Space-time code designs with non-vanishing determinants for three, four and six transmitter antennas

The design of a linear space-time code with full rate, large diversity product, and non-vanishing minimum determinant of codewords continues to attract great attention. However, in most available no-vanishing determinant space-time codes for three, four, and six transmitter antennas, the average power at each layer is different, which results in a high peak to average power ratio. In this paper, a new cyclic algebraic space-time design scheme is proposed and the optimal codes in this class are provided by using some specific cyclic field extensions. Our proposed codes not only include the available non-vanishing determinant cyclotomic space-time codes for three, four, and six transmitter antennas, but also have the desirable property that the optimal codes can be achieved with the same average power at each layer.