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A successive-relaying-aided network (SRAN) is designed for a multiuser spread-spectrum scenario conceived for noncoherent (NC) detection to convert the typical 50% half-duplex relaying induced throughput loss to a potential user-load reduction of the code-division multiple-access (CDMA) system, where the NC allows us to avoid the extra power consumption imposed by channel estimation. We commence by evaluating the NC discrete-input-continuous-output memoryless channel (DCMC) capacity of both the amplify-and-forward-based (AF) and decode-and-forward-based (DF) SRANs in the direct-sequence CDMA (DS-CDMA) uplink (UL). While NC detection has the added benefit of eliminating both the pilot overhead and the power-hungry channel estimation, it tends to form an error floor at high Doppler frequencies. We mitigate this problem using multiple-symbol detection, which increases the detection complexity upon extending the detection window. Finally, a relay-aided soft-input-soft-output multiple-symbol differential sphere detection (SISO-MSDSD) CDMA regime is proposed, which significantly reduces the system's complexity without sacrificing its performance.