# Double-Scale Adaptive Transmission in Time-Varying Channel for Underwater Acoustic Sensor Networks
## 3 Double-Scale Adaptive Transmission Mechanism for UASNs
### Adaptive Transmission Framework  
To improve energy efficiency and reliability of underwater acoustic communication, a double-scale adaptive transmission mechanism is proposed based on the fluctuation characteristics of underwater channel, as shown in Figure 3. The transmission framework consists of two parts, namely double-scale prediction and adaptive transmission. In double-scale prediction, the historical channel state series is decomposed into large-scale and residual series, which will be predicted by a novel \(k\)-nearest neighbor search algorithm with sliding window and auto-regressive algorithm, respectively. In adaptive transmission, an energy-efficient transmission algorithm is designed to solve the problem of long-term modulation and coding optimization.  
To reduce the complexity of scheduling, the transmitter of a CH or a CM node uses the same modulation and coding mode in a large-scale time. In this way, the modulation and coding mode only needs to be scheduled once for each large-scale period. For the convenience of description, epoch and slot are used to refer to large-scale and small-scale time, respectively. A large-scale epoch consists of \(N_{large}\) slots, as shown in Figure 4.  
In detail, the large-scale decision aims to predict large-scale channel states and determine the modulation and coding mode for each large-scale epoch. As it is difficult to predict the future channel state in each slot, the average channel state of each large-scale epoch in the future is predicted for schedule. Large-scale channel state is defined as the average channel state in a large-scale epoch. Then, based on the present buffer state and predicted large-scale channel states, the modulation and coding mode in each future large-scale epoch will be scheduled.  
Then, given the scheduled modulation and coding mode, the small-scale decision operates to predict the channel state of the next slot and control the transmission power. To improve the accuracy of prediction, the channel state in each slot is predicted based on series decomposition.  
In a large-scale epoch, the average channel change should be less than a certain threshold \(D_{t}\), so that the same modulation and coding mode can be allocated for the slots in this large-scale epoch. Thus, the algorithm calculates the average time \(T_{large}\) required for channel state change \(D_{t}\) and takes \(T_{large}\) as the length of large-scale epoch. \(D_{t}\) is given as  
\[D_{t}=\frac{h_{max}-h_{min}}{2M}, \tag{11}\]  
Figure 4: Large-scale epoch and small-scale slot.  
Figure 3: Double-scale adaptive transmission mechanism.  
where \(h_{max}\) and \(h_{min}\) are the best channel state and worst channel state, respectively, and \(M\) is the number of modulation and coding modes.  
At the beginning of a slot, packets are sent by the transmitter. Before the end of the slot, an acknowledgment packet is sent from the receiver to the transmitter via an error-free channel, including the number of packets successfully decoded and the received signal-to-noise ratio (SNR) of each packet.