<p>Cognitive radio (CR) has emerged as a compelling solution to address the spectrum scarcity challenge and enhance overall spectral efficiency. Its primary objective is to advance spectrum sensing capabilities, facilitating the identification of primary users and enabling secondary users to effectively exploit spectral opportunities. Spectrum sensing operations are inherently confined to predefined time intervals, which are further segmented into sensing and transmission phases. The quality of spectrum sensing crucially hinges on the duration of the sensing phase, where a more extended sensing time yields superior detection performance and reduces the likelihood of false alarms. Consequently, the development of an optimization framework becomes imperative to navigate the intricate trade-off between sensing time and throughput. This study introduces a novel optimization model for spectrum sensing in CR systems, grounded in energy detection and wavelet denoising techniques. The investigation encompasses the evaluation of key performance metrics such as detection probability, false alarm probability, number of sensing samples, optimized sensing durations, and maximum attainable throughput across various signal-to-noise ratios (SNRs). Simulation outcomes substantiate the efficacy of the proposed model by substantially mitigating false alarms, enhancing detection probabilities, and determining optimal sensing durations across diverse SNR scenarios and varying sample sizes. Specifically, the optimized sensing durations are identified as 1.6667&#xa0;ms for 10,000 sensing samples, 8.3333&#xa0;ms for 50,000 sensing samples, 16.6667&#xa0;ms for 100,000 sensing samples, and 33.3333&#xa0;ms for 400,000 sensing samples. Consequently, this model not only augments the spectrum sensing process within CR systems but also furnishes a robust real-time solution for CR networks, surpassing existing methodologies in terms of performance and efficiency.</p>