Full Rate L2-Orthogonal Space-Time CPM for Three Antennas

To combine the power efficiency of continuous phase modulation (CPM) with enhanced performance in fading environments, some authors have suggested to use CPM in combination with space-time codes (STC). Recently, we have proposed a CPM ST-coding scheme based on L²-orthogonality for two transmitting antennas. In this paper we extend this approach to the three antennas case. We analytically derive a family of coding schemes which we call parallel code (PC). This code family has full rate and we prove that the proposed coding scheme achieves full diversity as confirmed by accompanying simulations. We detail an example of the proposed ST codes that can be interpreted as a conventional CPM scheme with different alphabet sets for the different transmit antennas which results in a simplified implementation. Thanks to L²-orthogonality, the decoding complexity, usually exponentially proportional to the number of transmitting antennas, is reduced to linear complexity.