OPTIMUM DETECTION OF LASER SIGNAL THROUGH M TURBULENT ATMOSPHERE

Abstract

The invention of laser in 1960, triggered the imagination of a large number of communication engineers to develop a sophisticated communication system for hand ling huge amount of information. Considerable amount of work has been done towards inventing new forms of modulation and detection techniques with such coherent sources. It is now possible to establish in practice real communica tion systems involving extremely large band widths. These efficient optical communication systems have the added advantage of high achievable directivity, increased antenna gain and higher data rates. Laser communication systems operate at carrier frequencies in the interval of 101%z to 101^Hz. The attri butes of large information band width and narrow transmitted beams of laser systems compared to radio frequency commun ication system are simply a result of high frequency of optical waves, narrow spectral width and coherence. x - For laser communication, the channel or medium of transmission may be earth's atmosphere, closed optical waveguide, or vacuum. For short distance transmission any sort of guiding technique may be employed, but for long and medium distances, transmission through atmosphere becomes inevitable. The propagation characteristics of atmosphere have been the subject of investigation for several decades particularly at radio frequency. The advent of laser spurred renewed activities in the optical and infrared region of the spectrum. The hope for use of lasers for communication through atmosphere was hampered some what due to the adverse role played by atmospheric effects as reported by Subramanian [l55j. Propagation through turbulent atmospheric channel has been reviewed by Strohbehn [152], Lawrence and Strohbehn C1011, Brookner [17][18] ,Kennedy and Karp £89 J. There are a number of propagation effects due to the random spatially and temporally varying refractive index. The ultimate atmos pheric limitation on propagation at optical frequencies can be established by applying communication theory ideas to adequate statistical models of atmospheric channel. In the turbulent case one is faced with a slowly varying fading channel with amplitude variations having log-normal distribution C89J and the phase varia tions for which the probability distribution has been assumed as Tl6ifj i exp(<* cos 9) p(<P) = . "1T^(?4W- 2 * Io(c<) The function I {«<) is the Bessel's function of the first kind. °( is regarded as a parameter that controls the spread of the density. The transmitter sends a signal whose intensity is modulated with one of a set of M-possible intensities each T second long. One can associate a signal energy component mk for the k intensity. During an interval of T second, one of the M equal energy signal is known to be transmitted. During transmission through the atmosphere multipathing occurs due to inhomogeneities of turbulence. The signal is perturbed by background radiation noise, which is assumed to be white, stationary, Gaussian and statistically independ ent of the channel perturbations. The receiver determines with minimum probability of error as to which signal was transmitted. It does this by appropriately processing the received signal S. This operation consists of computing the a-posteriori probability of the M received signal and choos ing the one with the largest probability. An upper bound on average probability of error of multiphoton count laser system has been derived. The signal has been assumed to be disturbed by background radiation noise alone. It has also been mentioned that the probability of error bound can be used to attain any required standard of performance in terms of the allowable error. - xii - Analytical expressions have been derived for the a-posteriori probability of detecting M-possible signals, with multipathing and perturbed by random variations in phase and gain. Receiver structures are proposed which can imple ment the analytical expression giving the a-posteriori probability. Decision is given in terms of that signal which gives the maximum a-posteriori probability. The physi cal realizations of the proposed receivers are also discussed.