The complex sphere decoding has lower complexity compared with real sphere decoding for space-frequency block codes with PSK modulation.When the initial radius of the complex sphere decoder tends to infinity
sorting has high complexity.For symbols of PSK modulation
a new sorting method is proposed in every layer according to the zigzag rule centred the middle reference point in the angle dimension of the polar coordination.Through looking up the table
the sorted symbol sequence can be fast gained.Compared with the general complex sphere decoding algorithm
the sphere decoding algorithm through looking up table of sorted symbol sequence can save approximate 61% complexity for 16-PSK in 14dB average bit SNR.