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In this paper, we present a novel system for joint speaker identification and speech separation. For speaker identification a single-channel speaker identification algorithm is proposed which provides an estimate of signal-to-signal ratio (SSR) as a by-product. For speech separation, we propose a sinusoidal model-based algorithm. The speech separation algorithm consists of a double-talk/single-talk detector followed by a minimum mean square error estimator of sinusoidal parameters for finding optimal codevectors from pre-trained speaker codebooks. In evaluating the proposed system, we start from a situation where we have prior information of codebook indices, speaker identities and SSR-level, and then, by relaxing these assumptions one by one, we demonstrate the efficiency of the proposed fully blind system. In contrast to previous studies that mostly focus on automatic speech recognition (ASR) accuracy, here, we report the objective and subjective results as well. The results show that the proposed system performs as well as the best of the state-of-the-art in terms of perceived quality while its performance in terms of speaker identification and automatic speech recognition results are generally lower. It outperforms the state-of-the-art in terms of intelligibility showing that the ASR results are not conclusive. The proposed method achieves on average, 52.3% ASR accuracy, 41.2 points in MUSHRA and 85.9% in speech intelligibility.