K. Pavan Srinath

High-rate, 2-group ML-decodable STBCs for 2 m transmit antennas

A Space-Time Block Code (STBC) in K-variables is said to be g-Group ML-Decodable (GMLD) if its Maximum-Likelihood (ML) decoding metric can be written as a sum of g independent terms, with each term being a function of a subset of the K variables. In this paper, a construction method to obtain high-rate, 2-GMLD STBCs for 2m transmit antennas, m ≫ 1, is presented. The rate of the STBC obtained for 2m transmit antennas is 2m−2 + 1/2m complex symbols per channel use. The design method is illustrated for the case of 4 and 8 transmit antennas. The code obtained for 4 transmit antennas is equivalent to the rate-5/4 Quasi-Orthogonal design (QOD) proposed by Yuen, Guan and Tjung.

Improved Perfect Space-Time Block Codes

Perfect space-time block codes (STBCs) are based on four design criteria-full-rateness, nonvanishing determinant, cubic shaping, and uniform average transmitted energy per antenna per time slot. Cubic shaping and transmission at uniform average energy per antenna per time slot are important from the perspective of energy efficiency of STBCs. The shaping criterion demands that the generator matrix of the lattice from which each layer of the perfect STBC is carved be unitary. In this paper, it is shown that unitariness is not a necessary requirement for energy efficiency in the context of space-time coding with finite input constellations, and an alternative criterion is provided that enables one to obtain full-rate (rate of nt complex symbols per channel use for an nt transmit antenna system) STBCs with larger normalized minimum determinants than the perfect STBCs. Further, two such STBCs, one each for 4 and 6 transmit antennas, are presented and they are shown to have larger normalized minimum determinants than the comparable perfect STBCs which hitherto had the best-known normalized minimum determinants.

Single real-symbol decodable, high-rate, distributed space-time block codes

A scheme to apply the rate-1 real orthogonal designs (RODs) in relay networks with single real-symbol decodability of the symbols at the destination for any arbitrary number of relays is proposed. In the case where the relays do not have any information about the channel gains from the source to themselves, the best known distributed space time block codes (DSTBCs) for k relays with single real-symbol decodability offer an overall rate of complex symbols per channel use. The scheme proposed in this paper offers an overall rate of 2/2+k complex symbol per channel use, which is independent of the number of relays. Furthermore, in the scenario where the relays have partial channel information in the form of channel phase knowledge, the best known DSTBCs with single real-symbol decodability offer an overall rate of 1/3 complex symbols per channel use. In this paper, making use of RODs, a scheme which achieves the same overall rate of 1/3 complex symbols per channel use but with a decoding delay that is 50 percent of that of the best known DSTBCs, is presented. Simulation results of the symbol error rate performance for 10 relays, which show the superiority of the proposed scheme over the best known DSTBC for 10 relays with single real-symbol decodability, are provided.

Interference aligned space-time transmission with diversity for the 2 × 2 X-Network

It is well known that the interference alignment (IA) based transmission scheme proposed by Jafar and Shamai achieves the 4M over 3 sum-degrees of freedom (DoF) of the twotransmitter, two-receiver multiple-input multiple-output (MIMO) X-Network with M antennas at each node, referred to as the (2 × 2, M) X-Network. The Jafar-Shamai scheme assumes the availability of “global” channel-state-information at the transmitter (CSIT). “Local” CSIT based transmission schemes that couple IA with space-time block codes (STBC) in order to achieve the sum-DoF of the (2 × 2, M) X-Network are known specifically for M = 2; 3; 4. Further, these schemes have been proven to guarantee a diversity gain of M when finite-sized input constellations are employed. In this paper, an explicit transmission scheme that achieves the 4M over 3 sum-DoF of the (2 × 2, M) X-Network, for arbitrary M, is presented. The proposed scheme needs only local CSIT unlike the Jafar-Shamai scheme. In addition, it is shown analytically that the proposed scheme guarantees a diversity gain of M + 1 when finite-sized input constellations are employed.

Reduced ML-decoding complexity, full-rate STBCs for 4 transmit antenna systems

For an n<inf>t</inf> transmit, n<inf>r</inf> receive antenna system (n<inf>t</inf>× n<inf>r</inf> system), a full-rate space time block code (STBC) transmits min(n<inf>t</inf>, n<inf>r</inf>) complex symbols per channel use. In this paper, a scheme to obtain a full-rate STBC for 4 transmit antennas and any n<inf>r</inf>, with reduced ML-decoding complexity is presented. The weight matrices of the proposed STBC are obtained from the unitary matrix representations of a Clifford Algebra. By puncturing the symbols of the STBC, full rate designs can be obtained for n<inf>r</inf> < 4. For any value of n<inf>r</inf>, the proposed design offers the least ML-decoding complexity among known codes. The proposed design is comparable in error performance to the well known Perfect code for 4 transmit antennas while offering lower ML-decoding complexity. Further, when n<inf>r</inf> < 4, the proposed design has higher ergodic capacity than the punctured Perfect code. Simulation results which corroborate these claims are presented.

An Enhanced DMT-Optimality Criterion for STBC Schemes for Asymmetric MIMO Systems

For any nt transmit, nr receive antenna ( nt×nr) multiple-input multiple-output (MIMO) system in a quasi-static Rayleigh fading environment, it was shown by Elia that linear space-time block code schemes (LSTBC schemes) that have the nonvanishing determinant (NVD) property are diversity-multiplexing gain tradeoff (DMT)-optimal for arbitrary values of nr if they have a code rate of nt complex dimensions per channel use. However, for asymmetric MIMO systems (where ), with the exception of a few LSTBC schemes, it is unknown whether general LSTBC schemes with NVD and a code rate of nr complex dimensions per channel use are DMT optimal. In this paper, an enhanced sufficient criterion for any STBC scheme to be DMT optimal is obtained, and using this criterion, it is established that any LSTBC scheme with NVD and a code rate of min{nt,nr} complex dimensions per channel use is DMT optimal. This result settles the DMT optimality of several well-known, low-ML-decoding-complexity LSTBC schemes for certain asymmetric MIMO systems.

Fast-decodable MIDO codes with large coding gain

In this paper, a new method is proposed to obtain full-diversity, rate-2 (rate of 2 complex symbols per channel use) space-time block codes (STBCs) that are full-rate for multiple input, double output (MIDO) systems. Using this method, rate-2 STBCs for 4×2, 6×2, 8×2 and 12×2 systems are constructed and these STBCs are fast ML-decodable, have large coding gains, and STBC-schemes consisting of these STBCs have a non-vanishing determinant (NVD) so that they are DMT-optimal for their respective MIDO systems.

DMT-optimal, low ML-complexity STBC-schemes for asymmetric MIMO systems

For an n_t transmit, n_r receive antenna (n_t × n_r) MIMO system with quasi-static Rayleigh fading, it was shown by Elia et al. that space-time block code-schemes (STBC-schemes) which have the non-vanishing determinant (NVD) property and are based on minimal-delay STBCs (STBC block length equals n_t) with a symbol rate of n_t complex symbols per channel use (rate-n_t STBC) are diversity-multiplexing gain tradeoff (DMT)-optimal for arbitrary values of n_r. Further, explicit linear STBC-schemes (LSTBC-schemes) with the NVD property were also constructed. However, for asymmetric MIMO systems (where n_r <; n_t), with the exception of the Alamouti code-scheme for the 2×1 system and rate-1, diagonal STBC-schemes with NVD for an n_t ×1 system, no known minimal-delay, rate-n_r LSTBC-scheme has been shown to be DMT-optimal. In this paper, we first obtain an enhanced sufficient criterion for an STBC-scheme to be DMT optimal and using this result, we show that for certain asymmetric MIMO systems, many well-known LSTBC-schemes which have low ML-decoding complexity are DMT-optimal, a fact that was unknown hitherto.

On the Sphere Decoding Complexity of High-Rate Multigroup Decodable STBCs in Asymmetric MIMO Systems

A space-time block code (STBC) is said to be multigroup decodable if the information symbols encoded by it can be partitioned into two or more groups such that each group of symbols can be maximum-likelihood (ML) decoded independently of the other symbol groups. In this paper, we show that the upper triangular matrix R encountered during the sphere decoding of a linear dispersion STBC can be rank-deficient even when the rate of the code is less than the minimum of the number of transmit and receive antennas. We then show that all known families of high-rate (rate greater than 1) multigroup decodable codes have rank-deficient R matrix even when the rate is less than the number of transmit and receive antennas, and this rank-deficiency problem arises only in asymmetric MIMO systems when the number of receive antennas is strictly less than the number of transmit antennas. Unlike the codes with full-rank R matrix, the complexity of the sphere decoding-based ML decoder for STBCs with rank-deficient R matrix is polynomial in the constellation size, and hence is high. We derive the ML sphere decoding complexity of most of the known high-rate multigroup decodable codes, and show that for each code, the complexity is a decreasing function of the number of receive antennas.

Reduced ML-Decoding Complexity, Full-Rate STBCs for 2a Transmit Antenna Systems

For an