## 2 System Model  
Figure 1 shows the structure of the weighted multi-band FSK transceiver model with a DSSS. The turbo encoder has a rate of one-third. Information bits, \(K\), are passed though the encoder. After encoding, \(N\) coded bits are generated, and they are input to the interleaving block. The interleaving shuffles the input sequence to improve the performance of the encoder against noisy burst errors [15]. The interleaving output is then packetized with preamble. The packet has \(N_{p}(=N+n)\) bits, consisting of \(N\) bits of turbo-coded data, \(C=\{c_{0},\,c_{1},c_{2}\cdots,c_{N-1}\}\), and \(n\) bits of preamble data, \(P=\{p_{0},\,p_{1},p_{2}\cdots,p_{n-1}\}\). Preamble data are added to the encoded data to detect the start of the packet. After spreading by \(N_{c}\) chips, the Tx subband processing block in Figure 1 divides the bit column of the packet data into a group, and frequencies are allocated according to the group. In multi-band configurations, different \(N_{b}\) bands are used to combine and propagate \(M\)-FSK modulated signals. Orthogonal \(M\)-FSK modulation is a tone-based communication method that uses a fraction of the available bandwidth at any given time. Data are modulated at discrete subcarrier frequencies and one subcarrier \(f_{k,i}\), where \(i=[1:M]\) and \(k=[1:N_{b}]\), is transmitted at one moment in time for a specific duration, and the symbol of time is \(T_{s}\). \(M\) is the number of subcarriers required and is known as the modulator order. The transmitted multi-band \(M\)-FSK signal can be expressed by Equation (1):  
\[s(t)=\sum_{k=1}^{N_{b}}\sum_{i\in M}exp(j2\pi f_{k,i}t)\hskip 28.452756 pt0\leq t \leq T_{s} \tag{1}\]  
where \(j=\sqrt{-1}\), \(\{f_{k,i}\}\) represents the \(i\)-th tone at the \(k\)-th band. The received signal is expressed by Equation (2):  
\[r(t)=\sum_{l=1}^{L}s(t)h_{l}(t)+\eta(t) \tag{2}\]  
where \(l\) represents the \(l\)-th multi-path among a total of \(L\) multi-paths. \(h_{l}(t)\) is the channel response coefficient in path \(l\), and \(\eta(t)\) is Gaussian noise. The transmitter sends a packet that begins with a preamble sequence, and the receiver compares the received sequence with the preamble sequence in order to locate the start of packet. The comparison is effectively performed by correlating the received sequence with the preamble sequence [16]. When we correlate the received sequence with a reference preamble symbol, the correlation function \(C(t)\) is shown in Equation (3) [17]:  
\[C(t)=\sum_{m}r_{p}(t)*P \tag{3}\]  
where \(r_{p}(t)\) denotes the received preamble symbol, \(P\) denotes the reference preamble symbol. When the preamble and received sequence exactly align with each other, the correlation function, \(C(t)\), reaches the maximum value, and the start of the packet is located. The Rx sub-band processing block is a non-coherent FSK demodulator. The non-coherent receiver typically employs energy detection for each subcarrier. It separates the frequency band by a bandpass filter and detects the highest energy by an envelope detector for different frequencies. After Rx sub-band processing, due to reflections from multiple obstacles in the underwater environment, a RAKE receiver is designed to counter the effects of multi-path fading for spread spectrum communications. The RAKE receiver consists of multiple correlators, in which the receive signal is multiplied by time-shifted versions of a locally generated spreading code sequence. The delays in each received  
Figure 1: The structure of the multi-band FSK transceiver model with a DSSS. signal are compensated and are fed to the combiner, integrator, and comparator, which combines them suitably with different appropriate time delays. In particular, the RAKE receiver architecture allows for an optimal combining of energy received over paths with different [18].