Asymptotically-Optimal, Fast-Decodable, Full-Diversity STBCs

For a family/sequence of STBCs $\mathcal{C}_1,\mathcal{C}_2,\dots$, with increasing number of transmit antennas $N_i$, with rates $R_i$ complex symbols per channel use (cspcu), the asymptotic normalized rate is defined as $\lim_{i \to \infty}{\frac{R_i}{N_i}}$. A family of STBCs is said to be asymptotically-good if the asymptotic normalized rate is non-zero, i.e., when the rate scales as a non-zero fraction of the number of transmit antennas, and the family of STBCs is said to be asymptotically-optimal if the asymptotic normalized rate is 1, which is the maximum possible value. In this paper, we construct a new class of full-diversity STBCs that have the least ML decoding complexity among all known codes for any number of transmit antennas $N>1$ and rates $R>1$ cspcu. For a large set of $\left(R,N\right)$ pairs, the new codes have lower ML decoding complexity than the codes already available in the literature. Among the new codes, the class of full-rate codes ($R=N$) are asymptotically-optimal and fast-decodable, and for $N>5$ have lower ML decoding complexity than all other families of asymptotically-optimal, fast-decodable, full-diversity STBCs available in the literature. The construction of the new STBCs is facilitated by the following further contributions of this paper:(i) For $g > 1$, we construct $g$-group ML-decodable codes with rates greater than one cspcu. These codes are asymptotically-good too. For $g>2$, these are the first instances of $g$-group ML-decodable codes with rates greater than $1$ cspcu presented in the literature. (ii) We construct a new class of fast-group-decodable codes for all even number of transmit antennas and rates $1 < R \leq 5/4$.(iii) Given a design with full-rank linear dispersion matrices, we show that a full-diversity STBC can be constructed from this design by encoding the real symbols independently using only regular PAM constellations.Comment: 16 pages, 3 tables. The title has been changed.The class of asymptotically-good multigroup ML decodable codes has been extended to a broader class of number of antennas. New fast-group-decodable codes and asymptotically-optimal, fast-decodable codes have been include

Low ML-Decoding Complexity, Large Coding Gain, Full-Rate, Full-Diversity STBCs for 2 X 2 and 4 X 2 MIMO Systems

This paper (Part of the content of this manuscript has been accepted for presentation in IEEE Globecom 2008, to be held in New Orleans) deals with low maximum likelihood (ML) decoding complexity, full-rate and full-diversity space-time block codes (STBCs), which also offer large coding gain, for the 2 transmit antenna, 2 receive antenna ($2\times 2$) and the 4 transmit antenna, 2 receive antenna ($4\times 2$) MIMO systems. Presently, the best known STBC for the $2\times2$ system is the Golden code and that for the $4\times2$ system is the DjABBA code. Following the approach by Biglieri, Hong and Viterbo, a new STBC is presented in this paper for the $2\times 2$ system. This code matches the Golden code in performance and ML-decoding complexity for square QAM constellations while it has lower ML-decoding complexity with the same performance for non-rectangular QAM constellations. This code is also shown to be \emph{information-lossless} and \emph{diversity-multiplexing gain} (DMG) tradeoff optimal. This design procedure is then extended to the $4\times 2$ system and a code, which outperforms the DjABBA code for QAM constellations with lower ML-decoding complexity, is presented. So far, the Golden code has been reported to have an ML-decoding complexity of the order of $M^4$ for square QAM of size $M$. In this paper, a scheme that reduces its ML-decoding complexity to $M^2\sqrt{M}$ is presented.Comment: 28 pages, 5 figures, 3 tables, submitted to IEEE Journal of Selected Topics in Signal Processin

Multifunctional MIMO systems: A combined diversity and multiplexing design perspective

In this treatise we investigate the design alternatives of different multiple-input multiple-output schemes while considering the attainable diversity gains, multiplexing gains, and beamforming gains. Following a brief classification of different MIMO schemes, where the different MIMO schemes are categorized as diversity techniques, multiplexing schemes, multiple access arrangements, and beamforming techniques, we introduce the family of multifunctional MIMOs. These multifunctional MIMOs are capable of combining the benefits of several MIMO schemes and hence attaining improved performance in terms of both their bit error rate as well as throughput. The family of multifunctional MIMOs combines the benefits of both space-time coding and the Bell Labs layered space-time scheme as well as those of beamforming. We also introduce the idea of layered steered space-time spreading, which combines the benefits of space-time spreading, V-BLAST, and beamforming with those of the generalized multicarrier direct sequence code-division multiple access concept. Additionally, we compare the attainable diversity, multiplexing, and beamforming gains of the different MIMO schemes in order to document the advantages of multifunctional MIMOs over conventional MIMO schemes

Four-Group Decodable Space-Time Block Codes

Two new rate-one full-diversity space-time block codes (STBC) are proposed. They are characterized by the \emph{lowest decoding complexity} among the known rate-one STBC, arising due to the complete separability of the transmitted symbols into four groups for maximum likelihood detection. The first and the second codes are delay-optimal if the number of transmit antennas is a power of 2 and even, respectively. The exact pair-wise error probability is derived to allow for the performance optimization of the two codes. Compared with existing low-decoding complexity STBC, the two new codes offer several advantages such as higher code rate, lower encoding/decoding delay and complexity, lower peak-to-average power ratio, and better performance.Comment: 1 figure. Accepted for publication in IEEE Trans. on Signal Processin

Single-Symbol ML Decodable Distributed STBCs for Partially-Coherent Cooperative Networks

Space-time block codes (STBCs) that are single-symbol decodable (SSD) in a co-located multiple antenna setting need not be SSD in a distributed cooperative communication setting. A relay network with N relays and a single source-destination pair is called a partially-coherent relay channel (PCRC) if the destination has perfect channel state information (CSI) of all the channels and the relays have only the phase information of the source-to-relay channels. In this paper, first, a new set of necessary and sufficient conditions for a STBC to be SSD for co-located multiple antenna communication is obtained. Then, this is extended to a set of necessary and sufficient conditions for a distributed STBC (DSTBC) to be SSD for a PCRC, by identifying the additional conditions. Using this, several SSD DSTBCs for PCRC are identified among the known classes of STBCs. It is proved that even if a SSD STBC for a co-located MIMO channel does not satisfy the additional conditions for the code to be SSD for a PCRC, single-symbol decoding of it in a PCRC gives full-diversity and only coding gain is lost. It is shown that when a DSTBC is SSD for a PCRC, then arbitrary coordinate interleaving of the in-phase and quadrature-phase components of the variables does not disturb its SSD property for PCRC. Finally, it is shown that the possibility of {\em channel phase compensation} operation at the relay nodes using partial CSI at the relays increases the possible rate of SSD DSTBCs from $\frac{2}{N}$ when the relays do not have CSI to 1/2, which is independent of N