## 2 Model Using a Spread Spectrum Based on Turbo Equalization  
In the transmitter, as shown in Figure 1, the channel is coded through the (\(N\), \(k\), \(m\)) convolutional encoder and then an interleaving process is conducted to change the burst error into the random error. To spread the spectrum, a PN spread process, in which the PN code is multiplied by a coded signal directly, is conducted, and then PN code is transmitted through modulation. In the receiver, the multiple path effect is removed through the equalizer after modulation, and then PN de-spreading is conducted to make the spread spectrum data into the original spectrum. At the receiver side, as shown in Figure 1, the received signal distorted by multiple path channels is compensated by estimating channels and calculating a Doppler's offset value using the frequency compensation algorithm and \(r_{T}(n)\), which is the training data portion [13]. \(f_{d}\), which is a frequency compensation value, is transferred to the RAKE process. \(r_{d}(n)\), which is the data signal among the symbols received at the RAKE receiver, compensates the frequency using a frequency compensation value \(f_{d}\) and then is input to the turbo equalizer after the RAKE process. The RAKE process is as follows: The signal received at the RAKE receiver increases error due to the effect of fading, and induces interference between signals due to time delay. Thus, the RAKE receiver delays the signal arriving at the receiver through multipath as much as the chip length \(T_{c}\) of the PN code, thereby summing the calculated power of the received signal through the multipath. This process is not to sum all signals  
Figure 1: Turbo equalizer transceiver based on RAKE receiver: (**a**) Transmitter; (**b**) Receiver. delayed as much as \(T_{c}\), but only signals whose value is more than the threshold value from each of the branches are reflected to the output signal. The reason for this is that low-level signals whose value is lower than the threshold value can influence as an error component when producing a signal output. The threshold value is set to the second largest value after the largest value in the correlated values after de-spreading is conducted at each of the branches. Previous work [12] related to the successive interference cancelation (SIC) method, it required perfect channel estimation. Without perfect channel estimation, it cause performance degraded severely. Aspect to structure of RAKE receiver fields previous works, the receiver structure is very simple such as soft decision Viterbi decoder. In this paper, we employ turbo equalization technique combined with RAKE model to improve error performance. DFE as an outer codes and BCJR decoder as an inner codes, equalizer and decoder are connected through the interleaving and de-interleaving that update each other's information repeatedly. Iteratively exchange probabilistic information between inner decoder and outer decoder makes the error rates significantly. The proposed RAKE-based turbo equalization technique improves performance by addressing a drawback of the existing RAKE-based model, as it applies the phase shift keying (PSK) technique. When the underwater channel environment is expressed with the tap delay line according to multipath, the RAKE structure selects and utilizes the optimum channel taps. The receive signal due to time delay passes through the PN de-spreading process to remove PN components using as many \(T_{c}\) taps as the number of PN code bits. A correlation is calculated by re-multiplying the frequency compensation value \(f_{d}\) at each of the taps by the PN code used for spread spectrum at the transmitter side. This operation includes the PN de-spreading procedure as well. If the PN code is not delayed for the ideal amount of time, the largest correlation value is obtained. Otherwise, a very small correlation value is obtained.