A family of fast-decodable MIDO codes from crossed-product algebras over ℚ

Multiple Input Double Output (MIDO) asymmetric space-time codes for 4 transmit antennas and 2 receive antennas can be employed in the downlink from base stations to portable devices. Previous MIDO code constructions with low Maximum Likelihood (ML) decoding complexity, full diversity and the nonvanishing determinant (NVD) property are mostly based on cyclic division algebras. In this paper, a new family of MIDO codes with the NVD property based on crossed-product algebras over Q is introduced. Fast decodability follows naturally from the structure of the codewords which consist of four generalized Alamouti blocks. The associated ML complexity order is the lowest known for full-rate MIDO codes (O(M) instead of O(M) with respect to the real constellation size M ). Numerical simulations show that these codes have a performance from comparable up to 1dB gain compared to the best known MIDO code with the same complexity.