In this paper, we model the received signal of a single-input-multiple-output (SIMO) cognitive radio with in-phase and quadrature imbalance (IQI) in the transmitter. Then, the spectrum sensing problem is formulated as a composite hypothesis testing problem. We propose two new eigenvalue-based detectors based on the likelihood ratio test (LRT), Rao and Wald frameworks, i.e., the resultant LRT leads us to the Wald test. For the proposed Rao test, we find closed-form expressions for false alarm and detection probabilities under noise variance uncertainty in order to get the level of desired false alarm probability $p_{\text{fa}}$ , i.e., it is called a level $p_{\text{fa}}$ test. This is required for nonconstant false alarm rate (non-CFAR) such as the Rao test to guarantee that the obtained false alarm rate is always below a required level $p_{\text{fa}}$ . Additionally, an analytical formula for the probability of false alarm of Wald test is presented to confirm our simulation results. In this case, the proposed Wald detector is a size $p_{\text{fa}}$ test, called a CFAR detector. Detection performances of the proposed detectors are compared in different scenarios by extensive Monte Carlo simulations. It is shown that the Wald detector outperforms the proposed Rao one. Also, we show that the effects of transmitting IQI can be considered as a signal-to-noise ratio factor, just affecting the detection performance. Also, our performance results show that the proposed Wald detector is fairly robust to the receiver IQI when direct down-conversion receivers are exploited.
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