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In this paper, we introduce two new linear parallel interference cancellation (LPIC) detectors that are suitable for low to medium signal-to-noise ratio ill-conditioned communication systems and do not require knowledge of the noise variance but perform close to the linear minimum mean square error detector, which needs such information. Particularly, we focus in this work on fast linear parallel interference cancellation detectors that are asymptotically equivalent to the steepest descent and conjugate gradient algorithms, respectively, and show that they exhibit a spectral filtering property and semi-convergence behavior. Consequently, a deterministic stopping rule to stop the LPIC iterations that is independent of the noise level (known as the L-curve method) is investigated and tested. Simulation results are presented to support our theoretical findings.

Linear IC detectors for low to medium SNR ill-conditioned communication systems with unknown noise variance