Abstract: According to a first aspect, a novel method of performing an eight point quantization is developed. The eight point quantization consists of selecting one eight specific points depending upon the phase of the measured complex error signal. According to a second aspect, a novel method of performing eight-point quantization of an error signal by rotating a measured complex sample point by positive pi/8 and by negative pi/8. Two sign comparisons results in two control signals. These control signals used in conjunction with the signs of the real and imaginary parts of the variable being quantized results in all the information necessary to select one of eight equal and radially symmetric decision regions. According to a third aspect, an efficient hardware circuit implements the complex coefficient update algorithm using the quantization method according to the first aspect on the error signal.