Abstract: A three dimensional scanning beam system (100) and method (500) enable economical and efficient three dimensional scans of an environment. The system (100) includes a ranging apparatus (105), and a reactive linkage mechanism (110) having a first end (115) and a second end (120). The first end (115) is connected to the ranging apparatus (105) and the second end (120) is connected to an object (125) that moves the system (100) through an environment. In use acceleration of the object (125) with respect to the environment is converted by the reactive linkage mechanism (110) to motion of the ranging apparatus (105) with respect to the object (125), which increases the field of view of the ranging apparatus (105) with respect to the environment.

Abstract: Disclosed is a method of communicating a complex vector, using one or more index bits, the method comprising quantizing the complex vector using a codebook, the codebook comprising a plurality of complex vectors mapped from real vectors that lie on a reflected simplex where the simplex is of dimension one less than twice the length of the complex vector; indexing the quantized vector to form the one or more index bits; and transmitting the index bits to the transmitter, thereby communicating the complex vector.