A novel scheme of pilot design based estimation of sparse channel is proposed to get optimized pattern. An updating rule for probability of selected sub carriers is derived. Simulation results verify the performance of the system by comparing with LS channel estimation. A EEOPA is proposed so that the energy efficiency and the channel capacity is validated. sparse channel estimation is first introduced in orthogonal frequency-division multiplexing (OFDM)-based cognitive radio systems. Based on the results of spectrum sensing, the pilot design is studied by minimizing the coherence of the dictionary matrix used for sparse recovery. Then, it is formulated as an optimal column selection problem where a table is generated and the indexes of the selected columns of the table form a pilot pattern. A novel scheme using constrained cross-entropy optimization is proposed to obtain an optimized pilot pattern, where it is modeled as an independent Bernoulli random process. The updating rule for the probability of each active subcarrier selected as a pilot subcarrier is derived. A projection method is proposed so that the number of pilots during the optimization is fixed. Simulation results verify the effectiveness of the proposed scheme and show that it can achieve 11.5% improvement in spectrum efficiency with the same channel estimation performance compared with the least squares (LS) channel estimation.