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High signal-to-noise ratio (SNR) properties of the minimum output energy (MOE) receiver and the Capon channel estimation technique are analyzed in the case of large direct-sequence code-division multiple-access (DS-CDMA) systems. It is shown that if the noise power tends to zero and the system load is less than one, then the signal-to-interference-plus-noise ratio (SINR) of the MOE receiver tends to infinity and the Capon channel estimate converges to a scaled version of the channel vector of the user-of-interest. For the case when the system load is larger than one, an asymptotic SINR expression is obtained. Furthermore, expressions for the efficiency and asymptotic efficiency of the MOE receiver are derived. Simple approximations of (and upper/lower bounds on) these expressions are found and the effects of the system physical parameters on the performance of the MOE receiver are discussed.