An algebraic MIDO-MISO code construction

Multiple-input double-output (MIDO) codes are important in future wireless communications, where the portable end-user device is physically small and uses only two receive antennas. In this paper, we address the design of 4×2 MIDO codes. Starting from a 4×4 space-time block code matrix built from a cyclic division algebra, two ways of puncturing the code are presented, resulting in either a well-shaped MIDO code, or a MIDO code with some orthonormal columns, yielding fast maximum-likelihood (ML) decodability. The well-shaped MIDO code outperforms the fast decodable one through simulations, an indication that the shaping property stays an important code design criterion. We then provide a slightly modified version of the well-shaped MIDO code which both preserves the shaping and increases the orthogonality of its columns in an attempt to speed up the decoding of the code. Finally, we show that a multiple-input single output (MISO) code is actually embedded in the MIDO code, allowing the transmitter to choose between sending a MIDO or MISO code, without having to change the encoder. All the proposed codes have the non-vanishing determinant (NVD) property.