# Optimal Deployment of Vector Sensor Nodes in Underwater Acoustic Sensor Networks
## 2 Communication Performance Based on Single-Vector Sensors
### Underwater Acoustic Communication Using Single-Vector Sensors  
An acoustic vector sensor measures the particle motion produced by acoustic waves, which is a vector quantity described using the displacement, particle velocity, and acceleration, whereas a hydrophone measures the acoustic pressure, which is a scalar quantity. Most previous studies in underwater acoustic communication used hydrophone arrays to receive the communication signals [15; 16], but this approach has poor spatial efficiency (Figure 1a). In contrast, a vector sensor has good spatial efficiency because it measures the three directional vector quantities as well as the pressure change at a single point. Accordingly, it can be used as a SIMO system, as shown in Figure 1b [22; 23; 24]. In this paper, it is assumed for convenience that the vector sensor measures particle velocity and pressure simultaneously in two-dimensional (2-D) coordinates (i.e., horizontal and vertical components). Thus, the vector sensor can be considered a one-by-three SIMO system for underwater acoustic communication. Figure 2 shows a block diagram of a vector sensor communication system for decoding the communication data. To recover the baseband waveform, the three components of the communication signal are multiplied by \(e^{-i\omega t}\), where \(\omega\) is the angular frequency. Then the rest of the process is the same as that in Reference [13], i.e., the baseband data are passed through a low pass filter and an adaptive DFE with a recursive least-squares (RLS) algorithm [26]. Then the data from multi-channels are combined to improve the signal-to-noise ratio (SNR) by removing residual ISI [15; 26; 27]. The BER performance is finally evaluated. See [24] for a detailed description of vector sensor communication using particle velocity and pressure signals. Figure 1: Communication system layouts. (**a**) Vertical-pressure sensor array, (**b**) single-vector sensor. Figure 3 shows the communication performance (BER) as a function of receiver position, estimated from a three-channel vertical-pressure sensor array and a single-vector sensor in a 2-D underwater environment with acoustically hard and soft bottoms. For easier comparisons, a Pekeris waveguide with a water depth of 50 m and a water sound speed of 1500 m/s was assumed. In addition, it was assumed that the sound source was at a depth of 25 m and transmitted a BPSK communication sequence with a 1 kbps bit rate and a 10 kHz carrier frequency. The BER performance was obtained as a function of receiver position by varying the receiver depth from 5 m to 45 m at 5-m intervals, and by varying the source-receiver range from 75 m to 500 m at 25-m intervals. In the pressure sensor array, the element spacing was 1.5 m, which corresponded to 10 times the wavelength. The communication signals received at each hydrophone channel were simulated using the method described in Reference [13]. The underwater acoustic channel response at each channel point was predicted by the ray-based BELLHOP propagation model and was convolved with a representation of the BPSK sequence. A finite difference approximation method [28] was used to simulate the particle velocities received at the vector sensor. The particle velocity \(v(\mathrm{t})\) can be estimated by the time integral of the pressure  
Figure 3: Communication performance (BER estimates) as a function of receiver position. Left and right plots are for coarse sandy and silty bottoms, respectively. Upper and lower plots correspond to the performance results for a three-channel pressure sensor array and a single-vector sensor, respectively. Figure 2: Block diagram of a single-input multiple-output (SIMO) system using a single-vector sensor. \(P_{M}\) is an acoustic pressure. \(P_{r}\) and \(P_{z}\) are the horizontal and vertical components of the pressure equivalent particle velocities, respectively. gradient. The pressure gradient can be approximately estimated using two pressure signals received at two pressure sensors placed close together.