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In this paper, a new representation theory that provides an improved description of the channel statistics of multihop and tropospheric scatter communication links is presented. Two conceptually different representations are developed. These representations, which are based on the deviations from a lognormal distribution, are due to the variable skewness of the lognormal distribution, extremely flexible, and can provide, with the proper choice of parameters, a good approximation of a broad class of non-Gaussian distributions. In addition, since the statistics of these channels are primarily due to multiplicative noise disturbances and the lognormal distribution results from multiplicative events, the presented representations mathematically describe the statistics of these channels in terms of a reference distribution related to their underlying natural processes. The proper application of this representation theory to the problem of signal detection in such non-Gaussian noise environments results in improved near-optimum signal detection systems. These procedures will yield, with an appropriate adjustment of system parameters, near-optimum performance for a large class of non-Gaussian channel noise conditions. In addition, these detectors can be easily implemented in terms of available devices and can be modified to operate in an adaptive mode.