# Z-OFDM: A New High-Performance Solution for Underwater Acoustic Communication
## 5 Discussion  
In the Z-OFDM system, innovative designs have been implemented from both the transmitter and receiver. On the transmitter side, the modulator generates OFDM signals by loading data streams onto subcarriers and mapping them to corresponding carrier phases via ZoomIFFT. During this process, ZoomIFFT processes the spectrum with higher resolution, allowing for more subcarriers to be accommodated within the same bandwidth, thereby increasing the channel capacity. On the receiver side, the demodulator employs ZoomFFT to refine the spectrum of the received OFDM signal, which enables the receiver to more accurately recover the original signal. As a result, the SINR is improved, and the BER is reduced. Recently, FFT-based OFDM communication systems continue to be the focus of numerous studies [7; 60; 61]. In [60], an FFT size of 2048 is used, resulting in a spectral resolution of 46.875 Hz. The study mitigates ICI by improving Doppler shift compensation through the use of a non-uniform fast Fourier transform matrix (NFFT). Experimental results demonstrate that the proposed method achieves at least an 8 dB gain in system performance at a BER of \(10^{-1}\) compared to systems without Doppler compensation. In [61], the FFT size is 256, yielding a spectral resolution of 390.625 Hz. The study designs a preamble using a CAZAC sequence and develops a new time-frequency synchronization method for the OFDM system. Experimental results show that the proposed improvements lead to a significantly lower symbol error rate (SER) on the order of \(10^{-3}\). In [7], an FFT size of 1024 is employed, providing a spectral resolution of 7.8125 Hz. The study enhances system performance by introducing a novel CE technique and an intra-block CFO estimation method. Experimental results indicate that, after compensation, the system's BER is \(3.20\times 10^{-3}\) at an SNR of 30 dB. These studies, while achieving specific gains in BER, SER, and other  
Figure 10: BER over time varies underwater acoustic channel of unit time in Wuyuan Bay. metrics, still face limitations due to the inherent constraints of the FFT, such as increased computational complexity with larger FFT sizes. As shown in Table 2, Z-OFDM significantly outperforms traditional FFT-based OFDM in several key areas. On the transmitter side, the channel capacity is notably increased. Experiments conducted in an AWGN channel indicate that under the same condition of \(\frac{E_{k}}{N_{0}}=10\) dB, the Z-OFDM system (with a refinement factor \(D=2\)) achieves an increase in channel capacity by 0.2 bps/Hz compared to the FFT-based OFDM system. Moreover, when channel capacity remains constant, the Z-OFDM system can achieve up to a 3 dB gain over the FFT-based OFDM system. On the receiver side, the increased spectral resolution of Z-OFDM allows it to handle NBI more effectively, leading to lower BER and improved signal quality. Experiments show that under the same condition of \(\frac{E_{k}}{N_{0}}=10\) dB, the Z-OFDM system with a refinement factor \(D=2\) reduces the BER by 0.0683 and improves the SINR by 0.576 compared to the FFT-based OFDM system. When BER and SINR remain constant, the Z-OFDM system can also achieve up to a 3 dB gain over the FFT-based OFDM system. Additionally, Z-OFDM maintains computational efficiency, ensuring that these benefits are achieved without excessive processing overhead. In terms of computational complexity, as the refinement factor \(D\) in the Z-OFDM system increases, the spectral resolution becomes higher. To achieve the same resolution, the FFT-based OFDM system would be required to increase the FFT size, leading to a significant increase in computational complexity. However, the Z-OFDM system takes advantage of ZoomFFT, allowing its complexity to remain almost unchanged. The above comparison is made with the refinement factor \(D=2\). However, increasing the factor \(D\) can increase both the capacity and the SINR of the Z-OFDM system.