Distributed Space-Time Coding Based on Adjustable Code Matrices for Cooperative MIMO Relaying Systems

An adaptive distributed space-time coding (DSTC) scheme is proposed for two-hop cooperative MIMO networks. Linear minimum mean square error (MMSE) receive filters and adjustable code matrices are considered subject to a power constraint with an amplify-and-forward (AF) cooperation strategy. In the proposed adaptive DSTC scheme, an adjustable code matrix obtained by a feedback channel is employed to transform the space-time coded matrix at the relay node. The effects of the limited feedback and the feedback errors are assessed. Linear MMSE expressions are devised to compute the parameters of the adjustable code matrix and the linear receive filters. Stochastic gradient (SG) and least-squares (LS) algorithms are also developed with reduced computational complexity. An upper bound on the pairwise error probability analysis is derived and indicates the advantage of employing the adjustable code matrices at the relay nodes. An alternative optimization algorithm for the adaptive DSTC scheme is also derived in order to eliminate the need for the feedback. The algorithm provides a fully distributed scheme for the adaptive DSTC at the relay node based on the minimization of the error probability. Simulation results show that the proposed algorithms obtain significant performance gains as compared to existing DSTC schemes.Comment: 6 figure

Structured Dispersion Matrices From Division Algebra Codes for Space-Time Shift Keying

We propose a novel method of constructing Dispersion Matrices (DM) for Coherent Space-Time Shift Keying (CSTSK) relying on arbitrary PSK signal sets by exploiting codes from division algebras. We show that classic codes from Cyclic Division Algebras (CDA) may be interpreted as DMs conceived for PSK signal sets. Hence various benefits of CDA codes such as their ability to achieve full diversity are inherited by CSTSK. We demonstrate that the proposed CDA based DMs are capable of achieving a lower symbol error ratio than the existing DMs generated using the capacity as their optimization objective function for both perfect and imperfect channel estimation

Fast-Decodable Asymmetric Space-Time Codes from Division Algebras

Multiple-input double-output (MIDO) codes are important in the near-future wireless communications, where the portable end-user device is physically small and will typically contain at most two receive antennas. Especially tempting is the 4 x 2 channel due to its immediate applicability in the digital video broadcasting (DVB). Such channels optimally employ rate-two space-time (ST) codes consisting of (4 x 4) matrices. Unfortunately, such codes are in general very complex to decode, hence setting forth a call for constructions with reduced complexity. Recently, some reduced complexity constructions have been proposed, but they have mainly been based on different ad hoc methods and have resulted in isolated examples rather than in a more general class of codes. In this paper, it will be shown that a family of division algebra based MIDO codes will always result in at least 37.5% worst-case complexity reduction, while maintaining full diversity and, for the first time, the non-vanishing determinant (NVD) property. The reduction follows from the fact that, similarly to the Alamouti code, the codes will be subsets of matrix rings of the Hamiltonian quaternions, hence allowing simplified decoding. At the moment, such reductions are among the best known for rate-two MIDO codes. Several explicit constructions are presented and shown to have excellent performance through computer simulations.Comment: 26 pages, 1 figure, submitted to IEEE Trans. Inf. Theory, October 201

High rate space time code with linear decoding complexity for multiple transmitting antennas

The multipath nature of the wireless channel, results in a superposition of the signals of each path at the receiver. This can lead to either constructive or destructive interference. Strong destructive interference is frequently referred to as deep fade and may result in temporary failure of communication due to the severe drop in the channel\u27s signal-to-noise ratio (SNR). To avoid this situation, signal diversity might be introduced. When having more than one antenna at the transmitter and / or receiver, forming a Multiple-Input Multiple-Output (MIMO) channel, spatial diversity can be employed to overcome the fading problem. Space time block codes (STBC) have been shown to be used well with the MIMO channel. Each type of STBC is designed to optimize a different criteria such as rate and diversity, while other characteristics of the code are its error performance and decoding computational complexity. The Orthogonal STBC (OSTBC) family of codes is known to achieve full diversity as well as very simple implementation of the Maximum Likelihood (ML) decoder. However, it was proven that, with complex symbol constellation one cannot achieve a full rate code when the number of transmitting antennas is larger than two. Quasi OSTBC are codes with full rate but with the penalty of more complex decoding, and in general does not achieve full diversity. In this work, new techniques for OSTBC transmission / decoding are explored, such that a full rate code can be transmitted and decoded with linear complexity. The Row Elimination Method (REM) for OSTBC transmission is introduced, which basically involves the transmission of only part of the original OSTBC codeword, resulting in a full rate code termed Semi-Orthogonal STBC (SSTBC). Novel decoding scheme is presented, such that the SSTBC decoding computational complexity remains linear although the transmitted codeword is not orthogonal anymore. A new OSTBC, that complies with the new scheme\u27s requirements, is presented for any number of transmit antennas. The performance of the new scheme is studied under various settings, such as system with limited feedback and multiple antennas at the receiver. The general decoding techniques presented for STBC, assume perfect channel knowledge at the receiver. It was shown, that the performance of any STBC system is severely degraded due to partial channel state information, results from imperfect channel estimation. To minimize the performance loss, one may lengthen the training sequences used for the channel estimation which, inevitably, results in some rate loss. In addition, complex decoding schemes can be used at the receiver to jointly decode the data while enhancing the channel estimation. It is suggested in this work to apply adaptive techniques to mitigate the performance loss without the penalty of additional rate loss or complex decoding. Namely, the bootstrap algorithm is used to further refine the received signals, resulting in better effective rate and performance in the presence of channel estimation errors. Modified implementations for the bootstrap\u27s weights calculation method are also presented, to improve the convergence rate of the algorithm, as well as to maintain a very low computational burden

On channel estimation and optimal training design for amplify and forward relay networks

10.1109/GLOCOM.2007.763GLOBECOM - IEEE Global Telecommunications Conference4015-401

Distributed space-time block codes for two-hop wireless relay networks

Recently, the idea of space-time coding has been applied to wireless relay networks wherein a set of geographically separated relay nodes cooperate to process the received signal from the source and forward them to the destination such that the signal received at the destination appears like a Space-Time Block Code (STBC). Such STBCs (referred to as Distributed Space-Time Block Codes (DSTBCs)) when appropriately designed are known to offer spatial diversity. It is known that different classes of DSTBCs can be designed primarily depending on (i) whether the Amplify and Forward (AF) protocol or the Decode and Forward (DF) protocol is employed at the relays and (ii) whether the relay nodes are synchronized or not. In this paper, we present a survey on the problems and results associated with the design of DSTBCs for the following classes of two-hop wireless relay networks: (i) synchronous relay networks with AF protocols, (ii) asynchronous relay networks with AF protocols (iii) synchronous relay networks with DF protocols and (iv) asynchronous relay Fig. 1. Co-located MIMO channel model networks with DF protocols