In this paper we propose an energy-efficient and high-speed robust system design methodology targeting remote cardiac health monitoring. The proposed system comprises of two main moduleslow- complexity 3D CORDIC based FastICA followed by the adaptive permutation ambiguity solver to solve the permutation indeterminacy encountered in Independent Component Analysis (ICA) for artifacts removal from recorded 3-channel ECG signals within the remote health monitoring environment for cardiovascular patients. Since FastICA is computationally intensive, its direct architectural mapping from the algorithm may not result in an optimum architecture suitable for the resource constrained applications including remote healthcare. Therefore our proposed 3D CORDIC based FastICA system architecture would reduce the hardware complexity significantly. Unlike the existing approaches to solver permutation ambiguity, the proposed methodology takes into account the nonstationarity of the ECG signal thereby making this methodology more realistic. Since the proposed methodology is based on the adaptive template matching scheme, once the channel containing the intended ECG signal is detected, there is no need to continue this proposed methodology for the rest of the channels. Thus it saves computation time as well as minimizes the overall energy consumption of the system. The proposed methodology is tested using 275 ECG signal recordings of patients obtained from clinically well-known MIT-BIH PTB databases and real-life ECG data collected from University of Southampton hospital corrupted by an exhaustive set of 5 bodily artifacts and noise. The proposed methodology is found to save on the 55.55% of the otherwise incurred energy and 33.33% speed improvement as compared to the existing approaches.