**4.1 Frequency dependent component of SNR**

The narrowband Signal-to-Noise-Ratio (SNR) observed at the receiver, assuming no multi-path or doppler losses is given by:

$$\text{SNR}(r, f, d, t, w, s, P\_{\text{tx}}) = \frac{SL\_{\text{projecture}}(P\_{\text{tx}}, \eta, DI)}{\text{PathLoss}(r, f, d, t) \sum \text{Noise}(f, w, s) \times B} \tag{8}$$

where B is the receiver bandwidth and the Signal Level (SL), PathLoss and Noise terms have been previously developed.

Taking the frequency dependent portion of the SNR from Equation 8, as developed by Stojanovic (2006), is the *PathLoss*(*r*, *f* , *d*, *t*) ∑ *Noise*(*f* , *w*,*s*) product. Since SNR is inversely

Communication Networks 17

Short-Range Underwater Acoustic Communication Networks 189

The impact of changes in range can be seen if the vehicles moved from 100 m to 500 m (at wind state 0 m/s), the optimum signal frequency to maintain highest SNR decreases from 38 kHz to ≈ 28 kHz, Figure 9(b). Reduction in signal frequency implies a potential reduction in absolute bandwidth and with that a reduction in data rate which needs to be managed. This will be investigated further in the next sub sections. Figure 10 (a) and (b) show the optimum signal frequency verses range up to 500 m for the various parameters; temperature and depth, within the Thorp and Fisher and Simmons Absorption Loss models as well as the wind in the Ambient Noise model. The optimum frequency, decreases with increasing range due to the dominating characteristic of the absorption loss. It can be seen in Figure 10(a) that as the range increases there is an increasing deviation between the two models and between the parameters within the Fisher and Simmons model. There is approximately a 2.5 kHz difference between the models themselves at 500 m and up to 6 kHz when temperature increases are included. When wind is included, Figure 10(b), there is a dramatic change in optimum signal frequency at very short ranges and this difference reduces substantially over the range shown. This is due to the increasing significance of the Absorption Loss term relative to the constant Ambient Noise term (as it is not range dependent), which reduces the affect of the Noise term and therefore the wind parameter. In both Figure 10(a) and (b), the Fisher and Simmons model provides higher optimum frequencies due to the more accurate inclusion of the relaxation

(a) Comparison of Absorption Loss Parameters (b) Comparison with changes in wind (from

Having established that at different ranges there is an optimum signal frequency that provides a maximum SNR, assuming constant transmitter power and projector efficiency, there is therefore an associated channel bandwidth with these conditions for different ranges. To determine this bandwidth a heuristic of 3dB around the optimum frequency is used. Following a similar approach to Stojanovic (2006) the bandwidth is calculated according to the frequency range using ±3dB around the optimum signal frequency *fo*(*r*) which has been chosen as the centre frequency. Therefore, the *fmin*(*r*) is the frequency when

Fig. 10. Optimum Frequency determined from frequency dependent component of

Ambient Noise Characteristics)

frequencies of boric acid and magnesium sulphate.

narrowband SNR

**4.2 Channel bandwidth**

proportional to *PathLoss*(*r*, *f* , *d*, *t*) ∑ *Noise*(*f* , *w*,*s*) factor, the <sup>1</sup> *PathLoss*(*r*, *<sup>f</sup>* ,*d*,*t*)*Noise*(*<sup>f</sup>* ,*w*,*s*) term is illustrated in the Figures 9 (a) for longer ranges and Figure 9 (b) for shorter ranges. The first of these figures, shows various ranges up to 10km using Thorps absorption model (spherical spreading) and has been presented by several authors (Chen & Mitra, 2007; Nasri et al., 2008; Sehgal et al., 2009; Stojanovic, 2006). Figure 9(b) highlights shorter ranges of 500 m and 100 m and also illustrates the variation between the Thorp and Fisher and Simmons absorption loss models developed in Section 3.2.2.

Fig. 9. Frequency Dependent component of narrowband SNR

These figures show that there is a signal frequency where the frequency dependent component of SNR is optimised assuming that the projector parameters, including transmitter power and projector efficiency behave uniformly over the frequency band. The black dot at the apex of each of the three curves based on the Thorp absorption model indicate this optimum point. The two absorption models present similar responses and optimum frequencies. There is a minor variation in optimum frequency at 100 m where the absorption coefficient has a significantly lower contribution. The impact that the Ambient Noise component has on optimum signal frequency is seen most dramatically at the 100 m range when the wind state is changed from 0 to 2 m/s, the optimal signal frequency changes from 38 kHz to 68 kHz. From a communication perspective, if two vehicles were operating at 100 m and 38kHz and the wind state changed from 0 m/s to 2 m/s, there is a reduction of 9dB in the frequency dependent component of SNR. This is not an absolute reduction in SNR as the projector parameters and in particular the transmitter power level has not been considered here. It does however indicate the significant impact that wind and wave action can play with data communication underwater, and in addition this reduced SNR value does not include any increased losses associated with the increase scattering that wave action can generate. The impact of shipping, found in the Ambient Noise term, is not included here as its effect is minor on signal frequencies above 10kHz. In Section 3.2.2 Figure 4, temperature variations were seen to have the most impact on the signal frequency associated with the ranges of interest. Figure 9(b) illustrates this difference in terms of the frequency dependent component of SNR. This is further explored in Figure 10(a) in terms of the signal frequency variations over range.

16 Will-be-set-by-IN-TECH

illustrated in the Figures 9 (a) for longer ranges and Figure 9 (b) for shorter ranges. The first of these figures, shows various ranges up to 10km using Thorps absorption model (spherical spreading) and has been presented by several authors (Chen & Mitra, 2007; Nasri et al., 2008; Sehgal et al., 2009; Stojanovic, 2006). Figure 9(b) highlights shorter ranges of 500 m and 100 m and also illustrates the variation between the Thorp and Fisher and Simmons absorption loss

> (a) Longer Ranges (b) Short Ranges with channel parameter variations

These figures show that there is a signal frequency where the frequency dependent component of SNR is optimised assuming that the projector parameters, including transmitter power and projector efficiency behave uniformly over the frequency band. The black dot at the apex of each of the three curves based on the Thorp absorption model indicate this optimum point. The two absorption models present similar responses and optimum frequencies. There is a minor variation in optimum frequency at 100 m where the absorption coefficient has a significantly lower contribution. The impact that the Ambient Noise component has on optimum signal frequency is seen most dramatically at the 100 m range when the wind state is changed from 0 to 2 m/s, the optimal signal frequency changes from 38 kHz to 68 kHz. From a communication perspective, if two vehicles were operating at 100 m and 38kHz and the wind state changed from 0 m/s to 2 m/s, there is a reduction of 9dB in the frequency dependent component of SNR. This is not an absolute reduction in SNR as the projector parameters and in particular the transmitter power level has not been considered here. It does however indicate the significant impact that wind and wave action can play with data communication underwater, and in addition this reduced SNR value does not include any increased losses associated with the increase scattering that wave action can generate. The impact of shipping, found in the Ambient Noise term, is not included here as its effect is minor on signal frequencies above 10kHz. In Section 3.2.2 Figure 4, temperature variations were seen to have the most impact on the signal frequency associated with the ranges of interest. Figure 9(b) illustrates this difference in terms of the frequency dependent component of SNR. This is further explored in Figure 10(a) in terms of the signal frequency variations over range.

*PathLoss*(*r*, *<sup>f</sup>* ,*d*,*t*)*Noise*(*<sup>f</sup>* ,*w*,*s*) term is

proportional to *PathLoss*(*r*, *f* , *d*, *t*) ∑ *Noise*(*f* , *w*,*s*) factor, the <sup>1</sup>

Fig. 9. Frequency Dependent component of narrowband SNR

models developed in Section 3.2.2.

The impact of changes in range can be seen if the vehicles moved from 100 m to 500 m (at wind state 0 m/s), the optimum signal frequency to maintain highest SNR decreases from 38 kHz to ≈ 28 kHz, Figure 9(b). Reduction in signal frequency implies a potential reduction in absolute bandwidth and with that a reduction in data rate which needs to be managed. This will be investigated further in the next sub sections. Figure 10 (a) and (b) show the optimum signal frequency verses range up to 500 m for the various parameters; temperature and depth, within the Thorp and Fisher and Simmons Absorption Loss models as well as the wind in the Ambient Noise model. The optimum frequency, decreases with increasing range due to the dominating characteristic of the absorption loss. It can be seen in Figure 10(a) that as the range increases there is an increasing deviation between the two models and between the parameters within the Fisher and Simmons model. There is approximately a 2.5 kHz difference between the models themselves at 500 m and up to 6 kHz when temperature increases are included. When wind is included, Figure 10(b), there is a dramatic change in optimum signal frequency at very short ranges and this difference reduces substantially over the range shown. This is due to the increasing significance of the Absorption Loss term relative to the constant Ambient Noise term (as it is not range dependent), which reduces the affect of the Noise term and therefore the wind parameter. In both Figure 10(a) and (b), the Fisher and Simmons model provides higher optimum frequencies due to the more accurate inclusion of the relaxation frequencies of boric acid and magnesium sulphate.

(a) Comparison of Absorption Loss Parameters (b) Comparison with changes in wind (from Ambient Noise Characteristics)

Fig. 10. Optimum Frequency determined from frequency dependent component of narrowband SNR

#### **4.2 Channel bandwidth**

Having established that at different ranges there is an optimum signal frequency that provides a maximum SNR, assuming constant transmitter power and projector efficiency, there is therefore an associated channel bandwidth with these conditions for different ranges. To determine this bandwidth a heuristic of 3dB around the optimum frequency is used. Following a similar approach to Stojanovic (2006) the bandwidth is calculated according to the frequency range using ±3dB around the optimum signal frequency *fo*(*r*) which has been chosen as the centre frequency. Therefore, the *fmin*(*r*) is the frequency when

Communication Networks 19

Short-Range Underwater Acoustic Communication Networks 191

Thus using the optimum signal frequency and bandwidths at 100 m and 500 m found in the Section 4.1 and 4.2, the maximum achievable error free channel capacities against range are shown in Figure 12. The signal frequency and channel bandwidth values for 100 m were *fo* = 37kHz and B=47kHz and for 500 m were *fo* = 27kHz and B=33kHz. These are significantly higher than values currently available in underwater operations(Walree, 2007), however they provide an insight into the theoretical limits. Two different transmitter power levels are used, 150dB re 1*μ*Pa which is approximately 10mW (Equation 1) and 140dB re 1*μ*Pa is 1mW. Looking at the values associated with the same power level in Figure 12, the higher channel capacities are those associated with the determined optimum frequency and bandwidth for that range as would be expected. The change in transmitter power, however, by a factor of 10, does not produces a linear change in channel capacity across the range. These variations are important to consider as minimising energy consumption will be critical for AUV operations. In general, current modem specifications indicate possible data rate capacities of less than 10kbps (LinkQuest, 2008) for modem operations under 500 m, well short of these theoretical limits. This illustrates the incredibly severe data communication environment found underwater and that commercial modems are generally not yet designed to be able to adapt to specific channel conditions and varying ranges. The discussion here is to understand the variations associated with the various channel parameters at short range

that may support adaptability and improved data transmission capacities.

Ptx=1mW, Fo=27kHz Ptx=1mW, Fo=37kHz Ptx=10mW, Fo=27kHz Ptx=10mW, Fo=37kHz

100 300 500




SNR (dB) Values -9dB -1dB

**Range (m)**

Achieving close to the maximum channel capacities as calculated in the previous section is still a significant challenge in underwater acoustic communication. The underwater acoustic channel presents significant multipaths with rapid time-variations and severe fading that lead to complex dynamics at the hydrophone causing ISI and bit errors. The probability of bit error, BER, therefore provides a measure of the data transmission link performance. In underwater systems, the use of FSK (Frequency Shift Keying) and PSK (Phase Shift Keying) have occupied researchers approaches to symbol modulation for several decades. One approach is using the simpler low rate incoherent modulation frequency hopping FSK

0

50

8dB 18dB

Fig. 12. Theoretical limit of Channel Capacity (kbps) verse Range

**4.4 BER in short range underwater acoustic communication**

6dB 16dB

100

150

**Maximum Channel Capacity Achievable (kbps)**

200

250

*PathLoss*(*r*, *d*, *t*, *fo*(*r*))*N*(*fo*(*r*)) − *PathLoss*(*r*, *d*, *t*, *f*))*N*(*f*) ≥ 3*dB* holds true and similarly for *fmax*(*r*) when *PathLoss*(*r*, *d*, *t*, *f*))*N*(*f*) − *PathLoss*(*r*, *d*, *t*, *fo*(*r*))*N*(*fo*(*r*)) ≥ 3*dB* is true. The system bandwidth B(r,d,t) is therefore determined by:

$$B(r,d,t) = f\_{\max}(r) - f\_{\min}(r) \tag{9}$$

Thus, for a given range, there exists an optimal frequency from which a range dependent 3dB bandwidth can be determined as illustrated in Figure 11. The changes discussed in Section 4.1, related to changes in the optimum signal frequency with changes in range and channel conditions such as temperature, depth and wind. These variations are reflected in a similar manner to the changes seen here in channel bandwidth and in turn will reflect in the potential data transmission rates. Figure 11 demonstrates that both the optimal signal frequency and the 3dB channel bandwidth decrease as range increases. The impact of changing wind conditions on channel bandwidth is significant, however as discussed wind and wave action will also include time variant complexities and losses not included here. Temperature increases show an increase in channel bandwidth, at ranges of interest, due to the reduction in absorption loss as temperature increases, which means some benefits in working in the surface layers. The discussion here highlights that the underwater acoustic channel is severely band-limited and bandwidth efficient modulation will be essential to maximise data throughput and essentially that major benefits can be gained when performing data transmission at shorter ranges or in multi-hop arrangements.

Fig. 11. Range dependent 3dB Channel Bandwidth shown as dashed lines. Where Y-axis is the frequency dependent component of the narrowband SNR

#### **4.3 Channel capacity**

Prior to evaluating the more realistic performance of the underwater data communication channel, the maximum achievable error-free bit rate *C* for various ranges of interest will be determined using the Shannon-Hartley expression, Equation 10. In these channel capacity calculations, all the transmitted power *Ptx* is assumed to be transferred to the hydrophone except for the losses associated with the deterministic Path Loss Models developed earlier. The Shannon-Hartley expression using the Signal-to-Noise ratio, SNR(r), defined in Equation 8, is:

$$\mathcal{C} = B \log\_2(1 + \text{SNR}(r)) \tag{10}$$

where C is the channel capacity in bps and B is the channel bandwidth in Hz

18 Will-be-set-by-IN-TECH

*PathLoss*(*r*, *d*, *t*, *fo*(*r*))*N*(*fo*(*r*)) − *PathLoss*(*r*, *d*, *t*, *f*))*N*(*f*) ≥ 3*dB* holds true and similarly for *fmax*(*r*) when *PathLoss*(*r*, *d*, *t*, *f*))*N*(*f*) − *PathLoss*(*r*, *d*, *t*, *fo*(*r*))*N*(*fo*(*r*)) ≥ 3*dB* is true. The

Thus, for a given range, there exists an optimal frequency from which a range dependent 3dB bandwidth can be determined as illustrated in Figure 11. The changes discussed in Section 4.1, related to changes in the optimum signal frequency with changes in range and channel conditions such as temperature, depth and wind. These variations are reflected in a similar manner to the changes seen here in channel bandwidth and in turn will reflect in the potential data transmission rates. Figure 11 demonstrates that both the optimal signal frequency and the 3dB channel bandwidth decrease as range increases. The impact of changing wind conditions on channel bandwidth is significant, however as discussed wind and wave action will also include time variant complexities and losses not included here. Temperature increases show an increase in channel bandwidth, at ranges of interest, due to the reduction in absorption loss as temperature increases, which means some benefits in working in the surface layers. The discussion here highlights that the underwater acoustic channel is severely band-limited and bandwidth efficient modulation will be essential to maximise data throughput and essentially that major benefits can be gained when performing data transmission at shorter ranges or in

Fig. 11. Range dependent 3dB Channel Bandwidth shown as dashed lines. Where Y-axis is

Prior to evaluating the more realistic performance of the underwater data communication channel, the maximum achievable error-free bit rate *C* for various ranges of interest will be determined using the Shannon-Hartley expression, Equation 10. In these channel capacity calculations, all the transmitted power *Ptx* is assumed to be transferred to the hydrophone except for the losses associated with the deterministic Path Loss Models developed earlier. The Shannon-Hartley expression using the Signal-to-Noise ratio, SNR(r), defined in Equation

where C is the channel capacity in bps and B is the channel bandwidth in Hz

*C* = *Blog*2(1 + *SNR*(*r*)) (10)

the frequency dependent component of the narrowband SNR

*B*(*r*, *d*, *t*) = *fmax*(*r*) − *fmin*(*r*) (9)

system bandwidth B(r,d,t) is therefore determined by:

multi-hop arrangements.

**4.3 Channel capacity**

8, is:

Thus using the optimum signal frequency and bandwidths at 100 m and 500 m found in the Section 4.1 and 4.2, the maximum achievable error free channel capacities against range are shown in Figure 12. The signal frequency and channel bandwidth values for 100 m were *fo* = 37kHz and B=47kHz and for 500 m were *fo* = 27kHz and B=33kHz. These are significantly higher than values currently available in underwater operations(Walree, 2007), however they provide an insight into the theoretical limits. Two different transmitter power levels are used, 150dB re 1*μ*Pa which is approximately 10mW (Equation 1) and 140dB re 1*μ*Pa is 1mW. Looking at the values associated with the same power level in Figure 12, the higher channel capacities are those associated with the determined optimum frequency and bandwidth for that range as would be expected. The change in transmitter power, however, by a factor of 10, does not produces a linear change in channel capacity across the range. These variations are important to consider as minimising energy consumption will be critical for AUV operations. In general, current modem specifications indicate possible data rate capacities of less than 10kbps (LinkQuest, 2008) for modem operations under 500 m, well short of these theoretical limits. This illustrates the incredibly severe data communication environment found underwater and that commercial modems are generally not yet designed to be able to adapt to specific channel conditions and varying ranges. The discussion here is to understand the variations associated with the various channel parameters at short range that may support adaptability and improved data transmission capacities.

Fig. 12. Theoretical limit of Channel Capacity (kbps) verse Range

#### **4.4 BER in short range underwater acoustic communication**

Achieving close to the maximum channel capacities as calculated in the previous section is still a significant challenge in underwater acoustic communication. The underwater acoustic channel presents significant multipaths with rapid time-variations and severe fading that lead to complex dynamics at the hydrophone causing ISI and bit errors. The probability of bit error, BER, therefore provides a measure of the data transmission link performance. In underwater systems, the use of FSK (Frequency Shift Keying) and PSK (Phase Shift Keying) have occupied researchers approaches to symbol modulation for several decades. One approach is using the simpler low rate incoherent modulation frequency hopping FSK

Communication Networks 21

Short-Range Underwater Acoustic Communication Networks 193

A short range underwater network, as shown in Figure 1(b) is essentially a multi-node sensor network. To develop a functional sensor network it is necessary to design a number of protocols which includes MAC, DLC (Data Link Control) and routing protocols. A typical protocol stack of a sensor network is presented in Figure 14. The lowest layer is the physical layer which is responsible for implementing all electrical/acoustic signal conditioning techniques such as amplifications, signal detection, modulation and demodulation, signal conversions, etc.. The second layer is the data link layer which accommodates the MAC and DLC protocols. The MAC is an important component of a sensor networks protocol stack, as it allows interference free transmission of information in a shared channel. The DLC protocol includes the ARQ (Automatic Repeat reQuest) and flow control functionalities necessary for error free data transmission in a non zero BER transmission environment. Design of the DLC functionalities are very closely linked to the transmission channel conditions. The network layers main operational control is the routing protocol; responsible for directing packets from the source to the destination over a multi-hop network. Routing protocols keep state information of all links to direct packets through high SNR links in order to minimise the end to end packet delay. The transport layer is responsible for end to end error control procedures which replicates the DLC functions but on an end to end basis rather than hop to hop basis as implemented by the DLL. The transport layer could use standard protocols such as TCP (Transmission Control Protocol) or UDP (User Datagram Protocol). The application layer hosts different operational applications which either transmit or receive data using the lower layers. To develop efficient network architectures, it is necessary to develop network and/or application specific DLL and network layers. The following subsections will present MAC and routing protocol design characteristics required for underwater swarm networking.

> Application Transport Network Data Link Layer (DLL)

> > Physical

Medium access protocols are used to coordinate the transmission of information from multiple transmitters using a shared communication channel. MAC protocols are designed to maximise channel usage by exploiting the key properties of transmission channels. MAC protocols can be designed to allocate transmission resources either in a fixed or in a dynamic manner. Fixed channel allocation techniques such as Frequency Division Multiplexing (FDM) or Time Division Multiplexing (TDM) are commonly used in many communication systems where ample channel capacity is available to transmit information (Karl & Willig, 2006). For low data rate and variable channel conditions, dynamic channel allocation techniques

**5. Swarm network protocol design techniques**

Fig. 14. A typical protocol stack for a sensor network

**5.1 MAC protocol**

signalling with strong error correction coding that provides some resilience to the rapidly varying multipath. Alternatively, the use of a higher rate coherent method of QPSK signalling that incorporates a Doppler tolerant multi-channel adaptive equalizer has gained in appeal over that time (Johnson et al., 1999).

The BER formulae are well known for FSK and QPSK modulation techniques (Rappaport, 1996), which require the Energy per Bit to Noise psd, *Eb No* , that can be found from the SNR (Equation 8) by:

$$\frac{E\_b}{N\_b} = \text{SNR}(r) \times \frac{B\_c}{R\_b} \tag{11}$$

where *Rb* is the data rate in bps and *Bc* is the channel bandwidth. Equation 12 and 13 are the uncoded BER for BPSK/QPSK and FSK respectively:

$$\text{QPSK}: \qquad \text{BER} = \frac{1}{2}\text{erfc}[\frac{E\_b}{N\_0}]^{1/2} \tag{12}$$

*FSK* : BER <sup>=</sup> <sup>1</sup> 2 *er f c*[ 1 2 *Eb No* ] 1/2 (13)

Fig. 13. Probability of Bit Error for Short Range Acoustic Data Transmission Underwater

The data rates *Rb* used are 10 and 20 kbps to reflect the current maximum commercial achievable levels. Figure 13 (a) and (b) show the BER for *Eb No* and Range respectively. Taking a BER of 10−<sup>4</sup> or 1 bit error in every 10, 000 bits, the *Eb No* required for QPSK is 8dB for a transmitter power of 10mW and a data rate of 20kbps. This increases to 12dB if using FSK with half the data rate (10 kbps) and same Transmitter Power. From Figure 13 (b), these settings will provide only a 150 m range. The range can be increased to 250 m using QPSK if the data rate was halved to 10 kbps or out to 500 m if the transmitter power was increased to 100mW in addition to the reduced data rate. Transmitter power plays a critical role, as illustrated here, by the comparison of ranges achieved from ≈ 75 m to 500 m with a change of transmitter power needed from 1mW to 100mW for this BER.
