Cognitive radio (CR) incorporating orthogonal frequency division multiplexing (OFDM) is an intelligent spectrum sharing technique that acquires high data rate in frequency selective fading environment. OFDM has been successfully used for 4G and specific version of OFDM is being considered as the multiple access technology for 5G as well. However OFDM signal is more likely to have high peak‐to‐average power ratio (PAPR). Similarly, the sideband power of secondary or temporary users (SU) in CR can lead to interference to the licensed or primary users of the neighboring bands. In this work, an improved technique for the joint minimization of sideband power and PAPR using Zadoff‐Chu (ZC) sequence is proposed for CR based on OFDM technology. Furthermore, we propose a detection algorithm based on a binary hypothesis testing problem to recover the chosen ZC sequence at the receiver side eliminating the requirement of side information (SI) transmission. Simulation studies of the proposed method exhibits the efficiency of the concurrent reduction of PAPR and sideband power along with a huge bandwidth saving by the omission of the SI transmission.