For pt.I see ibid., vol.45, no.9, p.1101-11 (1997). An adaptive code-aided technique for the simultaneous suppression of narrow-band interference (NBI) and multiple-access interference (MAI) in direct-sequence code-division multiple-access (DS/CDMA) networks is proposed. This technique is based on the recursive least-squares (RLS) version of the minimum mean-square error (MMSE) algorithm for multiuser detection. The convergence dynamics of the RLS blind adaptive algorithm for suppressing the combined NBI and MAI are analyzed. The steady-state performance of this algorithm in terms of the signal-to-interference ratio (SIR) is also derived. Systolic array structures for parallel implementations of the RLS adaptive interference suppression algorithms are then proposed. Versions of the rotation-based QR-RLS algorithms for both the blind adaptation mode and the decision-directed adaptation mode are derived. These algorithms exhibit high degrees of parallelism, and can be mapped to VLSI systolic arrays to exploit massively parallel signal processing computation.