Sensor array is a group of sensors deployed in certain geometry pattern. The advantage of using a sensor array over using a single sensor lies in the factor that an array can increase the antenna gain in the direction of the signal while decreasing the gain in the directions of noise and interferences. In other words, sensor arrays can increase signal-to-noise ratio (SNR): magnify the signal while suppressing the noise. Another ability of sensor array is that is can detect the direction and distance of impinging signal sources. The technology to achieve this is called Array Signal Processing. Application examples of array signal processing include RADAR/SONAR, wireless communications, seismology, machine condition monitoring and fault diagnosis, etc.
The mathematical and physical principle behind array signal processing is that the information gathered by the sensor array displays some interrelationships that are functions of the array geometry and the temporal and spatial parameters of the signals, and the information can be used to estimate the characteristics of the impinging signals. This is known as parameter estimation.
Figure 1 illustrates a six-element uniform linear array. In this example, the impinging signal is assumed far-field so that it can be treated as planar wave.
Parameter estimation takes advantage of the fact that the distance from the source to each microphone in the array is different, which means that the signal recorded by each microphone will be phase-shifted replicas of each other. Eq. (1) shows the calculation for the extra time it takes to reach each microphone in the array relative to the array center, where c is the sound speed.
Each sensor is associated with a different delay. Although the delays are small but not trivial. In frequency domain, the delays display as phase shift among the signals received by the sensors. The delays are closely related to the incident angle and the geometry of the sensor array. Given the geometry of the array, the delays or phase differences can be used to estimate the incident angle. This the mathematical basis behind the array signal processing. Simply summing the signals received by the sensors and calculating the mean value give the following result:
Because the received signals are out of phase, this mean value does not give an enhanced signal compared with the original source. Heuristically, if we can find weights multiplying to the received signals to make them in phase before summing them together, the mean value will give an enhanced signal:
The process of multiplying a well selected set of weights to the signals received by the sensor array so that the signal is added constructively while suppressing the noise is called beamforming. There are a variety of beamforming algorithms for sensor arrays, such as The delay-and-sum approach, spectral based (non-parametric) approaches and parametric approaches. These beamforming algorithms are briefly described as follows.
Read more about Sensor Array: Delay-and-Sum Beamforming, Spectral Based Beamforming, Parametric Beamformers
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