This paper follows up the previous work on the linearly constrained, modified minimum mean-squared error(MMSE) detection for direct-sequence code-division multiple-access DS-CDMA) systems in fading channels. We find a condition to avoid the breakdown of joint modified MMSE detection and pilot symbol-aided channel estimation (PSACE). The linearly constrained, modified MMSE solution is theoretically shown to be robust against time variations in Rayleigh fading channels. This fact is consistent with the simulation results. We also show that under some conditions the linearly constrained, modified MMSE detection maximizes the output signal-to-interference-plus-noise ratio.(SINR)