Problem Formulation

In this chapter, we explain some important aspects of beam forming and differential arrays. The problem of a DMA design is formulated while we progress in defining some useful concepts. We start with the definition of the steering vector for a plane wave with the conventional anechoic far field model. We give the general definition of the beam pattern as well as its expression for directional arrays. We then derive the gain in signal-to-noise ratio (SNR), which can be very useful in the evaluation of DMAs under different types of noise. Finally, we discuss the Vander monde matrix, which always appears, explicitly or implicitly, in the design of DMAs.