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Effective solutions should be devised to handle the effects of shadow zones in Underwater Wireless Sensor Networks (UWSNs). An adaptive topology reorganization scheme that maintains connectivity in multi-hop UWSNs affected by shadow zones has been developed in the context of two Spanish-funded research projects. A mathematical model has been proposed to find the optimal location for sensors with two objectives: the minimization of the transmission loss and the maintenance of network connectivity. The theoretical analysis and the numerical evaluations reveal that our scheme reduces the transmission loss under all propagation phenomena scenarios for all water depths in UWSNs and improves the signal-to-noise ratio.

Underwater Wireless Communication Networks (UWCNs) are formed by sensors and Autonomous Underwater Vehicles (AUVs) interacting together to perform specific underwater applications such as collaborative monitoring or surveillance [

Shadow zones cause high bit error rates, losses of connectivity and dramatically impact communications performance. Some experiments show that for high frequencies signal levels are typically at least 40 dB less than those at the edges of the shadow zone [

For these reasons, in this paper we focus on communication reliability in the presence of shadow zones. We propose a distributed adaptive topology reorganization scheme that alleviates the effects of energy limitations and is able to maintain connectivity between sensor nodes in multi-hop three-dimensional UWSNs in the presence of shadow zones. Besides, it is able to estimate when the shadow zones have disappeared using double sensor units to restablish communication very quickly through the original acoustic wireless links. We study the effects of the proposed scheme in shallow (depth up to 100 m) and deep water. A two-path Rayleigh fading channel model and different propagation phenomena are considered: shallow water, deep water with convergence zones, deep water with deep sound channel and shallow or deep water with shadow zones.

According to the number of links in the three-dimensional UWSN affected by the shadow zone, three different cases have been introduced. In this paper we have extended our work in [

The theoretical analysis and the numerical evaluations reveal that the average transmission loss values are reduced significantly under all propagation phenomena for all water depths in UWSNs when the optimal locations are computed and the communication between sensor nodes is again restablished outside the shadow zone. The average SNR values have also improved significantly and are maintained for all frequencies.

The remainder of the paper is organized as follows: In Section 2, we discuss the related work. In Section 3, we analyze our system model. In Section 4, we state the location optimization problems and propose nonlinear programming (NLP) formulations. In Section 5 we present our numerical results. Finally, we draw the conclusions in Section 6.

Shadow zones represent a serious obstacle for good communication in UWSNs, because they cause network partition. Therefore, the proposal of solutions to handle their effects has been encouraged [

In addition, in [

In our proposed scheme sensor nodes are double units operating as a single sensor; they are decoupled into two sensor nodes in the presence of a shadow zone. One sensor node remains in the same position and estimates, as opposed to SZODAR [

Several papers have proposed options related to location optimization of sensor nodes underwater. In [

We consider a three-dimensional underwater sensor network for environmental monitoring (see

We consider the example of the tree-like topology shown in ^{4} $, whereas the cost of software modems that use generic hardware (off-the-shelf configuration) is around 10^{2} $; this cost decrease facilitates the deployment of sensor nodes to form underwater acoustic sensor networks. The double sensor nodes operate as a single sensor when the underwater communication is reliable. This fact changes in the presence of shadow zones.

Each intermediate node _{i}_{i i}_{+1} towards one-hop neighbor _{i}_{+1} is affected by the presence of a shadow zone computing the transmission loss _{i i}_{+1} [_{i i}_{+1}(_{i i}_{+1}(_{shadow zone}_{i i}_{+1}(_{shadow zone}

We distinguish between three different cases according to the number of links in the underwater sensor network affected by the shadow zone:

Case 1: Only the uplink _{i i}_{+1} between _{i}_{i}_{+1} is located in the shadow zone.

Case 2: The uplink _{i i}_{+1} between _{i}_{i}_{+1} and the uplinks _{(}_{i-}_{1)}_{k i}_{(}_{i-}_{1)}_{k}_{i}_{i}

Case 3: The uplink _{i i}_{+1} between _{i}_{i}_{+1} and the uplinks _{(}_{i}_{-1)}_{k i}_{(}_{i-}_{1)}_{k}_{i}, l_{(}_{i-}_{2)}_{k i-}_{1} between _{(}_{i-}_{2)}_{k}, ∀k_{(}_{i-}_{1)}_{k}_{(}_{i-x}_{)}_{k i-x}_{+1} between _{(}_{i-}_{x)}_{k}_{(}_{i-x}_{+1)}_{k}

_{i}

We assume that sensor nodes are located in a grid (see

In this case under the presence of a shadow zone the sensor node _{i}_{i}_{→1} and _{i}_{→2} as shown in _{i}_{→1} remains in the same location as the node _{i}_{i}_{→2} We formulate this problem as a Nonlinear Program (NLP).

We introduce the following notation:

_{i}_{+1} = (_{i}_{+1}, _{i}_{+1}, _{i}_{+1}) is the location of node _{i}_{+1}.

_{i}_{→2} = (_{i}, y_{i}, z_{i}_{→2}) is the new location of node _{i}_{→2}.

_{MAX}

_{Th}

_{i}_{→2 i}_{+1} refers to the transmission range of the acoustic link between nodes _{i}_{→2} and _{i}_{+1} expressed in meters.

α represents the absorption coefficient and has the units dB/Km.

_{sz}_{−}_{start}_{i}, y_{i}, z_{sz}_{−}_{start}_{sz}_{−}_{end}_{i}, y_{i}, z_{sz}_{−}_{end}_{i}, y_{i}_{sz}_{−}_{start}_{sz}_{−}_{end}_{sz}_{−}_{end}_{sz}_{−}_{start}

_{Bw}_{i}_{→2}.

_{Th}

_{i}, x

_{i}

_{+1},

_{i}, y

_{i}

_{+1},

_{i}

_{+1},

_{MAX},TL

_{TH}, α, χ

_{sz}

_{–}

_{start}, z

_{sz}

_{–}

_{end}, E

_{bw}, E

_{th}

_{i}

_{→2}∈ [0,

_{i}

_{→2 i}

_{+1}∈

^{+}

_{i}

_{→2 i}

_{+1}=

_{i}

_{→2 i}

_{+1}+

_{i}

_{→2 i}

_{+1}10

^{−3}+

_{i}_{→2} that minimizes the transmission loss and preserves the connectivity with node _{i}_{+1} preventing from network partition.

The absorption coefficient α is computed as derived in [_{i}, i^{2}.(_{b}/N_{0}_{Γ}(_{0}_{0}_{0}^{2}].(_{b}/N_{0}_{b}/N_{0}

Constraint (2) imposes that the transmission range should be lower than a threshold to ensure connectivity. Constraint (3) expresses that the transmission loss should be lower than a transmission loss threshold, that is, the maximum propagation loss for properly receiving the transmitted signal.

The SNR of an emitted underwater signal at the receiver can be expressed in dB by the passive sonar _{Th}

The signal level _{t}_{t}

In deep water the

We consider five different channel models:

Shallow water.

Deep water with convergence zones.

Deep water with deep sound channel.

Shallow water with shadow zones.

Deep water with shadow zones.

Constraint (4) imposes that the sensor node _{i}_{→2} should be located outside the shadow zone.

Constraint (5) states that the energy consumed by the electronically controlled engine to move the sensor to the optimal position should be lower than a threshold. It is defined as [_{Bw}_{Bw}_{s}

In this case under the presence of a shadow zone the sensor node _{i}_{i}_{→1} and _{i}_{→2}, as shown in _{i}_{→1} and _{i}_{→2} using NLP. Since the topology is tree-like, we assume several nodes _{(}_{i-}_{1)}_{k}_{i}_{i}_{→1} and _{(}_{i-}_{1)}_{k}_{i}_{→2} and _{i}_{+1} on the other hand should be maintained. The optimal location for the node _{i}_{→2} is obtained solving the _{i}_{→1}.

We define:

_{i}_{→1} = (_{i}, y_{i}, z_{i}_{→1}) is the new location of node _{i}_{→1}.

_{(}_{i-}_{1)}_{k}_{(}_{i-}_{1)}_{k}, y_{(}_{i-}_{1)}_{k}, z_{(}_{i-}_{1)}_{k}_{(}_{i-}_{1)}_{k}

_{i}, x

_{(}

_{i}

_{−1)}

_{k}, y

_{i}, y

_{(}

_{i}

_{−1)}

_{k}, z

_{(}

_{i}

_{−1)}

_{k}, H, R

_{MAX},TL

_{Th}

_{sz}

_{–}

_{start}, z

_{sz}

_{–}

_{end}, E

_{bw}, E

_{Th}

_{i}

_{→1}∈ [0,

_{(}

_{i}

_{−1)}

_{k i}

_{→1}∈

^{+}

_{k}TL

_{(}

_{i}

_{−1)}

_{k i}

_{→1}

The objective function of problem _{i}_{→1} that minimizes the transmission loss of the link _{(}_{i-}_{1)}_{k i}_{(}_{i-}_{1)}_{k}

Constraint (12) imposes that the transmission range should be lower than a threshold to ensure connectivity. Constraint (13) expresses that the transmission loss should be lower than a transmission loss threshold. Constraint (14) imposes that the sensor node _{i}_{→1} should be located outside the shadow zone. Constraint (15) states that the energy consumed by the electronically controlled engine to move the sensor to the optimal position should be lower than a threshold.

In this case the sensor node located at the lowest depth in the shadow zone _{i}_{i}_{→1} and _{i}_{→2} as shown in

The optimal placement for node _{i}_{→2} is obtained solving the _{i}_{→1} should move to (_{i}, y_{i}, z_{sz-end}^{+} is a very small value, that is, _{i}_{→1} moves vertically downwards outside the shadow zone. In this case, the connectivity with the nodes _{(}_{i-}_{1)}_{k}_{(}_{i-}_{1)}_{k}_{(}_{i-}_{1)}_{k}_{→1} and _{(}_{i}_{-1)}_{k}_{→2}. The node _{(}_{i-}_{1)}_{k}_{→2} remains in the same location as node _{(}_{i-}_{1)}_{k}_{(}_{i-}_{1)}_{k}_{→1}. The data sensed by _{(}_{i-}_{1)}_{k}_{→2} is sent through a wire between _{(}_{i-}_{1)}_{k}_{→2} and _{(}_{i-}_{1)}_{k}_{→1} to maintain communication inside the shadow zone. Generally speaking, the same process should be repeated for all the nodes down in the hierarchy _{(}_{i-x}_{)}_{k}_{(}_{i}_{-}_{x}_{)}_{k}_{→1} and _{(}_{i-x}_{)}_{k}_{→2}. The node _{(}_{i-x}_{)}_{k}_{→2} remains in the same location as node _{(}_{i}_{-}_{x}_{)}_{k}_{(}_{i-x}_{)}_{k}_{→1}. The data sensed by _{(}_{i-x}_{)}_{k}_{→2} is sent through a wire between _{(}_{i}_{-}_{x}_{)}_{k}_{→2} and _{(i-x)k→1} to maintain communication inside the shadow zone.

If the node _{(}_{i-x}_{+1)}_{k}_{→1} has already moved to a new location outside of the shadow zone and node _{(}_{i-x}_{)}_{k}_{→1}does not know its depth _{(}_{i-x}_{+1)}_{k}_{→1}, node _{(}_{i-x}_{)}_{k}_{→1} can move to (_{(}_{i-x}_{)}_{k}, y_{(}_{i-x}_{)}_{k}, z_{sz-end}_{(}_{i-x}_{+1)}_{k}_{→1} to find out the depth and afterwards compute its optimal location using this information.

Finally, the data sent towards the suface sink travels through the following nodes in the path using hierarchical routing: _{(}_{i-x}_{)}_{k}_{→2}, _{(}_{i-x}_{)}_{k}_{→1}, _{(}_{i-x}_{+1)}_{k}_{→1},…, _{(}_{i-}_{1)}_{k}_{→1}, _{i}_{→1}, _{i}_{→2}, _{i}, s_{i}_{+1},…, and the surface sink.

Generally speaking, the optimal location of the node _{(}_{i-x}_{)}_{k}_{→1} can be determined as follows. We define:

_{(}_{i-x}_{)}_{k}_{→1} = (_{(}_{i-x}_{)}_{k},y_{(}_{i-x}_{)}_{k},z_{(}_{i-x}_{)}_{k}_{→1}),∀_{(}_{i-x}_{)}_{k}_{→1}.

_{(}_{i-x}_{+1)}_{k}_{→1} = (_{(}_{i-x}_{+1)}_{k},y_{(}_{i-x}_{+1)}_{k},z_{(}_{i-x}_{+1)}_{k}_{→1}) is the new already established location of node _{(}_{i-x}_{+1)}_{k}_{→1} for a particular _{(}_{i-x}_{+1)}_{k}

_{(}_{i-x-}_{1)}_{k}_{(}_{i-x}_{-1)}_{k},y_{(}_{i-x-}_{1)}_{k},z_{(}_{i-x-}_{1)}_{k}_{(}_{i-x}_{-1)}_{k}_{(}_{i-x}_{-1)}_{k}

_{(}

_{i}

_{−}

_{x}

_{)}

_{k}, x

_{(}

_{i}

_{−}

_{x}

_{+1)}

_{k}, x

_{(}

_{i}

_{−}

_{x}

_{−1)}

_{k}, y

_{(}

_{i}

_{−}

_{x}

_{)}

_{k}, y

_{(}

_{i}

_{−}

_{x}

_{+1)}

_{k}, y

_{(}

_{i}

_{−}

_{x}

_{−1)}

_{k}

_{(}

_{i}

_{−}

_{x}

_{+1)}

_{k}, z

_{(}

_{i}

_{−}

_{x}

_{−1)}

_{k}, H, R

_{MAX},TL

_{Th}

_{sz}

_{–}

_{start}, z

_{sz}

_{–}

_{end}, E

_{bw}, E

_{Th}

_{(}

_{i}

_{−}

_{x}

_{)}

_{k}

_{→1}∈ [0,

_{(}

_{i}

_{−}

_{x}

_{)}

_{k}

_{→1 (}

_{i}

_{−}

_{x}

_{+1)}

_{k}

_{→1}∈

^{+}

_{(}

_{i}

_{−}

_{x}

_{−1)}

_{k}

_{(}

_{i}

_{−}

_{x}

_{)}

_{k}

_{→1}∈

^{+}

_{(}

_{i}

_{−}

_{x}

_{)}

_{k}

_{→1 (}

_{i}

_{−}

_{x}

_{+1)}

_{k}

_{→1}

_{k}

_{(}

_{i}

_{−}

_{x}

_{−1)}

_{k}

_{(}

_{i}

_{−}

_{x}

_{)}

_{k}

_{→1},

_{(}

_{i}

_{−}

_{x}

_{)}

_{k}

_{→1 (}

_{i}

_{−}

_{x}

_{+1)}

_{k}

_{→1})

_{(}_{i-x}_{)}_{k}_{→1} that minimizes the transmission loss of the link _{(}_{i-x}_{)}_{k}_{→1(}_{i-x}_{+1)}_{k}_{→1} and preserves the connectivity with node _{(}_{i-x}_{+1)}_{k}_{→1} preventing from network partition. The objective function 2 of problem _{(}_{i-x}_{)}_{k}_{→1}that minimizes the transmission loss of the link _{(}_{i-x}_{)}_{k}_{→1(}_{i-x}_{+1)}_{k}_{→1} or the link _{(}_{i-x}_{-1)}_{k}_{(}_{i-x}_{)}_{k}_{→1} with the highest transmission loss value and preserves the connectivity with node _{(}_{i-x}_{+1)}_{k}_{→1} and nodes _{(}_{i-x-}_{1)}_{k}_{(}_{i-x-}_{1)}_{k}_{(}_{i-x}_{)}_{k}_{→1} should be located outside the shadow zone. Constraint (23) states that the energy consumed by the electronically controlled engine to move the sensor to the optimal position should be lower than a threshold.

Now we study the performance of the proposed scheme under the presence of shadow zones via numerical evaluations. We distinguish between shallow and deep water. The five different channel models considered appear in Section 4. The parameters used in our evaluation are listed in

The whole seabed is divided into a 2D square grid of equal sizes ^{3} for shallow water and of 40,000 × 40,000 × 5,000 m^{3} for deep water. In shallow water, sensor nodes are located following a hierarchical structure at the depth levels of 25, 50, 75 and 90 m. In deep water, we study the communication between sensor nodes located following a hierarchical structure at the depth levels of 300, 350, 400 and 450 m.

We consider realistic cases where shadow zones can influence the propagation of sensors.

Now we compute the transmission loss threshold _{Th}

According to [^{ψdB}^{(}^{d}^{f}^{)/10}, _{N}

Based on the bit error rate _{b}

For ARQ, the cyclic redundandy check (CRC) block code detection mechanism is deployed. Assuming detection of all possible packet errors, the PER of a single transmission for a packet of

For FEC convolutional codes, the PER of a single transmission for a packet of _{b}_{c}_{c}

The relationship between the PER and _{Th}_{Th}_{Th}_{Th}

The FEC convolutional code with _{c}_{Th}^{−2} the maximum _{Th}

Now we analyze the energy consumed by the electronically controlled engine to move the sensors affected by the shadow zone to the optimal position. _{Th}_{Bw}

We consider a sensor node _{i}_{i}, y_{i}, z_{i}_{i}_{+1} is located at (_{i}_{i}_{i}_{+1}), _{i}_{+1} < _{i}_{i i}_{+1} is affected by a shadow zone with height (_{sz}_{−}_{end}_{sz}_{−}_{start}_{i}_{sz}_{−}_{end}_{i}_{+1} < _{sz}_{−}_{start}_{i}_{i}_{→1} and _{i}_{→2} and the optimal location of node _{i}_{→2} has been found using NLP solving the optimization problem

_{i i}_{+1} (between _{i}_{i}_{+1}) affected by the shadow zone (shallow water + shadow zone or deep water + shadow zone). _{i}_{i}_{→2} is found outside the shadow zone using our mathematical model; the transmission loss for the acoustic link _{i}_{→2 i}_{+1} (between _{i}_{→2} and _{i}_{+1}) (shallow water (optimal), deep water + convergence zone (optimal) or deep water + deep sound channel (optimal) has also been computed. The average transmission loss is increased when the frequency is increased and is higher for deep water + shadow zone than for shallow water + shadow zone. It is also higher for deep than shallow water. The transmission loss values are higher than the transmission loss threshold for deep water+shadow zone, which means that the transmitted signal will not be properly received. The average transmission loss values are reduced significantly when the optimal locations are computed and the communication between sensor nodes is again restablished outside the shadow zone. The maximum transmission loss improvement is of 4.9 dB for shallow water, of 45.1 dB for deep water + convergence zone and of 42.9 dB for deep water + deep sound channel. Therefore, we can conclude that using our mathematical model deep water + convergence zone shows the best improvement in the diminishment of the transmission loss.

We consider a sensor node _{i}_{i}, y_{i}, z_{i}_{i}_{+1} is located at (_{i}_{i}_{i}_{+1}), _{i}_{+1} < _{i}_{(}_{i-}_{1)}_{k}_{i}_{i}_{(}_{i}_{-1)}_{k}_{(}_{i}_{-1)}_{k}_{i}, k_{i i}_{+1} and _{(}_{i-}_{1)}_{k i}_{sz}_{−}_{end}_{sz}_{−}_{start}_{sz}_{−}_{start}_{i}_{sz}_{−}_{end}, z_{(}_{i}_{-1)}_{k}_{sz}_{−}_{end}, z_{i}_{+1} < _{sz}_{−}_{start}_{i}_{i}_{→1} and _{i}_{→2}. The optimal locations of node _{i}_{→2} and _{i}_{→1} have been found using NLP solving the optimization problems _{i}_{→1} (Case 2). For shallow water the value of _{sz}_{−}_{end}_{sz}_{−}_{start}_{(}_{i}_{-1)}_{k}_{sz}_{−}_{end}_{(}_{i-}_{1)}_{k i}_{sz}_{−}_{end}_{sz}_{−}_{start}_{(}_{i-}_{1)}_{k i}_{(}_{i-}_{1)}_{k}_{i}_{→1} with the highest value is minimized for shallow water. The transmission loss values are not affected by the shadow zone height but they are increased with the frequency to 41 dB for _{(}_{i-}_{1)}_{k i}_{sz}_{−}_{end}_{sz}_{−}_{start}_{sz}_{−}_{end}_{sz}_{−}_{start}_{(}_{i}_{-1)}_{k}_{sz}_{−}_{end}_{(}_{i-}_{1)}_{k i}_{(}_{i-}_{1)}_{k}_{i}_{→1} with the highest value is minimized for different propagation phenomena (deep water + deep sound channel, deep water + convergence zone). Deep water + convergence zone is the underwater propagation phenomena that suffers lower transmission loss and is more appropriate for underwater communication.

The transmission loss values are especially decreased with the shadow zone height for the frequency of 10 KHz; the reason is that the depth of the optimal location is increased when the shadow zone height is increased (_{sz}_{−}_{end}

We consider a sensor node _{i}_{i}, y_{i}, z_{i}_{(}_{i-}_{1)}_{k}_{i}_{i}_{(}_{i}_{-1)}_{k}_{(}_{i}_{-1)}_{k}_{i}, k_{(}_{i-}_{2)}_{k}_{i}_{i}_{(}_{i}_{-2)}_{k}_{(}_{i}_{-2)}_{k}_{(}_{i}_{-1)}_{k}, k_{(}_{i-}_{3)}_{k}_{i}_{i}_{(}_{i}_{-3)}_{k}_{(}_{i}_{-3)}_{k}_{(}_{i}_{-2)}_{k}, k_{(}_{i-}_{1)}_{k i}, l_{(}_{i-}_{2)}_{k}_{(}_{i-}_{1)}_{k}, l_{(}_{i-}_{3)}_{k}_{(}_{i-}_{2)}_{k}_{sz}_{−}_{end}_{sz}_{−}_{start}_{sz}_{−}_{start}_{i}_{sz}_{−}_{end}, z_{sz}_{−}_{start}_{(}_{i}_{-1)}_{k}_{sz}_{−}_{end}, z_{sz}_{−}_{start}_{(}_{i}_{-2)}_{k}_{sz}_{−}_{end}, z_{(}_{i}_{-3)}_{k}_{sz}_{−}_{end}_{i}_{i}_{→1} and _{i}_{→2}. Nodes _{(}_{i-}_{1)}_{k}_{(}_{i-}_{1)}_{k}_{→1} and _{(}_{i-}_{1)}_{k}_{→2}. Nodes _{(}_{i-}_{2)}_{k}_{(}_{i-}_{2)}_{k}_{→1} and _{(}_{i-}_{2)}_{k}_{→2}. Node _{i}_{→1} is relocated to (_{i}, y_{i}, z_{sz-end}^{+}is a very small value, _{sz}_{−}_{end}_{sz}_{−}_{end}_{(}_{i-}_{1)}_{k}_{→1} have been found with NLP solving the optimization problem _{(}_{i-}_{2)}_{k}_{→1} have been found with NLP solving the optimization problem

We consider four hierarchical levels with one node _{i}_{(}_{i-}_{1)}_{k}_{(}_{i-}_{2)}_{k}_{(}_{i-}_{3)}_{k}_{(}_{i-}_{1)}_{k i}, l_{(}_{i-}_{2)}_{k}_{(}_{i-}_{1)}_{k}, l_{(}_{i-}_{3)}_{k}_{(}_{i-}_{2)}_{k}

In this paper, a distributed adaptive topology reorganization scheme that maintains connectivity in multi-hop UWSNs affected by shadow zones has been developed in the context of two Spanish-funded research projects. It alleviates the effect of energy limitations and is able to maintain network connectivity in multi-hop three-dimensional UWSNs in the presence of shadow zones solving a location optimization problem.

Three different cases have been determined according to the number of links in the three-dimensional UWSN affected by the shadow zone. A mathematical model has been developed for each case to find the optimal placement for the sensor nodes, whose ongoing communications are being disturbed.

The average transmission loss values are reduced significantly (especially for deep water + convergence zone) when the optimal locations are computed and the communication between sensor nodes is again reestablished outside the shadow zone. Shallow water shows lower transmission loss values in comparison with the other propagation phenomena. Deep water + convergence zone suffers lower transmission loss values than deep water + deep sound channel and is more appropriate for underwater communication. Only in deep water the transmission loss values are especially decreased with the shadow zone height for the frequency of 10 KHz and only very slightly decreased for the frequencies of 0.1 KHz and 1 KHz; the transmission loss values don't vary with the shadow zone height in shallow water.

The average SNR values in the presence of shadow zones are negative, which indicates that the signal is below the noise level and transmission loss, and it can't be properly recovered. The average SNR values are increased significantly when the optimal locations are computed and the communication between underwater sensors is again reestablished outside the shadow zone. Furthermore, the improved SNR values are maintained for all frequencies. With shallow water the SNR values are better because in shallow water the transmission loss values are lower. The SNR values are higher with deep water + convergence zone than with deep water + deep sound channel. Nevertheless, in all cases the SNR loss values are increased outside the shadow zones.

This work was supported by the Spanish Government through projects TSI2006-13380-C02-01 and TSI2007-66637-C02-01.

Shadow zone formation beneath the mixed layer when sound velocity monotically decreases with depth.

Architecture for a 3D underwater sensor network.

Scenario in the 3D UWSN with a shadow zone (Case 1).

Scenario in the 3D UWSN with a shadow zone (Case 2).

Scenario in the 3D UWSN with a shadow zone (Case 3).

2D Square grid.

Corresponding ray trace for a source depth of 90 m.

Corresponding ray trace for a source depth of 75 m.

Corresponding ray trace for a source depth of 50 m.

Corresponding ray trace for a source depth of 450 m.

Corresponding ray trace for a source depth of 400 m.

Corresponding ray trace for a source depth of 350 m.

PER as a function of transmission loss for shallow water.

PER as a function of transmission loss for deep water.

Energy consumption in the sensor displacement.

Average transmission loss of a link as a function of frequency in shallow and deep water.

Average transmission loss of a link as a function of the shadow zone height in deep water.

Average SNR as a function of frequency in shallow and deep water.

Parameter Values.

Shallow water: 100 m | |

Deep water: 5,000 m | |

Shallow water: 16,000 × 16,000 × 100 m^{3} | |

Deep water: | |

40,000 × 40,000 × 5,000 m^{3} | |

25 | |

238 bytes | |

6 Kbps | |

15 °C | |

8 | |

35 ppt | |

_{t} |
Shallow water: 12 W |

Deep water: 40 W | |

47.69 dB | |

1500 m/s | |

0.5 m/s | |

_{Bw} |
10 W |

0.01 | |

_{MAX} |
Shallow water: 5,000 m |

Deep water: 11,000 m | |

_{Th} |
1,500 J |

_{Th} |
Shallow water: 112.5 dB |

Deep water: 129 dB |