Abstract: A system and method is provided for converting an input signal from a sequence of rectangular coordinate pairs to a sequence of polar coordinate pairs. The input signal includes a sequence of input vectors each including a pair of rectangular coordinates. A plurality of N input registers is configured to store an input vector of the input signal. The system includes a plurality of N CORDIC algorithm instances, each in communication with a corresponding one of the N input registers. Each CORDIC algorithm instance is configured to receive the input vector stored in the corresponding input register and to convert the received input vector to a corresponding output vector including a pair of polar coordinates. A recombiner is configured to receive the N output vectors and to recombine at least the N output vectors in sequence to form an output signal.

Abstract: In digital communications over a limited-bandwidth channel such as a radio-broadcast channel, multiple phase-amplitude shift keyed (MPASK) modulation is preferred using close packed hexagonal code. In quantizing such signals, a representation of an equalized received signal is transformed such that, to each symbol of the constellation, there corresponds a respective point on a square grid. A symbol of the constellation is determined as a quantized representative of the received signal by its selection as the one or the other of two symbols of the constellation having transformed representations at vertices of the square or rectangle in which the transformed signal lies. Such quantizing can be performed at a rate which is independent of the size of the constellation, and can be combined with similarly advantageous decoding in a receiver.