# Design and Evaluation of an Acoustic Modern
## 2 System Design  
### Direct Sequence Spread Spectrum (DSSS) Modulation  
As the principle of spread spectrum (SS) technology is well known, they are briefly reviewed here from an engineering viewpoint of the modem design. By directly modulating the information to be transmitted into a broad frequency band with a pseudorandom sequence and then recovering the transmitted information sequence through demodulation and de-spreading processes, a direct sequence spread spectrum (DSSS) is adopted to yield a strong anti-interference ability, a strong anti-multipath capability, and multiple user access capabilities and robustness under low SNR [9]. Moreover, differential coherent demodulation is employed to mitigate the time variations induced by UWA channels. The block diagram of DS-DBPSK (Direct Sequence-Differential Binary Phase Keying) modulation is shown in Figure 1.  
The frame structure of the system is displayed in Figure 2, which consists of two LFM signals and the data packet. While the first LFM signal acts as the synchronization header as well as the first reference for Doppler estimation, the second one is used as the second reference signal for Doppler estimation with a fixed interval between them. Considering the precision of Doppler estimation as well as the communication efficiency, the length of the fixed interval \(T_{tp}\) is set to be ten times the length of the LFM signal \(T_{syn}\). Meanwhile, a protection interval was inserted between the second LFM signal and the following data packet to avoid interference, the length of which \(T_{guard}\) equals the length of the  
be obtained by performing cross-correlation and then measuring the real interval \(T_{rp}\) of two correlation peaks associated with these two LFM signals. As the Doppler time domain expansion is equivalent to the degree of signal contraction or expansion [10], the Doppler factor can be calculated according to the following equation:  
\[\Delta\approx\frac{T_{rp}}{T_{tp}}-1. \tag{1}\]  
Generally, after estimating the Doppler, a resampling calculation can be directly used to compensate for it. As mentioned above, while it is pretty convenient to perform resampling in an offline manner by means of computation software such as Matlab, from the viewpoint of practical modem design the implementation of resampling poses significant difficulties for the microprocessor because of the real-time computational complexity involved. Considering that adjusting the AD sampling rate is equivalent to resampling the received signal, a novel Doppler correction approach, by directly tuning the AD sampling rate, is proposed to reduce the real-time computational complexity of the microprocessor and thus facilitate hardware implementation.  
Specifically, the total duration of a frame is 6.8 s for the proposed modem, corresponding to 510,000 samples under a signal sampling rate of \(f_{\mathrm{s}}\) = 75 K sps. With the traditional principle of software resampling, the original signal sequence needs to first be up-sampled by an integer factor of \(I\), and then the output sequence is calculated by a linear interpolation algorithm according to the following equation [11]:  
\[y(m+1)=(1-It_{m+1})y_{1}(m+1)+It_{m+1}Iy_{2}(m+1), \tag{2}\]  
where \(y(m+1)\) is the output after resampling, and \(y_{1}\) and \(y_{2}\) are the adjacent points after up-sampling. One may conclude from the algorithm equations that the computational complexity of the resampling process algorithm is \(O(m^{2})\), which means a large calculation requirement considering the frame duration of the proposed system. Instead, by the proposed Doppler correction method of adjusting the AD sampling rate, the Doppler compensation can be directly fulfilled at the same time as the analog-to-digital conversion process; thus, no additional calculation is needed in the microprocessor for the Doppler correction. In other words, the proposed hardware resampling scheme will enable the adoption of a low-cost microprocessor with a relatively low calculation capability and small memory space.