Threaded Algebraic Space-time Research Articles

Hybrid IRS and DFE Detection Scheme for MDL-Impaired Transmission With TAST Coding

Linear threaded algebraic space-time (TAST) codes have shown potential advantage in mitigating the mode-dependent loss in the few-mode-fiber-based mode-division multiplexing (MDM) system. However, the maximum-likelihood (ML) detector employed at the receiver of the MDM system greatly suffers from exponential computational complexity. In this work, we first examine the necessity of space-time coding in the MDM system. On this basis, a new hybrid detection, which integrates the improved reduced-search (IRS) method and the decision feedback equalizer (DFE), is proposed for the TAST-assisted MDM system, in which DFE is employed to detect the more reliable tributaries to obtain a near-ML solution, while IRS is responsible for finding the best solution in the remaining set with a reduced number of candidates. Simulation results show that the proposed detection method can achieve near-optimal solutions and has a low computational complexity. Moreover, it has the attractive advantage of flexible adjustment in the tradeoff between system performance and computational complexity.

On the Performance of Spatial Modulations Over Multimode Optical Fiber Transmission Channels

In this paper, we analyze the performance of coded and uncoded spatial modulations over multi-mode fiber optic channels with the mode-dependent loss (MDL) under the maximum likelihood (ML) and zero-forcing (ZF) detection schemes. We focus on the multi-dimensional modulations that satisfy certain orthogonality criteria such as the Threaded Algebraic Space-Time (TAST) codes. In particular, we link the post-detection signal-to-noise ratio (SNR) to the orthogonality defect factor (ODF) of the equivalent channel matrix by deriving their closed-form expressions as well as characterizing their statistical properties. Using the post-detection SNR and ODF properties, we develop upper and ad-hoc tight bounds on the error probabilities, which illustrate how these “orthogonal” spatial modulations mitigate the MDL under both the ML and ZF detection schemes. The obtained properties also allow us to propose a modification to the detection algorithm such that it still achieves an essentially optimal performance but at a much smaller cost than exhaustive or tree search algorithms. The theoretical results are validated numerically and by simulations.

Blind Interference Alignment With Diversity in <inline-formula> <tex-math notation="TeX">$K$</tex-math> </inline-formula>-User Interference Channels

In this paper, we propose blind interference alignment (BIA) schemes using reconfigurable antenna technology to achieve high degree of freedom (DoF) or diversity gain in K-user interference channels. First, two DoF-oriented BIA schemes are proposed that fully and partially align the inter-user interference, respectively. We compare the achievable DoF of the two schemes and show that the partial BIA scheme has higher DoF than the full BIA scheme under some conditions, and vice versa. Then, three diversity-oriented BIA schemes with space-time coding are proposed to achieve both spatial diversity gain and reconfigurable antenna pattern diversity gain. With different tradeoffs among the diversity gain, the rate and the decoding complexity, the BIA with threaded algebraic space-time (TAST) codes, the BIA with orthogonal space-time block codes (OSTBCs), and the BIA with multiplexing Alamouti codes are proposed, respectively. The BIA with TAST codes can achieve the full diversity and high rate with high decoding complexity. The BIA with OSTBCs can achieve the full diversity and the linear decoding complexity but has low rate. The BIA with multiplexing Alamouti codes can achieve high rate with low decoding complexity at the expense of full diversity loss.

Energy Spreading Transform Approach to Achieve Full Diversity and Full Rate for MIMO Systems

Full-diversity full-rate (FDFR) space-time codes achieve both high data rate and good reliability at the cost of high decoding complexity. In this paper, we propose a low-complexity MIMO scheme that achieves both full diversity and full rate over flat fading channels for a sufficiently large number of transmit and receive antennas. The proposed scheme is constructed by applying energy spreading transforms (EST's) to multiple data streams and spatially multiplexing the streams to multiple transmit antennas. Simulation results show that the proposed FDFR scheme outperforms the threaded algebraic space-time (TAST) code, which is a FDFR code based on maximum likelihood (ML) detection, when the number of transmit antennas (with the same number of receive antennas) are three and four. However, its detection complexity is only that of a decision-feedback detector.

Delay tolerant (delto) distributed TAST codes for cooperative wireless networks

In a distributed cooperative communication system, as the distances between different relay nodes and the receiving nodes may be different, so the performances of distributed space time codes at receiving nodes may badly be degraded if timing synchronization is not assured. In this article, extending the work of Damen et al. we introduce the design of distributed threaded algebraic space-time (TAST) codes offering resistance to timing delay off-set. We present some new and useful techniques of constructing delay tolerant TAST code for distributed cooperative networks, which, like their brethren codes, are delay tolerant for any delay profile and achieve full diversity for arbitrary number of relays, transmit/receive antennas, and input alphabet size. Our proposed codes with minimum lengths achieve better performances than the existing codes retaining full rate and full diversity with or without use of guard bands. Simulations results confirm our claim of obtaining better performances.

Bounded Delay-Tolerant Space Time Block Codes for Asynchronous Cooperative Networks

When distributed cooperative nodes are communicating with a destination, the received signal can be asynchronous due to the propagation or processing delays. This can destroy the space time block code properties designed initially for synchronous case. In this paper, a new construction method of bounded delay tolerant codes is presented. These new codes preserve the full diversity with optimal rates if the relative delays are in a designed delay tolerance interval. The general design method is based on the concatenation and permutation of optimal synchronous space time block codes and works for an arbitrary number of transmitting and receiving antennas. Examples of bounded delay tolerant codes based on the Alamouti code, the Golden code and Threaded Algebraic Space-Time (TAST) codes are given. Theoretical proofs are used to show that the new codes respect the design criteria. Simulation results manifest better error rate performance of the new codes compared to other known delay tolerant codes.

Block Layering Approach in TAST Codes

Threaded Algebraic Space Time (TAST) codes developed by Gamal et al. is a powerful class of space time codes in which different layers are combined and separated by appropriate Diophantine number . In this paper we introduce a technique of block layering in TAST codes, in which a series of layers (we call it Block layers) has more than one transmit antenna at the same time instant. As a result we use fewer layers (Diophantine numbers) for the four transmit antennas scheme, which enhances the coding gain of our proposed scheme. In each block layer we incorporate Alamouti’s transmit diversity scheme which decreases the decoding complexity. The proposed code achieves a normalized rate of 2 symbol/s. Simulation result shows that this type of codes outperforms TAST codes in certain scenarios.

Delay-Tolerant Distributed-TAST Codes for Cooperative Diversity

In cooperative networks using a decode-and-forward strategy, the multiple relays effectively transmit a distributed space-time code, the performance of which can be severely degraded when timing synchronization among the relays is not assured (e.g., in cases of broadcast to dispersed recipients or in networks without a shared, high-quality timing reference). Recent work by Xia and Hammons have investigated the design of distributed space-time codes that are delay tolerant, in the sense that full spatial diversity is achieved regardless of timing offsets. In general, the previously known space-time block codes belonging to the class of C-linear codes, however, which are important because they achieve full spatial diversity and admit near-optimal lattice decoding algorithms, are not delay tolerant. In this paper, we present a new family of such codes that are fully delay tolerant. The new codes generalize the threaded algebraic space-time (TAST) codes introduced by El Gamal and Damen. Like their brethren, the new distributed-TAST codes are effective and flexible, enabling use of different signaling constellations, transmission rates, numbers of transmit and receive antennas, and decoders of varying levels of complexity.

Linear Decoupled and Quasi-Decoupled Space–Time Codes

Space-time transmit diversity results in coupling of transmitted symbols across different antennas, which increases the complexity of maximum-likelihood decoding. Symbol coupling can be completely or partially avoided if the space-time code (STC) satisfies specific decoupling conditions; examples of such codes are orthogonal space-time block codes and quasi-orthogonal codes. In this letter, we study decoupling conditions for a linear full-diversity STC. Quasi-decoupled codes are proposed as a partially decoupled full-diversity STC of any rate for any number of transmit antennas with minimum decoding delay. By optimizing the coding gain of quasi-decoupled codes, it is shown that quasi-orthogonal codes have competitive performance with respect to the Alamouti code, and the more-recent threaded algebraic space-time (TAST) codes and ABBA codes. A general full-diversity decoupling condition is considered, and the general solution to this case, which also encompasses previously known orthogonal STCs, is derived

A New Representation of TAST Codes

A simple and general form of threaded algebraic space-time (TAST) codes and constellations for arbitrary numbers of transmit and receive antennas and arbitrary input alphabets is given and analyzed. This new form gives revealing insights on the TAST framework, elucidates the connection between space-time constellation expansion and the peak-to-average power ratio (PAR), and establishes the equivalence between a certain class of TAST constellations and constellations derived from division algebras

Noncoherent Space–Time Coding: An Algebraic Perspective

The design of space-time signals for noncoherent block-fading channels where the channel state information is not known a priori at the transmitter and the receiver is considered. In particular, a new algebraic formulation for the diversity advantage design criterion is developed. The new criterion encompasses, as a special case, the well-known diversity advantage for unitary space-time signals and, more importantly, applies to arbitrary signaling schemes and arbitrary channel distributions. This criterion is used to establish the optimal diversity-versus-rate tradeoff for training based schemes in block-fading channels. Our results are then specialized to the class of affine space-time signals which allows for a low complexity decoder. Within this class, space-time constellations based on the threaded algebraic space-time (TAST) architecture are considered. These constellations achieve the optimal diversity-versus-rate tradeoff over noncoherent block-fading channels and outperform previously proposed codes in the considered scenarios as demonstrated by the numerical results. Using the analytical and numerical results developed in this paper, nonunitary space-time codes are argued to offer certain advantages in block-fading channels where the appropriate use of coherent space-time codes is shown to offer a very efficient solution to the noncoherent space-time communication paradigm.

Linear threaded algebraic space-time constellations

Space-time (ST) constellations that are linear over the field of complex numbers are considered. Relevant design criteria for these constellations are summarized and some fundamental limits to their achievable performances are established. The fundamental tradeoff between rate and diversity is investigated under different constraints on the peak power, receiver complexity, and rate scaling with the signal-to-noise ratio (SNR). A new family of constellations that achieve optimal or near-optimal performance with respect to the different criteria is presented. The proposed constellations belong to the threaded algebraic ST (TAST) signaling framework, and achieve the optimal minimum squared Euclidean distance and the optimal delay. For systems with one receive antenna, these constellations also achieve the optimal peak-to-average power ratio for quadrature amplitude modulation (QAM) and phase-shift keying (PSK) input constellations, as well as optimal coding gains in certain scenarios. The framework is general for any number of transmit and receive antennas and allows for realizing the optimal tradeoff between rate and diversity under different constraints. Simulation results demonstrate the performance gains offered by the proposed designs in average power and peak power limited systems.