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This paper investigates the problem of cooperative spectrum sensing in cognitive radios with unknown parameters in the likelihood function. We first derive the optimal likelihood ratio test (LRT) statistic based on the Neyman-Pearson (NP) criterion at the fusion center for hard (one-bit), soft (infinite precision) and quantized (multi-bit) local decisions. This NP-based LRT detector is feasible only if primary signal statistics and channel parameters are known. This assumption may not be realistic in cognitive radio systems. Thus, we propose a linear composite hypothesis testing approach which estimates the unknown parameters, and further simplify it so that it does not even require these estimates. Under the scenarios of: i) unknown primary signal and channel statistics; and ii) unknown primary signal statistics but known channel statistics, we apply the proposed test and also, for case ii), derive the locally most powerful (LMP) detector for weak signals. For performance analysis and threshold setting, we derive the distributions of the linear test and LMP statistics under the signal-absent hypothesis. Our simulation results show that the linear test performs very closely to the optimal LRT while not requiring the primary statistics. As a result, this method enhances robustness in cooperative spectrum sensing to uncertainties in channel gains and signal statistics.