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In this paper, we propose asynchronous non-orthogonal communication between distributed sensors and a data fusion center via asynchronous direct-sequence code-division multiple access (DS-CDMA). Furthermore, we evaluate the performance of such a system in the presence of local-sensor and channel errors due to multiple-access interference (MAI) and noise. We derive the optimal Bayesian receiver for this system operating over both a simple AWGN channel and a Rayleigh-fading channel, assuming full knowledge of the channel fading coefficients. The optimal receiver is shown to have exponential complexity as a function of the number of sensors. A set of low-complexity partitioned receivers are then proposed and analyzed in relation to the optimal one. These partitioned receivers are based on well-known linear and nonlinear multiuser detectors for DS-CDMA. The synchronous DS-CDMA case was studied previously, and it is shown here that the degradation induced by moving to an asynchronous model is relatively small for the optimal receiver. Moreover, we provide compelling evidence that the quality of the local-sensor decisions is the limiting factor in fusion performance for fading channels with high signal-to-noise ratio.