE Communications Letters.

[23]  Isaac Todhunter,et al.  Treatise on integral calculus , 1889 .

[24]  Robert F. Pawula,et al.  Refinements to the theory of error rates for narrow-band digital FM , 1988, IEEE Trans. Commun..

[25]  R. F. Pawula.  Offset DPSK and a Comparison of Conventional and Symmetric DPSK with Noise Correlation and Power Imbalance , 1983, MILCOM 1983 - IEEE Military Communications Conference.