Statistical behavior of a fading signal

A general analysis of the statistical behavior of the envelope of a fading signal V (t)eiϕ(t) is presented in this paper. The statistics include the probability P(V ≤ L) that the amplitude V (t) will fade below a specified signal level L; the expected number N(L) of fades of V (t) below L per unit time; and the average duration t(L) of fades below L. The model for the fading signal is a constant vector plus a random interfering vector which represents the resultant of all the received extraneous signals and noise. The theoretical results agree with three empirically observed power relationships obtained in deep fades of nondiversity signals: P(V ≤ L) ∝ L2, N(L) ∝ L and t(L) ∝ L. The theoretical results are applicable to a wide class of fading problems. The analysis includes the previous works of Rice, Nakagami, Norton, Vogler, Mansfield, and Short as special cases.

[1]  Arvids Vigants,et al.  Number and duration of fades at 6 and 4 Ghz , 1971 .

[2]  W. T. Barnett,et al.  Microwave line-of-sight propagation with and without frequency diversity , 1970, Bell Syst. Tech. J..

[3]  Arvids Vigants,et al.  The number of fades in space-diversity reception , 1970 .

[4]  A. Rosenbaum,et al.  Binary PSK Error Probabilities with Multiple Cochannel Interferences , 1970 .

[5]  Paul H. Deitz,et al.  SATURATION OF SCINTILLATION MAGNITUDE IN NEAR-EARTH OPTICAL PROPAGATION. , 1969 .

[6]  A. Vigants,et al.  Space-Diversity Performance as a Function of Antenna Separation , 1968 .

[7]  R. Clarke.  A statistical theory of mobile-radio reception , 1968 .

[8]  David A. deWolf,et al.  Saturation of Irradiance Fluctuations Due to Turbulent Atmosphere , 1968 .

[9]  H. Lenzing,et al.  Excitation of Higher-Order Antenna Modes by Multipath Propagation , 1967, IEEE Transactions on Communication Technology.

[10]  K. Morita,et al.  Design of Space Diversity Receiving and Transmitting Systems for Line-of-Sight Microwave Links , 1967, IEEE Transactions on Communication Technology.

[11]  David L. Fried,et al.  Measurements of Laser-Beam Scintillation in the Atmosphere: Errata , 1967 .

[12]  K. Pearson.  Method for the prediction of the fading performance of a multisection microwave link , 1965 .

[13]  Joseph F. Ossanna,et al.  A model for mobile radio fading due to building reflections: Theoretical and experimental fading waveform power spectra , 1964 .

[14]  P. Beckmann,et al.  Amplitude-probability distribution of atmospheric radio noise , 1964 .

[15]  A. B. Crawford,et al.  Studies in tropospheric propagation beyond the horizon , 1959 .

[16]  S. O. Rice,et al.  Distribution of the duration of fades in radio transmission: Gaussian noise model , 1958 .

[17]  P. Gudmandsen,et al.  Statistical data for microwave propagation measurements on two oversea paths in Denmark , 1957 .

[18]  K. A. Norton,et al.  The Probability Distribution of the Amplitude of a Constant Vector Plus a Rayleigh-Distributed Vector , 1955, Proceedings of the IRE.

[19]  David Durand,et al.  The Distribution of Length and Components of the Sum of $n$ Random Unit Vectors , 1955 .

[20]  Ray S. Hoyt.  Probability functions for the modulus and angle of the normal complex variate , 1947 .

[21]  W. M. Sharpless,et al.  Measurement of the Angle of Arrival of Microwaves , 1946, Proceedings of the IRE.

[22]  A. B. Crawford,et al.  Further Observations of the Angle of Arrival of Microwaves , 1946, Proceedings of the IRE.

[23]  M. Slack.  The probability distributions of sinusoidal oscillations combined in random phase , 1946 .

[24]  S. Rice.  Mathematical analysis of random noise , 1944 .

[25]  S. O. Rice,et al.  Distribution of the extreme values of the sum of sine waves phased at random , 1955 .

[26]  A. B. Crawford,et al.  Selective fading of microwaves , 1952 .

[27]  K. Norton,et al.  The Probability Distribution of the Phase of the Resultant Vector Sum of a Constant Vector Plus a Rayleigh Distributed Vector , 1952 .

[28]  O. E. De Lange,et al.  Propagation studies at microwave frequencies by means of very short pulses , 1952 .

[29]  S. O. Rice,et al.  Statistical properties of a sine wave plus random noise , 1948, Bell Syst. Tech. J..

[30]  W. Bennett.  Distribution of the sum of randomly phased components , 1948 .