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Spread spectrum receivers with generalized selection combining (GSC) RAKE reception were proposed and have been studied as alternatives to the classical two fundamental schemes: maximal ratio combining and selection combining because the number of diversity paths increases with the transmission bandwidth. Previous work on performance analyses of GSC RAKE receivers based on the signal to noise ratio focused on the development of methodologies to derive exact closed-form expressions for various performance measures. However, some open problems related to the performance evaluation of GSC RAKE receivers still remain to be solved such as the exact performance analysis of the capture probability and an exact assessment of the impact of self-interference on GSC RAKE receivers. The major difficulty in these problems is to derive some joint statistics of ordered exponential variates. With this motivation in mind, we capitalize in this paper on some new order statistics results to derive exact closed-form expressions for the capture probability and outage probability of GSC RAKE receivers subject to self-interference over independent and identically distributed Rayleigh fading channels, and compare it to that of partial RAKE receivers.