## 5 Simulation Results  
### Simulation Environment  
To verify the interference cancellation performance of the proposed method, computer simulations are conducted. Figure 7 illustrates the transceiver structure used for simulation. Figure 6: Spectrum before cancellation (**left**) and after cancellation (**right**) with proposed fine frequency shift when \(f_{I}=50.4/256T\). The proposed system transmits short messages of 197 bits. A cyclic redundancy check (CRC) parity of 11 bits is added to the transmitted message, resulting in 208 bits. These bits are then encoded using a polar code [28] with a code rate of 1/2, producing 416 bits. Then, QPSK modulation is performed, and a cyclic prefix (CP) and pilot are added, resulting in a total of 268 symbols being transmitted. For improved performance in low-SNR environments, repetition transmission can be employed, where the 268-symbol frame is repeatedly transmitted. This process can be considered as performing DSSS with an all-one spreading code. Polar codes are known for their excellent error correction performance when transmitting short messages, and in this paper, we use the polar code employed in the uplink of 5G mobile communication systems [28]. In practical scenarios, interference is typically perceived as degraded channel quality. Under such conditions, the system would likely adopt the lowest modulation order, such as QPSK, to ensure reliable communication. However, when the interference is strong, even QPSK may fail to restore the received signal accurately. In such cases, the proposed NBI cancellation technique can effectively improve performance. For higher-order modulation schemes, the proposed NBI cancellation technique is also expected to improve BER performance in the presence of NBI. However, higher modulation orders generally require a high SNR to achieve the desired BER performance, even in the absence of NBI. In such cases, residual NBI after cancellation may severely degrade BER performance. For these reasons, the computer simulation in this paper focuses exclusively on QPSK. At the receiver, after the CP is removed, a fine frequency shift is applied, followed by NBI cancellation, as described in Sections 3 and 4. After that, the fine frequency shift is restored, and equalization and QPSK demodulation are performed to output the log-likelihood ratio (LLR). The equalization is performed as follows: the maximum length of the CIR estimate is 12, so the CIR is estimated from the 48-symbol pilot. The detailed frequency-domain equalization process follows Section 2. If repetition transmission is used at the transmitter, the LLRs are accumulated by the number of repetitions. Finally, the transmitted message is recovered through polar decoding. Two types of channel models are considered: the AWGN (Additive White Gaussian Noise) channel and the ETU (Extended Typical Urban) channel model from 3 GPP [29]. The ETU channel model used in this paper is a quasi-static model. Within a single packet duration, the channel remains fixed and does not change over time. However, the channel is randomly regenerated for each packet transmission. This approach ensures that the BER stays within a reasonable range. Excessively high BER due to poor equalizer performance would make it difficult to compare the NBI cancellation performance effectively. The quasi-static nature of the ETU channel model was chosen to facilitate a fair and meaningful comparison. The time delay and gain  
Figure 7: Transceiver model for simulation. profiles of the ETU channel model are shown in Table 1, and the simulation environment is summarized in Table 2.  
The simulations were performed using MATLAB R2024a. Specifically, the encoder and decoder for polar codes were implemented using the 5G NR Toolbox, while the channel model was created using the LTE Toolbox. The remaining blocks were directly coded using the MATLAB Communication Toolbox. As shown in Figure 7, a single packet consists of a 197-bit message, and the BER is measured by transmitting over 50,000 packets for each SNR value.