To efficiently use frequency resources, the next 6th generation mobile communication technology must solve the problem of out‐of‐band emission (OoBE) of cyclic prefix (CP) orthogonal frequency division multiplexing (OFDM), which is not solved in 5th generation technology. This study describes a new zero insertion technique to replace an existing filtering scheme to solve this internal problem in OFDM signals. In the development of the proposed scheme, a precoder with a two‐dimensional structure is first designed by generating a two‐dimensional mapper and using the specialty of each matrix. A spectral shaping technique based on zero insertion instead of a long filter is proposed, so it can be applied not only to long OFDM symbols, but also very short ones. The proposed method shows that the transmitted signal is completely blocked at the bandwidth boundaries of signals according to the current standards, and it is confirmed that the proposed scheme is ideal with respect to bit error rate (BER) performance because its BER is the same as that of CP‐OFDM. In addition, the proposed scheme can transformed into a real time structure through vectorizing process with minimal complexity.

This paper proposes a method that can reduce the complexity of a system matrix by analyzing the characteristics of a pseudoinverse matrix to receive a binomial frequency division multiplexing (BFDM) signal and decode it using the least squares (LS) method. The system matrix of BFDM can be expressed as a band matrix, and as this matrix contains many zeros, its amount of calculation when generating a transmission signal is quite small. The LS solution can be obtained by multiplying the received signal by the pseudoinverse matrix of the system matrix. The singular value decomposition of the system matrix indicates that the pseudoinverse matrix is a band matrix. The signal-tointerference ratio is obtained from their eigenvalues. Meanwhile, entries that do not contribute to signal generation are erased to enhance calculation efficiency. We decode the received signal using the pseudoinverse matrix and the removed pseudoinverse matrix to obtain the bit error rate performance and to analyze the difference.